Math | Arthur's Anydex: The Index of Anything

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Mathematics: Anything Index of Education

Note: This started as my Asian American "races in math" page, but has been extended to include the "reform math wars" as well. Most math reform programs are programs for the "dummies", not the kids who study hard and memorize everything and get top SAT scores. The problem is that they isolate precisely what makes Asian kids succeed (drill, rote learning, memorization, single minded pursuit of high skills and test scores) and make sure that nobody will do it.

Another feature of this math page is a grade-level spectrum and definition for most math concepts and a ---- appropriate ---- determination of tests or standards which have been set by committees at levels which cannot be reasonably expected to be met by most (90% pass rate) students.

Starting Links

Contents :( bad :) good



Grade level spectrum

Kindergarten
count to 10
add to 5
sutract from 5
square, circle, triangle, rectangle

G1
add to 10
sub from 10

? draw oblique projection of blocks DS

G2
add to 20
sub from 20

? subtract 19 from 31 by using negative numbers DS
? use 3 x 50 = 150 DS 

G3

add sub money
multiply to 10 x 10

? count two handfuls of rubber bands but don't add DS
? how many cats in 144 legs by drawing DS

G4
probability: certain/uncertain

? stem and leaf plot SF
? find item with most < x on a frequency histogram WASL
? compute probability as a ratio WASL
? construct symmetric figure on pegboard WASL
? solve ax + bx = c by guess and check WASL
? independent probability WASL
? cost a parts list a + 2b @$2.15 each + 3c + 5 ft @ $2 per foot WASL
? compare concentration ratio lemonade / water WASL
? compute height of flagpole by its shadow and short object WASL
? construct blocks from picture DS

G5
area=height x width


G6

G7

G8

G9 Algebra 1


Also see test scores, awards

Asians get the highest math test scores (except in Seattle and other
cities where Whites are unusually advantaged and Asians highly
disadvantaged), and the are over-represented in advanced math classes
and colleges and selective high schools with high math scores.

IF YOU CAN ONLY READ ONE
INTRODUCTION TO REFORM MATH AN WHY IT IS DESTRUCTIVE, ESPECIALLY FOR
MINORITIES, READ THIS REPORT FROM THE TEXAS PUBLIC POLICY
FOUNDATION


Math Reforms are also listed in this area.

Spectrum
--------
Good Buzzwords

Escalante
Rote Learning
Rank Ordering
Memorization
Sequential learning
Drill
All Children will do their best
Memorization of Multiplication Tables
Long Division
Manual Calculation
Norm-Referenced multiple choice tests
 (SAT, CTBS, ITBS)
Saxon
Hirsch / Core Knowledge
Basic Skills
Direct Instruction
Sequential Instruction
Abstract
Mathematically Correct
Automaticity
Content
Scientist / Engineer / Mathematician
Tutoring
Kumon


Bad Buzzwords
--------------------------
Student Centered
Spiral Curriclum
More than one answer or method
Not relying on memory or speed
Not practicing learned procedures
Standards Based
Research Based
Technology
Invented Mathematics
National Science Foundation
NAEP
Skills for the 21st Century
Deep, Balanced Mathematical Learning
Calculators
Learn More Mathematics
Math Educator
Mathematics for All
Math Power
Exploration Learning
Child-Centered
New Math
Whole Math
Reform Math
Multicultural inclusive math
Rote skills are bad
Standards Based Math
New Standards (NCEE)
All Children Will Succeed
Open-Response Criterion Referenced Tests
Constructivism
Connections
Context
Higher Order Thinking
Real World
Problem Solving
Math Communication
Integrated Math (no sequence, mixed with nonmath)
Applied
John Dossey
National Council of Teachers of Mathematics NCTM standards
Mathland
U Chicago
CMP
Investigations
Interactive Mathematics
Mathland
Everyday Mathematics
Thinking skills
Process

Links
The Math Forum


@@Abacus

MENTAL MATH ON MENTAL ABACUS
z46\clipim\2000\11\02\abacus\abacus.htm Oct 30 ABCNEWS.com - Anazan
is computing to 8 places on a mental abacus in no time flat. wow!

SF SUPERMATH USES MENTAL ABACUS
z55\clip\2002\04\abcus.txt
After students spend time in SuperMath class . . . 
Things just click Cicero A. Estrella, Chronicle Staff Writer Friday,
April 26, 2002 Mina Watanabe expects silence from her students.
Students who complete the basic program can multiply and divide three
figures by one figure, and add and subtract a string of up to 10
double-digit numbers. At the highest levels of SuperMath, square
roots, cubic roots and other complex calculations are not a problem. 

@@Acute Obtuse Angles (Geometry)

Definition
Acute = less than 90 degrees
Obtuse = more than 90 degrees

Grade Level Spectrum

G2-3  British Columbia Standard
G4    MCAS Massachusetts G4 Test
G4    North Carolina Public Schools InfoWeb
----- too low -------------------------
G5    Boulder Valley School District
G5    Advanced Learning System
G5    Nevada 1998
G6-8  Arizona Standards
Mid   Addison Wesley Middle School Math
Coll  http://www.geom.umn.edu/ U Minn Geometry Center
NA    CA 1998

British Columbia Ministry of Education
classify given angles as acute, right, obtuse, straight, or reflex
Grade 2-3

http://downtownweb.com/k-12-education/software/phonics/als/mathematics/ma5.h
tml
Advanced Learning System
Mathematics Grade Level 5

Boulder Valley School District
http://bvsd.k12.co.us/curriculum/math/elementary/geometry.html
In fifth grade, students will
1. understand the characteristics of equilateral, isosceles, and scalene
triangles and acute, obtuse, and right angles;

G6-8 Arizona Standards (Achieve)
http://www.achieve.org/a_dir/achieve/achieve.nsf/
4f3ab134c1989eb68525644300601a36/ee9840d1075e97d9852565880000fba6?OpenDocume
nt
PO 4. Measure and label specified angles (e.g., alternate interior,
obtuse, acute, right, corresponding . . . ) (Grades 6 - 8)


G4 North Carolina Public Schools InfoWeb Strategies for Instruction
in Mathematics Instructional Services North Carolina Department of
Public Instruction Grade 4 Objective 2.5
On a geoboard, make triangles which illustrate acute, obtuse and
right angles.

http://www.mathsurf.com/8/ch8/nature/index.html
Elements of Geometry: Addison Wesley Middle School math

From Pythagorean Theorem Home Page
http://www.geom.umn.edu/~ekeel/Project/promenu.html
http://www.geom.umn.edu/~ekeel/Project/tri3.html
Triangles can be classified in the following manner:

   1.By ANGLES
        1.acute triangle- a triangle with 3 acute angles
        2.right triangle- a triangle with one right angle
        3.obtuse triangle- a triangle with one obtuse angle
        4.equiangular triangle- a triangle with 3 congruent 60 degree angles


@@Addition

@@Advantage (America vs. Asians)

\doc\96\03\whyadd.txt "Why Johnny Can't Add, Subtract" Investor's
Business Daily April 25, 1996 p. 1 In 3 decades, the SAT math scores
fell from 492 to 473, about 3%. The top 5% of the US high school
students score about as well as the top 50% in Japan, or the median.
The California State University system increased those who were
judged to need remedial math from 30% in 1989 to 54% in 1994.
(comment, this doesn't jibe with the 2 year advantage shared with
Asian Americans in math)

\priv\95\19\ussmart.txt Tests put U.S. students among best - and
worst Tacoma News Tribune Story Number: 56007 12/10/95 Shankar
Vedantam Taiwan 11-yr olds in 1991 National Center for Education
Statistics test scored the same as American 13-yr olds (2 year gap)
(Story does not mention similar gap between Asian Americans and
whites)

@@Affective

Intrusive assignments in Pre-Algebra II
parent in the Mead School District, the first
assignment for a 7th Grade Pre Algebra II.  It is now on my website at
http://www.icehouse.net/lmstuter/page0243.htm day 1
http://www.icehouse.net/lmstuter/page0244.htm day 2



@@Algebra

Algebra is normally where the college track starts, with 9th grade. Some districts don't think it's appropriate for 8th grade, but 1/4 of 8th graders took algebra in 1996, according to the NAEP. In California, eventually 44% take algebra, 25% geometry, 6% trig and calculus.

Milwaukee requires ALL 9th graders to take algebra. In the last four years only 54%, 56%, 55% and 53% in 1996-97 passed Algebra in the 9th grade. In 1999, all 8th graders will be required to take algebra. The Equity 2000 program by the College board requires districts to require algebra of all 9th graders and geometry of all 10th graders.

In San Jose, Blacks and Hispanics are under-reprsented in algebra courses, but so are Whites, because of Asians, who get best scores and are twice as likely as whites to take the course in grade 8. Despite poverty, Asians are half as far ahead of whites in pass rates as blacks are behind. Blacks score better than the Hispanics in San Jose.

Santa Rose also finds blacks and Latinos under, but Asians over-represented in 8th grade Algebra.


Grade Level Ranking
--------------------------------------------
2nd  Gregory Smith prodigy
2nd  2008 2nd Grade math standard
  Kimmy has 7 more than Hazel, they have 20 total, how many do they have?
  http://hu1st.blogspot.com/2008/01/washingtons-new-2nd-grade-algebra-and.html
5th  Dave Cole's saturday class
7th  Connected Mathematics: solve 6x + 3 = 4x + 9
  http://connectedmath.msu.edu/mathcontent/algebra.html
8th  Palm Beach County required for all, 10% in 2002
8th  Russia
8th  1999 US Dept Ed goal
8th  1999 all Milwaukee 8th graders required
8th  25% of US kids
8th  Santa Rosa CA starts
8th  Bellevue WA new '98 curriculum
8th  CA 1998 state framework
8th  Renton calculus track
9th  Milwaukee 40% fail rate, required for all
9th  Renton college track
9th  All Milwaukee 9th graders required in 1998. Only 50% pass.
9th  NAEP expectations
9th  Most school standards, "tradition"
9th  Virginia standards
12th Kentucky (vs. 8)
12th nearly 100% of SAT students

Pass Rates By percent
------------------------------------------------------
100% Some say other nations put all kids in grade 7
100% Russian middle school claim
100% Some city and state goals
100% Wayne Bishop's Daughters 8th grade by Texas exam
 99% Aransas Pass TX (WB)
 97% White/Black SAT taker
 72% Singapore TIMSS 8th grade
 67% VA 2000 pass geometry  statewide
----- No state cross section over 65% ----------------
 66% Taipei TIMSS 8th grade
 65% VA 2000 pass algebra 1 statewide
 55% Pass required algebra in Milwaukee 9th grade
 55% CA alg + geometry White/Asian
 51% CA alg + geometry black
 44% VA 2000 pass algebra 1 black
 40% VA 2000 pass geometry black
 40% Russia TIMSS 8th grade
 33% Hispanic Black high school grad
 33% World Average 8th grade TIMSS
 30% Texas (WB)
 29% US TIMSS 8th grade
 15% Dallas ISD (WB)
 10% HS seniors who can use starting algebra

Percent Taking Algebra
93%  before or during HS US
52%  Algebra 2 in HS US
64%  Algebra 1 in HS US
30%  before high school US
1994 Digest of Education Statistics

%%Accelerated

2nd Grade algebra by Ideal
Image posted at:
http://www.arthurhu.com/images/2000/03/15/alg2.gif
2nd grade Get Your Hands on Problem Solving Ideal:
85 cents for a snack, nickels, dimes and quarters, same number of 
nickels and dimes but fewer quarters than dimes. What coins do
they have?

You can't even solve this with standard algebra since all you know
is that the number of quarters is less than the dimes!

try with two quarters
 5  5  5
10 10 10
25    25
---------- 
40 55 95 too many quarters

try with one quarter
 5  5  5  5
10 10 10 10
25    
---------- 
40 55 70 85

Requires 12 2 digit additions with carry!

What if they had pennies, nickels and dimes, two times as many
nickels as dimes, one more penny than dimes? (multiplication is not
taught in g2!)

1 dime = 1+1+10+5+5=22
1 pen 1  1
1 dim 10 
2 nic 5  5
2 dimes = 43
3 pen 1  1  1
2 dim 10 10
4 nick 5  5  5   5
3 dimes = 64
4 pen 1 1 1 1
3 dim 10 10 10 
6 nic 5  5  5  5  5  5   
4 dimes = 
5 pen 1 1 1 1 1
4 dim 10 10 10 10
8 nic 5  5  5   5  5  5  5  5  
----------------------------------------
Requires 43 2 digit addition with carry to solve.
How many 2nd graders can add 43 2 digit numbers without an error?


8TH GRADE ALGEBRA BETTER, US LAGS IN MATH GRADE LEVEL
timsmath.txt">
For the value of algebra in 8th. grade:
 Third International Math and Science
 Study [TIMSS] report "Do Gatekeeper courses expand education
options?"
 http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=1999303
"enrollment in gatekeeper couirses, such as algebra and foreign
language in eighth grade helps students reach higher levels in the
mathematics and foreign language pipelines.  For example: --Students
who enrolled in algebra as eighth-graders were mroe likely to reach
high-level math courses ... in high school than students who did not
enroll in algebra as eighth-graders.
From: Pursuing Excellence: Initial Findings from the Third International
 Study of Math and Science, Chapter 4: the Context of Learning
http://nces.ed.gov/pubs98/twelfth/chap4.html

Curriculum A comparison of the topics covered in the mathematics and
science general knowledge assessments with curriculum frameworks did
reveal that both general knowledge assessments covered content that
is introduced later in the U.S.  curriculum than it is introduced, on
average, in the other TIMSS countries as a whole.14
[8th grade useless if it does not account for best students taking
algebra, US sequence is good enough for MIT, best engineering
school in the world, while Russian economy is a mess]

ALGEBRA REQUIRED OF ALL BY G8?
http://www.chicago.tribune.com/version1/article/0,1575,SAV-9909270075,00.html
\clip\99\18\earlalg.ttx Chicago Tribune Tuesday, September 28, 1999
EARLY ALGEBRA IN CRETE-MONEE'S EQUATION DISTRICT OFFERS CLASSES FOR
YOUNGER PUPILS By Kathleen Knowles-Wantuch. Special to the Tribune.
Tribune staff writer Stephanie Banchero contributed to this report.
September 27, 1999
honors algebra, once reserved for high school freshmen, is now being
taught to high-achieving 7th graders. Although the middle school has
offered the class to 8th graders for years, the program was expanded
to 7th graders ... the state's new learning standards set for the
Illinois Standards Achievement Test expect 8th graders to know
algebra by the time they take the test in the spring.  When they
enter high school they will be taking Algebra II, advanced placement
calculus, and multivariate calculus. 

%%Advanced

Mr Smith Goes to College Seattle Times Sept 8, 1999 p. A2 Jennifer
Lenhart Washington Post. Gregory Smith at 10 will study Calculus,
completed completed algebra 1 in 18 months at age 7

You have to master arithmetic before
tackling Algebra

1/3 WORLD, US, 2/3 SINGAPORE 8TH GRADERS PROFICIENT IN ALGEBRA
z47\clip\2000\12\math8.htm US eighth-graders beat global average in
math By Gail Russell Chaddock (chaddockg@csps.com) Staff writer of
The Christian Science Monitor 12/6/2000

A club has 86 members, but 14 more girls than boys. How many 
boys and girls?
x = number of boys
x + (14 + x ) = 86
2x + 14 = 86
2x + 14 - 14 = 86 - 14
2x / 2 = 72 / 2
x = 36 boys
86 - 36 = 50 girls
-------------------------------------------------------------
72% Singapore
66% Taipei
40% Russia
33% World Average
29% US
Source: Boston College, TIMSS

%%Algebra Project

ROBERT MOSES ALGEBRA PROJECT - ALGEBRA AS CIVIL RIGHT
z48\clip\2001\03\moses.txt
http://www.chron.com/cs/CDA/story.hts/editorial/840954
HoustonChronicle.com March 5, 2001, 10:49PM Right to learn math new
'radical' cause By E.J. DIONNE "full citizenship depend crucially on
math and science literacy."


%%All

Liberals and conservative reformers both appear to support requiring
Algebra of all students instead of traditional top 1/2 or 1/4.
Liberals want to require it to be mastered by end of grade 8 instead
of traditional grade 10, and to integrate it into K-6.

True traditionalists only permit students who have mastered
arithmetic to even take Algebra, starting in grade 9. Some argue
whether integrated math is even algebra at all.

%%Against

LOW PERFORING STUDENTS MIS-PLACED IN ALGEBRA AT 2ND GRADE MATH LEVELS
\clip\2008\09\algall.txt
http://ednews.org/articles/29027/1/New-Study-Shows-the-Unintended-Consequences-of-Moving-More-Pupils-Into-Eighth-Grade-Algebra-and-Other-Advanced-Math-Classes/Page1.html
"No social benefit can be produced by placing students in classes for
which they are unprepared."

New Study Shows the Unintended Consequences of Moving More Pupils Into
Eighth Grade Algebra and Other Advanced Math Classes a.. By Brookings
Institute 
"Despite being enrolled in Algebra I, Geometry, and Algebra II,
misplaced eighth graders have NAEP scores well below average for
fourth graders. In fact, they know about as much math as a typical
second grader. The report reproduces several sample NAEP items to show
the gaps in knowledge among these low-scoring students on key
pre-algebra concepts such as percentages, decimals, and fractions.
The study also gives detailed information about the characteristics of
these misplaced students, their families, and their schools. It finds
that they are disproportionately black and Hispanic; have parents
whose own education is below the national average; come from
low-income households; attend large urban schools with predominantly
low socioeconomic status populations; and have math teachers with less
experience and mathematics training than the typical teacher of
advanced math students in eighth grade."
www.brookings.edu/reports/2008/0922_education_loveless.aspx

REQUIRE ALGEBRA FOR ALL WHEN THEY DON'T EVEN KNOW 56/7?
z47\doc\web\2001\01\sayall.txt
"This Says It All" by Dan Umbarger and Donna Garner January 4, 2001
It makes absolutely no sense to tell people everybody is enrolled in
a college prep course if they can't even master the multiplication
tables.

z45\clip\2000\09\algeb.doc THE MALEVOLENT TYRANNY OF ALGEBRA Gerald
W. Bracey To Appear in Oct Education Week - Algebra for All will be a
disaster. CA will make algebra proficiency a graduation requirement,
but almost nobody needs to know algebra.

NO REASON TO REQUIRE ALGEBRA OF ALL STUDENTS
z45\clip\2000\10\algall.txt
http://www.educationnews.org/when_was_the_last_time_you_used_.htm oct
2000 EducationNews.org The World's Leading Source of EducationNews 7
Days a Week October 9, 2000 Center for the Study of Jobs and
Education in Wisconsin When was the last time you used Algebra?  By
Dennis W. Redovich Algebra was useless for most students forty years
ago when I taught it in high schools and it is useless for most
students, except as a screening device for college, in the year 2000.
Sen. Charles Poochigian, R-Fresno. "Except for special-education
students ... I don't think there's a single kid who can't learn
algebra." the Milwaukee Public Schools leads the nation in failing
algebra students. MPS 9th graders have been required to take algebra
since 1993-94 when the pass rate was 54%. MPS Accountability reports
show the percentage of 9th graders passing in the last three years as
follows: 1996-97 55%, 1997-98 56%, and 1998-99 60%.  What is the
rationale for requiring all students to meet college entrance
requirements to graduate from high school? The reason, of course, is
that there is no rationale for these school reforms.

%%For 

ALGEBRA REQUIRED FOR FLA GRAD, 100% PALM BEACH 8TH GRADE
http://www.palmbeachpost.com/news/content/auto/epaper/editions/wednesday/news_f
3767dc561f061b500dc.html?urac=n&urvf=10638037402810.3035347880821241
From the Palm Beach Post -- Sept. 17
Eighth-graders must take algebra next school year
By Mary Ellen Flannery, Palm Beach Post Staff Writer
Wednesday, September 17, 2003
Last year, 1,315 eighth-graders in Palm Beach County took algebra, or about 10 
percent of all eighth-graders. Nationwide, about 20 percent of eighth-graders 
complete algebra or another higher-level math course.
Florida doesn't require students of a particular age to take algebra, although 
they do require completion before graduation,
In Milwaukee, which has had an algebra-for-all program 
since 1994, educators report 40 percent of ninth-graders failed algebra in 2000 
and that ninth-graders constitute more than 40 percent of dropouts.

GENERAL MATH SHOULD BE DISCONTINUED, ALGEBRA FOR ALL
z47\clip\2000\12\algall.txt From the Washington Post
http://www.washingtonpost.com/ac2/wp-dyn/A23855-2000Dec18?language=printer
Extra Credit (Education) Tuesday, December 19, 2000 ; Page A19, The
Washington Post www.aera.net/pubs/eepa University of
Wisconsin-Madison study by Adam Gamoran and Eileen C. Hannigan in the
fall issue of Educational Evaluation and Policy Analysis said
students who took algebra improved 8 points between eighth and 10th
grades on a general math test, while those without algebra improved
only 4 points.

SHOULD US/CA ADOPT ALGEBRA FOR ALL
z47\clip\2000\12\algca.txt
http://www.sacbee.com/news/projects/algebra/121400.html State's new
algebra goals are a shock to the school system By Deb Kollars Bee
Staff Writer (Published Dec. 14, 2000) "in Germany, Japan, Argentina,
Korea, France all students are expected to conquer beginning algebra
routinely in the sixth or seventh grade -- and study it thoroughly
until they reach high school. Seventh and eighth grade are notorious
for being wastelands of arithmetic -- fractions, decimals,
multiplication, division -- that students have seen before.  "

DUMP WIMP ARITHMETIC TO BEAT NEW MATH PROFICIENCY GRAD EXAM
z42\clip\2000\07\ohmath.txt Wednesday, June 14, 2000, Akron Beacon
Journal.  Math instruction to change Akron Public Schools step up
focus on proficiency BY REGINALD FIELDS Beacon Journal staff writer
[This sounds bad. Kids can't hack the basics, so you kick everybody
into the hardest track???]  "the district plans to deny students the
option of taking easier classes in secondary schools.  ``We're
eliminating all lower-level math courses'' at the high school level,
said Donna Loomis, director of secondary instruction." [you have to
take the accelerated algebra or nothing]

NCTM STANDARDS - ALGEBRA / GEOMETRY FOR ALL BY 8TH GRADE
April 13,2000 - new NTCM standards say students must master basics of
algebra and geometry by the end of 8th grade.  Seattle Times New math
guidelines aP Nicole Ziegler Dizon Students must know more than the
basics, number crunching is not enough.
z40\clip\2000\02\apmath.txt
http://seattletimes.com/news/nation-world/html98/math13_20000413.html
Thursday, April 13, 2000 New math guidelines 'set higher standards'
for students by Nicole Ziegler Dizon The Associated Press 

KY State reform law requires algebra for graduation
z40\clip\2000\04\kera.txt A New Direction KERA changes way schools
teach, students learn 10 April 2000 By Mark Cooper Messenger-Inquirer

NO ALGEBRA, NO DIPLOMA
\clip\99\21\allalg.txt Published Thursday, December 16, 1999, in the
San Jose Mercury News JOANNE JACOBS High school graduates should at
least know their algebra Low math standards shortchange us all [about
one-third of graduates don't take any algebra]

PETE WILSON SAYS TO TEACH ALGEBRA TO ALL
Tuesday, September 28, 1999  c1999 San Francisco Chronicle
URL: http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/1999/09/28
/ED38466.DTL
Higher Goals for Exit Exams California cheats its students by
expecting too little Pete Wilson, Bill Evers Unfortunately, the math
test planning committee, appointed by State Superintendent of Public
Instruction Delaine Eastin, has chosen to continue to avoid algebra.
It is time to insist that our schools teach algebra to all students.

%%Elementary

http://www.ncitela.org/downloads/math/Math4.pdf
z39\clipim\2000\02\14\Math4.pdf
use variable for number of pages left in book x = 
if x = (a - b) - c and a is 10, b is 3 and c is 4, what is x?
area = height x width. If area = 200 and height is 10, what is width?
find area of L shaped area with dimensions
draw graph of y = 3x
length of line segment (6,-4) (21,-4)
draw radius, diameter
draw two lines of symmetry
know right/acute/obtuse
1/4 of circle to degrees
#edges on rectangular prism
recognize flat figure folds into cube
scalene isoceles right triangle
rhombus vs. parallelogram
median (halfway) and mode (most common)
all possible outcomes coin plus 1 die

%%Level

The earliest track for algebra is grade 7, some want to start in
grade 8. Normal start is grade 9, but nationally, half of kids never
take algebra. Some teachers start as early as grade 5. Some state
standards want to integrate concepts as early as elementary. Some
textbooks and assessments put this at 4th grade, Alabama puts in
in 11th grade, even though not all are required to take algebra

     slow     fast
G6  middle 1 pre-alg
G7  middle 2 alg1
G8  middle 3 alg1
G9  algebra  alg 2

Algebra I Grade Spectrum
--------------------------
G7 Russia
G8 1999 National Science Foundation Goal
G8 1999 US Dept of Education Goal
G9 Traditional
G9 NAEP
G9 Traditional Andover elite high school

%%Pass Rates

Mickey VanDerwerker Sent: Thursday, October 05, 2000 4:33 AM In order
to graduate from a Virginia high school, among other things, you need
to take and pass two math courses (choose from Algebra 1, geometry,
algebra 2).  This means passing by teacher grades.  You must also
pass one of the high stakes standardized test at the end of those
courses to get the required "verified credit."
Thus far, our pass rates are as follows:
Algebra 1:  65% (African American:  44%)
Geometry:  67%  (African American:  40%)
Algebra 2:  58%  (African American:  36%)

%%Project, The Algebra 

Wayne says it's flakey fluff.
Another popular destination is the murder site of Medgar Evers.
Moses has all the right words and Inglewood Unified has all the right
test results.  Guess which is actually going to open doors for the
low socioeconomic minority children being served?

%%Real Life

z41\clip\2000\05\algbook.txt Houston Chronicle April 26, 2000,
10:26PM Experts say few algebra books enter real life into the
equation WASHINGTON (AP) -- Why can't the kids learn algebra? Because
the books they use don't explain how algebra calculations will relate
to everyday life, a panel of scientists said Wednesday. "Just
figuring out how to drive a truck route using the least amount of gas
is a mathematical problem," said George Nelson, director of the
American Association for the Advancement of Science's long-term math
and science education campaign.

[[Alabama

ALABAMA ADOPTS EXIT EXAM FROM HELL Birmingham News: Students facing
tougher exit test February 27, 1999 Students facing tougher exit test
CHARLES J. DEAN News staff writer 02/26/99 Question: Ryan makes $3
per hour more than Scott. If 3 times Ryan's rate plus 4 times Scott's
rate is $65, what is Ryan's hourly wage? Answer: $11.

[[Bellevue

"Middle schools go fast-track" Seattle Times Jan 21, 1998 Mike
Lindblom New curriculum encourages algebra at 8th grade.

[[California

elite private school has most
thru alg 1 in g7, 100% proficient by g8. Accelerated school is
below grade level because of nsf mctm math. Japanese g7 is like
saxon

http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm This Framework
focuses on presenting a curriculum that will prepare all children by
the end of seventh grade to begin to study algebra and geometry in
the eighth grade. This change has been adopted not only by the
California Standards Commission but also by vote of the committee
that developed this Framework. The Framework describes an
introductory algebra course for the eighth grade, followed by
geometry in the ninth grade and advanced algebra in the tenth grade,
or the alternative of a comparable three-year integrated program.

\clip\98\03\racegap.txt
San Francisco Chronicle 2/1/98 Editorial The
Great Divide In American Education

Complete Algebra 2 and Geometry
-------------------------------
55% White/ Asian
51% Black
35% Latino

California School District
Placement of top quartile in algebra
(student choice?)
-----------------------------------
100.0% Asian
 87.5% White
 51.0% Black
 42.0% Latino

Asians in 3rd quartile more likely than
Black or Hispanic in 4th quartile.


[[Cole

Dave Cole teaches 5th
graders to solve ax + bx = c.

[[Kentucky

http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.html
G8 is "ideas", hard algebra is a G12 standard.

[[Louisiana


Louisiana Contents Standards Algebra, in the K-8 classrooms,
refers to informal explorations and understandings of symbolism. It
is beneficial to introduce the algebraic terminology (equation,
inequality, variable, etc.) in the early grades. In this way high
school students will be able to understand algebra as a natural
outgrowth of their study of various number properties.

[[Milwaukee

Milwaukee has 37th percentile mostly inner city youths, and requires
ALL to take algebra. This is a BAD idea if they can't even master
basic math.

COLLEGE BOARD TELLS DISTRICTS TO TEACH ALEBRA TO ALL
Here's Y the teaching of algebra in the US has been such a big flop.
Wall Street Journal June 16, 1998 p. A1. US books teach too many
topics over and over. Only 40% of 2nd grade, 30% of some 8th grade
books have any "new" content. Grouping by ability dropped in the 70s,
but math tracks kids into what they are sure to pass, not what they
"need". TIMSS show 4th grade arithmetic is OK. The College Board
Equity 2000 program has signed up Milwaukee and 8 other cities,
requiring them to teach algebra to all 9th and geometry to all 10th
graders. Seniors must pass algebra and math proficiency test to pass,
but nearly half, 90 of 200 seniors are retaking the tests for the 3rd
time.  Lack of algebra is blamed for 100 point SAT difference, five
years ago fewer than 1/4 of Blacks and Hispanics took algebra vs.
about 1/2 of whites.  Milwaukee 10th graders are at the 37th
percentile nationally. Low income students who take algebra go to
college at middle class rates. 1/3 of US students missed 20% off of
$1,250 stereo, 1/9 could plot a graph.

MPS REQUIRES PASSING ALGEBRA TEST TO REACH 10TH GRADE, FLUNKS 50%
MPS exaggerates drop out rate to
signal crisis Dennis W. Redovich Greendale WI, Letter from Leon
Todd that MPS is the only district in the nation with such a drastic
standard that Milwaukee requires ALL 9th graders to take algebra. In
the last four years only 54%, 56%, 55% and 53% in 1996-97 passed
Algebra in the 9th grade. " MPS received an award for substituting
algebra, which many failing students in all probability may never
use, for consumer or ecomonic math which employers minimaly need
students to master for most twenty first century employment."
Students that did not pass the exam were held back at the ninth
grade.  "high skill jobs of the future that require algebra and
"high" academic skills simply don't exist for most graduates and
especially for poverty class people of color."

[[SAT


Percentage by race:

 \doc\95\12\sat95bk.wk1
 1995 Scholastic Aptitude Test Breakdown by Ethnicity
 Data from the College Board
 Data Entry and Analysis by Arthur Hu

Figues: Percentage taken, test score gap vs. white, SAT math score.

                White          Black             Hisp             Asian
 Math Coursework     Gap           Gap               Gap              Gap
 Overall               0  498       -110    388        -72   426         40
 538
 Algebra         97    0  498  96   -110    388  97    -73   425  94     37
 535
 Geometry        95    0  504  90   -109    395  94    -73   431  94     36
 540
 Triginometry    55    0  539  43   -106    433  42    -68   471  64     26
 565
 Precalculus     38    0  573  24   -104    469  32    -77   496  54     18
 591
 Calculus        23    0  613  12   -105    508  16    -76   537  40     13
 626
 Computer Math    9            10                10               13

[[US Dept of Education

\doc\web\99\13\muchmath.txt "HELPING
YOUR CHILD LEARN MATH" US DOEd We now believe that by the end of
the eighth grade, students should have mastered the fundamentals of
algebra and geometry to be ready for high school and on track for
college and the workforce.

zip36\clip\99\17\failam.txt \clip\99\17\failam.txt 9/1/99 THE
CONSPIRACY OF IGNORANCE Part 3 of 4 From today's Washington Times.
This is the third of four excerpts from Martin Gross' new book, "The
Conspiracy of Ignorance: The Failure of American Public Schools."

Luther Williams of the National Science Foundation says American schools
are backward in math. "Basic arithmetic [not algebra and geometry] is
still the staple of eighth-grade math," he laments. Almost half of public
high school grads have never taken intermediate algebra and only one in
eight have studied vital trigonometry.



[[Virginia:

http://www.pen.k12.va.us/go/Sols/math.html#GradeEight
8th grade is preparation for algebra, so algebra would be G9

NAEP - grade 8 math is different from algebra, so would be G9

%%Gambill

GAMBILL ALGEBRA METHOD \clip\99\15\gambill.txt
http://www.oregoneducation.org/math/gambill.htm ..signed up
voluntarily to take the 15-county Annual Algebra I Contest at 9:00
morning. The results of the Preliminary are the same as they have
been for the past 7 years, with my students "totally dominating,"
taking 95% of the top places.

%%Neccesary?

Bracey says most people don't
even need to know algebra.

%%Pass rate

Bishop cites high pass rates
100% Wayne Bishop's Daughters 8th grade by Texas exam
 99% Aransas Pass TX (WB)
 30% Texas (WB)
 15% Dallas ISD (WB)

%%Race

Los Angeles Times Wednesday, December 9, 1998 ON LEARNING / RICHARD
LEE COLVIN A Call to Refocus Our Country's High Schools By RICHARD
LEE COLVIN Two-thirds of Latino and African American students have no
understanding of geometry or algebra when they graduate. In fact, the
average Latino or African American 17-year-old is about as skilled
mathematically as the average white 13-year-old.  That means they are
unprepared for college or the workplace.

---------------------------------------------
\clip\97\27\minmath.txt
http://www.pressdemo.com/news/11-20/st005.html Santa Rose Press
Democrat Nov. 20, 1997 Few minorities enrolled in Santa Rosa
accelerated classes By ROBERT DIGITALE Press Democrat staff writer
Enrollments in middle school accelerated classes in Santa Rose:
Slater middle school 15% latino vs. 6% english 3% algebra.
Asians over-represented in 13 of 20 accelerated categories
Blacks under-represented in 17 ot 20 categories.

\doc\web\99\07\solrace.wk1

Virginia SOL Standards of Learning Test Results by Race

Data fromVirginia Department of Education as published in

Washington Post 5/13/99


In Virginia, Asians scored as much as 50% higher in algebra and some
other topics than whites, ev ery other subject was equal or better.
Blacks did more poorly in all subjects, with pass rates as low as 13%
in algebra.  and history, much lower than traditional norm-referenced
tests. Considering the amount of writing required, the impact on
Asians seems to be minimal on this test.

Ranked by Asian - Asians better or equal than whites in all subjects

                                                Index

Subject         White   Black   Asian   HispanicWhite   Black   Asian   Hisp
anic
Algebra II           34%     13%     50%     26%    100%   -262%    147%   -
131%
Algebra I            46%     20%     61%     33%    100%   -230%    133%   -
139%
History from 100     49%     17%     62%     33%    100%   -288%    127%   -
148%
Geometry             59%     25%     67%     47%    100%   -236%    114%   -
126%
History to 1000      68%     38%     77%     52%    100%   -179%    113%   -
131%
US History           36%     12%     39%     19%    100%   -300%    108%   -
189%
Chemistry            60%     31%     62%     41%    100%   -194%    103%   -
146%
English*             77%     55%     78%     64%    100%   -140%    101%   -
120%
Earth Science        69%     31%     68%     51%    100%   -223%   -101%   -
135%
Biology              81%     50%     79%     61%    100%   -162%   -103%   -
133%

\doc\96\04\sjalgebr.wk1

San Jose Unified Algebra Pass W1.00 B-1.23 H-1.30 A1.08 O-1.06
Eastside Union W1.00 B-1.17 H-1.30 A1.10 O-1.32

Percentage of students passing Algebra in two San Jose school districts
by ethnicity
Note that Asians are half as far ahead of whites as Blacks are behind.

 San Jose Unified School District ...
        1991-92         1994-95         Passing
...     Taking  Passing Taking  Passing Index
Asians       262     98%     282     94%    1.08
Whites       649     90%     793     87%    1.00
Others        36     83%      60     82%   -1.06
Total      1,430     87%   1,889     80%   -1.09
Blacks        52     73%      76     71%   -1.23
Hispanic     431     77%     678     67%   -1.30
 Percent taking(     72%             86%

 East Side Union High School District ...
        1993-94         1994-95         Passing
        Taking  Passing Taking  Passing Index
Asians     1,265     94%   1,680     91%    1.10
Whites       702     89%     947     83%    1.00
Total      3,067     86%   4,548     78%   -1.06
Blacks       194     80%     280     71%   -1.17
Hispanic     867     74%   1,595     64%   -1.30
Others        39     77%      46     63%   -1.32
% Taking             56%             80%

Source: San Jose Unified School District, East Side Union High School
District.  based on chart in San Jose Mercury news May 18, 1995
DOWNSIDE OF 'STAND AND DELIVER' MATH PROGRAM S.J. RESULTS: AS
ENROLLMENT EXPANDS, SO DOES PERCENTAGE OF STUDENTS FLUNKING.
Rankings and index by Arthur Hu

doc\94\7\algebrar.wk1 Algebra score by courses taken, 1990 NEAP
taking algebra in Grade 8: W1.0 B-2.57 H-1.80 A2.11
test score taking algebra - W 0 B-36 H-27 A+9
Asians taking G8 math same as black taking Algebra

%%Rate

z45\clip\2000\08\testgap.txt Academe Today Friday, August 25, 2000
Girls Catch Up With Boys in Math, Report Finds, but Overall Student
Gains Have Slowed By JULIANNE BASINGER Thirteen percent of female
17-year-olds taking the test in 1999 had enrolled in pre-calculus or
calculus courses, compared with 4 percent in 1978. More than half the
young women taking the test in 1999 had taken advanced algebra, while
only 37 percent of those in 1978 had done so.

\clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for
Math Problems RICHARD LEE COLVIN (New math, math reform backlash
against "fantasy lunch")
http://www.math.uic.edu/~cpmp/archive9701.html This fall, the
National Assessment of Educational Progress said 17-year-olds are no
stronger in math than 20 years ago. Only six of 10 high school
seniors can compute with decimals, fractions and percentages. Fewer
than one in 10 can use beginning algebra.


%%Required

New reformers say that since algebra is a "gatekeeper" an associated with high performance, then all students should be required to take it. Traditionally, only a small percentage were thought to be capable enough to master it or even need it if they weren't going to college. Some districts and states are setting up standards requiring algebra for all such as Minneapolis. On the plus side, more kids are passing algebra than were even trying before. On the other hand when 50% of kids who take it are failing, they may be driving up dropout rates, and it's pointless to require what kids won't or can't do.

George Cunningham says just because the best students take algebra, it doesn't automatically mean that all students should take it.



ONLY HALF ARE PASSING ALGEBRA, BUT MORE ARE TRYING, GOALS IS 8TH GRADE
2/28/99 Milwaukee Journal Sentinel: Algabra policy alters MPS
dynamics Requirement has affected course passing rates, fueled debate
about its merits By Joe Williams of the Journal Sentinel staff
February 28, 1999

"the requirement has driven up dropout rates because some students
have not been properly prepared to handle the course"

"One statistic, in particular, leaps off the pages of MPS reports:
There are more kids passing algebra now than were even taking the
subject in 1991.. only about half -- 53% -- of the freshmen who are
taking algebra in the district are passing the course. When algebra
was an elective in 1991 -- when the question of requiring the course
first came up -- 74% of algebra students were passing the course."

"believes a majority of the students who are failing algebra now
would have likely failed any math class they were taking.  Those
students have extremely weak backgrounds in math, don't do the
homework or simply miss school so much they are incapable of passing,
many educators said... when students attend algebra class regularly,
about four out of five tend to pass the course...students who had an
"A" or "B" average had an average daily attendance rate of 95% over
the duration of the semester. Students who were failing the course
attended school only 65% of the time. "

"adult critics of the algebra requirement that the subject is not
needed in the real world -- something that drives math teachers crazy"

"by the class of 2004, for example, all MPS students will be required
to demonstrate a proficiency in algebra by the end of eighth grade.
" [Comment currently only the fastest AP calculus tracks require
students to finish algebra in grade 8]


ALASKA STANDARDS TO REQUIRE ALL STUDENTS TO LEARN ALGEBRA

TEXAS TO ADD ALGEBRA TO EXIT EXAM
November 25, 1998, 08:07 p.m.  Proposals would raise TAAS bar Moses
wants to tighten ratings, add math test Moses said he will formally
propose next week that the Algebra I end-of-course exam be added to
the accountability system

MPS REQUIRES PASSING ALGEBRA TEST TO REACH 10TH GRADE, FLUNKS 50% MPS exaggerates drop out rate to signal
crisis Dennis W. Redovich Greendale WI, Letter from Leon Todd:
MPS is the only district in the nation with such a drastic standard
that Milwaukee requires ALL 9th graders to take algebra.

2/11/98 Austin American Statesman Algebra 1 only recently became a
required math course for most students. (Texas)

%%Simple

%%Standards

[[Algebraic expressions

a * 2
2t + 4

G7 Nevada
G8 Mathematics unlimited 1988

[[Evaluate given variable values

compute A = l * w given l=2 w=6

G8 Nevada
G8 Mathematics unlimited 1988

[[Solve for unknown working backwards

G8 Mathematics Unlimited textbook 1988

[[Solve for equation ax + bx = c

G4 www.passthewasl.com flashcards (2 + x) * 3 = 15
G4 Guess and check WASL apples and pears
G8 Algebra 1
G9 Integrated math 1

Traditionally, this sort of problem is taught in algebra 1 in grade
9, maybe grade 8. I have a whole sequence of pre-1990 math textbooks
from G1 to G8, none of them have problems of this type.

Example 1. There are 18 pieces of fruit, twice as many apples as
oranges, half as many pears, how many of each fruit?

Example 2. There are 5 more crows than cows in a farmer's field.
There is a total of 52 legs on all of the animals.  How many crows
and how many cows are in the field?

However, mid 1990s NCTM inspired assesments and textbooks expect
children in G4 and G5 to solve these problems with guess and check! It has also appeared in the 7th
grade test.

G3-5 Massachusetts
    "know and apply algebraic procedures for solving equations and
    inequalities." (yeah, right)
G4  1997 WA WASL 4th grade "how many bicycles", no solution
G5  New Progress in Mathematics, by Rose Anita McDonnell
G7  1999 WA WASL 7th grade "14 fruit", no solution
G8  2007 WA standards draft "solve linear equations"
G8  2001 Singapore "solve linear equations"
G12 Nevada
G9-12 DODDS
G12 New Jersey
    Solve equations and inequalities of varying degrees

Elementary Algebra Part I by Denholm
Dolciani, Cunningham 1970 Houghton Mifflin: tells how to solve
this problem AFTER nearly a whole book of algebra.

WA EALR benchmarks
http://cisl.ospi.wednet.edu/ComSL/MATHBMK.html
G4 solve simple equations using blocks, sticks, beans, pictures, etc.
G7 set up and solve single-variable equations
G10 create and solve equations and inequalities, evaluate and
  simplify expressions

DODDS Introductory Algebra and Geometry
3. Write numerical or algebraic expressions for expressions in words.
4. Solve and check equations involving signed numbers.
5. Use the distributive property to simplify numerical expressions.
6. Write equations to represent real situations.

[[Polynomials

G9 Algebra 1

@@Alebra Textbook Review

\clip\2009\11\Lee-math-textbooks
http://keen-studios.net/files/mathchoice/Lee.pdf
John M. Lee of University of Washington Dept of Mathematics
Reviews Prentice Hall: Algebra 1 and Algebra 2
"These books are solid, well organized, and mathematically sound.
Computational algorithms and formulas are clearly stated and well
motivated by examples and hands-on activities. The use of graphics
to call out important principles is very effective"

Key Curriculum Press: Discovering Algebra
My first impression is that these books have far too much verbiage for
students to read and too little in the way of clearly stated
mathematical principles. Definitions, computational algorithms, and formulas
seem to be stated vaguely when they are stated at all. For example, a relation
is defined as "any relationship between two variables" [a circular definition]

@@Algorithms



@@All
@@All students

END TRACKING
ALGEBRA FOR ALL
NCTM STANDARDS
BREAK DOWN GENDER AND RACE NUMBERS
http://www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma12000.htm
The Goal and Seven Components of The Equity 2000 Districtwide Reform Model
North Central Regional Education Laboratory
* end tracking and raise standards for all students
* requirement that all students complete algebra by the ninth grade
and geometry by the tenth grade, and including reform of the
curriculum to reflect standards set by the National Council of
Teachers of Mathematics and other discipline-based organizations.
# Establishment of ongoing professional development for teachers,
counselors, and principals to increase their professional knowledge
and skills and to raise their expectations for students.
# Improvements in schools' involvement with students' parents and
families to create a consistent climate for learning as well as to
empower parents to be advocates for their children's education.
# Use of student course enrollment and achievement data broken down by
ethnic group and gender to monitor progress toward reform goals

* all members of the school community will need to reexamine their beliefs,
expectations, and cultural sensitivities;
* develop a shared vision of equity and excellence in mathematics education;
* determine their new roles and responsibilities in supporting equitable mathematics education for all student

* All schools involved in reform will have to understand and share the
??democratic vision?? that underlies the Standards and address the issues
of power and practice raised by the Standards.

ALL STUDENTS MEANS ENSURING EQUITY
Ensuring **Equity** and Excellence in Mathematics In Reaching All Students
With Mathematics (Cuevas & Driscoll, 1993b), an NCTM task force gave
special attention to programs that work to ensure equity and ...
www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm

Educators and community members are beginning to recognize that most
students, including a disproportionate number of women, minorities,
and the poor, leave school without the mathematical skills they need
to thrive in an increasingly complex, global economy.

Behind Goals 2000 and the NCTM standards is the conviction that all
students can learn a significant core of mathematics and that the
entire school community must have high expectations for every child's
mathematics education.

foster cultural and linguistic diversity in an effort to increase the
participation and success of underrepresented groups.

OPPOSITION: Some people believe that inherent
differences in ability among males and females, racial and
socioeconomic groups, and individual students make high expectations
for all students unrealistic and ill-conceived. Although research
generally has discredited this view, the debate has been reopened by a
recent book, The Bell Curve: Intelligence and Class Structure in
American Life, by Murray and Herrnstein.

Parents of minority students are concerned about new math standards
and curricula that deemphasize paper-and-pencil computation.
Computation skills often are associated with mathematical competence,
and the lack of mastery of these skills has been used to justify
denying opportunities to minority students. Therefore, these parents
are not convinced that mathematics reform is in the best interests of
their children (Secada, 1994).

Morris KLINE - 1962- On The Mathematics Curriculum of The High School
The mathematics curriculum of the high school should provide for the
needs of **all students**: it should contribute to the cultural background
of the general ...  michel.delord.free.fr/kline62.html

ALL INCLUDES DISABLED USING NCTM CURRICULA
Including All Students in Meaningful Mathematics: The Story of Darrell. Judith Storeygard Cornelia Tierney, TERC. This article tells the story of Darrell, ...
escholarship.bc.edu/education/tecplus/vol1/iss3/art4/
because a few of his teachers knew how to teach mathematics to a range
of learners using NCTM standards-based mathematics curricula and
because he became aware of how he learns mathematics best, Darrell
began to progress towards the end of elementary school. Students with
disabilities, like Darrell, all deserve the chance to participate in
meaningful mathematics.

Science and Mathematics for All Students [Its Just Good Teaching] File
Format: PDF/Adobe Acrobat - View as HTML Mathematics for All Students
are mirrored in its. content and organization. ... adopt to increase
all students’ participa-. tion in mathematics and science. ...
www.nwrel.org/msec/images/resources/justgood/04.97.pdf

Mathematical Proficiency for All Students
Mathematical Proficiency For All Students. Adding It Up: Helping Children Learn Mathematics cover: click for full report Are the nation's schoolchildren ...
www4.nationalacademies.org/onpi/webextra.nsf/web/proficiency?OpenDocument

RAND | Monograph/Reports | Mathematical Proficiency for All ...
Mathematical Proficiency for All Students. Toward a Strategic Research and Development Program in Mathematics Education. Cover: MR-1643 | Mathematical ...
www.rand.org/pubs/monograph_reports/MR1643/index.html

Appendix: Table of Standards - Number and Operation NCTM's visionary
document for teaching mathematics at any level. ... Pre-K–2
Expectations: In prekindergarten through grade 2 **all students** should–
...  standards.nctm.org/document/appendix/numb.htm

http://www.mste.uiuc.edu/courses/ci332fa02/
Elementary Mathematics Instruction
What is mathematical power?
The National Council of Teachers of Mathematics (NCTM) has called for
fostering the mathematical power of ALL students (1989). 

EXPERTS QUESTION ONE MATH TEST FOR ALL
z74\CLIP\2003\10\mathstin.txt
New York Post
STATE'S HS MATH PROGRAM 'STINKS' 
By KENNETH LOVETT and CARL CAMPANILE 
Members of the panel also raise the question of whether it's
educationally sound to require all students - college bound or not -
to pass an identical math-skills test. 
October 8, 2003


@@Angles

%%vertical

Vertical Angles
G5?  Michigan G.GS.05.03 Identify and name angles on a straight line and vertical angles.
     http://www.eup.k12.mi.us/608973121310511/blank/browse.asp?a=383&BMDRN=2000&BCOB=0&c=55564&608973121310511Nav=|734|&NodeID=734
G6   CA  Identify angles as vertical, adjacent, complementary, or supplementary
     http://www.cde.ca.gov/be/st/ss/mthgrade6.asp
G6?  Indiana Identify and draw vertical, adjacent, complementary, and supplementary angles
     and describe these angle relationships. Solve problems involving an unknown angle.
     http://www.indianastandardsresources.org/standard.asp?Language=English&Subject=math&Grade=6&Standard=4
G7   identify vertical angles
     www.mathscore.com/math/free/lessons/California/7th_grade/Identifying_Angles_lesson.html
G7   Maryland Use vertical, adjacent, complementary, or supplementary angles
     http://www.mdk12.org/instruction/curriculum/mathematics/standard2/grade7.html
G8   Virginia relationships between vertical angles
     http://www.knowledge.state.va.us/main/sol/solview.cfm?curriculum_abb=MAT&category_abb=8
G8-12 prove relationships between angles in polygons by using properties
     of complementary, supplementary, vertical, and exterior angles
     http://www.cde.ca.gov/be/st/ss/mthgeometry.asp
G10  Solve problems involving complementary, supplementary, congruent, and vertical angles
     http://intranet.cps.k12.il.us/Standards/CAS/CAS_Mathematics/Math_10th_Grade/10SG9-Math/10sg9-math.html
Geom VA solve practical problems involving complementary, supplementary,
     and congruent angles that include vertical angles
     http://www.knowledge.state.va.us/main/sol/solview.cfm?curriculum_abb=MAT&category_abb=GEO


@@Applications of Mathematics

A key notion of reform is to apply mathematics to the "real world"
instead of studying abstract mathematics and algebra or geometry.
Critics say that introduces a lot of stuff which has nothing to do
with mathematics, and causes skipping a lot that does have to do with
algebra.


"Modern math book offers clue to lack of
student's abilities" Seattle Times Dec 28, 1997 p. B5 Robert
Supino (letters to editor) Much of the book is not algebra, in fact
the algebra is difficult to find.  The emphasis on application makes
it not really a math text but a bad physical science text.


@@Arise

Innovative new math program that claims to teach exclusively
in "real world" settings, but not rated highly by skeptics

Home Page
Project ARISE (Applications Reform In Secondary Education) is a
3-year college-preparatory mathematics program, in which all math is
taught in the context of real-world problems and settings.  Hogan
Senior High School, located in Vallejo, CA, is one of 15 national
pilot sites, and the only one located in California.

ARISE is a comprehensive curriculum development project funded by a
National Science Foundation (NSF) grant to the Consortium for
Mathematics and its Applications (COMAP). It is developing a 9th-
through 11th-grade secondary mathematics core curriculum in which **
applications of mathematics play a primary role. **


ARISE is a core curriculum; it is a program that allows students
"in", not keep them "out". It demonstrates that mathematics doesn't
have to be ability-grouped in order to be effective. It answers the
age-old question, "When am I ever going to have to use this?", so
that students can concentrate on the learning. It simultaneously
prepares students for college and for vocations. It is equally
effective in block schedules and in traditional schedules. It can be
an alternative program, an academy program or the program for a math
department. It is a model of what the NCTM Standards were addressing,
an actual mathematics curriculum, and a source of new teaching
materials on applications of mathematics.

So, here's an honest admission: students won't be exposed to the same
level of algebraic symbol manipulation that they would by taking 2
full years of algebra in high school. There's no way they could!
However, most students who DO take 2 years of algebra in high school
don't really know their algebra. A lot of them have to retake courses
again when they get to college.

Will students be prepared for college by studying ARISE? While it's
too early to quote statistics, my feeling is that "Some will; some
won't!"

 Testing processes are being adjusted to reflect what the NCTM
Standards have charted as the course for math education, and will
align themselves with the Assessment Standards relatively soon (at
least in our lifetime).

Marti Gaydish: Negative Review of Arise math pr
ogram

@@Area

Circle area (2 PI R squared)
G5 Dist of Columbia - pi times radius squared
   http://www.k12.dc.us/dcps/Standards/Grade-level/Grade%205/WS-math-5-ad4.pdf
G6 Connected Mathematics (PI R squared not in student book)
G6 GA
   public.doe.k12.ga.us/DMGetDocument.aspx/6th%20Grade%20Unit%205%20Circles%20and%20Graph%
G6 CT
G6 CA
   www.cde.ca.gov/be/st/ss/mthgrade6.asp


@@Arithmetic


Ability level


%%Addition
--------

Add to sum = 10 by counting
K Lk Wash
G1 Oak Harbor Christian School
G1 Japan

Add to 10 + 10 = 20 by counting
G1 CA 1998
G1 Lk Wash
G2 Oak Harbor Christian School

Add 3 numbers
G1 Scott Forseman

Commit math facts add/sub to 20 to memory
G1 CA 1998
NA WA

Add 2 digit whole numbers on paper with carry
G2 CA 1998
G2 Lk Wash
G2 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm

Add 3 digit whole numbers
G2 CA 1998
G2 Japan
G3 Lk Wash

Add 5 digit whole numbers
G3 CA 1998

Add whole numbers and simple fractions
1 1/2 + 1/2
G3 Los Angeles

Memorize addition table
(equivlant to 2 digit adding?)

Add money amounts (2 digit decimal)
G4 WA Assessment
G4 LkWash
G7 WA Benchmark
G8 Vermont

Add any decimal amount w/o calculator
G4 Addison Wesley 1991
G5 Lk Wash
G7 WA Benchmark
G7 LA Benchmark
G7 Nebraska 1940s
NA Vermont

Add any decimal amount with calculator
G6 Lk Wash

Add scientific notation
G9 LA


%%Subtraction
-----------

Subtract from 10 K->1

Subtract from 20

Subtract 2 digit with borrow
G2 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm

Subtract from 100

Subtract 3 digit
G3 Lk Wash

Compute change from 1 dollar on paper
G4 Lk Wash

Compute change from 1 dollar in head
NA

Subtract multiple digit whole numbers on paper
G4 WA
G4 Vermont

Subtract decimal numbers on paper
NA Vermont

Subtract any amount on calculator
G5-8 Vermont


%%Multiply
--------

Concrete Multiplication
-----------------------
G1 Draw 3 hats, each with 2 feathers and 3 buttons Lk Wash homework
   z39\clipim\99\15\3hats.efx
G2 Lk Wash

Memorize multiplication table
-----------------------------
G2 Japan 1990
G3 California '98
G4 California '97
--- do not memorize multiplication table ---
NA Alaska
NA Massachusetts
NA Minnesota
NA Washington EALR
NA Lake Washington SD


Multiply to 20 x 20
-------------------------
- Not common in US, common in Germany, Japan

Multiply 2-3 by 1 digit whole number
-----------------------------------
G4 WW Assessment
G4 Lk Wash
G4 1998 Mass MCAS test

Multiply 2 by 2 digits by drawing pictures (I'm
not kidding!)
------------------
G4 America's Choice New Performance Standards (NCEE)

Multiply 3 by 2 or 3 digits
G3 Japan
G4 1964 Addison Wesley
G5 British Columbia

http://www.thecrimson.harvard.edu/opinion/article.asp?ref=7818 May
04, 2000 New Battles in the Math Wars By WILFRIED SCHMID 
What is 256 times 98? Can you do the multiplication without using a
calculator? Two thirds of Massachusetts fourth-graders could not when they
were asked this question on the statewide MCAS assessment test last year. 


Multiply 4 by 2 digits
G4 WA Assessment
G5 Lk Wa

Multiply with decimal money w/o calculator
-------------------------------------------
G4 WA Assessment
G5 1964 Addison Wesley
G5 Lk Wa
G7 WA Benchmark
NA Vermont

Multiply with 1 decimal by estimation
G5 Houghton Mifflin  1.3 * 3

Multiply with decimal w/o calculator
G4 WA Assessment
G5 Lk Wa
G6 1964 Addison Wesley
G7 WA benchmark
G7 1940s Nebraska
NA Vermont

Multiply with sign
G7 WA benchmark

Multiply any amount with calculator
G7 WA benchmark
G5-8 Vermont


%%Division
--------

Sharing Division
G1 Scott Forseman

"Concrete" Division
G1 Washingon 10 feet, how many people? Problem solving with no
   instruction in division.
   http://www.utdanacenter.org/wamathrevision/index.php
G2 Lk Wash
G2 1 card = 3 marbles, how many cards for 24 marbles? Dale Seymour

Equal share division
G2 Utah
   www.uen.org/core/txFile.do?courseNum=5020&fname=math2.pdf 

Equal shares with remainder
G2 California
   "Use repeated subtraction, equal sharing, and forming
   equal groups with remainders to do division."
   www.cde.ca.gov/be/st/ss/mthgrade2.asp

Calculator Division
Prek-4 Massachusetts 1996

Divide 2 by 1 digit with remainder
G2 Wash State 2007 share 38 cents among 3. Problem
   solving with no instruction in equal shares with
   remainder
G3 Japan
G4 Lk Wash
G4 British Columbia http://www.est.gov.bc.ca/.curriculum/www/irps/mathk7/_4n
umno. htm
G4 1998 Mass MCAS
NA Massachusetts 1996

Divide 3 by 1 digit
G3 Japan
G3 1970 Holt
G4 1998 Mass MCAS test
G4 1998 CA Standards
G5 British Columbia http://www.est.gov.bc.ca/.curriculum/www/irps/mathk7/_4n
umno. htm
NA Massachusetts 1996

Divide by 10s
G4 1970 Holt
NA Massachusetts 1996

Divide by 2 digit whole number w/o calculator
G4 Japan
G4 Addison Wesley 1991
G4 Vermont
NA Massachusetts 1996


Long division 4 over 2 digits whole numbers

G4 WA Assessment (60 / 12 = 5, estimate 4 dig / 2 digit)
G4 Addison Wesley 1990 Math 4 textbook
G5 Omitted by Investigations/TERC
G5 Lk Wash
G5 '97 CA (Hard) Math Framework http://www.cde.ca.gov/cilbranch/eltdiv/mathf
w.htm#4-7
G5 Kentucky http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.html
G5 Virginia http://www.pen.k12.va.us/go/Sols/math.html
G5 San Marino CA 3 div by 2 digit
     http://www.san-marino.k12.ca.us/~valentine/fifth/fifthcu. html#MATH
G5 North Carolina http://www.dpi.state.nc.us/Curriculum/Mathematics/grade5.h
tm
     Explain the division process with 1 and 2 digit divisors.
NO British Columbia
NO Wisconsin "selecting and applying algorithms* for division"
 http://www.wisgov.state.wi.us/MSMath.htm
NO '97 CA fuzzy math standard, ommitted on purpose
NO Louisiana http://www.doe.state.la.us/os2httpd/public/contents/math97. htm

NO Nebrask State 1997 http://nde4.nde.state.ne.us/IPS/Issu/mathSTAND.html
NO Washington Benchmark "divide whole numbers"
NO Minneapolis
NO Massachusetts "select and use an appropriate method for computing
  from among mental arithmetic, paper-and-pencil, calculator"

Long division is needed to understand
higher concepts like polynomial factoring, rational numbers.
http://www.csun.edu/~hcbio027/standards/conference.html/
Conference on Standards-Based K-12
Education California State University Northridge Transcript of R.
James Milgram (Mathematics Professor, Stanford)

Money division .xx by whole number

Long division with decimal w/o calculator
G5 1970 Holt Exploring Elementary Mathematics
G6 1964 Addison Wesley Elementary School Mathematics
NA Lk Wash
NA Vermont
NA Massachusetts 1996

Divide with sign
NA Massachusetts 1996

Divide any decimal without calculator
G5-8 Vermont
G7 Mathematics unlimited
G7 1940s Nebraska

Fractions
---------

Add with like denominators
G4 Lk Wash

Compare fractions with fraction strips / benchmark fractions
G6 - Connected mathematics (common denominators not covered)

Add, subtract, multiply, divide with unlike denominators
G5 Lk Wash

Add fractions with common (but not lowest) denominator
G6 Connected Mathematics

Add and subtract fractions using factoring to find least common denominators
G7 1997 California framework
G6-G8 Omitted by Connected Mathematics, only common denominators.



@@Asian 

Asians have the highest quantitative and math scores of any race, the
scores of Asians Americans are just as high as those of Korea, Taiwan
or Japan, about 2 years ahead of white Americans. Asians with english
as 1st language score just as high in verbal as well. Yet Asians
emphasize obedience, rank order testing, conformity and rote
learning, not "progressive" learning styles which have been offered
as the antidote for American kids.

At worst, Asians score only slightly worse than average. More
typically, Asians score as well a communities the next level up in
income, no matter how bad the schools are.

See testing
See Asian Textbook
SAT test

%%Not Applicable

Some claim that Asian methods aren't
applicable since they are teaching to the same race, and suicide
rates are high. In fact, Asians have the fewest "role models" but
the best scores, in the US, Whites have the highest youth suicide
rates.


@@Assessment

Below is the address for NWREL's latest assessment model for problem solving
in mathematics.  The site includes a scoring guide, samples of scored
student work and information about the model.  Check it out at:
http://www.nwrel.org/msec/mpm/index.html.
Mathematics and Science Center
Northwest Regional Educational Laboratory
101 SW Main St. Suite 500
Portland, OR 97204
(503)-275-0689
(800) 547-6339 ext.689
(503) 275-9584 FAX
mcintosr@nwrel.org
http://www.nwrel.org/msec


@@Backlash

%%Defence

http://www.mathematicallysane.com/mission.htm Mathematically Sane
Promoting the rational reform of mathematics education For too long,
however, the public has heard primarily from the side of the
traditionalists. MathematicallySane.com has been developed to balance
the equation. 

http://www.mathematicallysane.com/analysis/survival.htm
Z50\clip\2001\07\survive.htm
Surviving the Math Wars:
Reflections From the Front Lines
Submitted by W. Gary Martin 



%%Offence
LA BATTLE TO KILL FUZZY MATH FOR MINORITIES
http://www.latimes.com/CNS_DAYS/990813/t000072042.html
zip36\clip\99\16\fuzzmat.txt
Friday, August 13, 1999 Order to Scrap New Math Texts Rescinded L.A.
Unified: In clash of philosophies, books were approved, then
eliminated and finally reinstated.  By LOUIS SAHAGUN, LA Times Staff
Writer Moving to quell a furor over traditional versus progressive
math instruction, Los Angeles schools Supt. Ruben Zacarias on
Thursday rescinded an order by his top staffers to eliminate
textbooks used in a federally funded enrichment program for poor
minority students.  

PARENTS FIGHT AGAINST CORE PLUS
\clip\98\02\edcli2.txt Detroit Free press 1/19/98 Bloomfield parents
fight for old math They say new method hurts kids BY TRACY VAN
MOORLEHEM Free Press Education Writer

\clip\98\03\reed\reed.htm CA MATH PROFESSORS SPEAK OUT AGAINST CLAIM
OF "CONSENSUS" ON FUZZY MATH.
http://ourworld.compuserve.com:80/homepages/mathman/reed.htm
(Mathematically Correct) For the record, the omission of long
division with 2 or more digit divisors was a conscious decision. I
pointed out in writing and in oral comments before the Commission
that this was missing.

@@Basic Skills

%%Harmful

@@Manual Computation


NEW MATH STANDARDS DEEMPHASIZE PAPER AND PENCIL COMPUTATION
Ensuring **Equity** and Excellence in Mathematics In Reaching All Students
With Mathematics (Cuevas & Driscoll, 1993b), an NCTM task force gave
special attention to programs that work to ensure equity and ...
www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm

Parents of minority students are concerned about new math standards
and curricula that deemphasize paper-and-pencil computation.
Computation skills often are associated with mathematical competence,
and the lack of mastery of these skills has been used to justify
denying opportunities to minority students. Therefore, these parents
are not convinced that mathematics reform is in the best interests of
their children (Secada, 1994).

TEACHING HOW TO MULTIPLY AND DIVIDE IS DANGEROUS
z39\clip\2000\01\leiwand.txt It's Time To Abandon Computational
Algorithms By Steven Leinwand (2/9/94)/Education Week It's time to
recognize that, for many students, real mathematical power, on the
one hand, and facility with multidigit, pencil-and-paper
computational algorithms, on the other, are mutually exclusive. In
fact, it's time to acknowledge that continuing to teach these skills
to our students is not only unnecessary, but counterproductive and
downright dangerous.

ORIGINAL CONTENTS OF PDF ARTICLE
http://my.nctm.org/ebusiness/productcatalog/Temp_Images/666_contents.pdf
17. The Harmful Effects of Algorithms in Grades 1– 4 . . . . . . . . . . . . . . 130
CONSTANCE KAMII
University of Alabama at Birmingham, Birmingham, Alabama
ANN DOMINICK
South Shades Crest Elementary School, Hoover, Alabama

http://members.aol.com/vlorbik/amstalk.html
Some Contradictions of Education Reform:
Constructivism, High-Tech, and Multi-Culti
Owen Thomas 
Constructivism.
EXHIBIT A: Quotes taken from "The Harmful Effects of Algorithms in
Grades 1--4", by Constance Kamii & Ann Dominick in The Teaching and
Learning of Algorithms in School Mathematics (NCTM Yearbook, 1998).

    "The teaching of algorithms is based on the erroneous assumption
that mathematics is a cultural heritage that must be transmitted to
the next generation." (p.132)

    "Some leaders in mathematics education also began to say that we
must stop teaching algorithms because they make no sense to most
children and discourage logical thinking." (p.141) 

I only wish these quotations could be allowed to speak for themselves.
But apparently some people don't not find them as outrageous as I do;
these ideas are taken seriously by the NCTM, after all. (The National
Council of Teachers of Mathematics needs no introduction to the
audience of my talk -- suffice it to say here that they're the
professional organization most aligned with Math Ed "reform").

Basic Skills Versus Conceptual Understanding/ H. Wu
http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf This
view echoes one that is held by many educators, among them Constance
Kamii. Kamii is generally acknowledged to be a leading advocate of
this point of view. A much quoted recent article co-authored by Kamii
and Ann Dominick is provocatively entitled

“The Harmful Effects of Algorithms in Grades 1-4.”7 Its main thesis is
this: Algorithms not only are not helpful in learning aritha metic,
but also hinder children’s development of numerical reasoning....

We have two reasons for saying that algorithms are harmful: (1) They
encourage children to give up their own thinking, and (2) they
“unteach” place value, thereby preventing children from developing
number sense....

The persisting difficulty [with standard algorithms] lay in the
column-by-column, single-digit approach that prevents children from
thinking about multidigit numbers.

This then brings us to an impasse, according to Kamii and Dominick:
Children can have conceptual understanding of numbers without learning
algorithms, or they become mathematical error-prone robots. Which do
we prefer? Invoking Piaget’s constructivism [sic],

Kamii and Dominick recommend that

Children in the primary grades should be able to invent their own
arithmetic without the instruction th are now receiving from textbooks
and workbooks.

 AMERICAN EDUCATOR/AMERICAN FEDERATION OF TEACHERS FALL 1999


http://www.eiu.edu/~scienced/5660/gotta/G-4_R-1.html
  the harmful effects of algorithms . . . in primary arithmetic
constance kamii ( she wrote the autonomy article ) and barbara a. lewis
teaching k8 --- january 1993
Two educators argue the case for "constructivism" as opposed to "traditional math"

http://www.ericdigests.org/2004-3/math.html
ERIC Identifier:  ED482725
Publication Date: 2003
Author: Roh, Kyeong Ha
Source: ERIC Clearinghouse for Science Mathematics and Environmental Education

Problem-Based Learning in Mathematics. ERIC Digest.
Kamii and Dominick(1998), and Baek (1998) have shown, though, that the
standard arithmetic algorithms would not benefit elementary students
learning arithmetic. Rather, students who had learned the standard
addition algorithm seemed to make more computational errors than
students who never learned the standard addition algorithm, but
instead created their own algorithm.

http://www.learner.org/channel/workshops/lala/resources.html#kamii
(has picture)
Constance Kamii
University of Alabama at Birmingham

Professor of Early Childhood Education at the University of Alabama at
Birmingham, Constance Kamii studied under Jean Piaget for a dozen
years, first as a postdoctoral research fellow and later as an adjunct
professor at the University of Geneva. She developed a preschool
curriculum based on Piaget's theory, especially in science,
mathematics, and the sociomoral realm, and is now developing an
elementary math program based on his theory. Kamii is the author of
Young Children Reinvent Arithmetic; Young Children Continue to
Reinvent Arithmetic, 2nd Grade; and Young Children Continue to
Reinvent Arithmetic, 3rd Grade.

Further Readings by Constance Kamii

Kamii, C. 1984. Young children reinvent arithmetic. New York: Teachers
College Press.

Kamii, C., and DeVries, R. 1980. Group games in early education.
Washington, DC: National Association for the Education of Young
Children.

Kamii, C., and Dominick, A. 1997. "To teach or not to teach
algorithms." Journal of Mathematical Behavior. 16(1): 51-61.

Kamii, C., and Ewing, J. K. 1996. "Basing teaching on Piaget's
constructivism." Childhood Education. 72: 260-264.

Kamii, C., Lewis, B. A., and Livingston, S. J. 1993. "Primary
arithmetic: Children inventing their own procedures." Arithmetic
Teacher. 41(4): 200-203.

INVENTED MATH ENDORSED IN AUSTRALIA
www.aare.edu.au/02pap/mci02517.htm
DEVELOPING INFORMAL WRITTEN COMPUTATION
Alistair J. McIntosh
University of Tasmania 
Paper presented at the Annual Conference of the Australian Association
for Research in Education, University of Queensland, Brisbane,
December 2002

There is a related change in approach to written computation advocated
and described, though less clearly, in official documents. For example
the National Statement on School Mathematics (Australian Education
Council, 1991, p. 109) states that:

The development of flexible computational skills can be inhibited by
emphasising the practice of standard paper-and-pencil methods to the
exclusion of all other methods.

It is far more realistic to use a
combination of mental and informal written methods most of the time,
with paper-and-pencil recording seen as providing memory
support...Consequently less emphasis should be given to standard
paper-and-pencil algorithms and, to the extent that they continue to
be taught, they should be taught at later stages in schooling.'

Some researchers in the UK, the USA and the Netherlands (Kamii &
Dominick, 1989; Hiebert et al, 1997; Carroll& Porter, 1998, Thompson,
1999) have made valuable contributions in this field, but to date
there has been little research undertaken to assist teachers in moving
forward in this area

http://www.math.umd.edu/~jnd/The-Math-Wars.html

Similarly, in their much quoted 1998 article, "The Harmful Effects of
Algorithms in Grades 1-4", Constance Kamii and Ann Dominick wrote:
"Algorithms not only are not helpful in learning arithmetic, but also
hinder children's development of numerical reasoning ..."

Invoking Piaget's constructivism, Kamii and Dominick wrote: "Children
in the Primary grades should be able to invent their own arithmetic
without the instruction they are receiving from textbooks and
workbooks."


www.aare.edu.au/00pap/hei00259.htm
Mental computation: Is it more than mental architecture?
Ann Heirdsfield
Centre for Mathematics and Science Education
Queensland University of Technology
Victoria Park Road,
Kelvin Grove 4059
Presented at the Annual Meeting of the Australian Association for Research in Education
Sydney

Literature at national and international levels argues the importance
of including mental computation in a mathematics curriculum that
promotes number sense (e.g., Klein & Beishuizen, 1994; McIntosh, 1998;
Reys, Reys, Nohda, & Emori, 1995; Sowder, 1992; Verschaffel & De
Corte, 1996; Willis, 1992). It has been posited that when children are
encouraged to formulate their own mental computation strategies, they
learn how numbers work, gain a richer experience in dealing with
numbers, develop number sense, and develop confidence in their ability
to make sense of number operations (Kamii & Dominick, 1998; Reys &
Barger, 1994; Sowder, 1990).

Carroll (1997) and Kamii, Lewis, and Livingston (1993) documented the
mental and written computational procedures invented by children who
are active in their learning. They showed that children could produce
a wide variety of efficient strategies that exhibited sound number
understanding even though there was little direct teaching of
algorithms. They also found that the active development of knowledge
encouraged children to participate in the construction of problems and
the explanation of solution strategies.

In Queensland, there are few reform classrooms and the traditional pen
and paper algorithms are still taught out of context and in situations
where children have little or no input into constructing problems and
explaining solutions. As Cooper, Heirdsfield and Irons (1995 & 1996)
reported, this has resulted in a tendency for Queensland children to
use strategies for mental computation that reflect the procedures
underlying the pen and paper algorithms regardless of their knowledge
and ability to use more efficient strategies.

File Format: Microsoft Word - View as HTML
Some experts in the United States provide evidence that the teaching of standard formal written algorithms is counter-productive (Kamii & Dominick, 1997). ...
www.ltag.education.tas.gov.au/focus/beingnumerate/ApproachingComputation.doc

International advice and practice is still evolving, with research on
the development of non-standard but formal algorithms being developed
particularly in the Netherlands. Some experts in the United States
provide evidence that the teaching of standard formal written
algorithms is counter-productive (Kamii & Dominick, 1997). However the
Australian and Tasmanian documents all take the same basic stance:
Young children should be encouraged to explore and invent informal
paper-and-pencil methods to supplement mental and calculator methods
(National Statement, p. 111).  They [Band B students] should devise a
variety of paper-and-pencil computational strategies, record the
results of their thinking in their own way, and progress towards
efficient, though not necessarily standard, procedures (National
Statement, p. 117).  At Level 2, a student: 2.16 Uses a variety of
strategies, including regrouping, to assist in adding and subtracting
whole numbers when unable to compute mentally (National Profiles, p. 42

GUIDELINES FOR PAPERS SUBMITTED TO THE NINTH DOSME, SHBIE, UBD ...
File Format: Microsoft Word - View as HTML
Firstly, there has been a growing swell of criticism directed towards
the teaching of algorithms in the early primary years (Kamii &
Dominick, 1998; ...
math.ecnu.edu.cn/earcome3/TSG2/07_RegICMIwhite05%5BFinal%5DAllan_EDITED%5B1%5D.doc


@@Bellevue

http://www.jt-actuary.com/Library/hnrsmath.doc
.html
Where is Math Going in Bellevue? John Tupper
CMP math really sucks, what the hell are you guys thinking??


@@Benchmarks by keyword

Links to math grade level benchmarks, by task, survey of different
national and state standards and assessments.




%%States

\clip\98\02\statest.txt Education Week 1/98: States Set To Examine
How To Make Testing Nationally Comparable By Millicent Lawton (states
worried about tests too easy, not too hard) The meeting is the first
event organized by Achieve, the Cambridge, Mass.-based independent
resource center for governors and business leaders on academic
standards and assessments.

@@Birthday Paradox

1993 8th grade text, teacher ed
The following problem appears the Teacher's Edition of "Mathematics in
Action" (1993) published by Macmillan/McGraw-Hill, an 8th grade text.

How many people would you have to ask for there to be a better than
50% probability that two of them will have the same birthday?
 
 You may be surprised to find out that the answer is just 24 people, even
 though there are 366 possible birthdays. 

 Maryland 8th grade assessment
problem with incorrect solution.

 Solution


@@Brain

%%Gender Differences

MATH, NAVIGATION DIFFERENCES IN BRAIN - RATS TOO
z56\clip\2002\05\sexbrain.txt z56\clipim\2002\05\20\sexbrain\sexbrain.htm
http://www.sciam.com/2002/0602mind/0602kimura.html
SEX DIFFERENCES IN THE BRAIN
Men and women display patterns of behavioral and cognitive differences
that reflect varying hormonal influences on brain development by
Doreen Kimura
Men better at 1) 3D rotation, predicting paper folding outcome 2)
aiming projectiles 3) mathematical reasoning
Women better at 1) rapidly identify matching objects 2) recall from
reading or list of words 3) fine motor coordination - placing pegs 4)
mathematical calculation
Note - these are precisely the tasks on the WASL test.

Male and female rodents have also been found to solve problems
differently. Christina L. Williams of Duke University has shown that
female rats have a greater tendency to use landmarks in spatial
learning tasks, as it appears women do. In Williams's experiment,
female rats used landmark cues, such as pictures on the wall, in
preference to geometric cues: angles and the shape of the room, for
instance

%%General

z50\clip\2001\08\mathbrai.txt
The Times  (London)
TUESDAY AUGUST 28 2001
Problems with maths linked to early birth
BY DAVID CHARTER, HEALTH CORRESPONDENT
Neuro-imaging showed that there was a specific area in the left parietal
lobe where children with normal calculation ability had more grey matter
than those with a specific learning deficit in this ability.

@@Burrill

Gail Burrill, president of the NTCM, vice-chair of Clinton math assessment c
ommittee


@@Calculators

Reform math believes that with the advent of the calculator, no one
will have to be taught or know arithmetic. Reaction is to ban use of
calculators in lower grades.


%%Cheating

zip38\clip\99\19\calc.txt
GRAPHING CALCULATORS TOOLS FOR LEARNING AND CHEATING Calculators with
an attitude Legitimate tools for high school math students, or
weapons for lazy cheaters? By JENNIFER LEE New York Times Fri, 08 Oct
1999 Students figure out assembly language, devise cheating programs
and games for calculators.


%%Controversy

http://dallasnews.com/metro/51545_TEACHERS19.html Math teachers
adding technology to help students' skills multiply 03/19/2000 By Ian
McCann / The Dallas Morning News Ann Brooks, a teacher at Richardson
West Junior High School, has used graphing calculators in her
geometry classes since she started teaching three years ago.  "They
help the kids learn the concepts," Ms. Brooks said.

RDYARROW GATHERS ANTI-CALCULATOR
ARTICLES Kids only learn to copy from the display, they don't
understand the underlying math, contrary to the claim that
calculators lead to understanding beyond the calculation of the
answer.

PARENTS FORCE ORE TO PUT NO-CALCULATOR QUESTIONS BACK ON EXAMS
Educators are divided on use of calculators in early grades Scott
Learn Newhouse News Service. Seattle Times 2/21/99
\clipim\99\02\26\calc.tif Math questions without calculators added to
Oregon state math tests after parents ask how to check if children
know manual calculation. Last year half of Ore 5th graders used
calculators in class, all by 10th grade according to NAEP surveys.
NCTM advocated their use in every grade in 1990s.

%%Race 
%%Disadvantaged

BLACKS, POOR MORE LIKELY TO USE CALCULATORS, WORSE OUTCOMES
z49\clip\2000\12\calcrace.txt Calculators May Be the Wrong Answer As
a 'Digital Divide' Widens in Schools By DANIEL GOLDEN Staff Reporter
of THE WALL STREET JOURNAL
http://interactive.wsj.com/archive/retrieve.cgi?id=SB976838326811281152.djm

The Brookings Institution found:
% using calculators every day
50% black
44% Hispanic
27% White

45% subsidized lunch
29% non lunch

42% parents not finished high school
28% college graduate parents

2.0 Public school relative to
1.0 Private school

Kentucky statewide math test 
43% fifth graders in Jefferson County, 30% black
33% statewide 10% black

Pennsylvania 5th graders taking state math test using 
calculators almost every day
5%   overall 
9%   black
8.5% Hispanic
4.4% White
4.1% Asian

Not meeting standards in Maine math test
47%  everyday calculator use
23%  2 or 3 times per month

Analyzing data from the National Assessment of Educational Progress,
every_day calculator users scored lower than less_frequent users,
both overall and within each racial group. 

John S. Bradley, a program manager with the National Science
Foundation, maintains that calculators generally improve student
scores Lee V. Stiff, president of the math_teachers council, contends
that more than 100 studies __ based on testing students with and
without calculators, as well as classroom observation __ show that
calculators can improve student achievement, problem_solving, and
understanding of mathematical ideas.

%%Testing

z41\clip\2000\05\montalg.txt From the Washington Times, Metropolitan
Section, C1, Monday, May 8, 2000 Maryland: Algebra funds OK’d ~
Montgomery seeks $$$ to improve scores By Gerald Mizejewski ­ The
Washington Times. Just 36 percent of county ninthgraders passed final
exams in Algebra 1 in January, the first time educators have used
standardized grading scales.  Grades among minorities are even worse.

Montgomery County Public Schools
have high SAT averages, yet their algebra tests have huge failure rates.

Fri, 15 Oct 1999 From: cassidy@pacifier.com
You can find the restrictions on calculator use in any SAT booklet --
Here are the types NOT allowed:

Calculators with QWERTY keypads (TI92, HP95, etc.)
Calculators with paper tape
Calculators that make noise or "talk"
Calculators that require an electrical outlet
Pocket organizers
Hand held laptop computers
Electronic writing pads and pen-input devices

%%United Kingdom

\clip\98\03\edclip2.txt Christian Science Monitor 1/28/98 Trash the
Calculator, It's Back to Basics in Britain Calculators for children
under 8, for example, have been banned.



@@Calculus

dx/dy, differentials, integrals, and all that. Usually college level,
but taught to upper small percentage of high school students,
sometimes for AP credit. The Efficacy Institute believes that ALL
students are capable of mastering AP Calculus. Also see
testing: AP Calculus

%%All

physics and calculus should be included in all high school curricula.

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z45\doc\web\index\calcprob.txt

Jeff Howard of the www.efficacy.org believes that all students are 
born with the innate ability to achieve AP calculus by the end of 
high school. This is one sample problem:

Sample problems:
http://www.collegeboard.org/ap/calculus/
http://www.collegeboard.org/ap/calculus/frq00/pdf/calc_ab_all.pdf
Graphic calculator is required.
Let R be the shaded region in the first quadrant enclosed
by the graphs of y = e^(-x^2), y = 1 - cos x and the y-axis
as shown in the figure above
a) find the area of the region R
b) find the volume of the solid generated with region R
   is revolved about the x-axis
c) the region R is the base of a sold. For this solid, each
   cross section perpendicular to the x-axis is a square.
   Find the volume of this solid.

I peeked at the solution, and had to download the manual to
a calculator to get the complete keystroke solution to this
problem. I'll send $10.00 to the first correct and complete
solution to this problem, and I'll post the solution next
week.

Actually I haven't figured out how to derive the formula for
(b) yet. One thing for sure, we sure as hell couldn't tackle
this one in my 1976 freshman Calculus class at MIT!

Is there anyone alive who believes this is a reasonable 
expectation for a high school graduation exam? Because if
you don't scream loud and hard, your state will probably 
decide to add it to your graduation requirements soon. 
They're at algebra now, but just wait for 10 years.

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>>\doc\95\14\mathtake.wk1
Source: SAT scores from The College Board, special compilation
SAT Took Calculus W23%(1.0) B12%(-1.9) H16%(-1.5) A40%(2.0)
Increase 1990-95  W21% B33% H23% A5%

Nearly half of Asian SAT takers have taken Calculus, twice the rate
of whites, who are two times the rate of Blacks. However minorities show
the most improvement.

>>\doc\96\01\hedsmith.txt "America Not Competitive" NW Asian Weekly
July 15, 1995 Hedrick Smith in "Rethinking America" points out 6% of
US, vs. 40% of German and 94% of Japanese students in high school
study calculus. filed under asian.education.calculus

\priv\95\12\blakcalc.txt - San Jose Mercury June 25, 1992 "Keys to the
Scientific Kingdom" Minorities in calculus workshop (article text)

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Even though it hasn't been proven that all students can master
arithmetic or algebra, some insist that nearly all can master
calculus by end of high school. It's still a freshman topic at MIT.

long time homeschooler and scientist Art Robinson: Most children are
capable of finishing calculus between ages 14 and 17.

Bellevue Superintendent Paul Riley: I believe everyone should be
taking calculus in high school, but we're not set up for that yet.

The Efficacy Institute believes that ALL
students are capable of mastering AP Calculus.


%%Bosangue's Calculus Study

BLACKS BEAT ASIANS????? IN CALCULUS??? NAAAAAH!
Blacks and Hispanics who took a calculus workshop got better grades than Asians or Whites. asian.education.math Long-Term Effectiveness of the Calculus Workshop Model Martin Vaern Bosangue et al, Mt San Antonio Community College Study of California Calculus College Students 1990-91 compared to minorities who participated in a Calculus workshop. Black/Latino WShop NonWS Filip Asian White All Study Hours 8.23 6.88 4.00 5.77 6.76 6.20 Group Hours 4.09 1.83 0.56 1.15 0.62 1.13 Involve 8.51 7.54 5.67 6.07 7.08 6.58 HS GPA 3.35 3.29 3.34 3.38 3.37 3.35 SAT Verbal 408 383 461 373 469 411 SAT Math 517 491 555 569 589 557 Parent Ed 2.12 2.08 3.00 2.57 3.19 2.72 Course Grade 2.43 1.47 1.18 1.60 1.68 1.58 Index W1.00 BH1.44(1.14) A-1.05 Note that Black and Latino who took the course had better grades than Asians or Whites with higher SAT Math scores, though non-workshop minorities got worse grades, and Blacks and Hispanics generally score worse in most math courses than Whites or Asians. Blacks in the workshop spent much more time on homework than Whites or Asians, but started out with lower math test scores and grades. Date sent: Thu, 08 Jan 1998 23:02:05 -0800 From: Bruce Crawford Arthur, The Drew book I read was "Aptitude Revisited: Rethinking Math and Science Education for America's Next Century." The Johns Hopkins Press, 1996. ISBN 0-8018-5143-2. I can't remember the price, but it was fairly expensive for its length, about 225 pages. Bosangue is a colleague of Drew's. He also did studies with Hispanics and got similar results. It's truely amazing what a difference good study habits close-coupled with effort makes. %%Links http://integrals.wolfram.com/ Mathematica On-line integral calculator http://www.sicyon.com/ Integral/roots calculator @@Charts Bar Charts K - cut out pictures, paste bar chart, pick highest Pie Charts K - draw pie charts in Georgia Reform math gets kids drawing pie, bar, and line charts as early as kindergarten in format most adults never had to learn in high school. Life is going to be one big Powerpoint presentation in the 21st Century. Pie Charts introduced in Kindergarten?? @@Chinese American Psychological Association VOLUME 29 , NUMBER 6 -June 1998 Dipping math scores heat up debate over math teaching psychologists differ over the merits of teaching children ‘whole math.’ By Bridget Murray Monitor staff http://www.apa.org/monitor/jun98/math.html Students need directed instruction because they aren’t naturally motivated to learn, as the constructivists believe, he says. In a recent study of 372 Chinese and American sixth-graders, 12th-graders and older adults, Geary found that Chinese children outperformed American children on computational and reasoning measures. However, Chinese and American older adults performed much the same, and IQ scores in the two countries were also similar. The study appeared last year in the Psychonomic Bulletin & Review (Vol. 4, No. 3, p. 425–430). According to Geary, America’s math performance sags because our country lacks a rigorous, sequenced national math curriculum like China’s. US MATH REFORM MAY BE MISGUIDED: AMERICANS ALREADY OUTPERFORM ASIANS IN FUZZY PROBLEM SOLVING MATH, LAG IN SYSTEMATIC FORMAL INSTRUCTION http://www.aera.net/uploadedFiles/Publications/Journals/Educational_Researcher/3405/03%20Wang.pdf Educational Researcher Vol 34 No. 5 pp. 3-13 Comparitive Studies on U.S. and Chinese Mathematics Learning and the Implications for Standards-Based Mathematics Teaching Reform. by Jian Wang and Emily Lin Chinese students often outperform US students. Chinese Americans also outperform Caucasian and other Asian American students, even before formal schooling, overall. This is cited as the reason for pushing radical new tranformational reforms in mathematics education as "standards based education", often criticized by many for deliberate omission of the teaching of systematic arithmetic methods in favor of open problem solving. However, test details show that Chinese students do not perform better at tasks such as graphing, and open ended problem solving that is such a priority for American reformers, and that the advantage of Chinese may be due to structered and systematic instruction by their parents. @@City %%Los Angeles z48\clip\2001\02\lamath.txt http://www.newtimesla.com/issues/2001-02-22/stewart.html 02/22/2001 Math War A rumble over an essential math text was one of four events that, taken together, show how hard L.A. Mummified reformers must work. By Jill Stewart @@CMSP Comprehensive Math and Science Program funded by NSF brought Pasadena HS from 26 to 57th percentile at algebra level math (successful fuzzy math program?) @@College Headlines are common that it's ridiculous so many college students need remedial math, but nobody's asking if it's ridiculous to require college students to take college level math beyond intermediate algebra, since it's not even required on the SAT, or for high school graduation. %%Remedial COLLEGE LEVEL MATH REQUIREMENT = INT ALGEBRA IS EXCESSIVE AT CC'S z55\clip\2002\04\mathcoll.txt http://www.sunspot.net/news/local/bal-md.math15apr15.story?coll=bal%2Dlocal%2Dheadlines Unequal equation between college, math, study shows High standards contribute to low graduation rate at BCCC, Abell reports; Requirements seen as roadblock By Alec MacGillis Sun Staff Originally published April 15, 2002 "Of the 1,350 first-time students who entered BCCC in the fall of 1997, 12 had graduated four years later; almost all of its students need remediation in math or English. " "95 percent of entering students last year needed remedial math" "test questions: "Find the equation of the circle at (-4,-4) and radius of 3" and "In how many different ways can three spades be drawn from a standard deck of cards?" Embry notes the SAT does not test intermediate algebra, and many top private colleges no longer require math courses for graduation. " @@Combinations and @@Permutations How many different ways can you order N items? If the order matters, it's a permutation. If it doesn't matter, it's called a combination. Most schools introduce this at middle or high school level. Every college math department includes this in a probability course. But NCTM based tests try to introduce this at elementary level. Here's a good definition from the The University of Saskatchewan http://www.usask.ca/education/ideas/tplan/mathlp/a2.htm Permutation - an arrangement of objects in which order is important There are 6 Permutations of ABC ABC ACB BAC BCA CAB CBA Find the number of permutations of the letters p, q, r, and s. Solution 4 x 3 x 2 x 1 = 24 ways 1*2*3 or n! (factorial) Another variation is how many ways can you combine 3 breads with 3 spreads to make different sandwiches. http://www.usask.ca/education/ideas/tplan/mathlp/a6.htm Combination - a selection in which the order is not important (groupings) How many groups of three letters are there if choosing from the letters A, B , C, D, E? Solution There are 5P3 = 5! / (5-3)! = 60 ways to arrange 3 letters. But for each arrangement of three letters, 6 arrangements are the same group. For example, arrangements using the letters Grade Level Spectrum -------------------------- G4 1998 MA MCAS test 2! problems ---- appropriate ---- G6 1998 CA Standards G7 Katy Junior High G7 Tucson Az District G8 Nevada 1998 G8-12 G8-12 Kings County CA G11-12 Instructional Television G11-12 Minnesota Standards Coll Most Colleges include it in probability courses Permutation G12 Nevada G4 1998 MA MCAS Prob 27 - list different ways to arrange 3 stations Prob 32 - how many numbers can you create with digits 1,5,8 Katy Texas Junior High http://www.katy.isd.tenet.edu/kjh/mathematkjh.htm G7 7th Grade - Math 7 includes ... permutations and combinations in application problems. G7 Benchmarks-Mathematics-Middle School (Tucson Az) http://instech.tusd.k12.az.us/esmsmath-b.htm G8 Orange County Framework Orange County Frameworks for Higher Achievement 1998 http://www.ocps.k12.fl.us/framework/ma/resource/links/241.htm G8 investigates combinations and permutations. http://kings.k12.ca.us/math/lessons/teamwins.htm G8-12 Kings County CA HS Minnesota 9-12 Mathematics (achieve) http://www.achieve.org/a_dir/achieve/achieve.nsf/25827e48252eaa2e85256443005 20ee4/43eed95af0cc74ac852565470072356c?OpenDocument Understand the following concepts related to uncertainty: a. randomness b. permutations c. combinations HS Instructional Television Parade of Programs Combinatorics Grades: 11-12 http://llwisc.wecb.org/ITV/Mathematics/Combinatorics/2._Fundamental_Counting _Prin.html The Fundamental Counting Principle is introduced with the question, "What are the chances of rolling two ones and a two with three dice?" The total number of outcomes are shown and counted. This leads to the development of the general formula of the total number of possible arrangements. Finally the program defines a permutation as an ordered arrangement of things drawn from a given number. HS PRECALCULUS TEXTBOOK http://www.thomson.com/brookscole/math/book_tours/stewart_pre/toc.html Precalculus: Mathematics for Calculus, 3/e by James Stewart, Lothar Redlin, and Saleem Watson 11. Counting and Probability 11.2 Permutations and Combinations HS Permutations and combinations North Quincy High School Mathematics Department Curriculum Guide DISCRETE MATHEMATICS http://ci.quincy.ma.us/qps/nqhs/math/dismath.htm (Now if every 4th grader is supposed to know how to count and compute combinations, why does every college include it in probability?) CCO Northern Virginia Community College http://www.nv.cc.va.us/home/jhorn/MTH182.5OU.htm The student will learn to use elementary counting techniques and will learn to distinguish between permutations and combinations and compute both. CO Purdue School of Engineering and Technology http://www.engr.iupui.edu/~orr/webpages/cpt122/syllab.htm College CPT 122 Finite Mathematics - Syllabus CO AMAT3403 E --- Probability 3E - Australian Defence Force Academy, University College Handbook - UNSW Laws of probability, permutations and combinations. @@Communication A big part of math reform is "math communication" or writing a big essay on how you solved a problem, even though most math is simply working out the numbers, not a research paper. @@Common Denominators (See Fractions) G6 1998 CA standard http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G6 1998 CA Common denominators are used to compare fractions and to solve other problems arising from proportions. %%omitted http://www.wgquirk.com/NCTM2000.html The phrase "common denominator" is not found in PSSM. NCTM 2000 @@Community College www.cascadia.ctc.edu Cascadia Community College From printed 2000 guide: Math for Life 3 unit price, cost, hourly wages, proportional scaling Math for Life 4 fractions, decimals, American metric, money, portioning Math for Life 5 (GED) begin prep use formulas, percents in word problems credit finance, simple geometry, calculators Math for Life 6 (GED) finish prep solve problems with formulas, bar circle graphs, ratio, proportion. (grade 6/7) Prealgebra algebraic geometric notation, abstract representations from arithmetic. Integrated Math 1 "introduces linear algebraic thnking and brings in related concepts from geometry and triginometry. Learners will develop study skills and habits, team skills , and the ability to express math in many forms while work with both abstract and real world applications. Int Math 2 mostly algebra, right triangle trig, probability, number theory Int Math 3 log, exponentials, geometry, trig, probabioity, modeling techniques @@congruent Triangle G1 - Saxon video G2 - NCTM check congruence by moving one geoboard shape to cover another. http://standards.nctm.org/document/eexamples/chap4/4.2/index.htm G2 - CA 2.2 two congruent right triangles can be arranged to form a rectangle http://www.cde.ca.gov/be/st/ss/mthgrade2.asp G3 - Kansas 3.1.K4 parts of congruent triangles find angle measures http://www.kerc-ks.org/Benchmark_ind_list.aspx?stan_con_grade_id=13605&con_id=2&grade_no=08&stan_id=3596 G5 - Indiana identify congruent triangles using equilateral, isosceles, acute, and obtuse http://209.85.173.104/search?q=cache:QaqkGhCc8vQJ:www.doe.state.in.us/standards/docs-Math/2006-Math-Grade05.doc+congruent+triangle+grade+standard&hl=en&ct=clnk&cd=19&gl=us G7 - Identify corresponding parts of congruent triangles www.emsc.nysed.gov/3-8/module5.doc G8-12 CA Students prove that triangles are congruent or similar http://score.kings.k12.ca.us/standards/geometry.html @@Connected Mathematics @@CMP Popular NSF funded math program developed at Michigan State University. Generates controversy. Middle school version of Seymour Investigations Asks students to write about a "number you especially like". Students compare fractions with folded paper strips, common denominators are not even mentioned in the book although parents letter, website, and spokeswoman say students are expected to learn how to use common denominators. Students are asked to develop their own way to add, subtract, multiply and divide mixed fractions but no complete method is explained or presented. Revolt in Plano Texas and New York city. Home page: http://www.math.msu.edu/cmp/Overview/Glance.htm "Research results consistently show that CMP students outperform other students on tests of problem-solving ability, conceptual understanding, and proportional reasoning. And CMP students do as well as, or better than, other students on tests of basic skills. " CHANGES GUIDE http://www.phschool.com/sales_support/Tours/Prentice_Hall/CM2/CMP2_Changes_At_a_Glance%201%20.pdf Adds mean, dividing by fraction but still has no instruction on any complete method, only asks students to devise one. Only parent's letter mentions standard fraction methods despite claim that students are expected to use common denominators to add fractions. geoncyn: Tue, 27 Apr 2004 10:20:56 EDT Bits and Pieces II p. 22 I think have that "textbook" around here somewhere - is that the bright pink one with roller-skates/puppy on the front cover? It looks like an early elementary book at first glance. It's insane. NO instruction whatsoever. The worst of the worst. PIE CHARTS, ASK YOUR PARENTS TO TEACH YOU WHAT'S NOT IN THE BOOK, NO INSTRUCTIONS AGAIN sample Connected Mathematics Grade 6: My kid's section on pie charts is "based on what you know, create a pie chart from this data" No instruction whatsoever. CONNECTED MATHEMATICS: CHOOSE A NUMBER THAT YOU ESPECIALLY LIKE CUT OUT FRACTION STRIPS, NOT COMMON DENOMINATORS http://www.massnews.com/past_issues/2000/10_Oct/1000math.htm z45\clip\2000\09\invest.txt Boston Spends $4M to Avoid Math Basics. Massachusetts News Published: Oct,2000 Author: Paul Moreno Boston Schools: these programs help students "develop their own algorithms," parents ...petitioned against "Connected Math" when they found that it gave sixth-graders assignments like this: "Choose a whole number between 10 and 100 that you especially like" .. in New York rebelled when they found out that it asked sixth-graders to add fractions by folding paper strips instead of by converting to common denominators," says The New York Times. CONNECTED MATH HAS NO INSTRUCTION IN PERCENT, OR FRACTION MATH article Adding fractions: You in a group will devise at least one and preferably two methods to add fractions. Here are examples to try it on. CMP2 gives more examples, and calls it an "algorithm" evidently in response to the complaint that the standard algorithm is not taught, but there is still no description of a complete, correct method. 1st 71 page 1 month booklet uses fraction strips and benchmark fractions to compare fractions, but NOT lowest or any common denominator. One exercise works with least common multiple, but it is not formally introduced as a correct method. From Elizabeth Phillips of CMP Bits and Pieces 1 develops understanding of equivalence, ordering, and comparing fractions. The focus is on the act of partitioning into equal-size pieces, and then repartitioning and renaming smaller and smaller parts. In addition, the units focus on the various meaning of fractions: fractions as parts of whole, fractions as measures or quantities, fractions as indicated divisions, fractions as decimals and fractions as percents. Various representations are used with an emphasis on fraction strips and number line. Least common denominator is not discussed in Bits and Pieces I since the students do not need it to compare fractions. The students are encouraged to compare fractions in a variety ways through the various problems that the explore. One method which I did not expect is that some students found it easier to compare fractions by finding common numerators and then comparing denominators. Some look at how far fractions are from one or some other whole number. The same student will use different methods depending on the problem and context. They use the one that makes sense and is efficient to do within the context. If these student strategies are shared and discussed by the class, it enriches all students' understanding of fractions and in particular, equivalent fractions. You can look at some interesting student work on comparing fractions in the attachment that I am sending. See pp. 66-67. If you can not open this attachment, you can view it at our website at: http://www.connectedmath.msu.edu/rnd/past.html While we do not focus on LCD we do however, emphasize common denominators, particularly in Bits and Pieces II and Bits and Pieces III which develop the algorithms for fractions and decimals. It seems to me that requiring LCD just adds an unnecessary layer to the problem-common denominators are just as efficient. Elizabeth Phillips ephillip @math.msu.edu Hu - The back of the parent's letter states that the students should understand how to use common denominators to add, multiply numerators and denominators to multiply and use reciprocals to invert and multiply to divide, but none of this is in the student textbook which like the first version asks students to devise their own "algorithm" when you look up the page in the index for addition algorithm, etc. There is NOTHING in the books that gives a complete, correct method to any of the 4 functions with fractions. Their web SOME KIDS LIKE CONNECTED MATH, LOTS OF SUPPLEMENT NEEDED z75\clip\2003\10\cmp.txt Providence Journal Julia Steiny: Slater kids connect with math Sunday, October 26, 2003 "I'm good at this math, but I wasn't good at the other math. Actually, I was so bad at the other math that I got held back and I had to change schools. But this math . . . I don't get it all the time at first, but after awhile, I always get it. I like it." %%Algebra http://connectedmath.msu.edu/mathcontent/algebra.html In Variables and Patterns (Grade 7), students solve linear equations using a variety of methods including graph and tables. As students move through the curriculum, these informal equation- solving experiences prepare them for the formal symbolic methods, which are developed in Moving Straight Ahead (Grade 7), and revisited throughout the five remaining algebra units in eighth grade. Solve 2x + 3 = 9, x + 3 = 9 / 2, Use properties of equality and numbers to solve each equation for x: 6x + 3 = 4x + 9 %%Review http://www.pearsoned.com/RESRPTS_FOR_POSTING/MATH_RESEARCH_STUDIES/M15.%20CMP_Final_Report.pdf Most teachers like the program, but the few criticisms are scathing "STUDENTS DO NOT HAVE THE SKILLS NECESSARY TO SUCCEED IN POST HIGH SCHOOL MATH CLASSES! Unless the curriculum is heavy supplemented, students have no mastery of math facts, fractions, decimals, percents, and integers. Students at our school have used Investigation/Connected Math for the past 6 years. 3 years ago after many complaints by parents, parent/students were given a choice of Core Plus or Alg/Geometry. We currently have 13 classes of Alg and 1 class of Core Plus. Student are very poorly prepare to take Algebra. The decision to change to this reform curricula was made by administrators against the recommendation of all but one secondary math teacher." ""It teaches nothing. It does not help parents. Discovery is for science not math. Students do not know simple mult. tables, can 't read, but we are expected to have students excel????" %%Plano Texas Plano Unofficial CMP Math page \clip\99\17\conmath.txt CONNECTED MATH UNDER FIRE IN TEXAS 9/7/99 By Andrea Billups THE WASHINGTON TIMES In Texas, six families from Plano filed a class-action lawsuit late last month claiming their children were not learning in the connected math program, and were not given the option of a more traditional math course -- a violation, they say, of the Texas Education Code. The "connected math" program taught in the Plano Independent School District and used in several school districts around the nation has been criticized by parents, including several in Montgomery County, Md PLANO PARENTS SUE OVER CONNECTED / INVENTED MATH zip36\clip\99\16\planoma.txt The Plano Star Courier. Publication date - Wednesday, August 25, 1999 Parents to file lawsuit today against PISD Organizers claim the district ignored their right to offer input into their children's education By JONATHAN M. BELL Staff writer Parents of Plano students will file a class action lawsuit today claiming the Plano Independent School District ignored their fundamental right to have direct input in the education of their children. The lawsuit stems from a year-long struggle over connected math, a new middle school math curriculum. TEA finds CMP is not compliant with state standards PLANO PARENTS SUE FOR ALTERNATIVE TO HATED "CONNECTED" MATH \doc\web\99\10\planrit.txt The Plano ISD has now adopted the Addison-Wesley (Dale Seymour) Connected Math Program districtwide. In the process of doing so, they ignored, pushed aside and derided the concerned parents who noted a number of problems with the curriculum. At "informational" seminars scheduled throughout the district, officials directed that parents be forbidden from even handing out written materials regarding the program. PLANO PRODUCES DISTRICT RESPONSE TO MATH PROTESTS \doc\web\99\07\conmath.txt For those of you following our effort to rid our school district of Connected Math, here is an update. We direct mailed a petition to about 5000 families of future 6th, 7th and 8th graders and have managed to collect 500, so far, asking for an alternative math class. \clip\99\planmath.txt Parents asking state agency to look into math program School board to vote on textbook Tuesday 03/16/99 By Sandy Louey / The Dallas Morning News Plano district officials said the math curriculum in the schools need to move away from memorization and toward problem-solving and understanding Plano parents against connected math, says that 6 out of 1000 adopting is already failure for nsf math. Articles on Plano protests Letter shows how NSF funded math has sparked protest. In Plano, parental concern over neglected skills have provoked demands that the school provide alternative traditional curriculum ("School district should scrap Connected math experiment," Plano Star Courier, August 12, 1998). The administration of Plano Independent School District implemented Connected Mathematics without review or approval of the Plano School Board %%National WASHINGTON DC CMP rejected in DC suburb and Singapore Math Textbooks Piloted NORTH PENN GETS RID OF CMP z75\priv\2003\11\npenn.txt Reds1122 aol.com was instrumental in killing CMP http://www.phillyburbs.com/intelligencerrecord/news/news%5Fintell/1625921.htm Board subtracts new math program By John Anastasi http://www.zwire.com/site/news.cfm?newsid=4789671&BRD=2275&PAG=461&dept_id=466404&rfi=6 New math gets scaled back http://www.zwire.com/site/news.cfm?newsid=4800668&BRD=2275&PAG=461&dept_id=466401&rfi=6 No final answer‚ but new math is on way out http://www.philly.com/mld/inquirer/news/local/states/pennsylvania/counties/montgomery_county/3459656.htm The inquirer (a strong Merlino supporter) Their report was bias and full of incorrect data. The professors found the Ridley numbers incorrect and other incorrect info. http://209.164.32.120/smni/002/bwFamily-720x300-v01.html the letters to the editorial. I will not deal with the Inquirer because of their bias article. I wonder how they felt when we won. But the letters will give you an idea of what the opposition will try to present. http://www.thereporteronline.com/site/news.cfm?newsid=4862383&BRD=2275&PAG=461&dept_id=466404&rfi=8 Merlino's comments about NP pulling out. http://www.thereporteronline.com/site/news.cfm?newsid=4974105&BRD=2275&PAG=461&dept_id=466404&rfi=8 http://www.phillyburbs.com/couriertimes/library/2001news/863233.htm BRISTOL TOWNSHIP 'Core Plus' a plus or minus for students? A PA suburban school chooses a math program http://www.phillyburbs.com/couriertimes/news/news/0607math.htm A look at the history of these math education. http://www.csmonitor.com/sections/learning/mathmelt/p-2story052300.html LANDSDALE PA z56\clip\2002\07\mathfail.txt http://www.zwire.com/site/news.cfm?brd=2275&Nav_Sec=58218 New math gets scaled back ICHAEL ROCCO , Staff Writer 07/19/2002 The Reporter Lansdale, PA 19446 LANSDALE – New math nearly became extinct math at the North Penn School Board meeting Thursday night after a recommendation by North Penn School District Superintendent Bob Hassler on the much-debated Connected Mathematics .... was used in seventh grade last year‚ but numerous parents have complained that their children are not learning math basics... will use traditional textbooks as the foundation and base of the math program next year %%Review ================================================================== James Milgram reviews CMP Finds alleged study of CMP "evidence" is bogus. Says appears to be remedial in nature, and is confusing even to teachers. No definition of "mean". PARENTS WANT TO DISCONNECT FROM THIS MATH PROGRAM http://cmpinpisd.freeservers.com/ Connected Mathematics Disconnected Parents http://cmpinpisd.freeservers.com/page42.htm When these textbooks were reviewed for compliance to the Texas Essential Knowledge and Skills elements by the Texas Education Agency, they failed to address an average of 43.3% of those elements at each individual grade level. The teaching of Connected Math is characterized by group discovery of mathematical concepts with an emphasis on problem solving, communication, reasoning and connections (the National Council of Teachers of Mathematics goals). Due to the time consuming nature of the program, some classes only completed 4 of the 7 modules scheduled to be covered at a given grade level ================================================================ Mathematically Correct Review Grade 7 - GETS FAILING GRADE http://www.mathematicallycorrect.com/books7a.htm Mathematical Depth [1.7] There is very little mathematical content in this book. Students leaving this course will have no background in or facility with analytic or pre-algebra skills. The introduction to Part 1 says "Connected Mathematics was developed with the belief that calculators should be available and that students should decide when to use them." In one of the great understatements, the Guide to the Connected Mathematics Curriculum states, "Students may not do as well on standardized tests assessing computational skills as students in classes that spend" time practicing these skills. =================================================================== SINGAPORE MATH STINKS EXCEPT FOR MATH SKILLS AND PROCEDURES U Washington Dept of Applied Mathematics http://www.amath.washington.edu/~adams/comparisons.html Middle School Mathematics Comparisons for Singapore Mathematics, Connected Mathematics Program, and Mathematics in Context (Including Comparisons with the NCTM Principles and Standards 2000) Submitted to the National Science Foundation by the Dept of Applied Mathematics Univ. Washington Loyce M. Adams, K.K. Tun, Virginia Warfield Co-Principal Investigator, NSF projects: creating a Community of Mathematical Learners. ... Nov 2, 2000 http://www.amath.washington.edu/~adams/full.pdf Full report - How does Singapore compare since they come out at the top of international comparisons? Mathematics in context: Because MIC is so fixated on conceptual underpinnings, computational methods and efficiency are slighted. Formal algorithms for, say dividing fractions are neither taught nor discovered by the students. we feels a return to some middle ground is warranted. Students should have and understanding of equivalent fractions, decimals and percents before the middle grades. z58\clipim\2002\09\12\cmp.appendix.pdf (Connected Mathematics) CMP summary: We feel that CMP's overwhelming emphasis on conceptual development neglects standard computational methods and techniques. .. there is a danger here of producing students with conceptual understanding but limited computational skills. CMP admits that "because the curriculum does not emphasize arithmetic computations by hand, some CMP students may not do as well on parts of standardized tests assessing compuational skills as students .. that spend most of their time practicing such skills....implies we have still not achieved a balance. Singapore: http://www.amath.washington.edu/~adams/sing.appendix.pdf z58\clipim\2002\09\12\sing.appendix.pdf ..provide some unneccessarily sterotypical depictions of men and women..Does not recognize that some students learn better through guided discovery than a direct presentation... seems to be based on the view that the teacher is the primary disseminator of information. Objectives are not well aligned with those in the NTCM standards. Does an excellent job of helping students acquire mathematical facts and procedures through the many worked out examples and large number of practice problems in its textbooks. However, NCTM has identified other goals, most notably reasoning, communication, and connections (a larger conception of mathematics as a coherent whole that interacts with our world) ================================================================== GLOWING STUDIES OF RESULTS CREATED BY NSF MATH PROMOTERS http://www.csmonitor.com/sections/learning/mathmelt/p-3story052300.html TUESDAY, MAY 23, 2000 Flaws in the evaluation process Mark Clayton (claytonm@csps.com) The Department of Education's expert panel, assembled to find the best math programs in the United States, had a key problem, critics say. It relied heavily on studies of student achievement that were authored or co-authored by the directors of the programs themselves - Yet during his stint as an evaluator, Mr. Hoover also worked and studied at Michigan State, the same university that received the Connected Math project grants of more than $7.7 million. This institutional affiliation violates common standards for independent evaluation, ethicists say. ====================================================================== PORTLAND ORE FIXES KNOW FLAWS, OK WITH HATED SEYMOUR MATH \clip\99\19\conmath.txt From: cassidy@pacifier.com http://www.oregonlive.com/news/99/10/st101006.html New math settles in smoothly Portland allows modifications and adaptations, and the reception is an exception to what happens elsewhere Oregonian Sunday, October 10, 1999 By Betsy Hammond of The Oregonian staff A new way to teach math that asks students to discover concepts and probe deeply rather than memorize formulas and perform drills has generated protests in almost every large school district that has tried to make the switch. MONTGOMERY PROTESTS \clip\99\19\conmath.txt Divided on Connected Math For Some Parents and Experts, Curriculum Doesn't Add Up By Brigid Schulte Washington Post Staff Writer Sunday, October 17, 1999; Page A01 Fun? Math? Koutsos and his class at Montgomery County's Col. E. Brooke Lee Middle School are part of an experiment. Lee is one of five county schools testing a new way of teaching math. What is going on in Koutsos's classroom is at the heart of a passionate, often vitriolic debate that has shot through school districts nationwide and has now reached Montgomery. Arthur Hu Reviews: My experience: He's spending 3 hours generating some stupid chart of every possible move in a "factor game", Arthur, if your son was a homeschooler, hence a high level thinker, he would be programming his Factor Game in Logo. Dale From my free_for_a_whistle Logo1.doc: http://fehps.une.edu.au/f/s/curric/gClark/h.html Garry Clark.Information Technology and Mathematics Australia http://www.northnet.com.au/~mathsactivities/mathact.htm Mathematical Activities is a CD of 109 activities designed to reveal the level of mathematical thinking of young users and to improve their computing skills. http://www.northnet.com.au/~mathsactivities/stratgames.htm Factor Game Players, in turn, choose a number from the board and score that many points. The opponent obtains the sum of the factors of the number chosen that are available on the board. 70 PAGES BUT _NO_ INSTRUCTION ON HOW TO COMPUTE AVERAGE WITHOUT BLOCKS Text z75\clipim\2003\10\28\conmath.efx, .jpg 70 pages but the most important item in statistics, how to compute an average ISN'T THERE!!! By comparison, Saxon spends just 2 pages and spells out exactly how to compute an average. They waste no space or time on "line plots" (frequency histograms) or "steam and leaf" plots. Just ONE item on homework takes a math whiz 10 minutes out of target 30 minute homework time. %%Research ?? http://connectedmath.com/Book%20series.htm GRADE SIX Prime Time Number theory, including factors, multiples, primes and composites Data About Us Statistics, formulating questions, organizing, analyzing data. Shapes and Designs Polygons, angles, measuring two dimensional geometry. Bits and Pieces I Understanding fractions, decimals, percents, all the rational numbers. Covering and Surrounding Area and perimeter of polygons and circles. How Likely Is It? Probability: likely and unlikely. Making sense of the uncertainty of things. Bits and Pieces II Using the rational numbers (B&P I) with +,-,x,%, and division problems. Ruins of Montarek Spatial Visualization: Architectural and isometric representations. http://ra.terc.edu/publications/Alliance_Access/Vol3-No3/math-curriculum.html Choosing a Mathematics Curriculum Debbie Bird, who teaches sixth grade at Fort Fairfield, reports that the selection committee spent almost a full year reviewing mathematics curricula before selecting Connected Mathematics Program (CMP). She says it was time well spent. factor game: She realized that while her students were having fun playing the game, they were also encountering some complex mathematical concepts. " We played the factor game and then analyzed game strategies and this lead to a discussion of prime numbers, an advanced concept for my students." This hands-on experience with Connected Mathematics convinced Debbie that the program would work in her classroom. http://www.pearsonatschool.com/k12/teacher/cat Connected Mathematics , 2002: Data About Us Student Edition Extensively field tested middle school program that features an investigative approach to teaching statistics. For each investigation students do hands-on activities to discover key math concepts....SEE MORE $5.97 Grades: 6 http://www.math.msu.edu/cmp/RREvaluation/Achievement.htm#Mass Quantitative Research or Data The quantitative results consistently show that CMP students do as well as or better than other students on tests of basic skills. And CMP students outperform other students on tests of problem-solving ability (including multi-step problems), conceptual understanding, and proportional reasoning. NO HARM DONE TO 5TH GRADERS, SOLVING, BLACKS DO MUCH BETTER Lapan, R.T., Reys, B.J., Barnes, D.E., Reys, R.E. (1998). Standards-Based Middle Grade Mathematics Curricula: Impact on Student Achievement. Paper presented at the Annual Meeting of American Education Research Association in San Diego, California in April, 1998. Standardized measures of traditional mathematics achievement and mathematics problem solving were administered at the end of fifth grade for base line data and at the end of sixth grade after one full year of implementation. "No significant differences were found between the groups with respect to traditional mathematics achievement. However, students in the two standards-based curricula significantly outperformed the control group in mathematics problem solving. No gender differences in traditional mathematics achievement or mathematics problem solving were found. Mathematics problem solving scores for African American students in the two standards-based curricula were significantly higher than scores for African American students in the control group" (Lapan et al. 2). http://www.phschool.com/product_information/math/middle_grades/connected_math.html Student Materials Connected Mathematics is organized by grade level, with eight units for each grade level. 8 X 70 = 560 @@Connecting Math Concepts :) From: Keta Tom Prof. Bishop likes Saxon and Connecting Math Concepts, a Direct Instruction series published by SRA. @@Coordinate Grid %%Read points 1st quadrant (x,y positive) 3-5 Lk Wash 4 Addison Wesley Math 1991 4th WA Assessment 4 MCAS 1997 MA assessment -------------------------------- 5 Nevada 1998 7th WA Benchmark %%Plot points all 4 quadrants 6 Nevada 1998 WA 4th Grade Assessment - tell which 3 points will connect a straight line given x,y pairs. WA 4th Grade Benchmark - describe relative positions on a grid WA 7th Grade Benchmark describe location of objects on coordinate grids http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html @@Constructing Figures %%Closed Area with fixed perimeter G4 1998 MA MCAS test Construct 4 different closed areas with 2 sections of fence %%Math Problem G4 1998 MA MCAS test ---- appropriate ---- G4 1998 MA MCAS test Write 3 clues for another number game and number your clues. The game must have only one correct answer %%Parallel Perpendicular G4 1998 MA MCAS test (street, trapezoid) NA MA standards G4 1998 MA MCAS test Draw streets that are parallel, perpendicular, and intersection but _not_ perpendicular. Draw figure with four sides with 2 sides parallel and 2 sides not. %%Symmetric Figure G4 1997 WA WASL test G7 1997 WA Benchmarks @@Core Plus New NSF funded integrated math curriculum used in Michigan, perhaps least harmful of new systems, opposed by parents in many districts as too difficult for even A grade students or parents. First page of matrix chapter is all about ... the shoe business, with a one sentence mention that a matrix has rows and columns. "If Joe has an IQ of 75, Is Joe mildly mentally retarded?" Cover many topics traditionally covered in college linear algebra, or not at all, such as network theory. Does not teach basic high school solving algebra equations. Andover students who did well only got 1-5 percentile on college math placement, most had to take remedial math, were not even prepared well enough for college algebra. Study shows that Andover students who were 75th percentile in verbal were only 50 in math, while the other school with traditional math was 75th in math as well. %%abandon MARYSVILLE DUMPED CORE PLUS http://community.seattletimes.nwsource.com/reader_feedback/public/display.php?source_name=mbase&source_id=2010995832 Dorboln Marysville, WA February 9, 2010 at 9:26 AM Well said post. Discovering defintley did a lot of good in addressing many of the issues with Pure reform texts such as Core Plus as much as people are against the Core Plus series (and I am one of them), it did do a very good job of connecting equations to their graph, far better than what happens with traditional texts, which tend to just assume the student will put them together. Also, the CP approach to the quadratic formula is very good. Even though we have dumped Core Plus here, several of us still use several of the activites/investigations to augment the newer and more traditional texts. tkcris 9/23/2009 The East Valley district (Spokane) is abandoning CorePlus. Unfortunately they are phasing it out as the kids that have already started in it years past will finish in it. The curriculum will re-embrace the Glencoe traditional texts that were in storage. %Notes MILLIONS DANGLED TO SWITCH TO COREPLUS IF YOU THOUGHT THE OLD MATH WAS HARD.... z58\ahu\clip\2002\09\coreplus.txt mcall.com - Parents fear new math doesn't add up The Morning Call -- September 15, 2002 ... had received a five-year, $2.6 million grant from the National Science Foundation... to help school districts switch to standards-based math, ... Mathematics Project should find out this month if it will receive a $35 million federal grant to bring reformed math to school districts throughout the Lehigh Valley "All I see is poor grades, a lot of frustration and complaints that he hates math.''" "understanding how to solve for ''x'' in 2x + y = z doesn't do much good in Core-Plus, where one problem can require knowledge of algebra, statistics and geometry." SF CHRONICLE COVERS FAILURE OF NSF FUNDED REFORM MATH IN MICHIGAN \clip\99\08\labrat.txt High School Students And Lab Rats Debra J. Saunders Friday, March 12, 1999 San Francisco Chronicle http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/1999/03/ 12/ED101990.DTL MELISSA LYNN was shocked when she discovered that she placed in the bottom 1 percent of the University of Michigan math placement test. She had graduated from the affluent high-achieving Andover High School in Bloomfield Hills, Mich., with a 3.97 grade point average and A's in math. Full report on how Core Plus flunked out elite Andover students: ftp://math.stanford.edu/pub/papers/milgram/andover-report.htm \doc\web\99\02\pkmath.txt Backtalk Phi Delta Kappan February 10, 1999 The cover story, The Mathematical Miseducation of America’s Youth, by Michael Battista endorses the position the industry pushes..deep in the article, concedes advanced algebra students scored significantly better on paper-and-pencil algebraic procedures. see, "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later", by R. James Milgram, Department of Mathematics, Stanford University: ftp://math.stanford.edu/pub/papers/milgram/andoverreport.htm txt: \clip\99\06\coreplus.txt htm: \clipim\99\04\coreplus\coreplus.htm Andover had, at that time, a group of accelerated students who finished their high school education with calculus, because, currently, all students at Andover take Core Plus. Core Plus was phased in over a four year period. the results are not encouraging. ..almost all the Andover students were severely critical of the program, many bluntly blaming it for their difficulties in university level courses. .. by every measure such as ACT scores, SAT Math scores, grades in college math courses, core plus students fell short of Lahser students. [... even when compared with students who did not even take pre-calculus] useless for real life? the two Core Plus students at Andover who reported entering the work force directly after high school. The first of them says "The math program was good and bad. It tried to apply math to real life - but it didn't make a great attempt. I live on my own in [....], use math in all my taxes and bank account things, and I learned all that outside of the math program." other "I am currently working and feel that I cannot even do basic math calculations. I am missing too many fundamentals." "I feel that the preparation I received in H.S. with Core Plus was hardly adequate enough for college Algebra. The students were quite emphatic about where they felt Core Plus failed them. .. they did not feel it adequately prepared them for college mathematics classes. .. their basic math skills were too weak, three others felt that all they had learned from four years of Core Plus was how to use a TI 82 calculator. Median Percentile SAT-MATH SAT-VERBAL Andover, Core Plus 49 74 Lahser, Group 1 76 79 [two groups are comparable in verbal, but not in math] ANDOVER HIGH SCORES 1-5 PCT WITH CORE PLUS \doc\web\index\corefail.htm The Detroit News Metro Section June 17, 1998 Math debate heats up Professor won't give up controversial data on Core-Plus program in Bloomfield Hills By Rusty Hoover / The Detroit News BLOOMFIELD HILLS -- A math program at Andover High School that students say has cheated them out of a solid math education is now causing a second round of controversy. Detroit Free Press \clip\98\03\coreplus.txt http://www.freep.com/news/education/qmside19.htm Calculators do most of work in new math January 19, 1998 Core-Plus math is a curriculum developed at Western Michigan University. Since 1993, it been tested in 23 Michigan school districts. PARENTS FIGHT AGAINST CORE PLUS \clip\98\02\edcli2.txt Detroit Free press 1/19/98 Bloomfield parents fight for old math They say new method hurts kids BY TRACY VAN MOORLEHEM Free Press Education Writer Calculators do most of work in new math January 19, 1998 Core-Plus math is a curriculum developed at Western Michigan University. Since 1993, it been tested in 23 Michigan school districts. Instead of offering algebra, geometry and calculus as separate courses, Core-Plus integrates the major math disciplines into one four-year course, [lets students discover math rather being lectured to and memorizing] Escondiso flunks CPM, IMP, keeps core plus. Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski "Students in new math at Orange Glen, for example, scored an average of 477 on the SAT, while those in traditional classes at the same campus had average scores of 502. " "No data is available that indicates that the integrated math is a success," he said." %%review http://www.sbe.wa.gov/documents/1-15-09SBEHighSchoolMathematicsInitialrecs.pdf Rank: 1 Holt Mathematics traditional 2 Discovering traditional 5/6 Core PLus Math Integrated M1-3 @@Counting -------- Count to 10 Preschool->K age 2 - India Little Angels Kindergarten NYT 1/2/2008 K Lk Wash Count to 20 Preschool->K K Lk Wash Count to 100 Preschool->G1 G1 Lk Wash G1 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm Count to 1000 G2 CA 1993 G3 Lk Wash Count to 1,000,000 G4 Addison Wesley Math 1991 G4 Lk Wash G4 Vermont Count to 1,000,000,000 G5 Lk Wash %%Language Some "primitive" cultures don't even have words to count up to ten. But the people are capable of learning mathematics. Henry Harpening says the Northern Bushmen have words for 1-4, an expression "kills fingers for five", above that, nothing. abcdThe Naro only have words for 1, 2, 3. Francis Galton explored this area and reported how hard it was to ask Herero's for measures of distance or time as they had no words for numbers. They apparently counted to five with words one, two, three, many, and many-many. %%Monkeys MONKEYS CAN COUNT, HUMANS CAN AT 3 \clip\98\15\monkey.txt Count Monkeys Among the Numerate Study Finds Monkeys Can Count By Rick Weiss Washington Post Staff Writer Friday, October 23, 1998; Page A01 Monkeys have an innate ability to conceptualize numbers and can be taught to count at least to the number nine, according to a series of groundbreaking experiments that promise new insights into the evolution of intelligence. @@courses Even taking into consideration the high participation rate of Asians, Asians take a very high percentage (40%) of Calculus and Honors math courses, and get the best grades. Even when Blacks take the best math courses, they score more poorly than White and Asians who have taken much less math, though the White / Asian gap narrows by 75% when both take calculus. Blacks with the most math still scored lower than Asians with less than 1/2 year of high school math study. \doc\95\14\mathtake.wk1 Source: SAT scores from The College Board, special compilation SAT Took Calculus W23%(1.0) B12%(-1.9) H16%(-1.5) A40%(2.0) Increase 1990-95 W21% B33% H23% A5% Nearly half of Asian SAT takers have taken Calculus, twice the rate of whites, who are two times the rate of Blacks. However minorities show the most improvement. \doc\95\12\sat95bk.xls 1995 Scholastic Aptitude Test Breakdown by Ethnicity Data from the College Board Data Entry and Analysis by Arthur Hu White Black Hisp Asian SAT Math Coursework pct Gap math pct Gap math pct Gap math pct Gap math Overall 0 498 -110 388 -72 426 40 538 Algebra 97 0 498 96 -110 388 97 -73 425 94 37 535 Geometry 95 0 504 90 -109 395 94 -73 431 94 36 540 Triginometry 55 0 539 43 -106 433 42 -68 471 64 26 565 Precalculus 38 0 573 24 -104 469 32 -77 496 54 18 591 Calculus 23 0 613 12 -105 508 16 -76 537 40 13 626 Computer Math 9 10 10 13 Black Calculus is equal to Whites who took Geometry, Asian Algebra, or Hispanic precalculus Asians advantage falls to 13 points with Calculus vs. 40 overall Nearly half of Asians took Calculus, 2X rate of Whites, 4X rate of Blacks White Black Hisp Asian Years of Study pct verb math pct verbal math pct verbal math pct verbal math 4 70 521 62 406 62 451 77 558 3 27 450 33 361 35 390 20 469 2 3 402 4 332 4 356 3 449 1 0 395 0 319 0 329 0 428 1/2 or less 0 435 0 330 0 372 0 434 honors 29 597 18 487 25 518 42 619 42% (nearly half) of Asians took honors math courses compared to 29% White, 18% Black Black 4 year = White 2 year, Hisp 3 Year, Asian 1/2 year or less Blacks who took honors courses (487) still less than Whites overall (498) Asian honors is highest, even higher than Asian $70,000+ income @@CPM (College Preparatory Math / Integrated Math) CPM is an "integrated" math curriculum which does not require students to master and complete learning of basic concepts before going on to more advanced topics. Tigard-Tualatin (OR) school board voted to abandon the program in 2009 http://www.tigardtimes.com/news/story.php?story_id=124231554279260600 CPM a casualty of TTSD math war In a split vote, the school board sides with Parents for Math Choice and decides to return to a more traditional math program By Christina Cooke The Times, May 14, 2009 ...Parents for Math Choice, who said the CPM curriculum was not working for their children. “Given the level of unrest this adoption has caused in our community and even among our teaching staff, I’d prefer to take a step back to a more conservative approach,” “I don’t think it’s fair to throw out CPM when we haven’t used it for a year because it has a few gaps" teacher ... "“We see them understanding concepts more easily and much more deeply.” %%Against Mathematical ly Correct Escondiso flunks CPM, IMP Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski Effectiveness of CPM vs Traditional Math by a Robert W. Haswell, a high school teacher Traditional students trounce those taught algebra with CPM SECOND SEMESTER ALGEBRA FINAL EXAM SCORES GRADES TRADITIONAL CPM A 29.1% 4.5% B 25.5% 6.7% C 14.5% 9.0% D 18.2% 16.9% F 12.7% 62.9% Median 42 27 These figures show that 54.6% of the traditional students earned A or B grades on the multiple-choice portion of the final exam, while 11.2% of the CPM students earned A or B grades. This is almost FIVE TIMES as many A's and B's earned by the traditional students as the CPM students. It can also be seen that 79.8% of the CPM students earned D or F grades, while 30.9% of the traditional students earned D or F grades. Where's the Math http://www.intres.com/math/_disc2/0000004f.htm New Math From: High School Teacher Date: 30 Jan 1997 I only wish we had more parents in Ca. that would check out the new math that is being forced on many of us that teach math. I thank you for speaking up . I teach CPM1 and Trig at Xxxxxxx in Xxxxxx, Ca.I feel that mathland at the lower level anddrop from the group, indicate this in a message to the group and I will contact our postmaster requesting the change. %%For http://www.cit.state.vt.us/educ/alliance/programs.htm Included on a listing of successful programs self-identified by schools on the 1996 Vermont Alliance Survey. http://www.service.com/PAW/morgue/news/1996_May_29.MATH.html Palo Alto Weekly Wednesday May 29, 1996 SCHOOLS: Math program nears adoption Board to choose between two courses Thursday. Creative Publications' "MathLand," a popular and innovative, hands-on approach to math which has no textbook; Everyday Math has no text, but includes a journal which can be used as a workbook and a textbook and integrates basic concepts with newer approaches. KENT JUSTIFIES AND EXPLAINS EVERYDAY MATHEMATICS Philosophy Statement "What is Everyday Mathematics© and why are we involoved with it?" We have also heard about how poorly our students score in mathematics compared to other countries. Everyday Mathematics© attempts to remedy this problem by giving your child a wide range of mathematical experiences and ideas. We achieve this by integrating mathematics instruction into other curricular areas, like science, social studies, and the language of mathematics. @@Democratic vision EPAA Vol. 9 No. 11 Cochran-Smith: Constructing Outcomes in Teacher ... ... researchers, and policy makers committed to a democratic vision of society and to the vital ... Relationships between research and the NCTM standards. ... epaa.asu.edu/epaa/v9n11.htm http://www.ingentaconnect.com/content/routledg/ueee/2004/00000037/00000004/art00007 Review of the Year's Publications for 2003: Social Justice Education Authors: Susan Allen; Marcella Runell; Rani Varghese; Tanya Williams; Maurianne Adams; Elaine Whitlock Source: Equity & Excellence in Education, Volume 37, Number 4, December 2004, pp. 360-376(17) Publisher: Routledge, part of the Taylor & Francis Group [RTF] Theoretical Perspectives for Developmental Education File Format: Rich Text Format - View as HTML ... the significance of difference to a democratic vision of the future. ... the National Council of Teachers of Mathematics (NCTM) articulated a set of ... www.gen.umn.edu/research/crdeul/rtf/monograph/1-theoretical.RTF [PDF] 174 Wednesday Morning, April 13, 2005 File Format: PDF/Adobe Acrobat - View as HTML Achievement and NCTM Standards in Algebra I Classrooms. Belinda Gimbert, Pennsylvania State ... Mapping Diversity of Democratic Vision/Imagination for ... www.aera.net/uploadedFiles/Meetings_and_Events/2005_Annual_Meeting/Program/174-201%20Wednesday%20Morning.pdf Powell's Books - Education A collection of insights into what a democratic vision of literacy looks ... Dozens of ready-to-go activities to develop the NCTM's essential math skills. ... www.powells.com/usedbooks/Education.30.html Ensuring Equity and Excellence in Mathematics Behind Goals 2000 and the NCTM standards is the conviction that all students ... understand and share the democratic vision that underlies the Standards and ... www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm NCTM: News & Media: Past President's Messages NCTM and Democratic Principles In its long history, NCTM has rarely been ... Six important points to know about the vision of mathematics education set ... www.nctm.org/news/pastpresident/ http://www.nctm.org/news/pastpresident/2003-01president.htm NCTM once published some very useful yearbooks. Not only did NCTM once publish some very useful yearbooks, but it still does. Consider the most recent titles in the yearbook series: * 2002: Fractions and Rational Numbers * 2001: The Roles of Representation in School Mathematics * 2000: Learning Mathematics for a New Century * 1999: Developing Mathematical Reasoning in Grades K–12 * 1998: The (NOT) Teaching and Learning of Algorithms in School Mathematics * 1997: Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity I could go on with titles, but only the last one might be incorrectly construed as a "politically correct" publication as opposed to a "useful" book about mathematics. In each of the yearbooks, including the latter, NCTM has taken the stand that (1) all students can learn mathematics; (2) all students are valued in the process; and (3) not all students learn in the same way, so a teacher should know different ways to teach mathematics. These stands are simply restatements of basic principles stated in Principles and Standards for School Mathematics. If these stands represent "political correctness," then the Council should never waver. @@Dilation G8 WA 2007 Draft standard G7 NYS preserved and not preserved under a reflection, rotation, translation, and dilation ... www.emsc.nysed.gov/3-8/module8.doc G8 SC KCSD Curriculum Resources Apply dilation to a square, rectangle, or right triangle www.kershaw.k12.sc.us/district/curriculum/pacing_guides/pacing_math/grade8_math-curriculum_map.doc @@Discovering Algebra Discovering algebra and geometry by key curriculum press Seattle Math presentation http://www.seattleschools.org/area/board/08-09agendas/040809agenda/mathpresentation.pdf 2009-3-8 WA HS Curriculum StudyFile Format: PDF/Adobe Acrobat - View as HTML mathematics is by leaving important mathematics undefined and assumed. Parabolas are one case in point. In Algebra, on page 447, students are given the ... www.math.jhu.edu/~wsw/ED/SThs.pdf "Besides the flaws shared by all the programs, Discovering and Glencoe are mathematically unacceptable for additional reasons. Discovering places more emphasis on the study of graphs rather than the study of quadratic functions. Glencoe presents many unexplained, unjustified rules and procedures related to algebraic skills. Neither program helps students build an understanding of the structure of algebra." Only textbook graded as "unacceptable" OSPI Final Composite Score2 ST Mathematical Soundness Rating Holt 0.838 Meets minimum standard Discovering 0.835 Unacceptable Glencoe 0.826 Approaches minimum standard Prentice Hall 0.820 Unknown McDougal Littell0.783 Unknown CorePlus 0.780 Approaches minimum standard Condemned by Wheres The Math, nearing adoption by Seattle in 2009 Discovering Algebra Everett Parent complains about fuzzy Algebra http://www.youtube.com/watch?v=n340ROI8uYc&feature=channel_page @@Drill vs @@Deep Understanding PARROTS VS DEEP UNDERSTANDING 1960S AND NOW z74\clip\2003\10\mathdrill.txt http://www.newswithviews.com/Erica/Carle9.htm THE MATH WARS - 1960's REVISITED Erica Carle October 13, 2003 NewsWithViews.com @@Equity MULTICULTURAL AND GENDER EQUITY http://www.nctm.org/news/pastpresident/2003-01president.htm NCTM once published some very useful yearbooks. Not only did NCTM once publish some very useful yearbooks, but it still does. Consider the most recent titles in the yearbook series: * 1997: Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity See equity and excellence Ensuring Equity and Excellence in Mathematics Behind Goals 2000 and the NCTM standards is the conviction that all students ... understand and share the democratic vision that underlies the Standards and ... www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm @@Everyday Mathematics A Review of Everyday Math, by Tsewei Wang, Ph.D. (Department of Chemical Engineering) and J. Douglas Birdwell, Ph.D. (Department of Electrical and Computer Engineering)University of Tennessee http://www.lit.net/orschools/A_Review_of_Everyday_Math.pdf z75\clipim\2004\01\22\A_Review_of_Everyday_Math.pdf A summary overview: "Constructivist Mathematics in the Oak Ridge Schools" (Updated April 10, 2001) iposted at: http://www.lit.net/orschools/ z75\clip\2003\11\angrydiv.txt http://www.nypost.com/news/regionalnews/10120.htm New York Post ANGRY DIVIDE By CARL CAMPANILE November 6, 2003 -- A war over the city's new math curriculum erupted yesterday, with parents complaining they're befuddled by the new ways of teaching math - and so are their kids. ""We are starting to get a trickle of complaints from parents that are having trouble understanding parts of Everyday Mathematics and Impact Mathematics. Providing forums for parents to meet to get information and ask questions will alleviate many concerns,"" @@Factors G4 CA 1998 G4 MCAS 1998 prob 15 (convert class of 36 to 1/2, 1/3/ 1/6) G5-8 Mass Framework 1996 G4 CA 1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm The Standards require that students know the definition of prime numbers and know that many whole numbers decompose in different ways. G5-8 Mass Framework 1996 http://www.doe.mass.edu/doedocs/frameworks/Mathnumsense.html Grades 5-8 Learning Standards @@Federal EXPERTS ATTACK MATH TEACHING PROGRAMS \clip\99\20\nomath.txt http://www.latimes.com/news/learning/19991118/t000105076.html Los Angeles Times September 17, 1999 page A3 Education: Top mathematicians and scientists urge U.S. to withdraw endorsement of methods that leave out basic skills. Federal official says change is unlikely. By RICHARD LEE COLVIN, Times Education Writer Nearly 200 top mathematicians and scientists, including four Nobel laureates, are urging U.S. Secretary of Education Richard W. Riley to withdraw the government's endorsement of math programs that experiment with nontraditional teaching methods. SAUNDERS SKEWERS DeptED PUSHING FAILED FUZZY MATH TEXTBOOKS \clip\99\19\whermath.txt Where's the Math? San Francisco Chronicle DEBRA J. SAUNDERS Sunday, October 17, 1999 THIS MONTH, the U.S. Department of Education came out with a list of 10 ``exemplary'' or ``promising'' math education programs. Kings County fourth-grade teacher Doug Swords was shocked at the department's bad choices. Some three years ago, his school district adopted MathLand, a math curriculum that prefers not to give lessons with ``predetermined numerical results.'' The department of Educrats, oops, I mean, Education, rated MathLand as ``promising.'' DofEd BLESSES INVENTED MATH PROGRAMS October 6, 1999 Ed. Dept. To Release List Of Recommended Math Programs By Debra Viadero set this week to confer its seal of approval on 10 programs for teaching mathematics to students in kindergarten through 12th grade. [Every one reflects the under-fire NCTM standards which have drawn fire] ZIP37\clip\99\18\badmath.txt For More Information "Exemplary and Promising Mathematics Programs" is scheduled to be available online at www.enc.org/. Print copies are also available by calling (877) 4ED-PUBS. Connected Mathematics, designed for students in grades 6-8 Core-Plus Mathematics Project, an integrated high school program Interactive Mathematics Program, an integrated, problem-based high school curriculum Pact Algebra, a full-year, technology-based course for students in grades 7-12 Programs recommended for "promising'' status: Everyday Mathematics, a program for grades K-6 Mathland, also for grades K-6 Middle School Mathematics Through Application Project Number Power, a supplemental program for grades K-6 University of Chicago School Mathematics Project, a six-course curriculum for grades 7-12 SOURCE: U.S. Department of Education @@Fractions Grade level comparisons learn about fractions G1 Indiana www.doe.state.in.us/standards/docs-Math/2006-Math-Grade01.doc compare fractions with models G3 numbernut http://www.numbernut.com/standards_3.html G3 CA Compare fractions by drawings or concrete materials www.cde.ca.gov/be/st/ss/mthgrade3.asp G4 Ohio Use models and points of reference to compare commonly used fractions http://www.ohiorc.org/standards/ohio/grade/mathematics/grade4.aspx compare fractions with like denominators G3 Mathematically Correct http://www.mathematicallycorrect.com/kprea.htm compare fractions with common denominators compare fractions using common denominators 12 or less G4 Mathematically Correct http://www.mathematicallycorrect.com/kprea.htm G5 NY State Compare and order fractions including unlike denominators http://www.emsc.nysed.gov/ciai/mst/mathstandards/revisedg5.html G6 VA SOL compare and order 141.104.22.210/go/Sols/math6.doc NO G6 Connected mathematics %%Against \CLIP\2007\12\NOFRACT.TXT FRACTIONS SHOULD NOT BE TAUGHT UNTIL AFTER CALCULUS Educators divided by fractions debate http://www.delawareonline.com/apps/pbcs.dll/article?AID=/20071226/NEWS03/712260337/1006/NEWS Penn prof's book aims to ignite math ideas By MAUREEN MILFORD, The News Journal Posted Wednesday, December 26, 2007 "Our kids ... want to know why they are forced to do complicated and difficult calculations," said Dennis DeTurck, dean of the college of arts and sciences at the University of Pennsylvania. (Buy photo) Special to The News Journal/EMILY VARISCO Dennis DeTurck argues that as mathematics has evolved, so must the teaching of mathematics. PHILADELPHIA -- A few years ago, Dennis DeTurck, an award-winning professor of mathematics at the University of Pennsylvania, stood at an outdoor podium on campus and proclaimed "Down with fractions!" "Fractions have had their day, being useful for by-hand calculation," DeTurck said as part of a 60-second lecture series. "But in this digital age, they're as obsolete as Roman numerals are." "He believes fractions are important for high-level mathematics and scientific research. But it could be that the study of fractions should be delayed until it can be understood, perhaps after a student learns calculus, he said. Long division has its uses, too, but maybe it doesn't need to be taught as intensely." %%1/N One of N equal pieces G2 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm %%M/N Is division of M into N equal pieces G4 CA G5 Minnesota sample test (which pie is 3/5) CA standard 1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm The fraction m/n represents the equal division of m into n equal pieces. %%Unlike denominator Adding / Compare / Subtract or decimal 4th 2000 CA STAR assessment 4th Addison Wesley 1991 4th MA MCAS assessment ------------------------ G5 1998 CA Standards (vs assessment) G6 1998 Nevada G6 1940s Nebraska Ommitted NO CMP2 G6 compare fractions, no instruction for +,-,*,/ NO TERC G5 add, subtract, compare fractions http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm The fourth-grade Standards do not require any arithmetic with fractions; however, practice with addition and subtraction of fractions (like denominator) must be continued in this grade, because they become very important in fifth grade. G5: Adding fractions with unlike denominators and multiplying and dividing fractions. %%Part of Whole to Fraction G4 1997 MA Assessment 6 out of 36 students convert to pie slice G5 1998 MN Assessment (10+5+3+2 votes to pie slices) %%Reducing Fraction G4 1998 MA MCAS test (convert 18 out of 36 to 1/2) G4 1998 MN Assessment (convert 10/20 to 1/2) ---- appropriate ---- G6 1998 CA standard G6 1998 CA standard When reducing a fraction, the greatest common divisor of the numerator and denominator can be used as the common factor. %%Multiply set by fraction %%N/M fraction of whole number Traditionally covered at middle school, moved down as low as G4 Not G2 1998, 2005 CA Mathematics Framework www.erusd.k12.ca.us/ProjectALPHAweb/index_files/CA_MF/GLC&AoE_2.pdf "Students should not be expected to solve "2/3 of 15" numerically in second grade, because doing so requires them to multiply fractions and convert an improper fraction to a whole number." -------------------------------------- G4 1998 Scott Forseman math G4 1997 MA Assessment 1/2 x 250 G4 1997 WA Assessment 2/3 x 30 G5 1998 CA standard G5 Minnesota Assessment 5/6 x 24 G7 1980 Mathematics Unlimited G8 %%Convert Fraction to Decimal G4 MA 1998 Assessment (number line) ---- appropriate ---- G4 CA 1998 Teaching G6 Nevada standard 1998 G4 CA Teaching of the conversion of fractions to decimals http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm %%Multiply Large Number by Fraction G4 1998 MCAS Problem 15 (convert 6/12/18 out of 36 to 1/6-3-2) G4 WASL sample (mowing lawn) ---- appropriate ---- G6 CA 1998 standard There are 24 students in our class. two thirds of them passed the test. How many students passed the test?" %%Compare, Order Compare with same denominator 4th Core Knowledge 4th CA Math Framework WA 4th Grade framework identify, compare, and order whole numbers and simple fractions http://cisl.ospi.wednet.edu/ComSL/MATHBMK1.html Compare with different denominators Performance based assessments routinely test for this in 4th grade but most standards based benchmarks leave this to grade 7. Some tough standards like CA mention this in G5, but no standards mention this in grade 4. CA '98 4th Grade MA 4th Grade Assessment - compare 3/4 and 5/7 WA 4th Grade Assessment - compare probability based on fractions with different denominators, or dilution with different denominators. CA G5 11/1998 WA 7th Grade Benchmark - compare and order whole numbers, fractions, and dec imals http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm 11/1998 Students can use fraction equivalence skills in order to compare fractions 5/1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm#k-3 Understand the values of fractions with denominators to 12, including ordering or comparing fractions and mixed numbers with unlike denominators and the equivalence of decimals and fractions in simple cases %%Convert Fraction to Decimal and Percent G5 CA 1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G5 CA 1998 Fractions can be represented as decimals and as percents. @@Fundamental Changes California Mathematics Council May 1, 1993 Dear CMC Members: Last year the State of California issued a new Mathematics Framework for California Public Schools that recommends **fundamental changes in** the way we teach math. @@Gambling Slot machine has 3 items, but I can't find the odds on a typical machine of a jack pot. How many items per reel? @@Gender GENDER MATH GAP SMALLER IN ASIANS, BUT OBSERVERD FOR ALL CULTURES from http://www.mugu.com/cgi-bin/Upstream/Resources/misc.html upstream website "Among....mathematically gifted 13-year olds, [sex] differences favour males in mathematical reasoning ability, but not in verbal reasoning, where there are no [sex] differences. Our gifted males score approximately one half of a standard deviation higher than females on the SAT-M, our measure of mathematical reasoning. Males' SAT-M scores are also more dispersed {yielding an upwardly shifted distribution of male scores (Benbow, 1988, Behav.& Brain Sci.11}. The resulting proportion of males and females at age 13 at various cut-off scores on SAT-M is approximately as follows: > 500 (average score of college-bound 12th-grade [18-year-old] males): 2 : 1; > 600 : 4 : 1; > 700 (top 1 in 10,000 for 7th graders [13-year-olds] :13 : 1. These ratios have remained relatively stable over the past 20 years, and have now been observed among mathematically gifted students in the 3rd grade (8-year-olds), and cross-culturally (though they are smaller in Asian populations)." Camilla P. BENBOW & D.LUBINSKI, 1993, in Ciba Foundation Symposium 178, The Origins and Development of High Ability. Chichester : Wiley-Interscience. MALES SAT ADVANTAGE DOES NOT SHOW UP IN GENERAL POPULATION \clip\2002\01\gendtrail.txt Girls barely trail boys in mathematics http://www.eurekalert.org/pub_releases/2002-01/uonc-nsg011002.php Public release date: 11-Jan-2002 Contact: David Williamson david_williamson@unc.edu 919-962-8596 University of North Carolina at Chapel Hill New study: Girls barely trail boys in mathematics (SAT) About four times as many boys scored above 600 as girls did, and about 13 times as many boys scored above 700, she said. A male advantage was also evident among college-bound high school seniors. ... Among the findings were that girls had higher average math scores than boys until about age 11 and higher reasoning scores at ages 11 to 13. BOYS ONLY 1.5% BETTER AT MATH THAN GIRLS? z54\clip\2002\01\mathgend.txt http://www.suntimes.com/output/news/cst-nws-math13.html Boys may not be better at math after all January 13, 2002 BY TRISH WILSON investigators at the University of North Carolina at Chapel Hill published a report... They found that girls had higher average math scores than boys until about age 11 and higher reasoning scores at ages 11 to 13. Boys did tend to progress faster, and by the end of high school that learning edge resulted in a 1.5 percent advantage over girls, which is very small, Leahey said. \clip\98\19\gendmath.txt Kianian, Amin M., Gender and mathematics achievement parity: evidence from post-secondary education.., Vol. 116, Education, 06-01-1996, pp 586(7). (electric library) With respect to different aspects of mathematics achievement, the general consensus seems to indicate that females tend to perform better than males in computation, and males tend to perform better than females in problem solving (Hyde et al., 1990). Better verbal ability for girls and spatial ability for boys is also frequent finding (Maccoby and Jacklin, 1974; Werdelin, 1985; Kaur, 1992). A meta-analysis of the studies that have been done during the period of 1974-1987 on mathematics and gender has produced two general conclusions. First, the average gender gap is very small and statically insignificant. Second, the gender differences have declined over the years (Friedman, 1989). \clip\98\04\edbrief1.txt Ruth Schubert, "Boys develop an edge in math very early" Seattle Post-Intelligencer, February 3, 1998, B1 According to a University of Washington study of 276 mathematically precocious children, even before they reach first grade, more boys than girls are exceptionally talented in math. @@Geometry %%Congruent G2 Texas Core Curriculum http://www.trinity.edu/departments/education/TCKC/2math97.htm G3 California G3 Virginia G4 Addison Wesley Mathematics 1991 G4 Wisconsin %%3D Shapes Pyramid G4 Addison Wesley Mathematics 1991 G4 TAAS test G4 WA Assessment G3-5 Lk Wash G10 WA Benchmark @@Parallel %%Parallel Lines Lines or line segments which are in the same direction and will not meet. Grade Spectrum G1 A.G Bell 1999 1st/2nd grade class G4 Exploring Elementary Mathematics 1970 Holt Rheinhart Winston G4 MCAS G4 Core Knowledge G4 Addison Wesley Mathematics 1991 G4 Wisconsin G4 California http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G4 Washington Assessment G5-8 Colorado 1998 Standard %%Perpendicular G2 Texas Core Knowledge http://www.trinity.edu/departments/education/TCKC/2math97.htm G4 Mass MCAS G4 Core Knowledge G4 Addison Wesley Mathematics 1991 G4 California http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G4 1970 Holt Exploring Elementary Mathematics G5-8 Colorado 1998 Standard NA 1964 Addison Wesley %%Radius, Diameter G3 Japan G4 California G4 Wisconsin G5 Virginia G7 Washington %%Right Angle G4 Core Knowledge %%Similar Triangles, Proportionality 4 WA Asssessment (no 4th grade curriculums cover this) 7 VA Standards 7 WA Benchmark 8 NAEP Assessment Standards 8 Wisconsin Standards 9 British Columbia Standards Virginia Standards http://www.pen.k12.va.us/go/Sols/math.html The seventh-grade standards place emphasis on solving problems involving consumer applications and proportional reasoning. Wisconsin Standards Mathematics: http://www.wisgov.state.wi.us/MSMath.htm 8th grade: ratios and proportions (e.g., rates, scale drawings*, similarity* ) BC Standards http://www.est.gov.bc.ca/curriculum/curric/inmath11.htm http://www.est.gov.bc.ca/curriculum/curric/apag9.htm NAEP Standard G8 http://www.projmath.caltech.edu/index.htm Project Mathematics video series is for high school students. BC standards G9, G11 solve problems using the concept that, in similar triangles, corresponding sides are proportional WA G4 = use similar triangles to determine height of flagpole from fire hydrant shadow. WA Benchmark http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html understand the concepts of ratio and direct proportion @@Grade 1 Long time homeschooler and scientist Art Robinson: Our curriculum requires that, during the first year of school, the student learn to read well and also learn the addition, subtraction, multiplication, and division tables through 12s by instant, rote memory. http://www.robinsoncurriculum.com/ negative review: http://eho.org/features/robrev.htm @@Grade 2 z39\clipim\99\12\05\catfish.efx 2nd grade Catfish Soup My 2nd grader got this "Get Your Hands on Problem Solving Grade 2" - requires adding 3+6+9+12+15+18 = 63! Carla Cat sold catfish soup in her cafe this week. Carla sold 3 bowls. On Tuesday she sold 6 bowls. On Wednesday she sold 9 bowls. On Thursday she sold 12 bowls. If the pattern continued, how many bowls of catfish soup did Carla sell on Saturday. Bonus: How much soup did she make all week. Make up a price, how much money did she make? Comment - pattern is OK, but it is not appropriate to add up 7 2 digit numbers manually without instruction, 2nd grade is generally adding 2, maybe 3 number with carry. Multiplication was also not covered in this class. @@Grade 8 ONLY 1/3 OF 8TH GRADERS TAKING PRE- OR ALGEBRA, HALF OF ASIANS The 1990 NAEP Trial State Assessment California: 59% 8th grade math vs 36% pre-algebra or algebra, pre/algebra white 43% black 27% Hispanic 23% Asian 55% 30 min homework Nation 62% / 34%, 15-30 min homework @@Grade Level G=Grade level Multiply 3 x 2 digit G4-G5 323 x 45 Multiply money G5-G6 3.23 x 12 Multiply by decimal G5-G6 1.23 x 1.23 Divide 2 dig by 1 dig G3-G4 12 / 2 Div by 10s G4 120 / 20 Long Divide 3 dig by 1 dig G3-G5 124 / 2 Long Divide 3 dig by 2 dig G3-G6 122 / 12 Money division G4-G5 1.24 / 2 Long Divide 3 decimal by 3 decimal G5-G7 1.234 / 2.345 * many states no longer require teaching long division Probability G4-G7 (coin = 1 in 2, 1 marble out of 6) * pre-1970 textbooks do not cover probability in elementary school Pi, circumference G5-G6 Algebra - 8th to 9th grade (about half of Americans don't take algebra at all)

Graph

@@Graph graph y = 3x G4 CA 2000 STAR sample test
@@Great Mathematicians MATHEMATICS LIBRARY AT COLUMBIA U HAS PC MATHEMATICIAN PICS from h-bd 4/2002 John wrote: On the wall in the main room of the Mathematics Library at Columbia University are four huge pictures of mathematicians. Left to right, they are: Henri Poincaré, Sofia Kovalevskaya, Carl Friedrich Gauss and Emmy Noether. Male, female, male, female. .. A personal (but not particularly unfair) ranking of these 4 people by the magnitude of their mathematical talent, among all the mathematicians of history, would be something like: 8, 253, 1, 179

@@Guess and Check Tables

Grade Level Spectrum -------------------- G2 Eric AG Bell 2000 G4 Scott Forseman Math G4 WA WASL 4th grade sample problem (no solution given) G5 New Progress in Mathematics homework (no solution given) --- inappropriate ---- G7 Passport to Algebra and Geometry New assessments and textbooks expect 4th and 5th graders to solve unknowns such as 2x + 3 (x + 3) = 59 5x + 9 = 59 5x = 50 x = 10 which will be solved in minutes by algebra by constructing a table or making a drawing of all possible outcomes based on an initial,guess x=5 x+3=8 * ... x=9 12 56 x=10 13 59 Considering that any job that requies this skill will require algebra, this is a total waste of time better sprnt on teaching arithmetic.
Parent says his gifted son was able to guess and check a solution too. No algebra required?? Eric in 2nd grade AG Bell 2000: Guess and check: 63 cents of pennies, nickels and dimes same dimes as pennies, 3 more nickels than dimes how many (algebra problem!) 5th graders expected to solve for unknowns by constructing guess and check table instead of using algebra taught at grade 9. This is problem solving?? Passport to Algebra and Geometry (7th or 8th grade pre-algebra) tells how to solve a problem like this, and also shows how to use a table to solve the problem. source: http://project2061.aaas.org/newsinfo/press/attach_c.pdf \clip\99\03\attach_c.pdf @@Higher Standards Why does everyone have to be rocket scientist in the 21st century? Answer: this IS no reason other than as an excuse to spend more money on useless reforms. The Mystique of Math and Science in American Education and The Big Con in Education By Dennis W. Redovich What is the rationale for high stakes testing in mathematics and science for promotion and graduation in public elementary and secondary schools? @@Hispanic Achievement \clip\98\08\latmath.txt http://www.edweek.org/ew/current/31nctm.h17 Education Week 4/15/98 Latino Students' Math Scores Climb While Family Income Drops Washington [oh no, a study that shows that you don't have to wait for middle class equality with whites to achieve better] The math achievement of Latinos improved from the early 1970s to the early 1990s nationwide despite the simultaneous shrinkage in the family income for that group and the rise in Latino child poverty, a study by a California researcher shows. ...conflict with earlier research and challenge what the author argues is a widely held assumption among educators that the math achievement of students from lower income levels improves only as their socioeconomic condition improves. @@History MATH CONTENT BALLOONS FROM BASICS IN 1900S http://www.freepress.com/news/education/qmath30.htm zip36\clip\99\17\mathhist.txt Math topics multiply through years Texts add lessons as technology alters educational goals August 30, 1999 BY TRACY VAN MOORLEHEM Detroit FREE PRESS EDUCATION WRITER "The slim books [from the 1900s] are, in many cases, half as tall as their modern counterparts and a third as thick...In the last century, dozens of topics have been added to math curricula. The only topic that has fallen away, Ball said, is some of the bookkeeping arithmetic that was included in the early 1900s...It fueled a movement, which continues today, to make algebra more universal. More and more districts, including Detroit Public Schools, have an algebra requirement in middle or early high school. At the same time, mathematicians began to see the importance of adding statistics -- the study of the collection and analysis of data. " @@Holt Mathematics %%Review @@Homeschool http://www.oaknorton.com/SLTrib-grip.cfm Alpine in grip of 'math wars' Some parents reject the move from traditional teaching By Celia Baker The Salt Lake Tribune Disgruntlement over a math program that emphasizes conceptual understanding and downplays rote learning caused parents there to pull children out of neighborhood schools in favor of charter, private and home schools; circulate a petition calling for abolishment of "fuzzy" math curricula; and threaten to use a newly enacted law to form their own school district. z47\clip\2000\12\math1.doc Dale Reed's homeschool notes, recommends http://www.robinsoncurriculum.com/ mostly negative review at http://eho.org/features/robrev.htm and Saxon. @@Homework A big complaint about new-new math is homework the parents can't understand DON'T EVER GIVE US AN ASSIGNMENT LIKE THIS AGAIN OR LOSE RECESS I found out that the reason it was undone was because they did not understand HOW to do the work. I sat down and took a look at it. You (the paper) have got to be kidding!!! TEARFUL HOMEWORK HOUR Juanita Doyon 5/2001: The problem with the wonderful new curriculum is that it totally discounts the power of numbers in ones head and the power of studying for understanding rather than sweeping past and catching the crumbs. Trouble is, when kids catch nothing but crumbs at school for whatever reason, and are then sent home with work their parents can't comprehend, they don't even get table droppings of math, much less "higher level thinking skills." All they get is tearful homework hour and parents tearing their hair out! @@How http://www.amazon.com/gp/reader/0805831053/ref=sib_dp_pt/105-7617436-0319658#reader-link Fostering Children's Mathematical Power: An Investigative Approach To K-8 Mathematics Instruction Arthur J. Baroody, Ronald T. Coslick $77.13 (How do do math with TERC, EM, Mathland, etc.) "You probably have no difficulty determining the answer to 1/2 + 1/89. More than likely you would invert the divisor 1/8 and multiply. The point is that you have probably mastered the mechanics of elementary arithmetic -- you know how to add with renaming (carrying or borrowing), how to multiply with decimals, how to divide with fractions, and so forth ... but most teachers do not understand why these procedures work".. "why is it important for you to develop proficiency with such mathmematical processes as problem-solving, reasoning, conjecture-making and -testing and communicating? ... you may have had little or no experience in solving challenging mathematical problems @@Injury and @@Intrusive Survey DALE SEYMOUR G5 INTRUSIVE SURVEY INVESTIGATION | image http://www.arthurhu.com/2004/07/injury.txt Arthur Hu 7/25/2004 Investigation 5 * Session 1 --------------------------- Data: Kids, Cats, and Ads [And serious injuries???] "I felt nervous. I was nervous becuse its' hard to answer your problems and injuries in front of another person. " @@Issaquah 2003: The elementary grades have Trailblazers. the middle school has MaTHEmatics. The high school is in their second year of CPM (College Prepatory Math). @@Important Reformers say that the basics aren't important anymore, we need charts, statistics, higher order reasoning skills ACT: COLLEGE PROFS THINK BASIC MATH, NOT STATISTICS IS IMPORTANT A http://www.act.org/news/index.html May 9, 2000 Most basics: addition, subtraction, multiplication division, ratios, percentages algebraic equations statistics Least Z42\clipim\2000\06\23\actmath\actmath.htm similar pattern followed in teaching students to compute probability. Seventy-two percent of college teachers thought it not important while 41 percent of high school teachers thought it very important. The educators were in agreement, however, about teaching the basics: addition, subtraction, multiplication, division, ratios and percentages. College faculty chose addition, subtraction, multiplication and division as the most important skills to have, while high school teachers chose them as second most important, behind performing very simple algebraic equations. [Most state math assessments put most emphasis on statistics, not arithmetic] @@improvement SAT MATH ABOVE 650 DOUBLES FROM 1981 TO 1995 Bracey says SAT math scores are up Here are the relevant numbers: 1981 1995 # Above 650 70,307 132,898 % Above 650 7.1 12.4 # Taking SAT 993,672 1,067,993 \priv\96\16\educcruc.txt Education Week Volume 15, Issue 33, May 8, 1996 "Education Crucial in Modern Economy By Jeff ArcherThe report acknowledges some gains by the public schools, such as the doubling from 1982 to 1992 in the proportion of high school graduates who took advanced algebra, geometry, and trigonometry. \priv\95\10\betmath.txt - US students have improved by about one year of study in math tests from 1982 to 1992, and are taking more math courses. Reading and writing have not improved as much @@Integrated Schedule In an integrated schedule, one school's plan only spends 15 minutes per day on math.

G1-3 Schedule = 15 min math @@Integrated Math Courses (IMP, McDougall Littell) The NSF funded several integrated high school math programs, most of which have gotten terrible reviews from people who make a living with mathematics. Old: Spend one entire class learning how to solve y = mx + b. New: Spend class on 50 topics covering college level statistics, precalculus and linear algebra, and 1 page on solving y = mx + b. %%Critic (http://www.atmos.washington.edu/~cliff/Mathematics.ppt) \doc\web\2006\04 Excellent presentation on Integrated Mathematics by Professor Cliff F. Mass. %%General NEW CA STANDARDS PROPOSES INTEGRATED GEOMETRY ADDED TO ALGEBRA IN 8TH GRADE \clip\97\25\edclip11.txt Nov 5, 1997 "The fact that [the standards for] 8th grade changed from an algebra class to a mathematics class incorporating algebra and geometry is very consistent with what most other countries in TIMSS do," Mr. Schmidt wrote in a September letter to the commission. [mostly Asian countries]..He also objects to the introduction of geometry in the 8th grade, noting that many teachers at that level are not trained in the subject, and the integration of Algebra 1, geometry, and Algebra 2 throughout the high school grades. "The basic problem is that they spread all this material all over hill and dale," Mr. Evers said. "Overall, I don't think that if you have requirements, you should experiment with a whole state population of children. You should have only a proven, research-based curriculum. , rather than algebra, trigonometry, and geometry. It's just a minor detail that colleges have specific math entrance requirements, which the integrated math courses fail to meet. @@Interactive Mathematics Program (IMP) @@IMP A popular integrated college prep math program that emphasizes problem solving skills. Home Page Discussion Listserver< /a> Mathematical ly Correct IMP DELAYS QUADRATIC FORMULA UNTIL G12 ZIP37\clip\99\18\lamath.txt From: "Mike McKeown" Home Page The Interactive Mathematics Program (IMP) is a growing collaboration of mathematicians, teacher-educators, and teachers who have been working together since 1989. This group has created both an exciting full four-year secondary mathematics curriculum and a rich professional development program for secondary mathematics teachers. This new curriculum meets college entrance requirements and prepares students to use problem-solving skills in further education and on the job. "The IMP curriculum integrates traditional material with additional topics recommended by the NCTM Standards, such as statistics, probability, curve fitting, and matrix algebra. IMP units are generally structured around a complex central problem. " "Dr. Webb has found that IMP students do as well as students in traditional mathematics classes on standardized tests such as the SAT. This is especially significant because IMP students spend about 25 percent of their time studying topics that are not covered on these tests. To measure IMP students achievement in these other areas, Dr. Webb conducted three separate studies involving students at different grade levels and in different locations. The three tests used in these studies involved statistics, quantitative reasoning, and general problem solving. In all three cases, the IMP students outperformed their counterparts in traditional programs by a statistically significant margin, even though the two groups began with equivalent scores on eighth grade standardized tests." A Problem-Based Mathematics Curriculum IMP is designed to replace the four-course sequence typical of most high school mathematics programs with an integrated course. While the traditional Algebra I-Geometry-Algebra II/Trigonometry-Precalculus structure emphasizes rote learning of mathematical skills and concepts, the IMP curriculum is problem-based, consisting of four-to-eight-week units that are each organized around a central problem or theme. The "interactive" aspect of IMP refers, in part, to the program's emphasis on students interacting with each other by working in groups. Together, students tackle problems that usually are too challenging to be solved by any one individual %%Failure %%Failure Escondiso flunks CPM, IMP Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski "Students in new math at Orange Glen, for example, scored an average of 477 on the SAT, while those in traditional classes at the same campus had average scores of 502. " ""No data is available that indicates that the integrated math is a success," he said. " Whitney Young Teacher wonders if IMP is math for dummies. Students want real algebra and fear they will get stomped by traditional algebra students. http://www.math.uic.edu/~cpmp/archive9701.html The Interactive Mathematics Program Listserver \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN (New math, math reform backlash against "fantasy lunch") http://www.math.uic.edu/~cpmp/archive9701.html School offers students a choice, only 1/4 chooses reform math. " In trials across the country, IMP students have done no worse--but no better--on college entrance exams than students taught traditionally. Still, Martinez believes weaker students stick with math longer because they enjoy the unconventional approach." %%Anti FEATURED HORROR STORY BY WEEKLY STANDARD The Weekly Standard August 4, 1997 EXAM SCAM The Latest Education Disaster: Whole Math By Lynne V. Cheney Senior Fellow, American Enterprise Institute my file: \clip\97\20\examscam.htm "They lied to me, says Madalyn McDaniel of Atascadero, California. They completely betrayed me..." Received $9 million in federal funds for development. %%General Key Curriculum Press IMP Home Page Check out this exciting mathematics curriculum! The Interactive Mathematics Program is being heralded across the country as one of the freshest breaths of air in today's 9-12 mathematics classrooms. @@Intersect G3-4 New Jersey G4 Mass MCAS G4 Big Horn County Co too low ------------ G6 North Rockland New York ------------ appropriate G6 North Rockland Central School District N.Y http://norock.lhric.org/curric/curric.htm Math Curriculum http://norock.lhric.org/curric/mathgr6.htm G4 Big Horn County School District Wyoming http://w3.trib.com/~rmhs/district/currelemmath.html#fourth Identify how lines, rays, and segments are related to one another (perpendic ular, parallel, intersect). Standard 7 - Geometry and Spatial Sense - Grades 3-4 New Jersey Mathematics Curriculum Framework http://dimacs.rutgers.edu/nj_math_coalition/framework/ch07/ch07_03-04.html They recognize the concepts of point, line, line segment, ray, plane, intersecting lines, radius, diameter, inside, outside, and on a figure. @@Invented Math If you're leery of invented spelling, you'll love invented math. It is harmful to teach standard methods, so you must rely on kids to invent their own methods, so the research says. NCTM STANDARDS 2000 - INVENT MORE THAN ONE METHOD http://standards.nctm.org/protoFINAL/chapter5/number.html In the past, common school practice has been to present a single algorithm for each operation. However, more than one efficient and accurate computational algorithm exists for each arithmetic operation. In addition, if given the opportunity, students naturally invent methods to compute that make sense to them (Fuson forthcoming; Madell 1985). The conventional algorithms for multiplication and division should be investigated in grades 3–5 as one efficient way to calculate. Regardless of the particular algorithm used, students should be able to explain their method and should understand that many methods exist. 728/34: One was conventional, but she "didn't understand". Henry used an offbeat useless method, but he understood. Twenty 34s plus one more is 21. I knew I was pretty close. I didn't think I could add any more 34s, so I subtracted 714 from 728 and got 14. Then I had 21 remainder 14." http://standards.nctm.org/protoFINAL/chapter4/number.html In some cases, their strategies for computing will be close to conventional algorithms; in other cases, they will be quite different. Many times, students' invented approaches are based on a sound understanding of numbers and operations, and they can often be used efficiently and accurately. Some sense of the diversity of approaches students use can be seen in figure 4.3, which shows the ways several students in the same second-grade class computed 25 + 37 Moreover, students who used invented strategies before they learned standard algorithms demonstrated a better knowledge of base-ten concepts and could better extend their knowledge to new situations, such as finding how much of $4.00 would be left after a purchase of $1.86 MANIFESTO FOR INVENTED MATHEMATICS \clipim\99\05\08\nctm\nctm.html \clip\99\10\nctm.txt http://www.nctm.org/jrme/abstracts/volume_30/vol30-01-hiebert.html Journal for Research in Mathematics Education January 1999, Vol. 30, No. 1, Page 3-19 Relationships Between Research and the NCTM Standards James Hiebert, University of Delaware If ability to invent procedures to solve new problems is emphasized in the standards, then the research on students' creative problem solving is of great interest. Standards increasingly emphasize young students' inventions of arithmetic procedures because, in part, we know they are capable of such inventions. Mathematical inventions by students are not included in the Standards simply because students are capable of inventing; they are included because an additional value judgment has been made--that invention is an important mathematical process. EVERYDAY: TEACHING STANDARD ALGORITHMS FAILS - STUDENTS SHARE INVENTED MATH http://www.chattanoogafax.com/email .htm WEEK OF November 17, 1999 \clipim\99\20\evmath.txt California Rejects It After Reviews that Basic Methods Aren't Emphasized "They are free to choose their own method" he writes and then quotes from the curriculum's 3rd Grade Resource Book: "Drill tends to become tedious and gradually loses its effectiveness.....Everyday Mathematics believes in children sharing their own invented algorithms rather than teachers continuing to teach the standard paper-and-pencil algorithms as such....Research shows that teaching the standard algorithms fails with large numbers of children." @@Japan Standards Mathematics Program in Japan (Kindergarten to Upper Secondary School) Japan Society of Mathematical Education January, 1990. $4.75 Reprint by US Dept of Education, US Govt Bookstore ORAD 97-1029 Kindergarten - 4 hrs per day, 39 weeks per year - "children feel interested in numbers, quantities, and geometrical figures" 1st Grade - 2 digit numbers - add, subtract 1 digit - apply 1 digit to simple 2 digit add/sub - counting - comparing - sum / difference - direct measurement - read clock - +, -, =, ones, tens 2nd Grade - 4 digit numbers - add / subtract 3 digit numbers carry borrow - multiplication table 1x1 digit number - = > < not equal - measure in metric meter, liter - triangles, quadrilaterals, right triangles - tables and graphs 3rd Grade - ten thousands - 10 times, 100 times , 1/10 - multiply 2 or 3 by 1 or 2 digit numbers, - multiply in column form - division - divide in column form by 1 digit - decimal fraction, common fraction - abacus / soroban adding, subtracting - gram, kilogram, kilometer - compute time - isosceles equilateral triangles - angles - center, diameter, radius of circle - bar graph - numerator, denominator, second, equal, not equal, divide 4th Grade - measure angle - measure area of geometric figure - hundred million, trillion, billion - rounding - divide by 2 digit number - add sub fractions with common denominator - add decimals - multiply and divide whole numbers - measure area of squares and rectangles - degrees, half-rotation, full arc - parallel, perpendicular - parallelogram, trapezoid, rhombus - cube, rectangular paralleopiped - position of object in space - draw graph from table - fill in variable quantities in frames (square) - plane, proper fractino, improper fraction, quotient, 5th Grade - percent - read pie chart - Investigations: consruct pie chart with 1/10 tics - multiply and divide decimals - compare fractions - least common denominator - add and subtract different denominator fractions - area of triangle, parallelograms, trapezoid - area of polygon by triangle - area of circle - volume of cube and parallelopiped - per unit concept - speed - congruence - pi = ratio of circumference to circle to diameter - use letter x instead of square frame - circle graph, tape graph - common denominator, greatest common divisor, sector, central angle, per cent 6th Grade - divide = multiply by reciprocal - multiply and division as fraction - volume of pyramid, cylinder, circular cone, surface area - proportional relationships - line and point symmetry - scale drawings - ratio - direct proportion - inverse proportion - use table and graph in frequency distribution @@Japan Style The Japanese are said to have implemented US style reforms in their math, but this really isn't true. STEVENSON DOWN ON NCTM STANDARDS NCTM are fuzzy standards that aren't helpful to most students or teachers, and aren't what the Chinese and Japanese do. I met and talked with the author of this article Wayne Bishop this past weekend in California. Incidentally he was the Math teacher of Jamie Escalante of "Stand and Deliver". He has Japanese books, materials, and lessons that were translated to english, along with the TIMSS study, to prove his point. Wayne is an exciting man with extensive knowledge and background. It was a pleasure talking with him. Dr. William Pfeifer http://ourworld.compuserve.com/homepages/mathman/wbishop.htm Math Lessons from Japan The TIMSS and the Truth For the Record - LA Times page A3, 1/15/97 Math teaching--A Jan. 5 article in The Times on math instruction stated incorrectly that a Reform curriculum called the Interactive Mathematics Program is widely used in Japan. It is not. [The Japanese drill very hard on basics, the teacher is definitely in charge, and there is a right answer, and a best way to solve a problem.] @@Job http://www.kiva.net/~pdkintl/kappan/kbra9810.htm The Eighth Bracey Report on the Condition of Public Education By Gerald W. Bracey .. our obsession with math and science, which has led us to overstate the number of people who need high skills in these fields. Borrowing from the study by Anthony Carnevale and Stephen Rose (discussed in "The Statistics from Thin Air Award"), Samuelson concludes that scientists, computer scientists, engineers, accountants, programmers, and business financial officers -- people who need advanced math or science skills -- account for 4% of the work force. @@Kindergarten Usually - count to 10 - colors - shapes Sphere - California, WA draft 2007 Multiplication - WA draft 2007 Grandma went to visit her three grandchildren and discovered they each had holes in every finger of their gloves. She will sew up their gloves. How many glove fingers need to be fixed? %%India \priv\2008\01\indiaschool.txt http://www.nytimes.com/2008/01/02/business/worldbusiness/02japan.html?_r=2&ref=education&oref=slogin&oref=slogin India’s more demanding education standards are apparent at the Little Angels Kindergarten, and are its main selling point. Its 2-year-old pupils are taught to count to 20, 3-year-olds are introduced to computers, and 5-year-olds learn to multiply, solve math word problems and write one-page essays in English, tasks most Japanese schools do not teach until at least second grade. @@Kumon Math Centers Popular math tutor program Some links: http://www.kumon.com/home/ Kumon.com http://family.go.com/Features/family_1997_10/dony/dony107cramschools/dony107 cramschools2.html http://www.ncneuropsych.com/links.htm This is strange! The link to KUMON Math & Reading on a "psych" page! http://www.mcs.net/~shs/schools/math_howtorespond.html Down on the page toward the bottom is the ref to Kumon http://www2.gol.com/users/milkat/alternative.html A Japanese Home-Schooling resource site. http://www.socialresearch.nu/bellpedr.html "all-purpose" good site! It has info on much! @@Least Common Denominator Dale Seymour Investigations Grade 5 does NOT teach least common denominator to compare fractions, but uses fraction lines and a bunch of other ridiculous ways. LCM CAUSES FEAR OF FRACTIONS http://www.delawareonline.com/apps/pbcs.dll/article?AID=/20071226/NEWS03/712260337/1006/NEWS Posted by: Jerome Dancis- Thu Dec 27, 2007 12:17 pm 1. Striking fear in students while teaching fractions. A popular method for teaching addition of fractions (using the LCM) “has struck fear in students for many generations” warns the Mathematics Framework for California Public Schools Chapter 3 Page 154. And, in Appendix A Page 274, it warns: “Many students find these concepts (LCM and GCF) confusing” and advises against teaching the two concepts (LCM and GCF) in “succession”. But books do teach them in “succession” (and at least one book may double the confusion by teaching them in the same lesson.) There is more on “fear of fractions” and “things that terrorize … students” on Page 152. 2. Good ways to teach fractions. @@Least Common Multiple The least common multiple of 10 hot dogs and 8 bugs is union of prime factors: 2 x 5 union 2 x 2 x 2 = 2 x 2 x 2 x 5 = 40 Silly no-brainer method - contructs a guess and check table. Grade Level Ranking 4 WA Assessment (there are NO 4th grade curriculums which teach this!) 5 San Marino School Dist 5 Tatnall School 5 Bill Evers K12 standard ---- appropriate ---- 6 Nevada 1998 6 Ping Wang 6 Prince William County 6 Learn Online 6 CA 1998 standard 6-8 Lk Wash ---- too low ---- 7 VA Standards 7 WA Benchmark 7 Ontario Activities 8 Wisconsin 8 NAEP 8 Kentucky Core Content http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.h tml http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm Least common multiple Wisconsin G8 http://www.wisgov.state.wi.us/MSMath.htm B.8.6 Model* and solve problems involving number-theory concepts such as least common multiples NAEP Use factors and multiples to model and solve problems http://www.nagb.org/pubs/math/mchap3.html San Marino School District 5th grade http://www.san-marino.k12.ca.us/~valentine/fifth/fifthcu.html Ontario Ministry of Education and Training http://www.edu.gov.on.ca/eng/document/curricul/activity/day1/ d1-g7-me.html Mathematics: Grade 7 TOPIC: Multiples FOCUS OF ACTIVITIES: common multiples least common multiples Learn Online http://www.learnonline.com/aec_mathematics_mathematics6.htm Mathematics Content Standards for grades K-12 Submitted by Bill Evers, Commissioner http://www.rahul.net/dehnbase/hold/platinum-standards/alt5. html Grade 5 2.10 Students determine the least common multiple and the greatest common divisor of whole numbers. Novi Meadows School http://itc.novi.k12.mi.us/nmtech/objectives6.html 1609 Find least common multiple given I and 2 digit numerals. The Tatnall School 1501 Barley Mill Road Wilmington Delaware 19807 http://www.ravenet.com/tatnall/MScurric/MS5curr.html The fifth grade students completed their unit on number theory by learning h ow to find the greatest common factor and least common multiple of pairs of numbers. WA Assessment - determine least number of packages need to match up buns (10) and hot dogs (8) WA Benchmark 7th grade http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html understand the concepts of prime and composite numbers, factors and multiples, and divisibility rules http://204.122.127.80/MATH/GRADE6.HTM Prince William County Schools standards VA Standards 7th grade http://www.pen.k12.va.us/go/Sols/math.html#Grade Four 7.2 The student will find common multiples and factors, including least common multiple and greatest common factor. Ping Wang's Home Page http://juliet.stfx.ca/people/fac/pwang/mathpage/grade6.html @@Level Education Week Quality Counts "Race and Demography" Lynn Olson http://www.edweek.com/qc/intros/race.htm 1/98 Nationally, roughly 55 out of every 100 white and Asian students complete Algebra 2 and geometry. Only 35% of African-American and American Indian seniors take this math. Although one in four white seniors takes physics, only one in six black seniors and one in seven Hispanic seniors completes this course. \clip\97\24\edclip1.txt 10/26/97 Sacramento Bee Proposed math standards divide state's educators By Deborah Anderluh Bee Staff Writer The proposed standards call for every student to learn algebra, geometry and most of advanced algebra between grades eight and 10. Source: California State Department of Education Students who complete: 44% algebra 25% geometry 14% advanced algebra 6% trigonometry and calculus ONLY 7% OF NAEP 17 YR OLDS DEMONSTRATED BEGINNING ALGEBRA Shockingly few students perform at the top competency level (above 350). To reach that score on the math portion of the NAEP students need only demonstrate "the use of beginning algebra." Yet in 1996 only 7 per cent of 17- year-olds scored in this category. NATIONAL REVIEW, October 27, 1997 Right Data, Ed Rubenstein Riley Hauls Out Less-Than-Fresh Math Findings in Education Blitz By Millicent Lawton \clip\97\25\edclip5.txt The Education Department reports one in four 8th graders took algebra in 1996, according to data collected as part of the National Assessment of Educational Progress, vs 1 in five in 1992. @@Marxist Is this from Mao's China or the NCTM standards?? "Hungry Ghosts" by Jasper Becker (The Free Press, 1996, ISBN 0-684-83457-X.) True scientists were peasants filled with intuitive knowledge and led by Party members driven by revolutionary fervor...we reject the fetishism of figures which holds us in thrall...We reject the multiplication table as the basis for policy.'" "The People's Daily reported how students in one faculty of science and mathematics showed their disdain for basic theory by putting decimal points in the wrong place while others deliberately made mistakes when calculating square roots." @@Mastery Learning z87\clip\2005\04\mymathlab.txt http://www.mymathlab.com/ Our proposed solution to the problem is to change the system for teaching entry level math courses at DeVry to a mastery learning approach, supported by Pearson Education's MyMathLab software. Mastery learning is an educational philosophy, theory, and instructional strategy developed by Benjamin Bloom of the University of Chicago in the mid-1960s. In essence, mastery learning uses feedback and correctives to bring increasing numbers of students to a predetermined mastery criterion. It has been used successfully in thousands of classrooms @@Mathematical power PENCIL AND PAPER HINDERS REAL MATHEMATICAL POWER z39\clip\2000\01\leiwand.txt It's Time To Abandon Computational Algorithms By Steven Leinwand (2/9/94)/Education Week It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous. GOOGLE FINDS ONLY ONE MATCH "WHAT IS MATHEMATICAL POWER" http://www.mste.uiuc.edu/courses/ci332fa02/ Elementary Mathematics Instruction What is mathematical power? The National Council of Teachers of Mathematics (NCTM) has called for fostering the mathematical power of ALL students (1989). In its most recent articulation of Principles and Standards for School Mathematics (2000), NCTM has reinforced this call with a clear vision for school mathematics. Mathematical power involves * a positive disposition toward mathematics (e.g., the interest and confidence to learn and to use mathematics), * the skills to conduct mathematical inquiry (e.g., problem solving and reasoning skills), and * understanding (well-connected knowledge). This course considers how K-8 instruction can foster each of these components of mathematical power. MATH POWER PART OF NEW CALIFORNIA FRAMEWORK, BUT NOT DEFINED did Richard Lee Colvin blow the whistle on this pseudo-educational junk when it was first promulgated? Dom Rosa California Mathematics Council May 1, 1993 Dear CMC Members: Last year the State of California issued a new Mathematics Framework for California Public Schools that recommends fundamental changes in the way we teach mathematics. In this packet, you will find a general summary of this Framework, titled, "They're Counting On Us: Mathematics for Your Children's Future" and seven inserts for teachers that elaborate on topics such as curriculum and assessment. Although these inserts can be read in any order, we suggest the following sequence: What is Mathematical Power? Moving Beyond Exercises Assessing Mathematical Power http://math.coe.uga.edu/tme/issues/v10n1/3davis.pdf DF] What Seems to be Happening in Mathematics Lessons? Findings from ... File Format: PDF/Adobe Acrobat - View as HTML The 1998 NCTM Yearbook on algorithms notwith-. standing, we note that the last NCTM Yearbook ad-. dressing classroom issues, such as the role of practice, ... The Standards of the National Council of Teachers of Mathematics (NCTM, 1989) referenced by Forgione call for a balance of procedural and conceptual knowledge so that students gain mathematical power. Mathematics Curriculum Framework: Achieving Mathematical Power ... The core concept of this Massachusetts Mathematics Framework is that students develop mathematical power through problem solving, communication, reasoning, ... www.doe.mass.edu/frameworks/math/1996/content.html - 31k Fostering the mathematical power of children with behavioral ... 'Fostering the mathematical power of children with behavioral difficulties: the case of Carter. from Teaching Children Mathematics in Reference & Education ... www.findarticles.com/p/articles/mi_hb3451/is_200104/ai_n8218343 Amazon.com: Mathematical Power: Lessons from a Classroom: Books ... Amazon.com: Mathematical Power: Lessons from a Classroom: Books: Ruth E. Parker by Ruth E. Parker. www.amazon.com/Mathematical-Power-Lessons-a-Classroom/dp/0435083392 Children’s Mathematical Power It seems to me to be appropriate, for the purposes of initiating this discussion on Developing Children’s Mathematical Power , that an example of a child ... www.nku.edu/~sheffield/edgellpbyd2.html [PDF] MATHEMATICAL POWER FOR ALL STUDENTS K-12 File Format: PDF/Adobe Acrobat - View as HTML mathematics to express. mathematical ideas. precisely. Build a connection from. everyday, familiar language to. the power and precision of ... fcit.usf.edu/math/resource/mathpower/fullpowr.pdf (FACT standards) C&I 332: An Investigative Approach to Elementary Mathematics ... What is mathematical power? The National Council of Teachers of Mathematics (NCTM) has called for fostering the mathematical power of ALL students (1989). ... www.mste.uiuc.edu/courses/ci332fa02/ - 14k - Cached - Similar pages Date: Mar 27, 2000 3:40 PM Author: Domenico Rosa Subject ... What is Mathematical Power? Moving Beyond Exercises Assessing Mathematical Power Getting Started What is a Unit? Growth Patters: An example of a Unit ... mathforum.org/kb/plaintext.jspa?messageID=715845 - 6k - Supplemental Result - Cached - Similar pages TEACH MATHEMATICS FOR SOCIAL JUSTICE oslund home What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? ... www.msu.edu/~oslund/ - 14k - Supplemental Result - Cached - Similar pages TE 803: Professional Roles and Teaching Practice--Elementary Mathematics What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? In the upcoming semester, Joy, along with 18 interns in MSU's teacher certification program, will grapple with these big ideas while navigtating the day-to-day experiences of the internship. @@Linear Algebra @@Matrix Arithmetic Grade Level ------------------ Matrix addition, subtraction, scalar multiplication G8-9 Virginia Algebra I (achieve) G9-12 Utah (all) G11-12 Algebra 3 DODDS G9-12 Michigan (all) Matrix multiplication Matrix inversion NA WA NA Virginia G10 McDougall Little Integrated Math 2 Matrix solve systems of equations ----------------------------------- G12 Oregon CAM G9-12 New Mexico Use matrices to solve linear systems. @@Line Segment (line AB segment CD) G2 Texas Core curriculum http://www.trinity.edu/departments/education/TCKC/2math97.htm @@Logo Seymour Papert's turtle based programming language is a favorite of constructivists and people who advocate use of technology. Was a fad in New Zealand. Dale Seymour devotes an entire book to Logo in the third grade even though it admits most schools don't have an adequate number of Mac computers to use the unit. z50\clip\2001\07\logo.txt EducationNews.org Date 06-Jul-2001 Headline Improving numeracy: It is time to revisit logo! Logo was once heralded as the touchstone for raising educational standards through computer use. However, like so many things in our educational systems all over the globe, it was something of a passing fad. @@Long Division The toughest calculation on paper method is long division (dividing by numbers more than 1 digit), some believe that it has been made obsolete by the calculator, but others believe it should still be taught and assessed. TERC not only omits long division but claims mathematicans no longer use long division notation. Spectrum ------------------- 4th WA Assessment 5th Lake Washington NO New-New math CA '97 Standard \clip\98\03\reed\reed.htm PROPOSED NEW-NEW MATH CA STANDARD WOULD DROP LONG DIVISION http://ourworld.compuserve.com:80/homepages/mathman/reed.htm (Mathematically Correct) For the record, the omission of long division with 2 or more digit divisors was a conscious decision. I pointed out in writing and in oral comments before the Commission that this was missing. Undoubtedly some thought long division obsolete; others probably thought teachers would teach long division and that it need not be specifically mentioned. The problem with this latter view is that since long division was not an explicit expectation under the Commission's standards, teachers and testmakers could and would in good conscience omit it. Since it would not have appeared on a state standards-based test (had one been created under the Commission's standards), it would have widely been dropped from textbooks and curricula used around the state. Bill Evers Commissioner, Academic Standards Commission @@Mathematically Correct %%Against MATHEMATICALLY CORRECT ATTACKED AS ARM OF CONSERVATIVE RIGHT \clip\99\06\mathco.txt Are the traditionalists mathematically right? Columnist Rick Casey, San Antonio Express News Feb. 22, 1999 Our friends at the conservative Texas Public Policy Foundation have taken on another task. They want to teach your children math. Mathematically Correct named themselves, apparently with no sense of irony. They have several things in common with the left- wing politically correct. Both include intelligent, well- intentioned people. Both are ideologically based. Both are intolerant of those who think differently. And while the politically correct have an idealized view of the future, Mathematically Correct has an idealized view of the past. Improvement among Texas fourth- and eighth-grade students on another standardized test, the National Assessment of Educational Progress, has been among the best in the nation since 1990. @@Mathland Mathland is a complete K - 6 (OBE) Math program from Creative Publications. They say they are rigorous, but it is another OBE all students can learn, but we won't drill them on basics, let's let them spend a week talking about our dream house project math system. It features cutting out a "fantasy lunch" and writing about or doing plays about why 1+3=4. It has no textbook. Mathematical ly Correct MATHLAND REFUSES TO TEACH KIDS HOW TO MULTIPLY TWO NUMBERS! ZIP37\clip\99\18\lamath.txt From: "Mike McKeown" Mathematically Correct Links z46\doc\web\2000\11\mathland.txt http://www.southcountyjournal.com/sited/retr_story.pl/33642 SUMNER SCHOOLS Math program lacking Shortly after the beginning of the 2000/2001 school year, I began to question the recent adoption by the Sumner School District of Mathland in Grades K-6. SANTA ROSE FLUNKS MATHLAND SR board frowns on MathLand program Oct. 15, 1998 By ROBERT DIGITALE Press Democrat Staff Writer Santa Rosa school board members voiced strong displeasure Wednesday night with the results of the MathLand math program and directed their staff to work immediately to help students improve basic computation skills. \clip\98\14\mathland.txt DRAW AND KILL Diary of a Mad Math Teacher While lovers of new-new math trash the old math as Drill and Kill, they've sadly replaced it with Draw and Kill. Many children must be bored out of their skulls with all the drawing, cutting and pasting and writing about why 3+1=4. Leona notes that her students are itching for more equations. Indeed, on more than one occasion, they have said to her, ``Can we do some real math now?'' MATHLAND BLAME FOR SCORE DECLINE IN SF Thursday, Aug. 15, 1996 · Page A 4 San Francisco Examiner Mixed math test results leading S.F. district to rethink methods Students in City's elementary, high schools lose ground on basic skills test; superintendent cites new curriculum Venise Wagner "Superintendent Bill Rojas partly attributes the lesser elementary school performance to the district's year-old math curriculum. Called Mathland, it emphasizes concepts and problem-solving rather than rote drills. Rojas speculated that because 40 percent of the district's primary school children entered without preschool experience, many were not ready for such a conceptual approach. " http://www.sfgate.com/programs/srch_archive/srch_archive_ wrap?unregistered= true&WAISdocFile=/WAISlink/examiner/ archive/1996/08/15/NEWS16113.dtl&WAISdb Name=/doc_root/wais/ examiner/1996&WAISaction=retrieve&WAISdocID=5387710402+ 2+0+0& WAISheadline=Mixed+math+ MATHLAND IS _NOT_ RIGOROUS MATH, BASED ON OBE ASSUMPTION THAT ALL STUDENTS ARE CAPABLE LEARNERS (Tennisons from Oregon) DOD PARENTS RISE UP AGAINST MATHLAND From: "Michael L. Bledsoe" Date: 1997/05/14 Message-ID: <3379B4C5.4001@msw0.attnet.or.jp> Newsgroups: alt.internet.yokota.general (math correcct) This site is about Mathland and the other "fuzzy math" programs that the bureaucrats in the DoD schools, as well as those in the states, are using to replace quality education. About a year or so ago, Stars and Stripes printed a number of letters from concerned parents about these programs. The controversy was strong enough that here in Misawa there were even meetings with parents to show us that Mathland wasn't as bad as we had heard. Test Your Kid's Math Ability From: "Richard C. Webb" Date: 1997/06/20 Message-ID: <33AAD076.3E2@webblabs.com> Newsgroups: wi.general,milw.general Here is a link to the math placement test given to 12 year olds in Japan: http://www.japanese-online.com/math/index.htm Test your high school sons and daughters. Your middle-schoolers will likely fail miserably. If they do, demand a written explanation from your school's superintendent. Many schools in Wisconsin are using math curricula proven to result in failure to learn math. A few of these boondoggles are: Algebra: Themes, Concepts, Tools; Creative Publication Quest 2000 (Addison-Wesley) Quasar Everday Math (UCSMP) Mathland (Creative Publications) From someone whose boys have successfully dodged the New-New Math, best of luck to all of you in avoiding these abusive curricula. Richard C. Webb Hartland %%For Subject: Re: Just what is Mathland From: Central School Date: 1996/10/01 Message-ID: <32506332.7937@bc.cybernex.net> Newsgroups: k12.ed.math I am a fifth grade teacher in a district in northern NJ that adopted MathLand last year. We are beginning our second year with this program from Creative Publications. We are generally happy with the program. The children are asked to analyze their thinking as they complete math projects. In addition to practice with computation in context, they are encouraged to estimate, consider alternative solutions (when appropriate) or alternative methods, and communicate their findings. http://www.cit.state.vt.us/educ/alliance/programs.htm Included on a a listing of successful programs self-identified by schools on the 1996 Vermont Alliance Survey. http://www.service.com/PAW/morgue/news/1996_May_29.MATH.html Palo Alto Weekly Wednesday May 29, 1996 SCHOOLS: Math program nears adoption Board to choose between two courses Thursday. Creative Publications' "MathLand," a popular and innovative, hands-on approach to math which has no textbook; Everyday Math has no text, but includes a journal which can be used as a workbook and a textbook and integrates basic concepts with newer approaches. @@Math Central Math Central seems extremely dumbed down, covers 1-10 numbers in 2nd grade. Houghton Mifflin. Poor review of math central. Principal tells parents to hire tutors and supplement at home. @@Math Expressions - Replaced TERC in Bellevue - Preferred by teachers and students over TERC - Math Expressions does not have a student textbook(?) - Invented methods means it is still not truly traditional %%adopt http://www.wheresthemath.com/2008/03/09/bellevue-school-board-to-vote-on-new-elementary-math-curriculum/ http://www.wheresthemath.com/local-groups/bellevue-school-district/ Bellevue adopts math expressions to replace TERC investigations in 2008 "I can't believe how awful [TERC] it is in comparison to Math Expressions." "Math Expressions is the best the teacher has ever seen." "thrilled that he actually had a book that he brought home" %%algoritms. Mercer Island Math Fair 2009: "the actual teaching in grades 3-5 is having the students try out what they like and personally adopt their favorite. Many of these ME invented algorithms are 2 pass algorithms suitable for mental arithmetic but not well suited for paper. Like left to right subtraction." D. Myerson @@Math Power New buzzword thrown about by 90's reform math, used by CA reformers and Houghton Mifflin. @@Math Trailblazers MATH TRAILBLAZERS ANOTHER CONSTRUCTIVIST NIGHTMARE http://www.illinoisloop.org/mathtrail.html A review of Kendall/Hunt’s Math Trailblazers Second Grade, Unit 11: "Ways of Subtracting with Larger Numbers" By Rebecca P., April 2002 Any way but the standard way is OK. z55\clip\2002\04\mathtrail.htm @@ASVAB Military Entrance Exam ASVAB REQUIRES MANUAL ARITHMETIC Our senior high son just came back from taking the Military ASVAB Entrance Exam. No calculators are allowed to be used on the test. Students are to compute all calculations by hand. This included calculating square roots, long division which contained 3 digits in the divisors-- into decimals, complex multiplication, and various other tedious math computations. My son thanked me for reteaching long division to him 2 summers ago. I would have added calculation of square roots by hand if I had known. I guess the military wants their recruits to be strongly competent and efficient in classical math. Colleen F. Kennewick Here's one question with square roots: The value of the sq. root of 164 to the nearest integer is: A. 18 B. 108 C. 42 D. 13 @@Average @@Mean, Median, Mode, Range Most Likely Value 4th Grade New Standards (given raisins in 12 boxes, what is most likely value) 4th KIRIS released (given candy in 12 bags, organize, what is most likely value Average - informal splitting 2nd Exemplars Mean = Average = sum / number 4th MCAS assesment 4th Vermont (begin simple concepts) 4th Addison Wesley 1991 --------- assessment appropriate ------- 5th Ommitted by Investigations / TERC 5th Addison Wesley 1964 5th Holt 1970 5-8 Vermont - appropriately use 6th Connected Mathematics V2 (ommitted from V1) Median/Mode/Range 4th Kentucky KIRIS Assessment 4th WA Assessment 4th Wisconsin 4th New Standards 5th Kentucky Core Content Standards 5th Nevada 6-8 Lk Washington 7th BC Standard 7th WA Benchmark (4th = rough centrality) 13 Not on SAT test HOMEWORK - EVERYTHING _BUT_ AVERAGE zip63\clipim\2003\01\07\mathhome.efx Homegrown homework sheet has frequency histogram, range, median, mode, but NOT average. COLLEGE LEVEL SAT DOES NOT REQUIRE MEDIAN OR MODE z60\doc\web\2002\09\meanmode.txt Deanna M. De'Liberto 2002 As someone who was an assistant examiner at ETS and assembled forms of the SAT I...we do not expect students to know the terminology for mean, median, and mode. ..we asked the average or arithmetic mean Distribution with most below a value 4th WA Assesment (frequency histogram of battery life) 8th Voluntary National Test Kentucky KIRIS Open-Response Item Scoring Worksheets 1995-96 http://www.kde.state.ky.us/blrs/ocaa/dcad/97/M4/M4Q5.PDF Expects students to pick from the mode or median from a sample of bags. WA 4th grade assessment: pick frequency histogram chart with battery most likely to last at least 8 hours (pick the one with most values below a value) Wisc 4th grade: min, max, range, mode (most frequent value) median (middle value) New Standards Test: "predict" next value based on frequency histogram of 11 boxes of raisins. (kid has to make a wild guess within the range, pick the median, or compute a mean???) Mean BC Standards 4th grade - possible, impossible, certain, or uncertain compare outcomes using the terms equally likely, more likely, or less likely design and conduct experiments to answer their own questions 6th grade - compute experimental and theoretical probability, probability of dice. 7th grade = mode median mean determine measures of the distribution of a set of data: range extremes, gaps, and clusters quartiles WA 4th grade benchmark - use different measures of central tendency such as "most often" and "middle" in describing a set of data understand the difference between certain and uncertain events know how to list all possible outcomes of simple experiments (does NOT include precise computation of probability) 1997 version says mean, median and mode %%Exemplars Exemplars Task expects kids to know how to divide up whole numbers into parts, and then parts again. Correct answer - line up equal whole numbers. Then cut remaining pieces into parts, and distribute the parts. (???!) @@Measurement %%Appropriate Size 4th WA Assessment 4th NAEP Guidelines (estimate size) 8th NAEP Guidelines (picking unit) WA - the size of a notebook paper is approximately 20 mm, cm, or meters? NAEP - determine appropriate size of unit in problem situation. Do not assess at 4th, OK at 8th. estimate the size of an object - 4th grade OK. %%Conversion of Units 4th Virginia Standards 4th WA Assessment 5th Houghton Mifflin Math 1998 5-8 SC Standards 7th WA Benchmark 8th NAEP Guidelines 5th Houghton Mifflin Math 1998 Compare speed of animals measured in miles per hour vs inches per minute. 5-8 South Carolina Convert units within and, given appropriate conversion factors, between systems. http://www.achieve.org/ WA 4th grade asessment - bird feeder requires conversion from 60 inches to 5 feet, test does not give conversion table, rubric does not mention that conversion is neccesary. WA 7th grade standard understand the relationship among units within both the U.S. and metric syst ems http://cisl.ospi.wednet.edu/NAVIG/INFORM.html Virginia standards http://www.pen.k12.va.us/go/Sols/math.html http://cisl.ospi.wednet.edu/ComSL/MATHBMK1.html WA G4: Perimeter, Area, Volume NAEP Convert from one measurement system to another within the same system: Do not assess at 4th, OK at 8th. %%Area = Length Times Width 4th Core Knowldge 4th WA Assessment 4th Addison Wesley Mathematics 1991 5-8 LA Standard 7th WA Benchmark 8th KY Standard 8th NAEP Measure area by multiplying length and width NAEP http://www.nagb.org/pubs/math/mchap3.html Solve problems involving perimeter and area (e.g., triangles, quadrilaterals, other polygons, circles, and combined forms) # = very simple at 4th grade CT 4th Grade Assessment Estimate lengths and areas CT 6th Grade Assessment Compute area LA 5-8th Grade Standard Mapplying the concepts of length, area, surface area, volume, capacity, weight, mass, money, time, temperature, and rate to real-world experiences WA 4th Grade Assessment Sample: Which pizza is the best value, gives pictures of 4 rectangles with 2 digit sides. WA 7th Grade Standard http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html measure objects and events directly or using indirect methods such as finding the area of a rectangle given its length and width http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.html KY 8th Grade Standard: use formulas to find measurements of two-dimensional shapes, how two or more measurements are related (perimeter and area, time and distance, height and weight, etc.) http://www.pen.k12.va.us/go/Sols/math.html Virginia standards VA 2nd Grade - count squares for area VA 6th Grade - measure area %%Perimeter G2 Texas Core Curriculum %%Rate Ranking: 4th WA Assessment 7th WA Benchmark 8th NAEP WA 4th - Use ruler and stack of cards to determine how many cards a box will hold WA 7th - understand the concept of rate and how to calculate rates and determine units 8th NAEP Apply the concept of rate to measurment situations - do not assess at 4th, 8th OK. @@Mental math z47\clip\2000\12\mentmath.txt straits times 28 December Singapore Maths whiz uses parts of brain others cannot reach A team headed by Ms Nathalie Tzourio-Mazoyer of France's National Centre for Scientific Research (CNRS), working with neuropsychologists from Louvain University in Belgium, carried out PET brain scans on a noted German maths prodigy, Mr Rudiger Gamm, while he was doing [extreme mental] calculations. [like using hard drive for long term storage] that most people don't use. @@Metric JOKE - METRIC COMMONLY USED IN THE 'HOOD z47\clip\2001\01\metric.txt z47\clipim\2001\01\31\metric\metric.htm http://www.theonion.com/onion3703/metric_system_thriving.html [warning, a bit of 'hood stereotyping here] Department of Education: Metric System Thriving in Nation's Inner Cities "While the typical teen has only a vague notion of what a kilogram is, teens in the Cabrini Green housing projects in Chicago and the Watts neighborhood of Los Angeles were thoroughly familiar with this unit of metric measurement," @@Mexico Mexican schools are more run down, but have higher standards than new US schools! @@Middle School \clip\99\16\achmath.txt www.achieve.org Achieve and Ten States Form Partnership Tying Middle School Math Teaching and Testing to Common, Internationally Challenging Standards New Materials, Training, and Exam Based on Third International Math & Science Study Will Add More Algebra, Geometry to States' Offerings @@Money %%Coins 2nd graders are expected to do math aned distinguish between coins on the basis of black and white pictures of the heads on the coins, which do not say their value on the ITBS test. Some tests ask students how many different combinations of coins they can use, but do not specify if rarely used half dollars or dollar coins may be used. Some textbooks do use pictures of coins with the number of cents on them. Most children and many adults have no idea who the heads on the coins are. NOTES ON US COINS cents name color face says 1 penny copper Lincoln "one cent" 5 nickle silver Jefferson 10 dime silver FDR Roosevelt "one dime" 25 quarter dollar silver Washington "quarter dollar" 50 half dollar silver Kennedy The canadian penny I have gives the name of the head (Elizabeth II), and the number of cents (1)! Comments on coin problem and history ITBS notes @@More Than One Way to Get an Answer Another popular reform slogan. @@Mountain Math Mountain Math is a brand of Math software developed by: http://www.mtnmath.com/mtnmath.html It is used in Tennessee(at least): http://www.acorns.k12.tn.us/curricu/cu01001.htm http://guaraldi.cs.colostate.edu:2000/form @@Multiply @@Multiplication Introduction K - Little Angels India Kindergarten %%Colored pencils TERC asks students to use different colored pencils on a 10,000 grid to show decimal addition. TERC does not show conventional addition as it does not even cover regrouping in 2nd grade %%Repeated addition http://wgquirk.com/NCEE.html#good a total of 38 math-related "examples", with 19 at the 4th grade level in Volume 1, 12 at the 8th grade level in Volume 2, and 7 at the 10th grade level in Volume 3. ** 3 equally inefficient ways to multiply ** Task 3: Demonstrate multiple ways to multiply 62 x 85. Method 2: The student "added 85, 62 times." Method 3: "The student showed how the problem could be solved by making 62 circles with 85 stars in each circle." @@NCEE America's Choice Performance Standards z48\clip\2001\03\nceemath.htm http://wgquirk.com/NCEE.html#good a total of 38 math-related "examples", with 19 at the 4th grade level in Volume 1, 12 at the 8th grade level in Volume 2, and 7 at the 10th grade level in Volume 3. these standards have been benchmarked to the expectations of those countries with the highest student performance in the world." They say the ACPS have been reviewed by researchers and recognized experts in several other countries, including Germany, Japan, and Singapore, and "No reviewer identified a case of significant omission," and "None of the reviewers identified standards for which the expectations expressed in the standards were less demanding than those for students in other countries." ** 3 equally inefficient ways to multiply ** Task 3: Demonstrate multiple ways to multiply 62 x 85. Method 2: The student "added 85, 62 times." Method 3: "The student showed how the problem could be solved by making 62 circles with 85 stars in each circle." @@Negative Numbers G2 - Dale Seymour uses negative numbers, but not borrow/regroup! G4 - California Nevada Covina Valley Nebraska G6 - Washington State G6-8 Florida G8 Texas G8 Ohio Math Standard: Grade 4: Number & Number Relationships MATH CONTENT STANDARDS. GRADE: 4. ... including the use of standard and expanded form. Identify ... Use concepts of negative numbers (eg, on a number line, in counting ... www.cvusd.k12.ca.us/covina-valley/Tech_Plan/K-5Math/grade04_nos.htm - 10k - Texas G7 (A) compare and order non-negative rational numbers; G8 (A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals; Japan Nebraska G4. By the end of fourth grade, students will identify and demonstrate positive and negative numbers and zero. Vermont G3-5 b. Begin to use simple concepts of negative numbers, properties of numbers (e.g., prime, square, composite), three-digit and larger multipliers and divisors, rates, and the relationship among fractions, decimals, and percents; G7 (1) To help students deepen their understanding of the concept of numbers, through the enlarging of the scope of numbers to include positive and negative numbers. Ohio G8 - negative with color chips Nevada 4.1.4 By the end of fourth grade, students will identify and demonstrate positive and negative numbers and zero. Washington state EALR G6 understands negative numbers www.seattleschools.org/area/acastan/full/math.pdf California G4 1. Students understand place value of whole numbers and decimals to two decimal places, how these relate to simple fractions, and use concepts of negative numbers. www.achieve.org @@New Math Introduced in 1957 in response to Sputnik, it added a lot of set theory, abstractions, rigor, but it was a disaster. Nobody understood it. Only the top 10% got any benefit, the rest were swamped by abstract mathematics. Funding was pulled by the feds in 1972 after it was widely regarded as a failure. Some blamed it on mathematicians, but more likely it came from the educators. Forerunner to the new wave of failing "fuzzy" math. NEW MATH 1958-1972 WAS A DISASTER z49\clip\2001\04\newmath.txt New York Post LET'S SEE: 2,001-1,957 IS . . . By CARL CAMPANILE April 17, 2001 Educators first introduced what was called "the New Math" in 1957 There was more logic, more abstractions and more proofs," said Richard Raim, a math professor at the University of Rochester. "But it was a disaster. Nobody understood it. Some of the commercial textbooks were inferior - and wrong." Raim said only elite students - the top 10 percent - benefited from the New Math while the rest of America's kids were numb with numbers. The federal government stopped funding the New Math in 1972, after it was widely considered a flop. z49\clipim\2001\05\09\newmath\newmath.htm New Math 1960's parody by Tom Lehrer Hooray for New Math, New-oo-oo-Math, It won't do you a bit of good to review math. It's so simple, So very simple, That only a child can do it! SPUTNIK, NSF BEGAT NEW MATH http://www.math.rochester.edu:8080/u/rarm/smsg.html z40\clip\2000\03\whatmath.txt Ralph A. Raimi 22 October 1995 Whatever Happened to the New Math? (Sputnik) The year 1958 therefore kicked off the largest and best financed single reform effort ever seen in mathematics education, the School Mathematics Study Group (SMSG), upon which the National Science Foundation (NSF) spent millions of dollars over its twelve-year lifetime. The result, after twelve years, was total failure. By any reasonable measure, and measures were taken, school mathematics was worse off in 1975 than it had been in 1955. The idiocies of the older curriculum had in most places been removed, but often to be replaced with new ones. "Gerald W. Bracey" Yeah, well John, the last time people listened to mathematicians, we got The New Math. It was an absolute disaster (see the section on post-Sputnik reforms in either my book, Final Exam, or Charles Silberman's 1970 tome, Crisis in the Classroom). I do not come to this from a distance: I spent the summer of 1963 with the School Math Study Group (SMSG: Some Math, Some Garbage to us disrespectful graduate students) at Stanford helping mathematicians rewrite their New Math texts so that teachers, not to mention kids, could understand them. My experiences with mathematicians is that they can barely communicate with college students and are clueless when trying to cope with teachers and k-12 students. I suggest you go dig up the Post-Sputnik literature about what it means to know mathematics. It was the mathematicians who decided that third graders had to know what "null set" and "empty set" and "commutativity" and "associativity" and the "distribution law" meant. Really. Third grade. No joke. Wish I had kept the textbooks. \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN (New math, math reform backlash against "fantasy lunch") http://www.math.uic.edu/~cpmp/archive9701.html New math was a reaction to Sputnik. "Instead of starting out by 'borrowing' and 'carrying,' we want children to understand what they're doing." ". Children were drilled on fancy concepts like spelling "commutive property", which is simply 2 + 3 = 3 + 2, concern was that children were not picking up basic skills. "By 1966, the movement was unraveling amid concerns that students were not learning basic skills. Over the next decade, New Math was satirized as "hopelessly abstract, elitist, confusing and impractical,"" @@New Standards NEW STANDARDS RESULTS IN LOW MATH CAT PERCENTILES IN VERMONT Sixth grade test CAT California Achievement Test scores: Median National Percentile (MDNP) 1990 1996 Math Computation: 71.6 48.6 Math Concepts and Appl. 89.5 87.4 Total Math: 86.0 70.3 @@Newsgroup http://www.thinkspot.net/k12math/charter.html Charter for k12.ed.math

@@NCTM Standards

The National Committee on Teaching Mathematics created an influential new document on teaching mathetmatics in 1989 which unfortunately legitimized the movement to stop teaching arithmetic. Really. It focused not on raising math standards, but moving towards "fuzzy" math which seeks "natural learning styles", discourages drilling and paper and pencil tasks, and "performance-based" tasks based on "real life" instead of concentrating on mastering the basics, and proving that there is never just "one correct answer". Proponents say that not all students are good at memorization, and that all students should be exposed to all math, but this turns a class that teaches students how to be good at algebra with lots of practice into an "integrated class" which turns into algebra "apprececiation" - you can be a listener of Beethoven, but not a piano player than can perform it. Critics say that the NCTM standards are responsible for dumbing down math education, and are something to run away from. This is all really the application of political correctness to mathematics. It's all about destroying "eurocentric male dominated", and math for women, minorities and losers. It promises algebra and calculus for all, yet relies on assessing students before they've been taught anything. ORIGINAL VISIONARY DOCUMENT Appendix: Table of Standards - Number and Operation NCTM's visionary document for teaching mathematics at any level. ... Pre-K–2 Expectations: In prekindergarten through grade 2 all students should– standards.nctm.org/document/appendix/numb.htm %%Assessment DAS KAPITAL FOR MATH MATH POWER, MATH FOR WOMEN, MINORITIES AND LOSERS, ALL CHILDREN MUST LEARN ALGEBRA, CALCULUS, STATISTICS, NUMBER THEORY INTEGRATED INTO ELEMENTARY AND MIDDLE SCHOOL. ASSESS STUDENTS _BEFORE_ YOU TEACH THEM HOW TO DO IT z43\clipim\2000\06\26\nctm.efx z43\clipim\2000\06\26\nctm.txt Assessment Standards for School Mathematics Working Draft October 1993 (Joanne Mccann copy) For all students to achieve mathematical power, they need to be mathematical problem solvers, to value mathematics, to reason and communicate mathematically, and to be confident in using mathematics to make sense of rael-worls problem situations. The mathematics curriculum, instructional methods and the strategies used to assess student performance must be congruent with this notion of mathematical power There has been too much reliance on brief problems that can be quickly solved (multiple choice or closed, constructed-response items.. creates equity problem.. different curricular experiences to different social classes p14 judged in terms of several levels of performance from less to more rather than incorrect so students can demonstrate what they know and are able to do. p10 all students need to develop personal and robust understandings of algebra, geometry, triginometry, statistics, probability, discrete mathematics, and even calculus. Furthermore, many of these understandings can, and must be initially developed in elementary and middle school. balanced variety that reflect cultural diversity must be in the basic elements of reform p66 it took 8 perpl rods (invented spelling k-4) p85 and is intended to be used holistically, not point by point P31 must allow for studens use of alternative approaches.. to distinguish from an elegant solution from one that is merely brief requires mathematical knowledge and sophistication. Sample is 6 wk statistics unit about how many Hispanics and blacks are put into jail. 13 has defined every child as follows - students denied access to opportunity students who are black, hispanic, AmIndian, other minorities female as well as male who have not been successful as well as successful 22 the group of afam girls wanted to investigate racism in the school, but their work was sloppy and incomplete.. was worried they claim racism if i gave them low marks Foreign exams usually small number of probs 2-6 eith parts take 10-16 min, American 50 tasks 1-2min %%Documents http://www.nctm.org/standards2000/download.html \clipim\98\11\PSSMDRFT.pdf Draft of 1998 NCTM Standards 2000 Electronic Standards Featuring invented mathematics. z42\clipim\2000\05\23\mathskill\mathskill.htm Here are the new M ath Standards National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 1989.(Eisenhower National Clearinghouse for Mathematics and Science Education> %%Critic http://mathematicallycorrect.com/frankallen.htm

More Nctm Standards links

Mathematics Education

Uiuc Site

Misc. Commercial Sites

Misc. Educational Institution Sites

Misc. Internet Provider Sites

Misc. Non-Profit Sites

%%Against NCTM: WE WERE ONLY KIDDING ABOUT THROWING OUT ARITHMETIC z40\clip\2000\04\backmath.txt www.nytimes.com/library/041300math-test.edu.html New York Times April 13, 2000 Math Teachers Back Return of Education in Basic Skills By ANEMONA HARTOCOLLIS In an important about-face, the nation's most influential group of mathematics teachers announced yesterday that it was recommending, in essence, that the arithmetic be put back into mathematics, urging teachers to emphasize the fundamentals of computation rather than focus on concepts and reasoning. Lee V. Stiff, president elect of the mathematics teachers' council, insisted that despite the protests of parents, the old standards had not done any harm. NOW NCTM SAYS THEY NEVER WANTED TO BAN TEACHING MANUAL ARITHMETIC z40\clipim\2000\04\10\nctm\nctm.htm http://www.edweek.org/ew/ewstory.cfm?slug=31nctm.h19 April 12, 2000 Math Revisions Add Emphasis on Basic Skills By David J. Hoff NCTM BACKPEDALS FROM 89 STANDARDS, EMPHASIZES BASICS Education Week http://www.edweek.org/ew/current/10nctm.h18 \clip\98\16\nctmnew.txt [November 4, 1998] [Education Week on the Web] Math Council Again Mulling Its Standards By David J. Hoff Note - Washington state EALR standards and WASL assessments are based on the NCTM standards which are being revised because they were just plain silly. NTCM STANDARDS ARE TO BLAME FOR PROMOTING FUZZY MATH Investors Business Daily 'Standards' To Blame For Rise Of 'Fuzzy Math' Date: 4/3/98 Math Correct Cease Fire Terms and why the NCTM standards have been harmful to math teaching. %%Problems THEY'RE TAKING NOTES AND WORKING ON TEXTBOOK PROBLEMS INSTEAD OF PLAYING WITH MANIPULATIVES AND COMPUTERS \clip\98\08\latmath.txt http://www.edweek.org/ew/current/31nctm.h17 First-year teachers have a hard time putting the voluntary national standards for mathematics into practice in their classrooms, a small study by Illinois teacher-educators has found. (Takes too much time to play with manipulatives, not enough computers) half or more of the respondents to the questionnaire--all teaching in secondary schools--said they "seldom" or "never" used hand-on materials, or so-called manipulatives, and seldom or never used computers or had their students write about math. Half or more of the dozen respondents said their students engaged in the more traditional activities of working on problems from textbooks or taking notes during teacher presentations. %%Research Constructivist wonders if there is any research to back up constructivism? %%review AMS Report on NCTM Standards Date: 3/4/98 The American Mathematical Society committee to comment on the NCTM Standards and possible revisions to the standards has released its first and second reports. These are available on line at http://www.ams.org/government/nctm2000.html %%Revision z40\clip\2000\02\apmath.txt http://seattletimes.com/news/nation-world/html98/math13_20000413.html Thursday, April 13, 2000 New math guidelines 'set higher standards' for students by Nicole Ziegler Dizon The Associated Press %%Support CA STATE SUP AND NSF SUPPORT NTCM STANDARDS Date sent: Thu, 22 Jan 1998 17:11:45 -0700 (PDT) From: Charles L Hagopian Anyone can access California's reading and math standards at www.csbe.ca.gov. The standards that match NCTM standards were recommended by our standards commission and rejected by our state board. Our state superintendent has recommended that districts follow the commission standards instead of the board's standards. NSF has threatened to withhold funding if a district uses the state board's standards. %%Videotape study "Are the Japanese using progressive education?" Of course not, as the TIMSS videos and James Stigler's writings about them demonstrate so clearly. Here's a couple of sources that show that what the Japanese do is excellent instruction, not ed school panacea. http://mathematicallycorrect.com/wbishop.htm (Interview with Stigler on TIMSS) "Understanding and Improving Classroom Mathematics Instruction: An Overview of the TIMSS Video Study", by James W.Stigler and James Hiebert, Sept '97 Phi Delta Kappan: http://www.pdkintl.org/kappan/kstg9709.htm Wayne Bishop NCTM SAYS NEW STANDARDS ALREADY BEING IMPLEMENTED BY JAPANESE http://www.thonline.com/th/news/1996/th1121/stories/35200.htm \clip\97\28\ustud.htm November 21, 1996 U.S. students aren't at the top of the class Associated Press . Average: American teens score low in math, but better in science WASHINGTON (AP) - American eighth graders ranked 28th in math tests given to students in 41 nations, far behind Asian countries at the top of the list. The U.S. students made it into the top half in science, ranking 17th. The National Council of Teachers of Mathematics has a videotape study that shows Japanese teachers already were doing a better job implementing the kind of reforms the council advocates. In the United States and Germany, students are taught procedures for solving practice math problems, said Jim Stigler, who directed the classroom videotape study. In Japan, the goal is conceptual understanding, he said. Explore Math Lessons in Germany, Japan, and the United States http://nces.ed.gov/timss/video/jimvid1.htm %%Critical STEVENSON DOWN ON NCTM STANDARDS Dr. Harold Stevenson, author of THE LEARNING GAP and University of Michigan researcher who has for 15 years analyzed math education in Eastern Asia and the United States, wrote the following as a response to the previous posting about the NCTM standards: NCTM are fuzzy standards that aren't helpful to most students or teachers, and aren't what the Chinese and Japanese do. SAXON HATES THE NEW STANDARDS We do not need guidelines that recommend leaving students ill-prepared for chemistry and physics, and that ridicule preparation for calculus. NCTM STANDARDS CHANGES Word Problems and the NCTM Standards

Math Forum

The math reform movement is based on constructivism, and against drilling. It seeks to concentrate on "problem solving" skills, and relate math to real life like cooking. The NTCM standards and several new math text series funded by the National Science Foundation have done the most to promote the "new new" or "fuzzy" math. Most states have adopted "performance-based" assesments which promote reform math philsophy

Critics say it has resulted in plunging test scores which have provoked parent revolts in cities across the nation. Problem solving inevitably ends up asking 4th graders how to solve what traditionally were 7th grade ratio and proportion and 9th grade algebra problems by "figuring it out" rather than teaching the skills, or waiting until they are taught. They say that students learn more about how to write about answers than getting the right answer, indeed, one of the most important principals is that there isn't such as a thing as "one right answer", and students are encouraged or required to "construct" their own methods of computation rather than being shown how it has been done for the past 5 thousand years. Traditionalists call for a return to contents based teaching and drill based programs like that of John Saxon for students who are failing in math.

Protest Pages


z49\clip\2001\04\badnews.txt Date: Tue, 17 Apr 2001 BAD NEWS FOR
CHILDREN, GOOD NEWS FOR TUTORS By CARL CAMPANILE Parents can't help
their kids with homework because the new math is "unrecognizable" to
what they learned in school.  Students who aren't fluent in English
are particularly handicapped with constructivist math because so much
is based on reading passages and writing answers regarding math
problems.

z49\clip\2001\04\crewmath.txt
From: "Elizabeth Carson" 
Apr 17, 2001 SCHOOLS' ‘NEW MATH' = TROUBLE FOR CITY KIDS By CARL
CAMPANILE "The movement - initiated by District 2 in Manhattan and
pushed by former Schools Chancellor Rudy Crew - continues, even
though mathematicians at the city's elite high schools are against
it.  "

NSF $3.5M grant to implement math reform in NYC
z48\clip\2001\04\addup.htm New York Post: SCHOOL'S MATHEMATICS DON'T
ADD UP Sunday,April 8,2001 By ROD DREHER 'IWALKED out of there, and I
tell you, my head was spinning," the distressed caller told me. "It
was like a cult. It was like they were selling Amway or something."
It has also been ground zero for a local movement of parents
desperately worried that their children are being harmed by this fad.
Carson and others have long tried, and failed, to get the district to
agree to a public forum to discuss the pros and cons of
constructivist math.  Raimi discovered that the National Science
Foundation had authorized a $3.5 million grant to implement and study
math "reform" in District 2 schools, along constructivist lines. 

WSJ ED ON NEWNEW MATH: WE HAD TO DESTROY IT TO SAVE IT...
\clip\99\21\wsjmath.txt Wall Street Journal Lead Editorial January 4,
2000 Page A22 MATH WARS The reason for the New New Math, as for many
other curriculum reforms, is that teachers, school administrators and
their unions are tired of being blamed for statistical declines and
poor student performances.  So with math, as in their campaign to
dumb down the SAT, such educators work to destroy or reject the
standards that brought them trouble in the first place.  Children are
different nowadays, goes the line, and cannot be measured by old
benchmarks.

 Have
Math Fundamentals Gone Fuzzy?  by Betsy Van Dorn  Family Education

Issues against
- results in falling test scores from 90 to 61 (Palo Alto, U Chicago)
- based on reading, weak readers can't do it.
- often no textbooks
- relies on discovery learning, some hit right answer right away,
   others never get it
- takes lots of prep and time to assess 25 free response questions.
- few exercises, little practice



%%Activism

PARENTS SUCCEED IN NEARLY KILLING CONNECTED MATH
z56\clip\2002\07\mathfail.txt
http://www.zwire.com/site/news.cfm?brd=2275&Nav_Sec=58218
New math gets scaled back 
ICHAEL ROCCO , Staff Writer  07/19/2002 
The Reporter Lansdale, PA 19446
...Although scaled back considerably‚ parents against Connected Math
want it gone completely.  Trish Gallagher of Montgomery Township said
final exam test sores of students show Connected Math has failed. The
board’s action proves the point‚ she said.

z49\clip\2001\04\fightmat.txt
Front Page Headline: BIG FAT MINUS PARENTS & TEACHERS: 'NEW MATH' DOING A
NUMBER ON KIDS
Inside Headline: SCHOOLS' 'NEW MATH' = TROUBLE FOR CITY KIDS
SUM-THING IS WRONG: PARENTS AND TEACHERS, Carl Campanile
LET'S SEE: 2,001-1,957 IS . . , Carl Campanile
BAD NEWS FOR CHILDREN, GOOD NEWS FOR TUTORS , Carl Campanile

GET MAD, THEN GO AFTER THE BUREAUCRATS By ROD DREHER April 17, 2001
-- HERE'S how you become angry: Read up on what many New York public
schools are doing to math education, and how permanently crippled our
kids will be because of this "constructivist" fad.

%%Bush Initiative

BUSH FUNDS MATH BASICS STUDY
z60\clip\2002\11\bushmath.txt
http://edweek.org/ew/ewstory.cfm?slug=12math.h22
November 20, 2002 
Bush to Push for Math 
and Science Upgrade
By David J. Hoff
Washington
[of three...] Mr. Milgram helped rewrite the California math standards
that had reflected the NCTM's influence.

%%Civil Rights

NEW NEW MATH IS A CIVIL RIGHTS ISSUE
Z56\doc\web\2002\05\mathgood.txt
http://www.aera.net/pubs/er/pdf/vol31_01/AERA310104.pdf
Making Mathematics Work for All Children:
Issues of Standards,Testing, and Equity
by Alan H. Schoenfeld
“Mathematics Education is a civil rights issue,” says civil rights
leader Robert Moses The data have been clear for decades: poor
children and children of color are consistently shortchanged when it
comes to mathematics.

%%critical

*** EXCELLENT 2 PG SUMMARY OF FUZZY MATH BOMBING IN CANADA ****
z49\clip\2001\05\canmath.txt canmath.doc
http://www.globeandmail.com/gam/Education/20010505/COWENT05.html Go
figure, Ashley can't MARGARET WENTE Saturday, May 5, 2001 Caitlin
Kirby's only in Grade 4, but already she has hit the math wall.
Sometimes she lays her head down on her math homework and cries. "I'm
stupid!" she tells her mother Tressa.  "It's time to acknowledge that
continuing to teach these skills to our students is not only
unnecessary, but counterproductive and downright dangerous."  The new
curriculum also introduces kids to complicated concepts they don't
yet have the tools to master, such as geometry and probability
statistics.

z45\clip\2000\08\silber.txt Boston Herald:
http://www.bostonherald.com/news/columnists/silber08212000.htm `Old
math' fans should go forth and multiply by John Silber Monday, August
21, 2000 The Massachusetts Board of Education recently adopted a new
set of guidelines for teaching mathematics. A Boston math teacher was
quoted as saying, ``The new framework means going back to the way our
grandparents did it, which was a terrible way to do math.'' 

z41\clip\2000\05\flexmath.txt FUZZY ANSWERS / A SPECIAL REPORT The
New, Flexible Math Meets Parental Rebellion By ANEMONA HARTOCOLLIS
Three years ago, one of New York City's most adventurous school
districts set out to tackle a nagging problem: the math phobia that
afflicts many students, and the disparity between the test scores of
white middle-class students and their poorer black and Hispanic
counterparts.

DEPT OF ED MATH PROGRAMS OMIT TRADITIONAL MATH ON PURPOSE
z40\clip\2000\03\mathadd.txt
http://www.mathematicallycorrect.com/usnoadd.htm American School
Board Journal April 2000 MATH PROBLEMS: Why the U.S. Department of
Education's recommended math programs don't add up By David Klein The
standard algorithms for arithmetic (that is, the standard procedures
for addition, subtraction, multiplication, and division of numbers)
are missing or abridged in ED's recommended elementary school
curricula.  Steven Leinwand of the Connecticut Department of
Education was a member of the expert panel that made final decisions
on ED's "exemplary".. In a Feb. 9, 1994, article in Education Week,
he wrote: continuing to teach these [manual math] skills to our
students is not only unnecessary, but counterproductive and downright
dangerous."
There is a unifying ideology behind "whole math." It is advertised as
math for all students, as opposed to only white males. But the word
all is a code for minority students and women

z40\clip\2000\03\innum.txt
Politically Correct Math=Innumerate Children
by Wendy McElroy 
Saturday, March 18, 2000 
"A. If math were a color, it would be __, because __. 
B. If it were a food, it would be __, because __. 
C. If it were weather, it would be __, because __." 
grade school children discover the rules of multiplication and
subtraction by themselves without the tyranny of "teacher-imposed
rules." 


SAN GABRIEL PASAENA PAPERS FLUNK OUT MATHLAND, QUEST 2000
zip37\clip\99\18\fuzmath.txt 
San Gabriel Valley Newspapers
Group/Pasadena Star News FUZZY MATH FLUNKS OUT October 5, 1999 In
closing, we say dump the fuzzy math. Dump a curriculum called
MathLand.  Dump Quest 2000, which is used at Rowland Unified School
District. One analysis says this will leave students by the time they
reach 6th grade well behind the state standard.

THANKS TO ACTIVISTS MOST TEXAS DISTRICTS REJECT NSF-FUNDED FUZZY MATH TEXTS
html
\doc\web\99\07\nofuzzy.txt
Texas School Districts Reject "Fuzzy Math"
Textbooks -- Major Defeat for Statewide Systemic Initiative Texas
school districts have overwhelmingly rejected the latest fad in math
instruction. Sometimes called "fuzzy math," "whole math," and "new
new math," textbooks based on this pedagogical approach received only
4% of the textbook orders for second grade math, 2% for fifth grade
math, and 5.6% for seventh grade math. Ironically, those promoting
this approach refer to it as "standards-based math." 
[including' Everyday Mathematics published by Everyday Learning
Corporation; and Investigations in Number, Data and Space published
by Addison Wesley Longman; (fifth grade books) Everyday Mathematics;
and Investigations in Number, Data and Space; (seventh grade books)
Math Thematics published by McDougal Littell; and Connected
Mathematics

\clipim\98\03\newmath.tif New Math Misses Mark The Washington Times
Marion Kester Coombs Tuesday June 17, 1997 The National Science
Foundation funded development of MathLand, Interactive Math and Math
in Context.  Prodded by "A Nation at Risk", the NCTM in 1986
appointed a commision to come up with new standards - verbalization.
Everyday real world.  Guess and check. Manipulatives. Calculators and
computers.  Understanding vs. memorization. Teamwork. Repetition of
topics rather than sequential.

%%Deceptive

z55\clip\2002\04\mathref.txt
Math is a gatekeeper for success
Compass
Anchorage Daily News 
By P.T. Chang
Published: April 10, 2002)
Ed Reform Buzzwords
- Carnegie Foundation Math Teacher of the Year ED INDUSTRY
- Teachers must become facilitators of learning PROGRESSIVE
- The right answer does not indicate MASTERY of a subject OBE
- Math seems to be a high-anxiety subject #1 REASON FOR FUZZY MATH
- International community WORLD CLASS STANDARDS
- Success ALL MUST SUCCEED, BELOW HIGH STANDARDS IS A WORTHLESS FAILURE
Looks like even Asian American math teachers aren't immune
from fuzzy math standards.

%%Defence


FUZZY MATH WORKS WHEN TEACHERS RE-EDUCATED??
Z49\CLIP\2001\04\FUZZBETT.TXT  NY POST Wednesday,
April 18, 2001 DON'T ALLOW 'NEW MATH' TO MULTIPLY, REGENT SAYS By
KENNETH LOVETT, CARL CAMPANILE and IKIMULISA SOCKWELL-MASON
Professors at City College and the Freudenthal Institute in the
Netherlands retrained more than 400 teachers in Districts 2 through 6
in Manhattan.  Their analysis shows that students taught the New Math
scored better on city and state standardized tests in 1999.  In
grades 4 and 5, students in constructivist math scored at least 10
points higher. 


http://showmecenter.missouri.edu/showme/keynote1full.html
Standards Under Fire: Issues and Options in the Math Wars
Summary of Keynote Session by
James Fey, Professor, University of Maryland-College Park 
Show-Me Project Curriculum Showcase, May 21-23, 1999
For almost 30 years, evidence from international comparative studies,
our own National Assessment of Educational Progress, and the SAT/ACT
college admission testing programs has suggested that, in relation to
other countries that are our intellectual and economic competitors, 
• Our curricula do not challenge students to learn important topics
in depth; 
• Our teaching traditions encourage students to acquire routine
procedural skills through a passive classroom routine of listening
and practicing; 
• Our assessment of student knowledge emphasizes multiple choice and
short answer responses to low-level tasks. 




PARROT MATH WINS - REPEATED SUBTRACTION SAME AS LONG DIVISION??
http://www.pdkintl.org/kappan/kbec0003.htm
z40\clipim\2000\03\22\math\math.htm
The Politics of California School Mathematics: The Anti-Reform of 1997-99, 
by Jerry P. Becker and Bill Jacob
. His criticisms are revealing, including, for example, that
"students are never required to use the standard long division
algorithm" as required by California's grade 5 standards. Inspection
of Everyday Mathematics reveals that students do indeed study a minor variant
of the standard division algorithm that illustrates that repeated
subtraction enables one to calculate a long division. And even though
many students understand this process far better than the
conventional approach, it is now unacceptable for California's
students. Parrot math has scored a significant victory.

Latino Educator in LA Vows to Go on
Hunger Strike Over an LAUSD Board Claims LA district data shows
more minorities completing college prep math, school with high math
scores have reform math texts.
1) There has been an increased of 73% in the number of African
American students that complete, with a C or higher, the first
mathematics college-prep course. 

Wayne bishop says:
At this link is the real LA and CA data regarding integrated math of the genre
supported by Mr. Mendieta.  Essentially, every way you slice the data -
disadvantaged or not, LEP or not , male or female, SAT-9 or the standards-based
STAR augmentation, LA Unified (where this protest is to happen, tomorrow night
on my own campus) or California as a whole - the integrated programs which are,
Allah be praised, coded into the database (but not by specific program,
unfortunately) come in 5-15% below traditional programs.  The idea is that, if
you do enough project oriented math experiences and use enough group grading,
even empty chairs get college preparatory credit in math.  Ah... Reform!! 
Don't educate underrepresented minorities.  Lie to them.
      http://mathematicallycorrect.com/la.htm

REFORM MATH GIVES HIGHER, GENDER BALANCED TEST SCORES ON UK EXIT
EXAMS?  
\clip\99\12\mathnew.txt Mathematics for the Moment, Or the
Millennium?  By Jo Boaler Education Week March 1999
http://www.edweek.org/ search: standards and assessments

"On the national examination, three times as many students from the
heterogeneous groups in the project school as those in the tracked
groups in the textbook school attained the highest possible grade.
The project approach was also more equitable, with girls and boys
attaining the different grades in equal proportions.  "

Comment - I'd like to see the actual study, I don't believe this, 
most US projects show reform students don't master methods and score
LOWER on the SAT, not higher.


> Two articles from the last issue of the Phi Delta Kappan that
> gave significant attention to mathematics reform in the U.S. are
> now available on the Phi Delta Kappan website.
 Here are the articles and locations:
 "The Mathematical Miseducation Of America's Youth"
 By Michael T. Battista
 http://www.pdkintl.org/kappan/kbat9902.htm
\clip\99\03\25\mathmis\mathmis.htm

"Parrot Math" By Thomas C. O'Brien
http://www.pdkintl.org/kappan/kobr9902.htm
\clipim\99\03\25\parrot\parrot.htm d:\clip\99\10\parrot.txt

%%Falling Test Scores

Despite the claim that Reform math does not result in lower math performance, history is riddled with failures in affluent communities which have resulted in falling math scores, and high school seniors who find themselves graded for remedial math instead of calculus.



[[Andover

Andover High School Bloomfield Hills School District in Michigan
"Outcomes Analysis for Core Plus Students at Andover High
School: One Year Later", by R. James Milgram, Department of
Mathematics, Stanford University:
ftp://math.stanford.edu/pub/papers/milgram/andover-report.htm
txt: \clip\99\06\coreplus.txt
htm: \clipim\99\04\coreplus\coreplus.htm

almost all the Andover students were severely critical of the
program, many bluntly blaming it for their difficulties in university
level courses. .. by every measure such as ACT scores, SAT Math
scores, grades in college math courses, core plus students fell short
of Lahser students. [... even when compared with students who did not
even take pre-calculus]


[[Norwich, Vermont

\doc\web\99\03\vtfail.txt From: Nanny714@aol.com In our financially
well heeled community of Norwich, Vermont which has a close
affiliation with Dartmouth College, we pioneered mathematics reforms
in our state. Our mathematics test scores as measured by the
California Achievement Test dropped dramatically consistent with our
pioneering effort.

\doc\web\98\06\vermath.txt The following is an excerpt from a Valley
News [Vermont] article dated May 6, 1997 titled "Norwich Voices
Concern Over Low Scores On Test" by Kristina Eddy "The median score
for the sixth grade in math computation dropped from 72 in 1990 (it
was 67 in 1989) to 41 in 1991, and stayed between 44 and 50 for the
next five years (55 in 1997). " [New Standards curriculum]


[[California

\clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for
Math Problems RICHARD LEE COLVIN (New math, math reform backlash
against "fantasy lunch")
http://www.math.uic.edu/~cpmp/archive9701.html Performance in
elementary grades is shaky as well. Last year, after many California
schools began using Reform lesson plans, test scores immediately
plunged in Santa Barbara, San Francisco and elsewhere--stirring
parent revolts.


[[ Chicago University of Chicago

Child with 135-140 IQ Math falls
from 99.5% to only 29-52% in only 3 years of reform math in wealthy
Chicago suburb.


[[ Palo Alto

PALO ALTO MATH TEST SCORES FALL FROM 91 IN '92 TO 58 IN '94
http://www.sfgate.com/cgi-bin/chronicle/article.cgi?ED26421. DTL:/chronicle/
archive/1995/03/10
\clip\98\01\newnew.txt Friday, March 10, 1995 · Page A23 1998 San
Francisco Chronicle Problems of New-New Math "However, the
dissatisfied parents note the drop in the Stanford test's math
computation scores for that grade -- which plummeted from the 91st in
1992 to 58th in 1994." "Problem of the week:" ``There is no
solution,'' concluded Wayne Bishop of California State University at
Los Angeles' department of mathematics and computer science.

NEW NEW MATH DESTROYS PALO ALTO MATH SUPERIORITY Wednesday, February
22, 1995 · Page A20 ©1998 San Francisco Chronicle Palo Alto Parents
Upset by the Even Newer Math John Wildermuth, Chronicle Peninsula
Bureau
http://www.sfgate.com/cgi-bin/chronicle/article.cgi?MN51592. DTL:/chronicle/
archive/1995/02/22
The average eighth-grade scores in number concepts and math
applications have stayed around the 90th percentile, but computation
scores skidded from 91st percentile in 1992 to 79th in 1993 and 58th
in 1994. `I cannot believe that the parents of children in the
high-tech Silicon Valley will put up with this `there's no correct
answer' math,'' said Evers.


[[Lake Washington

One parent reports his daughter was getting only 50th percentile math
scores until he sent his daughter to a Christian school, and it
bounced up to 90%. Bruce Poehlman of Lake Wash SD.


[[Plano Texas

\clip\99\17\conmath.txt CONNECTED MATH UNDER FIRE IN TEXAS 9/7/99 By
Andrea Billups THE WASHINGTON TIMES The "connected math" program
taught in the Plano Independent School District and used in several
school districts around the nation has been criticized by parents,
Celia J. Chiu, pulled her son out of the Plano public schools last
year after his once-stellar math grades declined.

%%Homework (or lack of)

Subject:      Re: Just what is Mathland?
From:         righteye@interaccess.com (The Other One)
Date:         1996/09/29
Message-ID:   
Newsgroups:   k12.ed.math
I work for a new math curriculum called Math Trailblazers, written at
the University of Illinois at Chicago One of the hardest things for
parents of a child using a math reform curriculum is that there are
no (or few) pages of drill and practice coming home.  The empahasis
is usually on giving students meaningful problems to solve.  Many
times the students are encouraged to come up with their own stratgies
for solving the problems, they are given manipulatives to use to work
out their ideas, and they work in groups to communicate their
strategies.  This is why there is less work coming home, so I feel
parents and teachers have to communicate more themselves.

%%Failure

PROBLEMS WITH NEW NEW MATH
Date sent:        Tue, 3 Mar 1998 08:14:09 -0500
From:             Nancy Torborg 
Subject:          Re: Got any U of Chicago Math Results?

Dear Diane,
I've used "Math in Stride" (Addison Wessley) and "Mathland"; my daughter is
currently using "Quest 2000" (new to our district).

Your principal is right; it will take several years for students to
cultivate the "habits of mind" that these programs try to develop. These
programs do not directly teach algorithims; they rely on student discovery.
There are several problems with this approach.

1) What do you do with the student who makes the "discovery" early? Keep
them in a holding pattern? This would mean in order to keep things flowing,
you need to run an individual program for each child, according to their
progress.
2) I will tell you from experience that some kids NEVER make the
"discovery"; they need the direct instruction
3) These math programs are reading-based; if you have kids with
reading/language/learning problems, they are at a real disadvantage
4) The programs downplay memorization of basic math facts, which are an
inescapable part of the real-world
5) These math programs take an INCREDIBLE amount of teacher-prep and
evaluation time; any school district that's bought into these programs
never had to sit and "evaluate" 25+ "free responses" on a daily basis! I
ended up sacrificing other subject areas just to try to get through the
program.

As in everything in life, moderation is the key. While I think the
problem solving aspect of these programs is admirable, I think direct
instruction is still appropriate and needed for some topics.  Nancy
Torborg Amherst NH mailto:nancy@torborg.com
http://www.torborg.com/nancy


\clip\98\04\flunktes.txt San Francisco Chronicle, Sunday, February
15, 1998 FLUNKING THE TESTS by DEBRA J. SAUNDERS "trendy math --
write about math, but you don't have to be right about math"

LOTS OF CONCEPTS, BUT NO MASTERY
I discovered the results of this trend
in that while she understood lowest common denominators and greatest
common factors, it took her forever to figure out the problems
because she had never been taught her multiplication facts.

%%Justification

CPM cites professors
students should learn beyond the basics to solve problems when
calculators do the basic functions.  (\doc\web\98\01\cmp.txt)

%%Netherlands

NO-ALGORITHM MATH SUCCESSFUL IN NETHERLANDS FOR 30 YEARS?
z62\clip\2002\12\realmath.txt
http://educationupdate.com/archives/2002/dec02/issue/spot_mathtorrence.html
New York City December 2002
Realistic Math Makes Sense for Student
By Eve Torrence
I am a mathematician. I am a college professor. I am a mother ..at his
Dutch school.. they were not taught the carrying and borrowing
algorithms. This approach has been used successfully in Holland for
almost thirty years.. Realistic Mathematics Education (RME)...The
teacher uses the method of guided reinvention,

Realistic Mathematics Education
http://www.fi.ruu.nl/en/projects/realme.html
Since 1971, the Freudenthal Institute has developed a theoretical
approach towards the learning and teaching of mathematics known as
'Realistic Mathematics Education'. ... students should not be
considered as passive recipients of ready-made mathematics, but rather
that education should guide the students towards using opportunities
to reinvent mathematics by doing it themselves. 


%%New Articles

\clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for
Math Problems RICHARD LEE COLVIN (New math, math reform backlash
against "fantasy lunch")
http://www.math.uic.edu/~cpmp/archive9701.html Why can't math be for
everyone? Turn new math upside down by letting students discover
concepts in groups, the process of finding an answer was more
important than using a complex formula to get the right answer. CA
adopted a "mathematically powerful" math instruction framework.
"Education journals highlight ways to teach "African American math."
Conferences attracting 5,000 teachers suggest downplaying the
difficulty of classwork by basing problems on fairy tales."

Friday, December 19, 1997 · Page A31 © 1997 San Francisco Chronicle
DEBRA J. SAUNDERS -- Man of Science Has a Problem With Real Math
http://www.sfgate.com/cgi-bin/chronicle/article.cgi?file= ED67991.DTL&direct
ory=/chronicle/archive/1997/12/19
California's commitment to ``deep, balanced mathematical learning''
-- aka new-new math -- has resulted in computational deficiencies, as
well as general arithmetical idiocy. For some years, trendy
California educators have focused on students writing about math,
repeatedly explaining how equations work and exploring their feelings
about math... credit for wrong answers.  The result: In the last
National Assessment of Educational Progress math test, California
fourth-graders scored behind students from every state but
Mississippi and Louisiana. Only 13 percent were rated proficient.

DISTRICTS ALREADY COMMITED TO WHOLE MATH "HIGHER" STANDARDS
\clip\97\29\baytep.txt Saturday, Dec. 13, 1997 · Page A 1 ©1997 San
Francisco Examiner Bay tepid to math standards Educators question
sense of the state's new guidelines Julian Guthrie OF THE EXAMINER
STAFF [state needs to revise textbook, curriculum, asessment]

/images/972/112197/p23.gif Numbers Racket: 'Standards' Math is
Creating a Big Division in Education Circles Wall Street Journal Nov
5, 1997 [generally sympathetic to new math movement, but cites
vehement opposition]

 MATH TALK IN WSU PULLMAN

KID CAN'T DO CHANGE IN HIS HEAD
http://washingtonpost.com:80/wp-srv/WPlate/1997-11/02/164l- 110297-idx.html
11/2/97 Washington Post Math Teachers' Modern Ways Don't Add Up for
Everyone By Victoria Benning Washington Post Staff Writer

NCTM - WHY REFORM?
\doc\web\97\08\need4.txt
http://www.enc.org/reform/journals/ENC2280/nf_28015.htm#need

CHILDREN NEED TIME TO "DEVELOP", "The notion of a developmentally
appropriate curriculum is an important one.  ..encourages the
exploration of a wide variety of mathematical ideas in such a way
that children retain their enjoyment of, and curiosity about,
mathematics. It incorporates real-world contexts, children's
experiences, and children's language in developing ideas.  It looks
beyond what children appear to know to determine how they think about
ideas.

WORKSHEETS, COMPUTATIONAL RULES DO NOT FIT "NATURAL LEARNING
PATTERNS" Programs that provide limited developmental work, that
emphasize symbol manipulation and computational rules, and that rely
heavily on paper-and-pencil worksheets do not fit the natural
learning patterns of children and do not contribute to important
aspects of children's mathematical development.  "

HOW MANY SKILLS THEY ACQUIRE IS "NOT AS IMPORTANT" "Thus, how well
children come to understand mathematical ideas is far more important
than how many skills they acquire"

REASONING AND PROBLEM SOLVING "Developing these characteristics in
children requires that schools build appropriate reasoning and
problem-solving experiences into the curriculum from the outset."

Child with 135-140 IQ flunks out
in math because of new math program that wastes 3 weeks on a group
project on my the Romand Empire fell.

 The Second Great Math Rebellion By
Tom Loveless Few truisms exist in the politics of education, but
you can usually count on two things. When reformers seize control of
the policy agenda, whether at the local, state, or national level,
they almost always go too far in jettisoning what they don't like and
too far in embracing the new, unproven practices they favor.

How many coins... Another silly
hard math problem that doesn't teach anything.

\doc\web\97\08\uchimath.txt U of Chicago math program puts "higher level thinking" ahead of basics so most students are just lost. PALO ALTO PARENTS MOBILIZE AGAINST FUZZY MATH http://www.rahul.net/dehnbase/hold/ Are you concerned about: the de-emphasis on basic math skills? the lack of textbooks and standard student materials? the hours that your child spends writing and illustrating a Problem of the Week (P.O.W.) that took him/her fifteen minutes to solve? the fact that 8th grade standardized test scores in computation have plummeted from the 90th to the 58th percentile in the past two years? the level to which your child is challenged in math? the ability of teachers to meet all children's needs in a heterogeneous (mixed ability) class? the failure of PAUSD to communicate with parents before changing the entire direction of a successful math program? the fact that PAUSD seems to have a different view of mathematics than you do? http://www.ait.net/catalog/catpages/c223.htm It Figures Problem Solving in Basic Mathematics for Grade 4 Encourage students to apply mathematics skills, ideas, and problem-solving strategies to real-life problems. Fourth-grade students become effective problem solvers by understanding that the process of reaching a correct answer is as important as the answer itself. It Figures, Math Works, and Solve It correlate to 4th-, 5th-, and 6th-grade student editions of Addison Wesley "Mathematics" (1987) and "Mathematics K-8" (1985); Harcourt Brace Jovanovich "Mathematics Today" (1985, 1987); Heath "Mathematics" (1985, 1987); Holt, Rinehart and Winston "Mathematics Unlimited" (1987) and Holt Mathematics (1985); Houghton Mifflin "Mathematics" (1987) and "Mathematics K-8" (1985); Macmillan "Mathematics" (1987); and Scott, Foresman "Invitation to Mathematics" (1985) and "Mathematics K-8" (1983). REFORM MATH HITS TEXTBOOKS http://hepg.awl.com/AWBookCatalog/Search/results.asp? TERTIARY_ID=88 A Problem Solving Approach to Mathematics for Elementary School Teachers , Sixth Edition, Rick Billstein, Shlomo Libeskind, Johnny W. Lott, 0-201-56649-4 BLL focuses on math skills (in contrast to teaching methods) for the teacher education market with a hallmark problem-solving emphasis, critical thinking techniques and selected major math reform trends (such as group work, writing and increased technology) that leave students at the end of the course with a clear understanding of the type of content outlines, challenges and situations they will face in the elementary education math classroom.... NEW MATH TESTS ARE SUBJECTIVE, AMBIGUOUS, GRADED ON WORDING MORE THAN CORRECT ANSWER REFORM MATH IS BOGUS - IS MEMORIZATION AND FACTS GOOD OR BAD? \clip\97\20\newmath.txt Please go to the following web site and read what a Ph.D. mathematics professor at Dartmouth has to say about math education. http://www.wgquirk.com/wgquirk/ Read the following document. http://www.wgquirk.com/wgquirk/#Documents Memorize Multiplication Facts? Cheney - Yes, Romberg - Abstained WHOLE MATH IS THE NEW DISASTER The Weekly Standard August 4, 1997 EXAM SCAM The Latest Education Disaster: Whole Math By Lynne V. Cheney Senior Fellow, American Enterprise Institute my file: \clip\97\20\examscam.htm "They lied to me, says Madalyn McDaniel of Atascadero, California. They completely betrayed me..." REFORM MATH IS A MULTICULTURAL BUST LIKE WHOLE READING \clip\97\13\fuzzmath.txt http://www.usnews.com/usnews/issue/970526/26john.htm ON SOCIETY BY JOHN LEO That so-called Pythagoras "Deep Thoughts" started as Jack Handy's running joke on TV's Saturday Night Live--a series of mock-inspirational messages about life that make no sense at all. Now "Deep Thoughts" are available on greeting cards, including one that pokes fun at the fuzzy new math in the schools. MATH DRILL RAISES SCORES, BUT SPURNED BY REFORMERS. REFORM MATH FAD IS FAILING US STUDENTS, VALUE FEELING GOOD OVER TEST SCORES \clip\97\01\refmath.txt http://www.seattletimes.com/extra/browse/html97/math_010597. html Copyright © 1997 The Seattle Times Company Jan. 5, 1997 Math-teaching fads failing U.S. students by Richard Lee Colvin Los Angeles Times Now the "reform" movement rules, it puts more value on feeling good about math than high test scores. It includes "fantasy lunch", cutting out paper shapes which has more to do with art than math, students confused about trying to "discover" 1000 years of math concepts on their own in groups, banning textbooks with "too many" formulas, and relating to fairy tales. US Ed Secretary urged not "abandoning" the reform method, critics say that drill on addition and subtraction is what builds up the mind for harder tasks. (comment, this has got to be the dumbest way to teach math I've ever heard of, it almost guarantees Asian supremacy in math, they never stand for this silliness.) %%higher scores DISTRICTS ALREADY COMMITED TO WHOLE MATH "HIGHER" STANDARDS \clip\97\29\baytep.txt Saturday, Dec. 13, 1997 · Page A 1 ©1997 San Francisco Examiner Bay tepid to math standards Educators question sense of the state's new guidelines Julian Guthrie OF THE EXAMINER STAFF [state needs to revise textbook, curriculum, asessment] For Redwood City superintendent Ron Crates, the new math standards couldn't have come at a worse time. Five years ago, at a cost of nearly $700,000, the district adopted content performance standards that he says have resulted in higher test scores. The district also spent $2.5 million to retrain teachers to teach under the more rigorous standards. %%TQM Blomstom says that Seattle teachers were told to support the reform math textbooks @@Remedial Math Colleges find many college students aren't ready for college level math or english and require students to take remedial courses in algebra or english. \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN http://www.math.uic.edu/~cpmp/archive9701.html Math professors shake their heads at the skills of freshmen--54% in the CSU system have to take remedial math. "Things the average students would know backward and forward 12 years ago, these students don't know at all," said Jerry Rosen of Cal State Northridge, lamenting how students now use calculators to add single-digit numbers. z45\clip\2000\08\remedma.txt Cal State Puts Remediation on an 'Or Else' Basis University system combines a tough approach with efforts to help high-school students prepare By JEFFREY SELINGO Long Beach, Calif. Chronicle of Higher Ed August 4, 2000 http://chronicle.com/free/v46/i48/48a02701.htm Last fall, 74 percent of black freshmen and 65 percent of Hispanic freshmen in the university system needed remediation in math, com pared with 40 percent of white freshmen. In English, 64 percent of black freshmen and 62 percent of Hispanic freshmen needed remediation, compared with 29 percent of white freshmen. @@Rhomberg, Thomas University of Wisconsin education professor who lead development of the NTCM standards, dismisses value of basic skills tests like the TIMSS where US 8th graders did relatively poorly. Author of "Math in Context" published by Encyclopedia Brittanica, received $1,702,780 from the National Science Foundation to develoop it. Weekly Standard Aug 4, 1997. @@Rhombus Parallelogram with all sides equal Grade Spectrum G1 A.G Bell 1999 1st/2nd grade class G4 Exploring Elementary Mathematics 1970 Holt Rheinhart Winston @@SAT Scores asian.education.math doc\95\01\sat93us.xlw 1993 SAT Scores Ranked by Race and Gender (unpublished special tabulations, College Board) 559 Asian male 518 White male 512 Asian female (only 6 points below WM) 472 White female 451 Hispanic male 408 Hispanic female 400 Black male @@Saxon John Harold Saxon is a leading proponent of a system empasizing rote drill reputed to be a remedy for fuzzy new new reform math. Founded a publisher dedicated to mastery of phonics and math skills / facts. Hated by educator reformers who insist on avoiding learing detailed phonics or math exercises, especially so because evidence seems to show that Saxon's methods work extremely well, and there is little evidence that show that conventional reforms result in improved performance. Now the company is run by his first employee, Frank Wang, who was a 16 yr old high school junior looking for a summer job. There are many success stories, often in inner city or rural settings, but it is shunned by the mainstream which embraces "standards based" (or fuzzy) mathematics. Saxon Publishers Home Page Article B ibliography %%Anti VERY GOOD AT PROCEDURAL ACCURACY BUT ONLY ONLY LEARN A BUNCH OF TECHNIQUES Prof. Hung-Hsi Wu raps Saxon for falling short of California standards, rejected by CA board It is extremely good at promoting procedural accuracy. And what David says about building everything up in small increments, that's correct, but the great pedagogy is devoted, is used, to serve only one purpose, which is to make sure that the procedures get memorized, get used correctly. .hundreds of thousands of students thinking that mathematics is basically a collection of techniques. %%General LOS ANGELES NIXES SAXON DESPITE SUCCESS WITH MINORITIES z50\clip\2001\06\saxon.txt Not on the Same Page Some Educators Say Saxon Math Books Are Great Teaching Tools, but Many School Systems Refuse to Use Them By Jay Mathews Washington Post Staff Writer Tuesday, June 19, 2001; Page A09 MAYWOOD, Calif. Last year's state tests showed that the school's first-graders had climbed from the 28th to the 44th percentile using Saxon. Second-graders had jumped from 24th to 42nd. z43\clip\2000\07\saxon.txt Subject: Saxon math: practice, practice Gail Russell Chaddock (chaddockg@csps.com) Staff writer of The Christian Science Monitor 5.30.00 BACK TO BASICS Saxon math: practice, practice - We don't lecture about internal combustion engines, we take you for a drive around the block. link For details on Saxon's story, go to http://www.winonanet.com/taa/NOTABLE/saxon.html Texas Commissioner refuses to allow Saxon Texts despite high performance. School board rejects Saxon math despite high scores \clip\98\08\saxmath.txt Denver Post Jeffco schools subtract Saxon math By Janet Bingham Denver Post Education Writer May 8 1998 - JEFFERSON COUNTY - A group of parents Thursday lost their battle to keep the Saxon math textbooks as a central part of the curriculum at three Jefferson County elementary schools. doc\web\97\08\saxon.txt Parent says saxon fixed harm caused by U Chicago Everyday Math http://www.seattletimes.com/sbin/iarecord?NS-search-set=/ 3353b/aaaa006YQ53b e0f&NS-doc-offset=0& \clip\97\11\saxon.txt Seattle Times Local News : Feb. 9, 1997 Math + memory, math + memory . . . by E.J. Gong Jr. "The approach is simple: repetition with frequent quizzes and review exercises. Some educators swear by it, while many others just swear at it. " John Saxon, now deceased has a popular math drill program for students failing in math. %%Sequence G2 venn diagram line of symmetry deg far mult add sub 2 digit color 3 3/4 squares bar chart estimate pounds horizontal (diagonal) oblique parallel line survey with chart perimeter < > = adding coins math54 roman numeral 1/4 + 1/8 450 / 15 75% of 100 div by 2 digit int multi > 2 dig adding exponents 5^2 + 2^3 meter kilometer reading scales tic marks adding with regrouping tally (||||/) sales tax (given as .20, not computed as %) area = rows x columns (but not height x width) mixed num improper fraction adding decimal adding like denom fraction estimate area by counting grids mult 3 x 2 digit sphere pyramid cylinder sphere cone math65 parentheses multiplication table long division practice read unlabeled tics reading clock time hands parallel perpendicular intersecting right acute obtuse angle ruler to 1/4 inch short division long 1 4 +------- 4 | 5 6 4 1 6 vs 1 4 --------- 4 | 5 (1)6 perimeter circumference radius (but not c=2 pi r) length unit conersion meter cm yard ft inch eq fractions percent to name part of group mult by decimal prob as fraction area = row x col draw count squares div decimal change a @@Scale Drawings %%Read 4th WA Assessment (bird feeder) 4th New Standards (with help of professional carpenter) --------- too early ------- 6th Nevada 6th Japan 1990 8th NAEP 5-8 Vermont - make scale drawings 8th 2001 Singapore math 10th WA Benchmark %%Construct 7th Nevada 1998 Create scale drawings New Standards - 4th grade "applied learning project" is to create plans for a bike trailer "with the help of a professional carpenter" over a period of months, with several views. NAEP Make and read scale drawings - do not assess at 4, ok at 8th grade. WA 4th Grade Assessment - read drawing for bird feeder, it has a top view, and orthogonal 3D view to give dimensions from arrows. WA 10 Grade Benchmark http://cisl.ospi.wednet.edu/ComSL/MATHBMK3.html construct geometric models and scale drawings using tools as appropriate, for example, designing a house plan or building a model of a bridge @@Scientific Notation G6 Utah G6-8 Florida @@Scott Forseman Addison Wesley Math http://www.illinoisloop.org/sf.html#conclusion z68\clipim\2003\06\03\sfaw\safaw.htm Illinois loop says it's not as bad as some off the deep end books, but still insists on 4th grade stem and leaf plots, distracting sidebars which give parents ADD, and still does the "solve it 3 different ways", but at least the traditional way is ONE of the correct ways, unlike Dale Seymour which says death to arithmetic as we know it. @@Sequence %%Traditional "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later", by R. James Milgram, Department of Mathematics, Stanford University: ftp://math.stanford.edu/pub/papers/milgram/andover-report.html txt: \clip\99\06\coreplus.txt "Traditional" Calculus = College 1 ----------------------------------- G1-G6 Elementary K : counting to 20 G1: add sub to 10 G2: add sub to 20, mult G3: add sub to 100 mult divide G4: add sub to 1000, money, average, compare like fractions G5: add sub, mult, div to 2 decimals, percent, ratio? G6: add sub, mult div decimals, neg integers, ratio, proportion G7-G8 Middle School 1-3 G7: decimal math, exponents, sci notation, exact probability, total of products, compare fraction unlike denonominator, unit conversion, percent interest, discount, mult by fraction, volume = l x w x h, neg integers, probability as ratio, percent, fraction, similar triangles. G8: decimal math, pythagorean theorem, algebraic expressions, triginometry, solve 5x + 24 = 300, rotation scatter chart, prime factorization, divisibility, permutation, frequency table flagpole proportionality? 1980s ------------------------- G9: Algebra I (solve ax + bx = c) G10: Geometry (obtuse angle) G11: Algebra II G12: Pre-Calculus (Trigonometry and Topics in Advanced Algebra) College: Calculus 1960s --------------------- G9: Algebra I G10: Algebra II G11: Geometry G12: Triginometry (thanks to Lauren Scheffers) "in my generation we had six subject hours (55 minutes) per day. I had 4 years of math (algebra I & II, geometry, and trigonometry), 4 years of English with an elective of rhetoric (in the "missing" science year that follows), 3(?) years of science (chemistry, biology, physics), 2 years of history (U.S. and world), 2 years of a foreign language, 4 years of gym, and 1 "elective" hour. People tended to use that for study hall, home ec, shop, or in my case, orchestra for 4 years." Accelerated ------------ G8 Algebra I G9 Geometry G10 Algebra II G11 Pre-Calculus (Trigonometry and Topics in Advanced Algebra) G12 Calculus http://www.arthurhu.com/images/99/09/07/highmath.gif Renton High District 403 High School Registration Booklet Graduating class of 1998 & beyond This chart give an excellent view of different levels of traditional math, as compared to "integrated math" and the notion that all students must master algebra and geometry by the 8th grade. Accelerated->Calculus ----------------- G8 Algebra 1,2 G9 Geometry(2) 1,2 G10 Algebra 3,4 G11 Math Anal/Trig G12 Calculus College Prep Normal->Math Anal -------------------- G8 65 percentile Algebra Aptitude or 80% Math Placement G9 Algebra 1,2 G10 Geometry 1,2 G11 Algebra 3,4 G12 Math Anal / Trig Slow Algebra->Algebra 3,4 --------------------- G8 36-64 Algebra prep, 60% Math Placement G9 Algebra 1A, 1B G10 Algebra 2A, 2B G11 Geometry 1,2 G12 Algebra 3,4 Minimum ----------------------- G8 0-35 Algebra test, < 60 math place G9 none G10 Math 1,2 G11 Math Maintenance Math Applications G12 Consumer Math 1,2 %%Reform "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later", by R. James Milgram, Department of Mathematics, Stanford University: ftp://math.stanford.edu/pub/papers/milgram/andover-report.html txt: \clip\99\06\coreplus.txt Integrated Math G1-G5 Elementary G6-G8 Middle School 1-3 G10-12 Integrated Math 1-4 College Remedial->Algebra->Calculus @@Singapore Math Textbook http://www.rockymountainnews.com/drmn/opinion_columnists/article/0,2777,DRMN_23972_4987887,00.html Back to basics Vincent Carroll, editor of the editorial pages, Yes, Singapore - whose structured approach gives many progressive educators the fits. Perhaps mastery of the facts is not so mindless after all. US STINKS IN BASIC MATH, BUT GOOD AT 21ST CENTURY FUZZY APPLICATIONS z87\clip\2005\02\airstudy.htm AMERICAN INSTITUTES FOR RESEARCH® What the United States Can Learn From Singapore’s World-Class Mathematics System AIR Report in pdf at: http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf American Institutes for Research (AIR) February 7, 2005 New AIR Study Compares the Quality of U.S. Math Instruction with Singapore, a Recognized World Leader U.S. Trails, But Both Nations Could Learn from Each Other Although the U.S. mathematics program is weaker than Singapore’s in most respects, the U.S. system is stronger than Singapore’s in some areas. The U.S. frameworks give greater emphasis than Singapore’s to developing important 21st century mathematical skills such as representation, reasoning, making connections, and communication. The frameworks and textbooks also place greater emphasis on applied mathematics, including statistics and probability "Because topics are mapped out in such a general way, the NCTM requirements risk exposing students to unrealistically advanced mathematics content in the early grades. NCTM’s Pre-K–2 algebra topics, shown in Appendix: Exhibit B3–2, indicate that students should understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various contexts, all in the very early grades. Students are exposed to these complicated mathematical topics in kindergarten and first grade at the same time they are learning basic addition and subtraction. Singapore, in contrast, considers algebraic concepts to be advanced rather than introductory mathematics, so algebra is not introduced until the sixth grade. Overall, NCTM’s grade-band structure lacks the specificity needed to serve as a solid national content benchmark. The specificity and logic in Singapore’s spiral approach offer a more effective, bettersequenced framework for a mathematical curriculum." The California mathematics framework is modeled on Singaporean and Japanese frameworks. It is similar to the Singapore framework in that it is organized around a varying set of mathematical topics appropriate to the grades in which they are taught. "this approach means that Singapore relies on early high-stakes testing [but for sorting, not all pass at the same level], but it also holds teachers responsible for the success of all children and ensures that teachers devote more attention, rather than less, to students with greater academic needs." BOTH CHINESE AND MALAY SCORE 83/96 ABOVE AVERAGE, US BLACK AT 25 PCT "1999 TIMSS scores for its Malay and Chinese populations (Ministry of Education Singapore, 2000b). Although 96 percent of Chinese students performed better than the international eighth-grade mathematics average, Malaysian Singaporeans also did very well, with 83 percent scoring above the international average. Scores for Singapore’s Indian minority population were not available, but typically, students of Indian background outperform their Malaysian peers by a small margin. By comparison, in the United States, half of black eighth-grade students achieved no better than the bottom quarter of all international test takers (NCES, 2000)." "We first looked at the Singapore textbooks and workbooks, the Scott-Foresman student texts, and the Everyday Mathematics student journals to get an overall sense of how they address mathematical topics." "Singapore students are expected to complete about one thorough lesson focused on a single topic per week, while U.S. students are expected to complete about one lesson on a narrowly focused topic each day." "the Scott-Foresman textbooks cover the geometric properties of plane shapes, 3-D solid figures, symmetry, congruence, and transformations in all six elementary grades. The Singapore textbooks, in contrast, do not introduce 3-D solid figures and symmetry until grade 4." "The only statistics content in the Singapore grade 5 textbooks and workbooks is a single lesson on line graphs. The lesson consists of one line graph made by using a table of data on attendance at a swimming pool over a 5-month period." "Despite the generally poor showing of both U.S. textbooks in terms of teaching mathematical concepts, the nontraditional U.S. textbook, Everyday Mathematics, does do one thing much better than the Singaporean texts do. It poses interesting real-world problems and uses illustrations that demonstrate the practical application of mathematical topics," z84\clip\2004\06\singpore.txt Schools import Singapore math style Diagrams, models used to aid comprehension By Susan Ware, Boston Globe Correspondent | June 10, 2004 The students at the Varnum Brook Elementary School in Pepperell groaned in unison when teacher Karin Pillion announced they would do the next set of problems out loud -- without pencil, paper, or calculators. "What is 6 times .04?" Pillion began. @@Slope Intercept G8 WA 2007 Draft math standard "interpret meaning of graph's slope" @@Standards Posted Northshore Schools (Seattle Suburb) http://wo1.nsd.org/Apps/WebObjects/Standards.woa/1/wo/O91vLCwJWgxc2g4Ni9C1Hq9XogU/0.12 @@Social Justice TEACH MATHEMATICS FOR SOCIAL JUSTICE oslund home What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? ... www.msu.edu/~oslund/ - 14k - Supplemental Result - Cached - Similar pages TE 803: Professional Roles and Teaching Practice--Elementary Mathematics What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? In the upcoming semester, Joy, along with 18 interns in MSU's teacher certification program, will grapple with these big ideas while navigtating the day-to-day experiences of the internship. @@Standards Wars CA MATH STANDARDS WARS 12/97 "...school systems that embark on a course that substitutes computational proficiencies for a commitment to deep, balanced, mathematical learning." US "WORLD CLASS MATH STANDARDS" AREN'T WORLD CLASS AT ALL! z57\doc\web\2002\08\mathstan.txt z47\clipim\2002\08\06\mathstan.pdf http://www.aft.org/american_educator/summer2002/curriculum.pdf A Coherent Curriculum The Case of Mathematics By William Schmidt, Richard Houang, and Leland Cogan American Educator (AFT) Summer 2002 Note - the scattershot state standards are partly BECAUSE of reform efforts such as NCTM which deliberately call for putting high level math and algebra into grades as low as kindergarten. These were never aligned with standards of other nations. Ironically, Schmidt is one of the people calling for NCTM "higher order thinking" constructivist math, but this call for sane standards is a step forward. E. D. Hirsch, Mr. Core Curriculum also writes inside this article. State standards contrast to international standards - * "For instance, even more demanding topics such as geometric transformations, measurement error, three-dimensional geometry, and functions are intro-duced as early as first grade." * Prerequisite knowledge doesn’t come first. For example, the distributive property is intended to be covered in first grade, vs. grade four (and not earlier than grade three) in the top-achieving countries. * Stuff is taught in every grade instead of few topics over only 2 or 3 years. @@Statistics %%Frequency Table / Histogram Many new assessments include very complex frequency histograms or distribution tables as early as the 4th grade. In addition the WA test expects students to pick out the distrbution with the most items LESS than an amount. G2 Eric's 2nd Grade G4 Scott Forseman Math 1998 (called a line plot) G4 New Standards Assessment (raisins) G4 WA Assessment (battery) G4 KIRIS sample ---- appropriate ---- G6 Japan 1990 G7 WA Benchmark (freq table) G8 Nevada 1998 (frequency distribution) G9-12 VT %%Effective MAY 2004: ALL FUZZY MATH PROGRAMS ARE ACTUALLY UNPROVEN TO BE EFFECTIVE http://www.nap.edu/books/0309092426/html/ A report just released from the National Academies reveals all 13 National Science Foundation (NSF) funded mathematics programs lack adequate scientifically valid evidence of effectiveness. Among the programs deemed to be still experimental are NYC's universal elementary program Everyday Math, as well as several others used in some waivered K-12 schools. National Academies announcement: "Evaluations of mathematics curricula provide important information for educators, parents, students and curriculum developers, but those conducted to date on 19 specific curricula fall short of the scientific standards necessary to gauge overall effectiveness, says a new report from the National Academies' Mathematical Sciences Education Board." - Latest News From the National Academies, May 18, 2004 http://www.nas.edu/ %%Eric's 2nd grade graph2.gif Scott Forseman Addison Wesley p. 45 "Critical Thinking" Each * stands for 10 children More than 2 miles ****** 2 miles **** 1 mile ***** less than 1 mile *** How far do most students live from school? () 2 miles or more () 1 mile or less How many students live less than a mile from school () 50 () 30 The children who live more than 1 mile from school ride the bus. How many children ride the bus? () 100 () 50 How many children must get to school in other ways? () 30 () 80 This form of a chart is equivalent to a frequency histogram, this form of analysis is beyond the 7th grade EALRs since it involves evaluating distributions other than the central value. To determine where most students live involves either a) figuring out the half-way median point out of 18 students, or b) figure that 2 miles or more consists of the the first two sets, and 1 mile or less is the last two sets, and that the the first set is larger than the 2nd set. Either way is way beyond basic 2nd grade math skills which is basically addition and subtraction facts to 100 with regrouping, very simple fractions and very simple multiply divide. @@Square G5 GA Pi r squared http://www.glc.k12.ga.us/BuilderV03/LPTools/LPShared/lpdisplay.asp?Session_Stamp=&LPID=15155 G5 Everyday Math exponential notation for squared numbers is introduced http://www.mathematicallycorrect.com/books5h.htm G6 squared means second power www.achievementtech.com/files/OH_MathI.pdf @@Square Roots and Power Use square root to solve for radius given area of circle G6 Connected Mathematics teacher solution Not covered in student book until G8. G6 square roots that are whole numbers http://www.arlingtonschools.org/Curriculum/math6.html Estimate square root of non-square number G7 CA "find the two integers between which its square root lies" www.cde.ca.gov/be/st/ss/mthgrade7.asp G8 OH "estimate the square root of non-perfect" www.ode.state.oh.us/GD/DocumentManagement/DocumentDownload.aspx?DocumentID=14972 G8 WA 2007 math draft "explain why such a root is not a rational number" Basic Skill - Square root of (x) is number that multiplied by itself will result in x. G5 DODDS demonstrate square root G6-8 Lake Wash G7 California 1998 G8 DODDS graph square root (achieve) G8 Connected Mathematics Looking for Squares "introduces the term square root " http://mmmproject.org/cmp.htm Looking for Pythagoras Understand how to find the square root of a number http://schools.mukilteo.wednet.edu/staff/lapinskiij/math/level_5_math_syllabus.htm G8 Oregon recognize square root G9 Japan Japan http://www.achieve.org/achieve/ search for square root http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm @@Stem and Leaf Plot Grade level ----------- G4 Scott Foresman G5 Hougton Mifflin From Scott Foresman / Addison Wesley Math 4th grade: Create a table using place value to organize data into a histogram --------- 2 0 20 3 3 33 4 5 0 0 8 50,50,8 6 5 2 0 65,62,0 7 8 2 82 @@Story Problems 8-11 (stage 2) http://www.nrich.maths.org.uk/primary/current_month/penta.htm#5081 Train Timetable Three trains travel from City Station to Farmland Station on the same morning. The Express leaves City 10 minutes after the All Stations train, but arrives at Farmland 10 minutes before it. The All Stations takes 50 minutes to reach Farmland and arrives at 10:30. The Goods train leaves 20 minutes before the All Stations and arrives at Farmland 20 minutes after the Express. Work out the timetable. That is; what time does each train leave City Station and what time does each train arrive at Farmland Station? "Train Tunnel" comes from Teacher Tactics for Problem Solving by K. Stacey & B. Southwell. @@Sum of Products Most G4 textbooks do not teach kids how to construct totals of products such as total price of a number of repeated items. I have yet to find a single curriculum standard that specifies this ,even though grade 4 tests often have such problems. G4 1997 WASL WA test (bird feeder) G4 1998 MCAS MA test (prob 4 scores) @@Symmetry Also translation, rotation, reflection G2 Dale Seymour (construct symmetric figure) G2 Texas Core Curriculum (recognize line of symmetry) http://www.trinity.edu/departments/education/TCKC/2math97.htm G4 Washington EALRS (recognize) --------------------------------------------------- G5 Nevada - G5-8 Vermont rotational and bilateral in 2/3D G6 Japan standard 1990 G7 Washington EALRS (construct figure) @@Systems of linear equations G7 MarcoPolo NY - Lesson DetailCoordinate Geometry, (A.G.7) Graph and solve systems of linear equations www.nyiteez.org/MarcoPoloNY/ProgramDetail.php?CourseID=IL039791 G8 WA Math Draft 2007 "identify graphical solutions to systems of linear equations" @@Tally ||||/ ||||/ || = 12 Groups of 4 and slash for 5 G1 Scott Forseman 1998 @@Teacher %%China z57\clip\2002\08\chinmath.txt Creativity lacking in Chinese schools Seattle Post Intelligencer August 29, 2002 MADHU NARAYANAN UNIVERSITY STUDENT we saw rigorous math proofs and college-level physics. The nationalized curriculum packs an amazing amount of material into 12 years, and students emerge with a set of skills that would seem to put the average American high school graduate to shame. "American students aren't afraid to make mistakes, but our students are too worried about finding the one right answer." CHINESE TEACHERS LESS EDUCATED BUT BETTER AT MATH \clip\99\20\techchin.txt Rocky Mountain News November 14, 1999 http://InsideDenver.com/seebach/1114seeba.shtml Linda Seebach An American nightmare: mathematics education Only nine of the 23 US teachers got the right answer to 1 3/4 divided by 1/2 Chinese teachers usually have less formal education than Americans -- two or three years of normal school training after ninth grade -- yet all of the Chinese teachers got the correct answer to the division calculation. Ma also tested a group of Chinese ninth-graders. They did better than the American teachers too. Several confessed they had to look up the formulas for perimeter and area of a rectangle. Notices of the American Mathematical Society, which is available at www.ams.org/notices/199908/rev-howe.pdf online. ONLY 50% OF AMERICAN VS 100% OF CHINESE MATH TEACHERS SOLVE FRACTION PROBLEM http://www.arthurhu.com/99/07/asmath.txt From: "Mark J.K. Penzkover" Liping Ma has written a new book, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, Lawrence Erlbaum Associates. 50% of American but 100% of Chinese math teachers could solve moderately complex fraction problem. %%general WE NEED $5 BILLION / YR TO IMPROVE MATH z45\clip\2000\09\nsta.txt National Science Teachers Association: Legislative Update September 27, 2000 **Glenn Commission Issues Final Report on Science and Mathematics Teaching for the 21st Century** "We as a nation must take immediate action to improve the quality of math and science teaching in every classroom in the country. If we delay, we put at risk our continued economic growth and future scientific discovery," said Senator Glenn. The Commission estimates the action strategies for achieving the three goals will cost more than $5 billion annually. http://www.ed.gov/americacounts/glenn/ has .pdf, it promotes "discovery" math, discounts rote learning, calls for "high standards" It's building a "systems" approach to the math and science curriculum. Everything from certification to accreditation, training to curriculum development, standards to assessments, will all be leveraged toward the predetermined "international" outcomes. This guarantees that the curriculum and assessments will be dictated by UNESCO, regardless of local/state interests or control (what a joke!). TEACHERS MUST RELEARN CONSTRUCTIVIST MATH Canda paper EQAO has sponsored a second research paper "Varieties of Assessment: Issues >of Validity and Reliability" (June 1999) by Anthony Barley (Lakehead) and Alexandra Lawson (OISE). "From this perspective, teachers need to spend time relearning mathematics in a constructivist or problem-based manner in order to be able to teach in this fashion. Genuine mathematical reform of teachers' practices, the type of reform that might result in children understanding more about mathematics, is highly challenging." TRAINING TRADITIONAL OR INVENTED MATH? delay textbooks to meet new traditoinal CA standards \clip\99\15\mathte.txt Los Angeles Times July 23, 1999 http//www.latimes.com/HOME/NEWS/STATE/topstory.html Classes for Teachers Return to Basics, Especially Math SchoolsDistricts focus on notion that one can't teach what one doesn't know. Often that includes fundamentals. By RICHARD LEE COLVIN, Times Education Writer In the Los Angeles Unified School District, one in five math teachers are working under emergency permits, meaning they are not fully trained. But there's little evidence, researchers now say, that the billions of dollars spent on pushing such generic teaching techniques have had much, if any, impact on student achievement. MATH SCIENCE TEACHERS WITH "EMERGENCY" CREDENTIALS JUST AS GOOD, HAVE BETTER TEST SCORES \clip\99\14\teaccred.txt The Washington Post Effectiveness Of Teacher Certification Questioned By Kenneth J. Cooper and Jay Mathews Washington Post Staff Writers Thursday, July 15, 1999; Page A14 ... high school students whose teachers have emergency teaching certificates perform about as well in mathematics and science as students whose teachers hold regular teaching credentials. ... based on the test scores of a national sample of high school seniors and sophomores, runs contrary to the assumptions of a Clinton administration proposal to require states to stop issuing emergency teaching certificates as a condition for receiving federal education aid.... students whose teachers have college degrees in math or have been specifically certified to teach math score significantly higher on standardized tests than students whose teachers did not specialize.

@@Test Scores

Traditional math ends up with better test scores every time, or at best, equal. The claims is that there is NO evidence that NTCM methods result in lower scores, but this is almost always the case. %%Equal There are no programs at any level that share the core instructional features, have been implemented as intended for reasonable lengths of time, and show that students perform more poorly than their traditionally taught peers http://www.nctm.org/jrme/abstracts/volume_30/vol30-01-hiebert.html Journal for Research in Mathematics Education January 1999, Vol. 30, No. 1, Page 3-19 Relationships Between Research and the NCTM Standards James Hiebert, University of Delaware [yet cites controversy over poor Algebra performance in Riverside] Home Page The Interactive Mathematics Program (IMP) Dr. Webb has found that IMP students do as well as students in traditional mathematics classes on standardized tests such as the SAT. \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN (New math, math reform backlash against "fantasy lunch") http://www.math.uic.edu/~cpmp/archive9701.html School offers students a choice, only 1/4 chooses reform math. " In trials across the country, IMP students have done no worse--but no better--on college entrance exams than students taught traditionally. Still, Martinez believes weaker students stick with math longer because they enjoy the unconventional approach." %%Higher Scores There are _no_ studies that show higher math scores for new integrated math programs. %%Lower Block scheduling also results in lower SAT scores. MATHLAND BLAME FOR SCORE DECLINE IN SF Thursday, Aug. 15, 1996 · Page A 4 San Francisco Examiner Mixed math test results leading S.F. district to rethink methods Students in City's elementary, high schools lose ground on basic skills test; superintendent cites new curriculum Venise Wagner San Francisco students scored 50.3 in reading and 53.7 in math vs. national 50 Elementary math scores fell to 50.5 this year from 50.8 in 1995. High school scores dropped to 57.1 from 57.7. African Americans scored 36.7, down from 38.6 in 1995; Filipinos scored 50.7, down from 52. Nearly 50 percent of African American students were at the bottom 25 percent in math. About 57 percent of African American second-graders were at the bottom 25 percent. In the fifth grade the percentage was 52.8. VERMONT SHOWS MASSIVE FALL IN COMPUTATION SCORES Vermont pioneered NCEE program We pioneered the math. What they haven't told you is that the computation scores on our California Achievement Tests plummented during the time we were involved in this so-called "project" with no gains in the area of "concepts and applications." Our involvement began in 1990 and our children are tested in the fall of each year. Here are the math computation percentile score summaries for 6th grade on the CAT: FALL IN PERCENTILE FROM 72% TO 59% 1989: 67%; 1990: 72%; 1991: 41%; 1992: 50%; 1993: 49%; 1994: 44%; 1995: 49%; 1996: 49% RISE IN FAILURE FROM 9% TO 28% Here is the percent of kids scoring in the lowest quartile: 1989: 9%; 1990: **; 1991: 25%; 1992: 24%; 1993: 31%; 1994: 27%; 1995: 28%; 1996: 28% Finally, here's the difference between the scores on the "Total Battery" and the "math computation" scores: 1989: -10%; 1990: -13%; 1991: -34%; 1992: -32%; 1993: -32%; 1994: -32%; 1995: -29%; 1996: -30%] April 26, 1998 edition of the Riverside Press-Enterprise newspaper High failure rates and concerns that students are not learning the math skills they need has prompted a third of Inland high schools trying a new college-prep program to drop it. Riverside's Poly High School discontinued College Prepatory Mathematics [CPM] in June after only 27 percent of the Algebra I students earned a C or better. One semester after scrapping the program, the passing rate went up to 42 percent (Sharma, 1998) DOD STUDY SHOWS MINORITES HAVE LARGER GAP WITH REFORM MATH http://www.tppf.org/ecot.html \clip\99\02\ecot.htm SCHOOL DISTRICT ALERT FOR MATHEMATICS TEXTBOOK SELECTION Texas policy foundation. NSF funded books are ranked as unsuitable for algebra by 8th grade In 1995 the Department of Defense introduced two "standards" math programs ...standardized testing of the 81,140 students enrolled in "Mathland" (elementary school) and "Interactive Math" (middle school). The CTBS indicated that scores in computation had significantly dropped (9 points for grade 3, 12 points for grade 4, 11 points for grade 5, 10 points for grades 6 and 7, and 4 points for grade 8). Data generated by this study can be accessed on the Internet at http://206.86.183.194/math/McArthurText.htm. ANDOVER HIGH SCORES 1-5 PCT WITH CORE PLUS \doc\web\index\corefail.htm The Detroit News Metro Section June 17, 1998 Math debate heats up Professor won't give up controversial data on Core-Plus program in Bloomfield Hills By Rusty Hoover / The Detroit News BLOOMFIELD HILLS -- A math program at Andover High School that students say has cheated them out of a solid math education is now causing a second round of controversy. Escondiso flunks CPM, IMP Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski "Students in new math at Orange Glen, for example, scored an average of 477 on the SAT, while those in traditional classes at the same campus had average scores of 502. " ""No data is available that indicates that the integrated math is a success," he said. " @@Testosterone Testosterone levels may have something to do with male/female differences in math and verbal performance. zip37\clipim\99\09\06\test.efx Seattle Times June 16, 1996 Testosterone may have links to skills in English, math John Hopkins University found 11 men with low testosterone levels did worse in math but better in verbal tasks without treatment. @@Textbook %%AAAS middle school Major warning flags! [[Project 2061 Project 2061 promotes NSF funded math like connected mathematics Reform: Project 2061, the long-term math and science education reform initiative of the American Association for the Advancement of Science (AAAS) has made a major contribution to education reform efforts with this standards-based textbook analysis," Funded by the source of funding of worst math textbooks: The benchmarks-based approach to evaluation was developed with funding from the National Science Foundation. Funding for the middle school math book evaluation was provided by the Carnegie Corporation of New York Based on dreaded NCTM standards: he analysts evaluated textbooks on how likely they are to help students achieve six key learning goals from Project 2061 landmark Benchmarks for Science Literacy. These benchmarks are consistent with the widely accepted standards developed by the National Council of Teachers of Mathematics. The AAAS math reviews are available on line as .pdf files in the press relea se at \clip\99\03\aaas.htm http://project2061.aaas.org/newsinfo/press/rl012299.htm The entire document is 4 pages long (the total of 3 files). ratings \clip\99\03\attach_a.pdf http://project2061.aaas.org/newsinfo/press/attach_a.pdf benchmarks attach_b.pdf http://project2061.aaas.org/newsinfo/press/attach_b.pdf good/bad example http://project2061.aaas.org/newsinfo/press/attach_c.pdf \clip\99\03\attach_c.pdf Best: Dale Seymour, Mathscape, Math Thematics McDougal Littell Worst: Saxon, Scott Forseman, Passport McDougall Littell %%Addison Wesley Focus on Algebra "Rainforest Algebra" Rainforest Algebra 800 pages of junk vs. 200 page japanese book that just teaches algebra, links to other bad reviews. %%Asian %%Japanese %%Singapore @@singapore The claim is that the fuzzy math texts are just like the Asian books but you can be darned sure they don't leave out carry and borrow but put in sheet music to Bingo!. http://www1.moe.edu.sg/syllabuses/default.asp Link to pdf Prim, HS standards z48\clipim\2001\03\29\maths_pri.pdf 2001 Singapore Math Standards Maths_LowSec.def lower secondary school. Singapore fuzzy math: Mathematics education aims to enable pupils to: • acquire and apply the skills and knowledge relating to number, measure and space in mathematical situations that they will meet in life. • acquire mathematical concepts and skills necessary for a further study in mathematics or other disciplines. • develop the ability to make logical deduction and induction as well as to explicate their thinking and reasoning skills through the solving of mathematical problems. • use mathematical language to communicate mathematical ideas and arguments precisely, concisely and logically. • develop positive attitudes towards mathematics including confidence, enjoyment and perseverance. • appreciate the power and structure of mathematics, including patterns and relationships, and to enhance their intellectual curiosity. key features of the syllabus: • mental calculation • mathematical communication • practical uses of mathematics • investigative work • problem solving • critical thinking • creative work • use of information technology Continual Assessment It is important to carry out assessment on a continual basis. Teachers should use continual assessment to: • obtain information about pupils’ learning, suitability of teaching methods and materials and effectiveness of the teaching programme • identify any learning difficulties that pupils may encounter or misconceptions that they may have so as to plan effective remedial help • provide prompt feedback to pupils on their progress and attainment • promote pupils’ confidence in doing mathematics by focusing on what they can achieve rather than what they cannot NSF Report faults Connected mathematics for shorting basics, but knocks Singapore math for "higher order thinking" even though Singapore students scored higher in math ability. SINGAPORE FOLLOWED VERMONT MATH ADVICE April 2001: Representatives from Singapore visited Vermont for two years studying the Vermont's standards and assessment system....Marge Petite, Acting Commissioner of Education at the time, spoke to the Business Round Table extolling the visitations and how Vt. had been selected by Singapore. In her address she stated that she advised the Singapore delegations that it was necessary to reduce existing math content by 30%. Looks like they followed instructions! Fran Rice How to get actual Japanese or Singapore math texts for $20 a book Japanese grade 7-9 textbooks are available from the University of Chicago School Math Project at 773-702-9770 or e-mail ucsmp@cicero.uchicago.edu . Individual books cost $19. %%California z47\clip\2001\01\camath.txt Dec. 15, 2000 Curriculum Commission overrules advisors on math texts Traditional emphasis continues as commission recommends only algebra books for eighth grade By Colleen Flannery The Curriculum Development and Supplemental Materials Commission only approved traditional algebra texts over the objections of ... Instructional Materials Advisory Panel (IMAP), composed of K-12 teachers and math education experts, reviews each book carefully, noting corrections that should be made and where each book deviates from state standards. A Content Review Panel (CRP) made up of university math professors, some of whom helped write current state standards, also reviews the materials. %%Comprehensive Curriculum z62\clipim\2002\12\02\comp4.jpg 4th grade workbook: 287x43 _____ 3)368 ____r 2)271 add fraction, same denom 2/5 + 1/5 = 3/5 reducing fractions 1/2 = 2/4 = 4/8 5/15 = 1/3 10/15 = 2/3 add/sub mixed numbers: 9 1/3 + 3 1/3 = 12 2/3 7 3/8 - 4 2/8 = 3 1/8 add/sub decimals 6.4 + 5.3 93.6 - 79.8 %%Open Source Wikipedia-like project (some content from the wikipedia) online free alternative to textbooks. http://flexbooks-wiki.ck12.org/index.php/Frequently_Asked_Questions has reader reviwer ... I've looked at their 6th grade and Algebra "flexbooks" and find nothing alarming. The standard algorithms are presented in all their glory. %%Scott Forseman http://bg016.k12.sd.us/math.htm Grade 5 Math Links %%Singapore ARTICLE HAS SAMPLE PROBLEMS - NOT BEYOND STANDARD TRADITIONAL MATH z43\clipim\2000\06\26\muslim.txt Muslims worry about compulsory education By JAMIE TARABAY Associated Press Writer G3 - what is cost of 4 books @ $5 each G8 - what is probability of pulling 2 cards that add up to 11 http://www.singaporemath.com/. Books come in one semester sets. Each year uses two sets, for example grade 4 is 3B and 4A (for slightly lower level students) or 4A and 4B (for slightly higher level students). Each set contains th e text book and two work books for $18.50. z40\clip\2000\04\sing2.txt Subject: US education chief praises S'pore way MATHS AND SCIENCE By TRACYQUEK The Straits Times US education chief praises S'pore way MATHS AND SCIENCE By TRACY QUEK MATHEMATICS and science textbooks used in Singapore's schools provide students here with a firm grasp of these subjects. It is no wonder Singapore students outperform their peers around the world in international mathematics and science tests, said US Education Secretary Richard Riley yesterday. Mr Riley Singapore The Singapore Math books are for sale through a family business in Oregon, whose website is http://www.singaporemath.com/ A Washington Post columnist has an article about them, posted at http://washingtonpost.com/wp-srv/WPlate/2000-02/17/059l-021700-idx.html SOME ADOPTING ASIAN DRILL, SEQUENCE APPROACHES KUMON, SINGAPORE z40\clip\2000\03\ormath.txt http://www.washingtonpost.com/wp-srv/WPlate/2000-03/21/076l-032100-idx.html Looking East for Math Techniques Approach Initiated In Japan, Singapore Guides U.S. Pupils By Valerie Strauss Washington Post Staff Writer Tuesday, March 21, 2000; Page A11 if students learn solid, basic math, they should be able to pass any standardized test. Students in Taiwan, for example, were given the MSPAP math and science exams in 1998 and outscored Maryland children--even though the Taiwanese instructors didn't teach to that test. The aim of Kumon, like that of Singapore math, is to ensure mastery over basic skills so that the student will have a foundation for creative thinking. From: Gerald W. Bracey Sent: Monday, May 15, 2000 He should be reminded that the Singapore Minister of Education was here a couple of years ago looking for ways to make his kids more like ours. Someone asked him why, since he had the #1 test scores in the world. He said "That's all they can do--take tests." %%Basic College Mathematics z47\clip\2000\12\collmath.txt http://www.bluestockingpress.com/pages/frameset.html Mathematics The reason Bluestocking Press distributes Basic College Mathematics is because the mathematical explanations behind the problem solving are excellent. we believe that most seventh graders can comfortably use this book. [teachers can use as an aid] %%Homeschool Dale Reed reviews math books, has reservations about Saxon books which are very expensive. %%Math Central Houghton Mifflin Math Central is terrible fuzzy math that does not teach basics, yet given credit for raising math scores %%Mathematically Correct Review Algebra z42\clip\2000\06\algebra\*.htm http://www.mathematicallycorrect.com/algebra.htm 1/1999 http://www.mathematicallycorrect.com/books.htm 2nd Grade http://www.mathematicallycorrect.com/books2f.htm Addition and Subtraction "In their adamance that facts and algorithms have no place in modern math classes, the authors accept that some children, at the end of second grade, will still add and subtract by drawing pictures and counting, or by counting back and forth on a "100 chart." So much emphasis is placed on personal strategies that an entire activity is devoted to adding 29 + 12 (book 5 page 7)." There is no formal instruction in telling time. An entire book (number 6) is dedicated to measurement, yet no real world measuring device appears. There are no rulers, no measuring cups, no thermometers, no balances There is little or no mathematics of consequence in this book. This program is totally dedicated to discovery learning and away from mastery, depth, or any skill or understanding necessary to succeed in any mathematics based profession. The program claims to want to "ensure that all students are included in significant mathematics learning." They succeed part way, all students, living or dead, can participate. The second part, "significant mathematics learning," is missing. "There is nothing to recommend about this program. The use of this program in our public schools is a strong argument for vouchers." 5th grade 4.1 A- SRA/McGraw-Hill SRA Math: Explorations and Applications The second group contains two programs that might be reasonably effective and contain a fair degree of mathematical depth, but fall short of the expectations of this review. There are substantial differences between these programs, but both have the potential for success. However, achievement to the level expected in the review would require supplementation. 3.8 B+ Saxon Publishers Math 65: An Incremental Development 3.5 B Silver Burdett Ginn Mathematics - Texas Edition The third group contains three programs with ratings overall that are below the expectations of this review. All three are lacking an adequate introduction to negative numbers, for example. Achievement with these programs would be expected to be limited to modest levels without more substantial supplementation. 3.2 B- Scott Foresman Addison Wesley Math - Texas Edition 3.1 B- Harcourt Brace Math Advantage 3.0 B- McGraw-Hill Math in My World Finally, the last group contains the two programs that are not recommended f or fifth grade use. 2.3 C- Everyday Learning Corporation Everyday Mathematics 1.3 F Dale Seymour Publications Investigations in Number, Data, and Spa ce Seymour G2 book does not even tell how to add 2 digit numbers Seymour G5 book does not teach how to multiply 2 digit numbers, discourages the use of standard division method, no decimal multiplication or division The emphasis on having students to devise their own methods leaves open the possibility that the students will not achieve any regular and reliable approaches. This risk is aggravated by a limited number and range of practice items. 7th grade Overall Ratings Please read the individual reviews to determine if a particular book is likely to meet the needs of a particular school or district. As noted below, not all books with the same grade are equivalent in presentation or organization. A - Well suited to pre-Algebra. These books may be considered 8th grade texts in some areas, but should be considered for seventh grade students where possible, and were evaluated based on seventh grade criteria. 4.8 A Glencoe/McGraw-Hill Pre-Algebra, an Integrated Transition to Alge bra and Geometry 4.6 A McDougal Littell Passport to Algebra and Geometry 4.3 A Saxon Publishers Algebra 1/2 B - Possibly suited to pre-Algebra. Definitely suited to pre-pre-Algebra. A true pre-Algebra book in the same series would probably rate at the A level 3.8 B+ Scott Foresman/Addison Wesley Middle School Math Course 2 3.6 B Glencoe/McGraw-Hill Mathematics: Applications and Connections, Co urse 2 3.5 B Harcourt Brace Math Advantage Middle School II Preparation for Al gebra 3.5 B Prentice Hall Middle Grades Math: Tools for Success Course 2 C - Not suited to pre-Algebra. May do well in certain pre-pre-algebra situat ions 2.8 C+ Saxon Publishers Math 87 2.7 C McDougal Littell Passport to Mathematics, Book 2 D - Not suitable 2.2 D+ McDougal Littell Math Thematics F - Not suitable 1.7 F Dale Seymour Publications Connected Mathematics Progrma \clip\98\07\badtext.txt From the San Antonio Express-News http://www.expressnews.com/pantheon/news-bus/education/ 2401agta.shtml Group denounces algebra textbook By Anastasia Cisneros-Lunsford Express-News Staff Writer " ''The Texas Public Policy Foundation, I've never heard of them. I also have never heard of Mathematically Correct . . . I have questions that are unanswered,'' Rhume said. " ''Addison- Wesley Secondary Math: Focus on Algebra,'' which received a D-plus from the math advocates. The 843- page textbook is published by Scott Foresman/Addison-Wesley Publishing Co. The company also publishes the only A-rated textbook, written by Alamo Heights High School teacher Paul Foerster, called ''Algebra I: Expressions, Equations and Applications.'' The high school also uses Foerster's book. %%High School %%Houghton Mifflin Initial impressions of Houghton Mifflin K12 text Down on H-M math Houghton Mifflin's new math program, Math Central , is math power. With Math Central students develop a strong foundation in skills and concepts, and learn to investigate, reason, and explain. %%McDougall Littel Integrated Mathematics Issaquah 2003 considers dropping integrated math in favor of traditional sequence. Integrated Math spends very little time on traditional algebra story problems found on WASL. No guess and check strategy either. MCDOUGAL LITTELL INTEGRATED MATHEMATICS McDougal Littell series is Integrated Mathematics 1, 2, Rubenstein, Craine, and Butts NCTM inspired book. Adopted by Lake Washington SD, Issaquah MATHEMATICALLY CORRECT SLAMS MCDOUGALL LITTELL TEXT http://mathematicallycorrect.com/integrat.htm "I do know that after some familiarity with probably fifty secondary mathematics texts in more than three decades, this is the only one which has ever made me ill." claim that students can learn more mathematics than before and can have better retention of what they've learned. I couldn't use a standardized test this year: there are too many topics on it we've not covered. And retention is way down: Product page http://www.mcdougallittell.com/product/mathcat/intmath.htm http://www.winonanet.com/taa/NOTABLE/rubenstein.html Math author It was an ambitious objective -- to bring a wider range of mathematics to a wider range of students," we worked from NCTM's original recommendations and the syllabi in the core curriculum addenda book," Rheta Rubenstein's goal in writing the Texty-winning textbook series, Integrated Mathematics, was to provide quality math in a form that is accessible to all high school students The title of our McDougal Littell series is Integrated Mathematics 1, 2, and senior authors are Rubenstein, Craine, and Butts. Rubenstein, Craine, Butts All areas of mathmatics woven into an integrated three-year course [Issaquah, Lake Washington] The course summary is amazing in that it's supposed to replace the algebra 1 - geometry - algebra 2 sequence. Traditionally, you spent the entire year learning to be able to solve ax + bx = c by the end of the year. This textbook appears to have NO traditional algebra story problems, and only 5-6 pages devoted to solving equations. Now, solving ax + bx = c is 5% of the the 1st year content, and you get to learn a lot of "other" topics like graphs, statisics, linear algebra, not to mention "unit projects". They use require students to have $100 graphical TI-82 calculators which can invert matrices, solve systems of equations. It's like setting your M16 to full auto and letting these kids have it. There's no way kids are going to retain this stuff. Teacher comments the sharp kids who can pick it up instantly will love it, but the other kids? Some districts are giving this to 7th graders rather than 9th grade normal start. "You can learn more with Integrated Mathematics because the mathematics topics are integrated. Over a three-year period, this program teaches all the essential topics in a contemporary Algebra 1/Geometry/Algebra 2 sequence, plus many other interesting topics.. Algebra and Geometry are taught all 3 years, Topics from Logical Reasoning, Measurement, Probability, Statistics, Discrete Mathematics and Functions are interwoven throughout". Course goals: This new program has been written to prepare you for success in college, careers and in daily life in the 21st century. Explore and solve mathematical problems. Think critically. Work cooperatively with others. Communicate ideas clearly. Advantages: develops clear understanding of topics and strong problem solving skills by giving you opportunities to: get actively involved in learning - study meaningful mathematics - see connections among different branches - try a wide variety of problems , real-world and long-term projects - use calculators and computers http://www.mcdougallittell.com/product/mathcat/mcdmath.htm %%Middle school 2 middle school text series Mathematics in Our World (c) 1978, 1981 Addison Wesley Middle School Textbook , evidently Grade 7 Mathematics Unlimited (evidently G8 math, 2nd of two books) %%Modern Curriculum Press Mathematics Popular inexpensive math series for homeschooling, books are thin, but comprehensive, tear out sheets can be figured out without the teacher book. I rate it A or A-. Compare this 1/3 inch thick book to Dale Seymour's NCTM "Investigations" which is literally 2 feet of books but little or no actual math instruction on borrow, carry, or fractions. G1 and G2 have simple tear-out sheets http://mcschool.com/html/math.html $21.50 for teacher $12.95 for student %%New Progress in Mathematics Progress in Mathematics: K-6 Balances a traditional teaching approach with the NCTM Standards. by Rose Anita McDonnell, published by Sadlier-Oxford 1995 Home Page 5th grade workbook has problems with ratio, solving for algebra unknowns using tables which appears in middle school texts. %%Reform http://www.tppf.org/ecot.html \clip\99\02\ecot.htm SCHOOL DISTRICT ALERT FOR MATHEMATICS TEXTBOOK SELECTION Texas policy foundation. NSF funded books are ranked as unsuitable for algebra by 8th grade "Modern math book offers clue to lack of student's abilities" Seattle Times Dec 28, 1997 p. B5 Robert Supino (letters to editor) "The old algebra text I bought has nine chapters and 320 pages. There are only two colors gblack and red. The red is used to emphasize important points. There are no pictures, cartoons, or diversions. It is clear what each chapter in the book is covering and it all pertains to algebra. It was written by two authors, Lial and Miller, working together to make a new text" Modern text has five authors, and 10 "conceptualizers", nine chapters and 690 pages. Much of the book is not algebra, in fact the algebra is difficult to find. The emphasis on application makes it not really a math text but a bad physical science text. %%Review Arthur Hu Review 3/11/99 of McDougall Littel Integrated Math, Scott Forseman elementary math %%Saxon %%Scott Forseman Claims to be #1 math text publisher http://www.scottforesman.com Home page The KnowZone - http://www.scottforesman.com/kz/kzsite/index.htm Sample test questions Arthur Hu Review of G4 Negative review of Grade 4th grade math @@Investigations / Connected Mathematics %%Seymour, Dale @@Dale Seymour %%Dale Seymour @@TERC %%General http://archives.seattletimes.nwsource.com/cgi-bin/texis.cgi/web/vortex/display?slug=study24e&date=20040324&query=us%2Bexpert%2Bassesses%2Bdistrict%2Bcurriculum http://www.bsd405.org/TIMSS.html A Summary Profile of Mathematics and Science Education in the Bellevue School District Wednesday, April 07, 2004 The $300,000 study was funded by one anonymous parent donor, and was the result of parent concerns with TERC, CMP and Core-Plus. The programs were brought into the district in staggered implementation beginning 5 years ago. The purpose of this report, funded by the Bellevue Schools Foundation is to provide information to facilitate Bellevue's mission to achieve K-16 alignment for every student. This assessment of the current state of mathematics and science education in Bellevue is an essential benchmark against which future efforts towards the goal may be measured. z75\doc\web\2004\04\let-seattle-terc-030122.html http://www.math.nyu.edu/mfdd/braams/nychold/let-seattle-terc-030122.html Jodi Gable and Erin Johnson Bellevue WA While aspects of the review are highly technical, the following substantial and notable omissions from the TERC program include: Carrying algorithms for addition Borrowing algorithms for subtraction Multiplication algorithm of "complex" values (i.e., 3247 x 348) Long division Multiplication and division of decimals Addition, subtraction, and multiplication of complex fractions Division of fractions Calculating an average Area and perimeter formulas for rectangles and triangles A commie wacko NSF funded constructivist thematic multicultural inclusive math curriculum with lots of cutting pasting, singing, clapping, card games and god knows what else. TERC stands for Technical Education Research Centers. Investigations in Number, Data, and Space was developed by TERC and is published by Dale Seymour Publications, an imprint of Addison Wesley Longman, Inc. More information about Investigations can be found at: http://www2.lab.brown.edu/investigations/ Wisdom from TERC: -------------------------------- - Don't teach carry or borrow __4_r 2 - Don't teach 7)30 or long multiplication (WASL) - Don't teach common denominators to add fractions - Don't teach mean = sum of items / number of items - Don't teach volume = l x w x h - Don't teach any standard algorithms Steinbock bio of seymour The 6th grade version is connected mathematics. %%Against For those interested in the basic TERC Investigations program without the supplements written specifically for Washington State: http://www.math.jhu.edu/~wsw/ED/wswmathreviewterc.pdf (There is insufficient time for students to learn efficient standard method, lots of time spent on unusual strategies) vs Math Expressions (much better) "The primary problem with whole number multiplication in TERC Investigations is the lack of opportunity to develop fluency with the standard algorithm." "As an historical note, what they call the U.S. algorithm is in the first printed arithmetic book, printed in 1478, somewhat before the discovery of America." "teacher-class dialogue on page 146 of Unit 7. In it we have: This U.S. algorithm was created when all calculation was done by hand. There were no calculators and no computers, so people invented algorithms that had as few steps as possible and that they hoped would be accurate and efficient." TERC Hands-On Math: The Truth is in the Details An Analysis of Investigations in Number, Data, and Space by Bill Quirk "You are likely to have students who suggest the arithmetic mean, or as they may call it, the average. They may know how to find it with the "add-'em-all-up-and-divide-by-the-number" technique. Although this algorithm is often taught in elementary school, research has shown that it is often not understood, even by older students and adults. At this point, it is better to stay away from the mean and the confusion it may introduce." U9, Page 6 " "In the Investigations curriculum, standard algorithms are not taught because they interfere with a child's growing number sense and fluency with the number system." BA, Page 74 5th Grade card game comparing fractions without instruction in common denominators or conversion to decimals. z60\clip\2002\11\desmath.txt http://deseretnews.com/dn/view/1,1249,450014357,00.html Math war heats up in Alpine By Jeffrey P. Haney (Utah) Deseret News staff writer Hundreds of parents, teachers and students on both sides of the ideological battlefield packed district headquarters Tuesday to voice both support and displeasure for the math programs, called "Investigations of Space and Data" for grade schools and "Connected Math" for higher grades. NO INSTRUCTION IN MULTIPLICATION OR DIVISION IN LAKE WASH 3RD GRADE Link Hu looks over 3rd grade book. Turtle Logo is worse than useless without 10 Mac computers, the only mention of long division or multiplication is to NOT do it, the only method for volume that is not approved is V = L x W x H! 2+2=5: Fuzzy Math Invades Wisconsin Schools Leah Vukmir Wisconsin Interest http://www.wpri.org/WIInterest/Vol10No1/Vukmir10.1.pdf by Leah Vukmir z48\clipim\2001\02\22\wiscmath.pdf Has example of singing happy birthday, counting on 2 hands, adding 3 ways including calculator. SING HAPPY BIRTHDAY IN MANY LANGUAGES FOR 3RD GRADE MATH z45\clip\2000\09\invest.txt Boston Spends $4M to Avoid Math Basics. Massachusetts News Published: Oct,2000 Author: Paul Moreno Posted on 10/04/2000 09:08:40 PDT Investigations is also fashionably multicultural. "Sing 'Happy Birthday' and encourage students to sing along with you. Ask for volunteers to sing the song in their native languages. Connected Mathematics review http://project2061.aaas.org/matheval/toc.htm DALE SEYMOUR: MATH FOR DUMMIES THAT LOOKS LIKE ME zip37\doc\web\99\14\mathall.txt zip37\clipim\99\09\23\mathall1.tif zip37\clipim\99\09\23\mathall2.tif Dale Seymour's Investigations: Teaching Mathmatics to _All_ Students [Or Math for Dummies of Color and Gender] ....The curriculum was designed so every student can find himself or herself reflected in it at various places Lots of Papers by Authors: http://www.terc.edu/investigations/relevant/html/relevantarticles-map.html#Z STUDY SHOWS INVESTIGATIONS MAKES GAINS, DOES NO HARM Full Year Pilot Grades 3 and 4 Investigations in Number, Data, and Space® December, 1994 Jan Mokros, Mary Berle-Carman, Andee Rubin, Tracey Wright TERC, Cambridge, MA http://www.terc.edu/investigations/impact/html/eval-3-4.html the z49\clipim\2001\05\07\pilot34\pilot34.htm Investigations group made substantially greater gains than students in the comparison group, particularly for items involving understanding of number and geometry. On the written test, both comparison and Investigations students made substantial gains. We conclude that the Investigations curriculum has the potential to substantially deepen students' mathematical understanding. At the same time, it does not seem to stand in the way of performance on traditional tests of computation skills. For example, in the Elephant Problem (fourth grade) students figure out how many 60 pound dogs would weigh the same as a 3000 pound elephant. We found that some students knew that they should choose an operation and perform it, but didn't know which operation to use. On the other hand, students who were developing good number strategies approached the task by building up chunks of 60's in order to find out how many 60's would equal 3000 http://www.lab.brown.edu/investigations/resources/studresults/iccuwno.html Study 1: Learning Number Operations in Second Grade The Comparison classrooms used a curriculum that emphasized both invented procedures and traditional algorithms. Both groups were from suburban Boston schools, with the Comparison students having a smaller class size and being from a somewhat more affluent community z49\clipim\2001\05\07\mismath.htm The Mathematical Miseducation Of America's Youth By Michael T. Battista http://www.pdkintl.org/kappan/kbat9902.htm Phi Delta Kappan Feb 1999 RECENT NEWSPAPER and newsmagazine articles, ... have aimed a great deal of criticism at the current "reform movement" in mathematics education. ... they attempt to seize control of school mathematics programs and return them to traditional teaching -- that is, to the "basics." As they cite isolated examples of alleged failures of mathematics reform, they ignore the countless failures of traditional curricula These curricula focus on the basic skills of today, not those of 40 years ago. Problem solving, reasoning, justifying ideas, making sense of complex situations, and learning new ideas independently -- not paper-and-pencil computation -- are now critical skills for all Americans. Scientific constructivism is a well-developed scientific theory that has proved invaluable in understanding empirical research on students' learning of mathematics In the mathematics curricula recommended by NCTM and all other professional organizations that deal with mathematics education, the exclusive emphasis that traditional teaching places on paper-and-pencil computation has been __moderated__. INCREDIBLE CLAIMS THAT INVENTED MATH IS _BETTER_ THAN TRADITIONAL MATH in 2nd Grade http://www.terc.edu/investigations/impact/html/eval-2.goodrow.html adding subtraction better without regrouping?? This has to be completely bogus. The traditional kids think that 9 + 4 = 12 yet the 2nd grade constructivist kids somehow understand that 3 x 50 = 150 (3rd grade) and that 8 - 9 is negative 1 (4th grade). This proves that the constructivist group is well beyond grade level in math ability. DON'T CARRY, COUNT WITH BLOCKS OR FINGERS z41\clip\2000\05\flexmath.txt FUZZY ANSWERS / A SPECIAL REPORT The New, Flexible Math Meets Parental Rebellion By ANEMONA HARTOCOLLIS When she started second grade last fall, Sabina knew how to carry tens and add two-digit numbers, Mr. Schmid said. Sabina's teacher, who is well-intentioned but too inexperienced to deviate from the program, Mr. Schmid said, told the child that she was not allowed to use this method; she had to demonstrate her work with blocks or by counting on her fingers. http://www.nwrel.org/scpd/natspec/catalog/connected.htm cmp participants outperformed comparison students on problem solving and proportional reasoning John Hall hates it too the LK WA standards requires teaching regrouping which is not in this book Lake Washington to adopt Dale Seymour WARNING! Notes about radical footnotes, long class prep, Bingo (from Barney preschool song) Portland OR adopts invented math over objections. \clip\99\10\oremath.txt http://oregonlive.com/news/99/05/st051101.html New math programs get board approval Portland elementary and middle schools will change the way math is taught, making the district one of the nation's largest to do so Tuesday May 11, 1999 By Betsy Hammond of The Oregonian staff "The district has estimated it will cost $3 million to buy any new math series and the needed calculators and hands-on math tools for the district's 56,000 students. District officials also have said they would have to spend about $700,000 on training for teachers if the new series is to succeed. " Investigations is rated unacceptable by Mathematically Correct %%Research http://investigations.terc.edu/impact/impact-studies/modesofteaching.cfm R's work: 1 2\8\ 18 - 9 --- 1 9 I: How did you think about that one? R: Cause you can't take nine from eight, so you cross it out and get um, you cross it out, you cross the two out and make a 1 and take that one and put it with the 8, and the 8 has 2 numbers and then 9 plus 9 equals 18. (Looks to me they didn't teach the kid how to do regrouping properly) Figure 6: Standard subtraction algorithm in the Traditional group. N's work: 28 -9 __ 19 N: 28 minus 9 I: Now this one's tricky I: How come it is 19? Tell me what you think? N: Wait. um I: That's right. Why is it right? N: Because 9 minus 8 is -1. I: 9 minus 8? N: No, I don't want to start with that. Let's see Hmmm. I have to start with ath. 9 minus 8 equals negative 1 and negative 1 minus 20. That's 20 minus 1. Equals 19. @@Time %%Time conversions 24 hr = 1 day 60 min = 1 hr 60 sec = 1 min G2 Students will need to review time equivalencies, e.g., 1 minute equals 6 0 seconds http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G5 Nevada %%Days of Week K Nevada %%Months, Calendar G1 Nevada %%Calendar Arithmetic G5 Houghton Mifflin - use a calendar to count days between july 10 and aug 22. %%Read Time to Half Hour, AM PM G1 Nevada G1 Lk Wash %%Read Time to Quarter Hour G2 Lk Wash G2 Nevada %%Read Time to 5 minutes G2 CA 1998 %%Read Time to minute G3 Nevada G4 Addison Wesley Math 1991 %%Elapsed Time (Identify) G3 Nevada G4 Massachusetts %%Add Time within even hour %%Add Time over even hour No standards specify time arithmetic going beyond hours or AM/PM. G4 1998 MA MCAS test G4 1998 MN assessment ---- appropriate ---- %%Add Time over 12 hours G5 Minnesota 1997 assessment (take medicine every 4 and 6 hrs, when same time?) (trip starting at 9PM) %%Elapsed Time within same Hour G4 Addison Wesley Math 1991 G4 TX TAAS %%Elapsed Time within different hours G1 Scott Forseman 3 to 4:30 G4 Scott Forseman Math (no minute regrouping) G4 WA Assessment G5 Houghton Mifflin math (minute regrouping) ---- appropriate ---- %%Divide Time, Result in minutes G4 1998 MA MCAS test ---- appropriate ---- Timelines ----------- G3-5 Lk Wash @@Too Hard TEACHING MATH THAT IS TOO HARD KILLS MASTERY OF BASICS MATRIX INVERSIONS VS BASIC ALGEBRA AND ARITHMETIC http://www.baltimoresun.com/news/opinion/oped/bal-op.math02nov02,0,1068320.story Teaching too-hard math concepts does students no favors By Joseph Ganem November 2, 2009 We are in the midst of a paradox in math education. As more states strive to improve math curricula and raise standardized test scores, more students show up to college unprepared for college-level math... In many cases, incoming college students cannot do basic arithmetic, even after passing all high school math tests. ... I've seen how little understanding is conveyed by the grade-school math curricula. For example, the problems assigned to my children have become progressively more difficult through the years, to the point of absurdity. My eighth-grade daughter asked me one evening how to perform matrix inversions, a technique I teach in my sophomore-level college course on mathematical methods for physics majors. ... My other daughter struggled through a high-school trigonometry course filled with problems I might assign to upper-class physics majors. goodoc: Teaching too-hard math concepts @@Tracking Traditionalists like tracking when possible, but progressives say mixed grouping is best when all are held to one "high standard". UK RESEARCH SAYS MIXED-GROUPS BEST, TRACKING CAUSES LOW MATH OUTCOMES(?) z48\clip\2001\02\uktrack.txt http://www.independent.co.uk/news/UK/Education/2001-02/pupils190201.shtml Grouping by ability disadvantages bright pupils By Judith Judd, Education Editor 19 February 2001 "research suggests that countries where pupils are taught in mixed-ability groups tend to be more successful than others. Setting, it suggests, could be "the single most important cause of the low levels of achievement in mathematics in the UK". " @@Traditional The proof that we need reform math is the "research" and "ancedotal" evidence that most adults don't think they are good at math. Yet reform math doesn't even try to teach math like carry or paper multiply or divide at all. WHERE IS THE EVIDENCE THAT TRADITIONAL MATH DOES NOT WORK? z39\clip\2000\01\mamath.txt Teachers object to plan to alter math standards By Andreae Downs, Globe Correspondent, 2/6/2000 Sandra Stotsky, the state's deputy commissioner for academic affairs [proposes to throw out 1995 NCTM math standards] ''we have a significant database that these `traditional' methods haven't worked,'' said Susan Jo Russell of Technical Education Research Centers, who develops council-based curricula in urban schools. ''The last time we had research mathematicians write K-through-12 math curricula, we got New Math,'' said Kendall. [Nope that's when we let the educators do it] ''The traditional way in which math was taught - and for all intents and purposes that's what we've had for the last 30 to 40 years - was fairly ineffective for most kids,'' said Mary Eich, kindergarten-through-eighth-grade mathematics coordinator in the Newton Public Schools. ''We know this anecdotally by the number of adults who feel they are not good at math.'' @@Trailblazers DO NOT TEACH STANDARD METHOD UNLESS NO STUDENTS INVENT IT http://www.illinoisloop.org/mathtrail.html "Later in grade 2, systematic work begins on paper-and-pencil methods for subtracting two-digit numbers. Students are asked to solve two-digit subtraction problems using their own methods and to record their solution on paper. The class examines and discusses the various procedures that students devise. At this time, if no student introduces the standard subtraction algorithm, then the teacher does so, explaining that it is a subtraction method that many people use. The standard method is examined and discussed, just as the invented methods were. Students who do not have an effective method of their own are urged to adopt the standard method." Appendix D: Constance Kamii "The teaching of algorithms is based on the erroneous assumption that mathematics is a cultural heritage that must be transmitted to the next generation." Constance Kamii is a professor of education at the University of Alabama. She studied under Piaget, @@Triginometry Only about half of college bound students take triginometry in high school, compared to nearly all taking algebra. G8 - Singapore 2001 G10 - integrated high school math G11 - standard high school sequence %%SAT Percentage taking by race: \doc\95\12\sat95bk.wk1 1995 Scholastic Aptitude Test Breakdown by Ethnicity Data from the College Board Data Entry and Analysis by Arthur Hu White Black Hisp Asian Math Coursework Gap Gap Gap Gap Triginometry 55 0 539 43 -106 433 42 -68 471 64 26 565 @@United Kingdom New New Math in UK an obsessive preoccupation with things like networks, 'clock arithmetic', Venn diagrams, different bases for counting, matrices, transformations and a whole new vocabulary to describe things with which we had previously become familiar without needing to attach names to them. @@University TRADITIONAL UNIVERSITY CALLS FOR 4 YRS OF MATH STARTING WITH ALGEBRA z62\clip\2002\12\ncpath.txt http://www.rethinkingschools.org/archive/17_02/IBM172.shtml 'McDonald's or IBM' In North Carolina, eighth graders are forced to make decisions that will impact the rest of their lives Winter 2002/2003 "U-track: Algebra I and II, then Geometry and a higher-level math. Peacock acknowledges that students not placed in Algebra I in their freshman year will have a hard time getting into a four-year institution since they'll have to complete four math courses in a three-year period." @@University of Chicago http://www.enc.org/professional/federalresources/exemplary/promising/document.shtm?input=CDS-000496-496_31 The University of Chicago School Mathematics Project (UCSMP) has been designated a Promising mathematics program. (by the Dept of Ed) UCSMP is designed to revitalize the traditional mathematics curriculum, improve student achievement, and increase the number of students who take mathematics beyond algebra and geometry. UCSMP provides a variety of exercises for students. These are challenging and inviting to students including lower level students, students with language barriers, and accelerated students. mean score of percent correct of test items for the UCSMP classes on the HSST was 1.2 percentage points higher than comparison classes. Similar results were found in a 1987-88 evaluation of the Advanced Algebra component; UCSMP students scored 15.6% higher than comparison students on a test using 50 multiple choice and four open-ended questions. Statistically significant positive differences favoring UCSMP students were found in three areas: reading, applications, and technology The program has clear, challenging learning goals consistent with NCTM standards. The content is well aligned with those goals and is carefully developed from problem situations to real-world experiences. The goals emphasize skill development and application. @@Venn Diagram Venn Diagrams (union, intersection of sets) are generally not introduced until after the 4th grade, but some places introduce them as early as the 1st grade. Traditionally, most adults were not introduced until college. My son got Venn Diagrams as a READING exercise in 2nd grade (2000) Grade Level Ranking ------------------ 1st Bill Evers 2nd Bridlemile Elementary School Portland, Oregon 2nd AG Bell (reading) 3rd Ohio 4th WA Assessment 4th Maine 6th Our Lady of Peace 8th Virgina (after algebra) 9-12 Missisippi 12th Wisconsin Standards NA WA Benchmark NA Nevada NA Massachusetts NA California College - Traditional Gerald Bracey Consider a recent Washington Post article. While the focus of the piece was the math wars as they are being played out in Maryland, the article used a sixth grade classroom as its center. The story mentioned in passing that the teacher was using Venn diagrams in his instruction. Venn diagrams!?!?!? I encountered Venn diagrams for the first time in a logic course I took as a junior in college. Another Post reporter affirmed that he, too, had not seen them until well into college. Yesterday I heard the same thing from teachers in Los Angeles they had not used Venn's before college but were now, as early as third grade. from Date sent: Wed, 22 Mar 2000 22:41:19 -0500 The use of Venn diagrams would be worth looking into for someone, wish I had the time. I first encountered them in college; a recent Washington Post article matter of factly described their use in 6th grade math. I mentioned this in LA and was told that they show up as early as second grade. My audience was a group of math and science teachers. I have since heard of them in various English classes. If anyone has time to explore, I'd love to know what's up. AG Bell 2000 Eric in 2nd grade was asked to draw a venn diagram of what was different and common between the tortoise and hare as a reading exercise! z42\clipim\2000\05\12\eric2.efx AG Bell - given Venn diagram without name - likes peaches, likes peaches and grapes, likes grapes. Ohio G3 http://www.achieve.org/ 4.make and use a Venn diagram to collect and sort information. Mississippi 9-12th grade http://www.achieve.org/ draw a Venn diagram, create a flow chart http://www.pen.k12.va.us/go/Sols/math.html#Grade Four Virginia standards - Venn diagrams are presented in Geometry (after algebra, grade 8/ 9 http://oaktree.dpi.state.nc.us/Curriculum/Mathematics/Mth. LssnPlns/Mth.2.3. 2 Strategies for Instruction in Mathematics Instructional Services North Carolina Department of Public Instruction Grade 2 http://www.achieve.org/clearinghouse/main.html Maine 4th Grade ELEMENTARY GRADES 3-4 1.Create and use organized lists, tree diagrams, Venn diagrams, and networks. http://www.wisgov.state.wi.us/MSMath.htm Wisconsin G12 B.12.1 Use complex counting procedures such as union and intersection of sets and arrangements (permutations* and combinations*) to solve problems Alternative California Math Standards http://www.rahul.net/dehnbase/hold/platinum-standards/alt1. html Data Analysis - Grade 1 1. Students collect, organize, represent and compare categorical data on simple graphs and charts, and Venn diagrams. Mathematics Content Standards for grades K-12 Submitted by Bill Evers, Commissioner September 15, 1997 6th Grade Highlights Sixth grade mathematics scholars begin to write numerals using exponents, and divide with two and three digit divisors, dividends and quotients. Set study introduces the children to the Venn diagram. Our Lady of Peace School \clip\97\26\lady.txt http://www.mcps.k12.md.us/schools/damascuses/mediacenter.html The concept of using a Venn diagram, to compare and contrast information, is featured in our first grade classrooms. Damascus Elementary School Media Center Program Montgomery County Public Schools, Maryland Bridlemile Elementary School Portland, Oregon USA Second Grade Enrichment Activities By Month http://www.icon.portland.or.us/education/elem/bridlemile/St_ projs/2nd_grd/E r_mon.htm Math Create a Venn Diagram. Label and illustrate it. Explain your diagram to someone. The Saginaw Intermediate School District LEVEL: FIRST GRADE Compare and contrast using a Venn diagram. http://isd.saginaw.k12.mi.us/curriculum/k-12/first.html VENN DIAGRAM IS PROBABLY A LOT TO ASK FOR STATE ESSENTIAL 4TH GRADE STANDARD \doc\web\97\09\venn2.txt "Finally, if I understood your question correctly, I'm inclined to agree that it's a bit early to require that knowledge as a part of a state standardized test." @@Videotape Study by James W. Stigler comparing math teaching, US, Japan and Germany on CD-ROM. NCTM claims the Japanese are using their reforms, but the EdWeek example shows the Japanese concentrate on one concept, not the "integrated approach" where they introduce themes and topics which have nothing to do with math entirely. http://www.edweek.org/ew/vol-16/28vids1.h16 \clip\97\28\vcr.txt 4/9/97 Education Week From VCR to CD-ROM: A New Way of Viewing Los Angeles "This has enabled them to learn, for example, that 8th grade teachers in Japan give a coherent lesson tightly focused on one mathematical concept, while their U.S. counterparts tend to introduce many topics at a time. " http://nces.ed.gov/timss/97198-6.html To overcome this lack, and to understand how U.S. classroom teaching compares to that of other countries, NCES added an innovative new research methodology to the TIMSS project- videotaping and quantitative coding of a national sample of eighth-grade mathematics classes in Germany, Japan, and the U.S. Explore Math Lessons in Germany, Japan, and the United States http://nces.ed.gov/timss/video/jimvid1.htm @@Volume Lots of new standards calls for knowing complicated formulas for volumes of cylinders, spheres and truncated frustrums, which we all need in everyday life, right? %%Cone Some states require knowing the volume of a cone as early as grade 7 G7 2007 WA State Math Standards draft develop (not just use) formula for volume of pyramids and cones G8 McREL INSTITUTE MATHEMATICS STANDARDS AND BENCHMARKS GRADE 8 Use appropriate formula: volume of cone www.dpi.state.nd.us/title1/benchmrk/math/math8.pdf G8 Newark NJ teachers union http://www.ntuaft.com/njcccs/Webpage/contents/STANDARD%204.2%20grade%208.htm volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height G8 Grade 8 Measurement Kent, Ohio volume should be calculated for spheres and cones kent.k12.oh.us/boe/Meas_8.htm G11 2007 IMAGE Sample Book Mathematics Volume of a cone = pr. 2. h. www.isbe.state.il.us/assessment/pdfs/2007_IMAGE_Math_Sample_Gr11.pdf %%Cylinder G8 WASL expects students to tell which dimension to increase to double capacity of can, but G10 gives the formula for the volume of a cylinder. G7 2007 WA State Math Standards draft justify volume formulas for right circular cylinders G8 2001 Singapore math G10 WASL gives sheet with formula for volume G11 PA Math Grade 11 The volume V of a right circular cylinder like the one in the figure is given by the formula V = ... www.pde.state.pa.us/a_and_t/lib/a_and_t/m11.b.2.pdf G12 Ohio Resource Center NAEP Assessment Item, Grade 12: Find the Volume of a Right Circular Cylinder ohiorc.org/standards/ohio/search/mathematics/gli/205.aspx?page=1 %%Sphere G10 New Standards expects students to memorize volume of 1/2 of sphere and "truncated frustrum". @@wars z75\clipim\2003\11\20\mathshift\mathshift.htm Math shift draws unequal reactions Schools like new system, but some parents say it's 'fuzzy' Eric Hübler, Denver Post Education Writer Wednesday, November 12, 2003 - "I've heard about people who sell their homes and move to another town because they don't like our stuff," he said. Holt 1981: Which is a square? triangle? (simple) Everyday: which of these does not belong (one figure is not "regular" - much more difficult task) z75\clip\2003\11\mathbattt.txt http://www.projo.com/education/content/projo_20031116_edwatch16.dbd29.html Edwatch by Julia Steiny: Math-war battle lines are drawn Providence Journal November 16, 2003 "In fact, testing results such as the SATs did drop probably in part because of this airhead math, though the public was considerably less aware then of such tests than they are now." @@Weighted Scores WA Assessment - devise weighted scoring scheme to determine winner in 4 categories WA Benchmark - no such task listed. @@Whole math Case for brain based thinking and "whole mat h" @@Women (Disadvantage) VERBAL UP, MATH DOWN WHEN FEMALE ESTROGEN IS HIGH http://www.genderweb.org/~julie/medical/hormones/ability.html \clip\98\16\hormmath.txt Hormones Linked to Reasoning Ability Los Angeles Times at the annual meeting of the Society for Neuroscience last week in Toronto, psychologists Elizabeth Hampson and Doreen Kimura said tests on three groups of women showed muscular coordination and verbal facility increased by as much as 10 percent during periods of the month when levels of estrogen, the female hormone, were high. At the same time, the women's ability to solve problems involving spatial reasoning fell by a similar amount. [well that explains a lot about why men score higher in math and lower in verbal, doesn't it?] @@Word Problems READING IS OFTEN THE HARDEST PART OF WORD PROBLEMS z43\doc\web\2000\07\ted2.txt To: "Word problems for example generallly demand higher than grade level reading skills and comprehension--math is the least difficult part of word problems." @@workplace 8TH GRADE LEVEL MATH (NON-ALGEBRA) SUFFICIENT FOR MODERN NONPROF WORK Does Higher Tech Require Higher Skills? Gerald Bracey Phi Delta Kappan May 2001 p. 715 John Smith III of Michigan state University concludes that we don't have to be first in the world as in Goals 2000. "Managers and human resource personell corroborate that the equivalent of an 8th grade level of mathematics education [pre-algebra] is an adequate preparation for modern, nonprofessional work." @@world %%Czech Czech students excel at math, science Seattle Times Feb 15, 1998 p. A17 \clipim\98\03\czech.tif TIMSS finds Czech's among world's highest, Americans down the list. no-pain no-gain. US has friendly teacdhers and multiple choice tests. %%general US 4TH GRADERS ABOVE AVERAGE IN MATH AND SCIENCE "Digest of Education Statistics 1999." National Center for Education Statistics, * International Comparisons The results of a 1995 international assessment in math & science show that U.S. 4th & 8th graders compare more favorably with other countries in science than in mathematics. In mathematics, U.S. 8th graders scored below the international average, falling below 20 of the 41 countries tested. Fourth graders performed above the international average of 26 countries tested, scoring below seven countries, including Singapore, Korea, & Japan. Students at both the 4th & 8th grade levels scored above the international average in science. Eighth grade students in the U.S. were outperformed by nine out of 41 countries. Fourth grade students once again compared more favorably with their international counterparts than 8th grade students. Out of 26 countries who participated in the 4th grade assessment, only one country outperformed the U.S. students in science. US Dept of Education National Center for Education Statistics Pursuing Excellence (TIMSS findings report) http://nces.ed.gov/timss/97198-6.html \clip\97\28\teach\teach.htm CHAPTER 3 : TEACHING Says the Japanese have been studying American research into higher level thinking, discovering, etc. and are implenting these ideas. Americans tend to just give out concepts and routine exercises rather than pondering over problems with no obvious solution. Michigan State mathematics professor Bill Schmidt says we should teach fewer topics to mastery, not repeat them every year, hit more advanced math, less basic arithmetic in 5,6,7 JAPAN AND GERMANY HAVE MORE DIFFICULT MATH MATERIAL \doc\web\97\08\mathrept.txt Chancellor's Conference on School Excellence and Accountability Vanderbilt University June 4, 1997 Jeanne Griffith -- Third International Math & Social Studies Report The most enlightening piece of information for me was her discussion of the videotaped math lessons effort. One hundred math lessons were videotaped in each of three countries: Japan, the U.S., and Germany. These lessons were then transcribed and translated, and a panel of college math teachers reviewed them. The were ranked as high, medium, or low quality for math content. For the U.S., 87% were ranked LOW, 13% medium, and NONE HIGH. Germany and Japan both had a much smaller percentage of their lessons in the low category, and a significant percentage for each was in the high category. US DOESN'T TEACH ENOUGH "DEPTH" IN MATH? http://www.washingtonpost.com/wp-srv/WPlate/1997-01/23/104L- 012397-idx.html \CLIP\97\02\MATHPROB.TXT U.S. Struggles To Solve Its Math Problem Time, Teaching Style Appear to Be Factors By Rene Sanchez and Robert O'Harrow Jr. Washington Post Staff Writers Thursday, January 23 1997; Page A01 The Washington Post %%Korea North Carolina State University Libraries: http://library.ncsu.edu/MARION/AJW-3833 Rethinking the mathematics curriculum / edited by Celia Hoyles, Candia Morgan and Geoffrey Woodhouse. Ch. 17. New Goals and Directions for Mathematics Education in Korea / Hee-Chan Lew. Ch. 18 http://203.247.208.20/pro/rhc/nonmun/england3.htm \doc\web\99\01\korea.txt "The new goals and directions of mathematics education of Korea for the next century." Fuzzy math for Koreans. Author of the coument was Hee-chan Lew, Korea National University of Education. The new goals and directions of mathematics education of Korea for the next century "At the outward appearance, mathematics education of Korea seems to make a success. Very recently, Korea was ranked 2nd in the TIMSS and 9th in the IMO. Although this result needs to be analyzed closely, too many problems are being raised from the so called skill- and fact-oriented unflexible curriculum. Most students believe that mathematics is meaningless and only some specific students' possessions." %%Russia observations claims of Russian math superiority - algebra at grade 7, calculus by high school - are exaggerated. %%math US States vs. world on IAEP http://nces.ed.gov/pubs/esn/n25b.html #topic#: Anydex

#topic# | Arthur's Anydex: The Index of Anything

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Introduction

blah

Contents

@@Alphabetical Topic

%%Subtopic

\clip\97\27\iaep\iaep.htm
Math Education Home< /a> | Top of Index | Contents | Education Reform | Education | Asian Americans / Race

Mathematics: Arthur Hu's Index of Education

(c) Arthur Hu's Index please cite when using data from here arthurhu @ hufamily.com (no space) on how to get more complete data or complete text of these references

Note: This started as my Asian American "races in math" page, but has been extended to include the "reform math wars" as well. Most math reform programs are programs for the "dummies", not the kids who study hard and memorize everything and get top SAT scores. The problem is that they isolate precisely what makes Asian kids succeed (drill, rote learning, memorization, single minded pursuit of high skills and test scores) and make sure that nobody will do it.

Another feature of this math page is a grade-level spectrum and definition for most math concepts and a ---- appropriate ---- determination of tests or standards which have been set by committees at levels which cannot be reasonably expected to be met by most (90% pass rate) students.

Starting Links

Contents :( bad :) good



Grade level spectrum

Kindergarten
count to 10
add to 5
sutract from 5
square, circle, triangle, rectangle

G1
add to 10
sub from 10

? draw oblique projection of blocks DS

G2
add to 20
sub from 20

? subtract 19 from 31 by using negative numbers DS
? use 3 x 50 = 150 DS 

G3

add sub money
multiply to 10 x 10

? count two handfuls of rubber bands but don't add DS
? how many cats in 144 legs by drawing DS

G4
probability: certain/uncertain

? stem and leaf plot SF
? find item with most < x on a frequency histogram WASL
? compute probability as a ratio WASL
? construct symmetric figure on pegboard WASL
? solve ax + bx = c by guess and check WASL
? independent probability WASL
? cost a parts list a + 2b @$2.15 each + 3c + 5 ft @ $2 per foot WASL
? compare concentration ratio lemonade / water WASL
? compute height of flagpole by its shadow and short object WASL
? construct blocks from picture DS

G5
area=height x width


G6

G7

G8

G9 Algebra 1


Also see test scores, awards

Asians get the highest math test scores (except in Seattle and other
cities where Whites are unusually advantaged and Asians highly
disadvantaged), and the are over-represented in advanced math classes
and colleges and selective high schools with high math scores.

IF YOU CAN ONLY READ ONE
INTRODUCTION TO REFORM MATH AN WHY IT IS DESTRUCTIVE, ESPECIALLY FOR
MINORITIES, READ THIS REPORT FROM THE TEXAS PUBLIC POLICY
FOUNDATION


Math Reforms are also listed in this area.

Spectrum
--------
Good Buzzwords

Escalante
Rote Learning
Rank Ordering
Memorization
Sequential learning
Drill
All Children will do their best
Memorization of Multiplication Tables
Long Division
Manual Calculation
Norm-Referenced multiple choice tests
 (SAT, CTBS, ITBS)
Saxon
Hirsch / Core Knowledge
Basic Skills
Direct Instruction
Sequential Instruction
Abstract
Mathematically Correct
Automaticity
Content
Scientist / Engineer / Mathematician
Tutoring
Kumon


Bad Buzzwords
--------------------------
Student Centered
Spiral Curriclum
More than one answer or method
Not relying on memory or speed
Not practicing learned procedures
Standards Based
Research Based
Technology
Invented Mathematics
National Science Foundation
NAEP
Skills for the 21st Century
Deep, Balanced Mathematical Learning
Calculators
Learn More Mathematics
Math Educator
Mathematics for All
Math Power
Exploration Learning
Child-Centered
New Math
Whole Math
Reform Math
Multicultural inclusive math
Rote skills are bad
Standards Based Math
New Standards (NCEE)
All Children Will Succeed
Open-Response Criterion Referenced Tests
Constructivism
Connections
Context
Higher Order Thinking
Real World
Problem Solving
Math Communication
Integrated Math (no sequence, mixed with nonmath)
Applied
John Dossey
National Council of Teachers of Mathematics NCTM standards
Mathland
U Chicago
CMP
Investigations
Interactive Mathematics
Mathland
Everyday Mathematics
Thinking skills
Process

Links
The Math Forum


@@Abacus

MENTAL MATH ON MENTAL ABACUS
z46\clipim\2000\11\02\abacus\abacus.htm Oct 30 ABCNEWS.com - Anazan
is computing to 8 places on a mental abacus in no time flat. wow!

SF SUPERMATH USES MENTAL ABACUS
z55\clip\2002\04\abcus.txt
After students spend time in SuperMath class . . . 
Things just click Cicero A. Estrella, Chronicle Staff Writer Friday,
April 26, 2002 Mina Watanabe expects silence from her students.
Students who complete the basic program can multiply and divide three
figures by one figure, and add and subtract a string of up to 10
double-digit numbers. At the highest levels of SuperMath, square
roots, cubic roots and other complex calculations are not a problem. 

@@Acute Obtuse Angles (Geometry)

Definition
Acute = less than 90 degrees
Obtuse = more than 90 degrees

Grade Level Spectrum

G2-3  British Columbia Standard
G4    MCAS Massachusetts G4 Test
G4    North Carolina Public Schools InfoWeb
----- too low -------------------------
G5    Boulder Valley School District
G5    Advanced Learning System
G5    Nevada 1998
G6-8  Arizona Standards
Mid   Addison Wesley Middle School Math
Coll  http://www.geom.umn.edu/ U Minn Geometry Center
NA    CA 1998

British Columbia Ministry of Education
classify given angles as acute, right, obtuse, straight, or reflex
Grade 2-3

http://downtownweb.com/k-12-education/software/phonics/als/mathematics/ma5.h
tml
Advanced Learning System
Mathematics Grade Level 5

Boulder Valley School District
http://bvsd.k12.co.us/curriculum/math/elementary/geometry.html
In fifth grade, students will
1. understand the characteristics of equilateral, isosceles, and scalene
triangles and acute, obtuse, and right angles;

G6-8 Arizona Standards (Achieve)
http://www.achieve.org/a_dir/achieve/achieve.nsf/
4f3ab134c1989eb68525644300601a36/ee9840d1075e97d9852565880000fba6?OpenDocume
nt
PO 4. Measure and label specified angles (e.g., alternate interior,
obtuse, acute, right, corresponding . . . ) (Grades 6 - 8)


G4 North Carolina Public Schools InfoWeb Strategies for Instruction
in Mathematics Instructional Services North Carolina Department of
Public Instruction Grade 4 Objective 2.5
On a geoboard, make triangles which illustrate acute, obtuse and
right angles.

http://www.mathsurf.com/8/ch8/nature/index.html
Elements of Geometry: Addison Wesley Middle School math

From Pythagorean Theorem Home Page
http://www.geom.umn.edu/~ekeel/Project/promenu.html
http://www.geom.umn.edu/~ekeel/Project/tri3.html
Triangles can be classified in the following manner:

   1.By ANGLES
        1.acute triangle- a triangle with 3 acute angles
        2.right triangle- a triangle with one right angle
        3.obtuse triangle- a triangle with one obtuse angle
        4.equiangular triangle- a triangle with 3 congruent 60 degree angles


@@Addition

@@Advantage (America vs. Asians)

\doc\96\03\whyadd.txt "Why Johnny Can't Add, Subtract" Investor's
Business Daily April 25, 1996 p. 1 In 3 decades, the SAT math scores
fell from 492 to 473, about 3%. The top 5% of the US high school
students score about as well as the top 50% in Japan, or the median.
The California State University system increased those who were
judged to need remedial math from 30% in 1989 to 54% in 1994.
(comment, this doesn't jibe with the 2 year advantage shared with
Asian Americans in math)

\priv\95\19\ussmart.txt Tests put U.S. students among best - and
worst Tacoma News Tribune Story Number: 56007 12/10/95 Shankar
Vedantam Taiwan 11-yr olds in 1991 National Center for Education
Statistics test scored the same as American 13-yr olds (2 year gap)
(Story does not mention similar gap between Asian Americans and
whites)

@@Affective

Intrusive assignments in Pre-Algebra II
parent in the Mead School District, the first
assignment for a 7th Grade Pre Algebra II.  It is now on my website at
http://www.icehouse.net/lmstuter/page0243.htm day 1
http://www.icehouse.net/lmstuter/page0244.htm day 2



@@Algebra

Algebra is normally where the college track starts, with 9th grade. Some districts don't think it's appropriate for 8th grade, but 1/4 of 8th graders took algebra in 1996, according to the NAEP. In California, eventually 44% take algebra, 25% geometry, 6% trig and calculus.

Milwaukee requires ALL 9th graders to take algebra. In the last four years only 54%, 56%, 55% and 53% in 1996-97 passed Algebra in the 9th grade. In 1999, all 8th graders will be required to take algebra. The Equity 2000 program by the College board requires districts to require algebra of all 9th graders and geometry of all 10th graders.

In San Jose, Blacks and Hispanics are under-reprsented in algebra courses, but so are Whites, because of Asians, who get best scores and are twice as likely as whites to take the course in grade 8. Despite poverty, Asians are half as far ahead of whites in pass rates as blacks are behind. Blacks score better than the Hispanics in San Jose.

Santa Rose also finds blacks and Latinos under, but Asians over-represented in 8th grade Algebra.


Grade Level Ranking
--------------------------------------------
2nd  Gregory Smith prodigy
2nd  2008 2nd Grade math standard
  Kimmy has 7 more than Hazel, they have 20 total, how many do they have?
  http://hu1st.blogspot.com/2008/01/washingtons-new-2nd-grade-algebra-and.html
5th  Dave Cole's saturday class
7th  Connected Mathematics: solve 6x + 3 = 4x + 9
  http://connectedmath.msu.edu/mathcontent/algebra.html
8th  Palm Beach County required for all, 10% in 2002
8th  Russia
8th  1999 US Dept Ed goal
8th  1999 all Milwaukee 8th graders required
8th  25% of US kids
8th  Santa Rosa CA starts
8th  Bellevue WA new '98 curriculum
8th  CA 1998 state framework
8th  Renton calculus track
9th  Milwaukee 40% fail rate, required for all
9th  Renton college track
9th  All Milwaukee 9th graders required in 1998. Only 50% pass.
9th  NAEP expectations
9th  Most school standards, "tradition"
9th  Virginia standards
12th Kentucky (vs. 8)
12th nearly 100% of SAT students

Pass Rates By percent
------------------------------------------------------
100% Some say other nations put all kids in grade 7
100% Russian middle school claim
100% Some city and state goals
100% Wayne Bishop's Daughters 8th grade by Texas exam
 99% Aransas Pass TX (WB)
 97% White/Black SAT taker
 72% Singapore TIMSS 8th grade
 67% VA 2000 pass geometry  statewide
----- No state cross section over 65% ----------------
 66% Taipei TIMSS 8th grade
 65% VA 2000 pass algebra 1 statewide
 55% Pass required algebra in Milwaukee 9th grade
 55% CA alg + geometry White/Asian
 51% CA alg + geometry black
 44% VA 2000 pass algebra 1 black
 40% VA 2000 pass geometry black
 40% Russia TIMSS 8th grade
 33% Hispanic Black high school grad
 33% World Average 8th grade TIMSS
 30% Texas (WB)
 29% US TIMSS 8th grade
 15% Dallas ISD (WB)
 10% HS seniors who can use starting algebra

Percent Taking Algebra
93%  before or during HS US
52%  Algebra 2 in HS US
64%  Algebra 1 in HS US
30%  before high school US
1994 Digest of Education Statistics

%%Accelerated

2nd Grade algebra by Ideal
Image posted at:
http://www.arthurhu.com/images/2000/03/15/alg2.gif
2nd grade Get Your Hands on Problem Solving Ideal:
85 cents for a snack, nickels, dimes and quarters, same number of 
nickels and dimes but fewer quarters than dimes. What coins do
they have?

You can't even solve this with standard algebra since all you know
is that the number of quarters is less than the dimes!

try with two quarters
 5  5  5
10 10 10
25    25
---------- 
40 55 95 too many quarters

try with one quarter
 5  5  5  5
10 10 10 10
25    
---------- 
40 55 70 85

Requires 12 2 digit additions with carry!

What if they had pennies, nickels and dimes, two times as many
nickels as dimes, one more penny than dimes? (multiplication is not
taught in g2!)

1 dime = 1+1+10+5+5=22
1 pen 1  1
1 dim 10 
2 nic 5  5
2 dimes = 43
3 pen 1  1  1
2 dim 10 10
4 nick 5  5  5   5
3 dimes = 64
4 pen 1 1 1 1
3 dim 10 10 10 
6 nic 5  5  5  5  5  5   
4 dimes = 
5 pen 1 1 1 1 1
4 dim 10 10 10 10
8 nic 5  5  5   5  5  5  5  5  
----------------------------------------
Requires 43 2 digit addition with carry to solve.
How many 2nd graders can add 43 2 digit numbers without an error?


8TH GRADE ALGEBRA BETTER, US LAGS IN MATH GRADE LEVEL
timsmath.txt">
For the value of algebra in 8th. grade:
 Third International Math and Science
 Study [TIMSS] report "Do Gatekeeper courses expand education
options?"
 http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=1999303
"enrollment in gatekeeper couirses, such as algebra and foreign
language in eighth grade helps students reach higher levels in the
mathematics and foreign language pipelines.  For example: --Students
who enrolled in algebra as eighth-graders were mroe likely to reach
high-level math courses ... in high school than students who did not
enroll in algebra as eighth-graders.
From: Pursuing Excellence: Initial Findings from the Third International
 Study of Math and Science, Chapter 4: the Context of Learning
http://nces.ed.gov/pubs98/twelfth/chap4.html

Curriculum A comparison of the topics covered in the mathematics and
science general knowledge assessments with curriculum frameworks did
reveal that both general knowledge assessments covered content that
is introduced later in the U.S.  curriculum than it is introduced, on
average, in the other TIMSS countries as a whole.14
[8th grade useless if it does not account for best students taking
algebra, US sequence is good enough for MIT, best engineering
school in the world, while Russian economy is a mess]

ALGEBRA REQUIRED OF ALL BY G8?
http://www.chicago.tribune.com/version1/article/0,1575,SAV-9909270075,00.html
\clip\99\18\earlalg.ttx Chicago Tribune Tuesday, September 28, 1999
EARLY ALGEBRA IN CRETE-MONEE'S EQUATION DISTRICT OFFERS CLASSES FOR
YOUNGER PUPILS By Kathleen Knowles-Wantuch. Special to the Tribune.
Tribune staff writer Stephanie Banchero contributed to this report.
September 27, 1999
honors algebra, once reserved for high school freshmen, is now being
taught to high-achieving 7th graders. Although the middle school has
offered the class to 8th graders for years, the program was expanded
to 7th graders ... the state's new learning standards set for the
Illinois Standards Achievement Test expect 8th graders to know
algebra by the time they take the test in the spring.  When they
enter high school they will be taking Algebra II, advanced placement
calculus, and multivariate calculus. 

%%Advanced

Mr Smith Goes to College Seattle Times Sept 8, 1999 p. A2 Jennifer
Lenhart Washington Post. Gregory Smith at 10 will study Calculus,
completed completed algebra 1 in 18 months at age 7

You have to master arithmetic before
tackling Algebra

1/3 WORLD, US, 2/3 SINGAPORE 8TH GRADERS PROFICIENT IN ALGEBRA
z47\clip\2000\12\math8.htm US eighth-graders beat global average in
math By Gail Russell Chaddock (chaddockg@csps.com) Staff writer of
The Christian Science Monitor 12/6/2000

A club has 86 members, but 14 more girls than boys. How many 
boys and girls?
x = number of boys
x + (14 + x ) = 86
2x + 14 = 86
2x + 14 - 14 = 86 - 14
2x / 2 = 72 / 2
x = 36 boys
86 - 36 = 50 girls
-------------------------------------------------------------
72% Singapore
66% Taipei
40% Russia
33% World Average
29% US
Source: Boston College, TIMSS

%%Algebra Project

ROBERT MOSES ALGEBRA PROJECT - ALGEBRA AS CIVIL RIGHT
z48\clip\2001\03\moses.txt
http://www.chron.com/cs/CDA/story.hts/editorial/840954
HoustonChronicle.com March 5, 2001, 10:49PM Right to learn math new
'radical' cause By E.J. DIONNE "full citizenship depend crucially on
math and science literacy."


%%All

Liberals and conservative reformers both appear to support requiring
Algebra of all students instead of traditional top 1/2 or 1/4.
Liberals want to require it to be mastered by end of grade 8 instead
of traditional grade 10, and to integrate it into K-6.

True traditionalists only permit students who have mastered
arithmetic to even take Algebra, starting in grade 9. Some argue
whether integrated math is even algebra at all.

%%Against

LOW PERFORING STUDENTS MIS-PLACED IN ALGEBRA AT 2ND GRADE MATH LEVELS
\clip\2008\09\algall.txt
http://ednews.org/articles/29027/1/New-Study-Shows-the-Unintended-Consequences-of-Moving-More-Pupils-Into-Eighth-Grade-Algebra-and-Other-Advanced-Math-Classes/Page1.html
"No social benefit can be produced by placing students in classes for
which they are unprepared."

New Study Shows the Unintended Consequences of Moving More Pupils Into
Eighth Grade Algebra and Other Advanced Math Classes a.. By Brookings
Institute 
"Despite being enrolled in Algebra I, Geometry, and Algebra II,
misplaced eighth graders have NAEP scores well below average for
fourth graders. In fact, they know about as much math as a typical
second grader. The report reproduces several sample NAEP items to show
the gaps in knowledge among these low-scoring students on key
pre-algebra concepts such as percentages, decimals, and fractions.
The study also gives detailed information about the characteristics of
these misplaced students, their families, and their schools. It finds
that they are disproportionately black and Hispanic; have parents
whose own education is below the national average; come from
low-income households; attend large urban schools with predominantly
low socioeconomic status populations; and have math teachers with less
experience and mathematics training than the typical teacher of
advanced math students in eighth grade."
www.brookings.edu/reports/2008/0922_education_loveless.aspx

REQUIRE ALGEBRA FOR ALL WHEN THEY DON'T EVEN KNOW 56/7?
z47\doc\web\2001\01\sayall.txt
"This Says It All" by Dan Umbarger and Donna Garner January 4, 2001
It makes absolutely no sense to tell people everybody is enrolled in
a college prep course if they can't even master the multiplication
tables.

z45\clip\2000\09\algeb.doc THE MALEVOLENT TYRANNY OF ALGEBRA Gerald
W. Bracey To Appear in Oct Education Week - Algebra for All will be a
disaster. CA will make algebra proficiency a graduation requirement,
but almost nobody needs to know algebra.

NO REASON TO REQUIRE ALGEBRA OF ALL STUDENTS
z45\clip\2000\10\algall.txt
http://www.educationnews.org/when_was_the_last_time_you_used_.htm oct
2000 EducationNews.org The World's Leading Source of EducationNews 7
Days a Week October 9, 2000 Center for the Study of Jobs and
Education in Wisconsin When was the last time you used Algebra?  By
Dennis W. Redovich Algebra was useless for most students forty years
ago when I taught it in high schools and it is useless for most
students, except as a screening device for college, in the year 2000.
Sen. Charles Poochigian, R-Fresno. "Except for special-education
students ... I don't think there's a single kid who can't learn
algebra." the Milwaukee Public Schools leads the nation in failing
algebra students. MPS 9th graders have been required to take algebra
since 1993-94 when the pass rate was 54%. MPS Accountability reports
show the percentage of 9th graders passing in the last three years as
follows: 1996-97 55%, 1997-98 56%, and 1998-99 60%.  What is the
rationale for requiring all students to meet college entrance
requirements to graduate from high school? The reason, of course, is
that there is no rationale for these school reforms.

%%For 

ALGEBRA REQUIRED FOR FLA GRAD, 100% PALM BEACH 8TH GRADE
http://www.palmbeachpost.com/news/content/auto/epaper/editions/wednesday/news_f
3767dc561f061b500dc.html?urac=n&urvf=10638037402810.3035347880821241
From the Palm Beach Post -- Sept. 17
Eighth-graders must take algebra next school year
By Mary Ellen Flannery, Palm Beach Post Staff Writer
Wednesday, September 17, 2003
Last year, 1,315 eighth-graders in Palm Beach County took algebra, or about 10 
percent of all eighth-graders. Nationwide, about 20 percent of eighth-graders 
complete algebra or another higher-level math course.
Florida doesn't require students of a particular age to take algebra, although 
they do require completion before graduation,
In Milwaukee, which has had an algebra-for-all program 
since 1994, educators report 40 percent of ninth-graders failed algebra in 2000 
and that ninth-graders constitute more than 40 percent of dropouts.

GENERAL MATH SHOULD BE DISCONTINUED, ALGEBRA FOR ALL
z47\clip\2000\12\algall.txt From the Washington Post
http://www.washingtonpost.com/ac2/wp-dyn/A23855-2000Dec18?language=printer
Extra Credit (Education) Tuesday, December 19, 2000 ; Page A19, The
Washington Post www.aera.net/pubs/eepa University of
Wisconsin-Madison study by Adam Gamoran and Eileen C. Hannigan in the
fall issue of Educational Evaluation and Policy Analysis said
students who took algebra improved 8 points between eighth and 10th
grades on a general math test, while those without algebra improved
only 4 points.

SHOULD US/CA ADOPT ALGEBRA FOR ALL
z47\clip\2000\12\algca.txt
http://www.sacbee.com/news/projects/algebra/121400.html State's new
algebra goals are a shock to the school system By Deb Kollars Bee
Staff Writer (Published Dec. 14, 2000) "in Germany, Japan, Argentina,
Korea, France all students are expected to conquer beginning algebra
routinely in the sixth or seventh grade -- and study it thoroughly
until they reach high school. Seventh and eighth grade are notorious
for being wastelands of arithmetic -- fractions, decimals,
multiplication, division -- that students have seen before.  "

DUMP WIMP ARITHMETIC TO BEAT NEW MATH PROFICIENCY GRAD EXAM
z42\clip\2000\07\ohmath.txt Wednesday, June 14, 2000, Akron Beacon
Journal.  Math instruction to change Akron Public Schools step up
focus on proficiency BY REGINALD FIELDS Beacon Journal staff writer
[This sounds bad. Kids can't hack the basics, so you kick everybody
into the hardest track???]  "the district plans to deny students the
option of taking easier classes in secondary schools.  ``We're
eliminating all lower-level math courses'' at the high school level,
said Donna Loomis, director of secondary instruction." [you have to
take the accelerated algebra or nothing]

NCTM STANDARDS - ALGEBRA / GEOMETRY FOR ALL BY 8TH GRADE
April 13,2000 - new NTCM standards say students must master basics of
algebra and geometry by the end of 8th grade.  Seattle Times New math
guidelines aP Nicole Ziegler Dizon Students must know more than the
basics, number crunching is not enough.
z40\clip\2000\02\apmath.txt
http://seattletimes.com/news/nation-world/html98/math13_20000413.html
Thursday, April 13, 2000 New math guidelines 'set higher standards'
for students by Nicole Ziegler Dizon The Associated Press 

KY State reform law requires algebra for graduation
z40\clip\2000\04\kera.txt A New Direction KERA changes way schools
teach, students learn 10 April 2000 By Mark Cooper Messenger-Inquirer

NO ALGEBRA, NO DIPLOMA
\clip\99\21\allalg.txt Published Thursday, December 16, 1999, in the
San Jose Mercury News JOANNE JACOBS High school graduates should at
least know their algebra Low math standards shortchange us all [about
one-third of graduates don't take any algebra]

PETE WILSON SAYS TO TEACH ALGEBRA TO ALL
Tuesday, September 28, 1999  c1999 San Francisco Chronicle
URL: http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/1999/09/28
/ED38466.DTL
Higher Goals for Exit Exams California cheats its students by
expecting too little Pete Wilson, Bill Evers Unfortunately, the math
test planning committee, appointed by State Superintendent of Public
Instruction Delaine Eastin, has chosen to continue to avoid algebra.
It is time to insist that our schools teach algebra to all students.

%%Elementary

http://www.ncitela.org/downloads/math/Math4.pdf
z39\clipim\2000\02\14\Math4.pdf
use variable for number of pages left in book x = 
if x = (a - b) - c and a is 10, b is 3 and c is 4, what is x?
area = height x width. If area = 200 and height is 10, what is width?
find area of L shaped area with dimensions
draw graph of y = 3x
length of line segment (6,-4) (21,-4)
draw radius, diameter
draw two lines of symmetry
know right/acute/obtuse
1/4 of circle to degrees
#edges on rectangular prism
recognize flat figure folds into cube
scalene isoceles right triangle
rhombus vs. parallelogram
median (halfway) and mode (most common)
all possible outcomes coin plus 1 die

%%Level

The earliest track for algebra is grade 7, some want to start in
grade 8. Normal start is grade 9, but nationally, half of kids never
take algebra. Some teachers start as early as grade 5. Some state
standards want to integrate concepts as early as elementary. Some
textbooks and assessments put this at 4th grade, Alabama puts in
in 11th grade, even though not all are required to take algebra

     slow     fast
G6  middle 1 pre-alg
G7  middle 2 alg1
G8  middle 3 alg1
G9  algebra  alg 2

Algebra I Grade Spectrum
--------------------------
G7 Russia
G8 1999 National Science Foundation Goal
G8 1999 US Dept of Education Goal
G9 Traditional
G9 NAEP
G9 Traditional Andover elite high school

%%Pass Rates

Mickey VanDerwerker Sent: Thursday, October 05, 2000 4:33 AM In order
to graduate from a Virginia high school, among other things, you need
to take and pass two math courses (choose from Algebra 1, geometry,
algebra 2).  This means passing by teacher grades.  You must also
pass one of the high stakes standardized test at the end of those
courses to get the required "verified credit."
Thus far, our pass rates are as follows:
Algebra 1:  65% (African American:  44%)
Geometry:  67%  (African American:  40%)
Algebra 2:  58%  (African American:  36%)

%%Project, The Algebra 

Wayne says it's flakey fluff.
Another popular destination is the murder site of Medgar Evers.
Moses has all the right words and Inglewood Unified has all the right
test results.  Guess which is actually going to open doors for the
low socioeconomic minority children being served?

%%Real Life

z41\clip\2000\05\algbook.txt Houston Chronicle April 26, 2000,
10:26PM Experts say few algebra books enter real life into the
equation WASHINGTON (AP) -- Why can't the kids learn algebra? Because
the books they use don't explain how algebra calculations will relate
to everyday life, a panel of scientists said Wednesday. "Just
figuring out how to drive a truck route using the least amount of gas
is a mathematical problem," said George Nelson, director of the
American Association for the Advancement of Science's long-term math
and science education campaign.

[[Alabama

ALABAMA ADOPTS EXIT EXAM FROM HELL Birmingham News: Students facing
tougher exit test February 27, 1999 Students facing tougher exit test
CHARLES J. DEAN News staff writer 02/26/99 Question: Ryan makes $3
per hour more than Scott. If 3 times Ryan's rate plus 4 times Scott's
rate is $65, what is Ryan's hourly wage? Answer: $11.

[[Bellevue

"Middle schools go fast-track" Seattle Times Jan 21, 1998 Mike
Lindblom New curriculum encourages algebra at 8th grade.

[[California

elite private school has most
thru alg 1 in g7, 100% proficient by g8. Accelerated school is
below grade level because of nsf mctm math. Japanese g7 is like
saxon

http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm This Framework
focuses on presenting a curriculum that will prepare all children by
the end of seventh grade to begin to study algebra and geometry in
the eighth grade. This change has been adopted not only by the
California Standards Commission but also by vote of the committee
that developed this Framework. The Framework describes an
introductory algebra course for the eighth grade, followed by
geometry in the ninth grade and advanced algebra in the tenth grade,
or the alternative of a comparable three-year integrated program.

\clip\98\03\racegap.txt
San Francisco Chronicle 2/1/98 Editorial The
Great Divide In American Education

Complete Algebra 2 and Geometry
-------------------------------
55% White/ Asian
51% Black
35% Latino

California School District
Placement of top quartile in algebra
(student choice?)
-----------------------------------
100.0% Asian
 87.5% White
 51.0% Black
 42.0% Latino

Asians in 3rd quartile more likely than
Black or Hispanic in 4th quartile.


[[Cole

Dave Cole teaches 5th
graders to solve ax + bx = c.

[[Kentucky

http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.html
G8 is "ideas", hard algebra is a G12 standard.

[[Louisiana


Louisiana Contents Standards Algebra, in the K-8 classrooms,
refers to informal explorations and understandings of symbolism. It
is beneficial to introduce the algebraic terminology (equation,
inequality, variable, etc.) in the early grades. In this way high
school students will be able to understand algebra as a natural
outgrowth of their study of various number properties.

[[Milwaukee

Milwaukee has 37th percentile mostly inner city youths, and requires
ALL to take algebra. This is a BAD idea if they can't even master
basic math.

COLLEGE BOARD TELLS DISTRICTS TO TEACH ALEBRA TO ALL
Here's Y the teaching of algebra in the US has been such a big flop.
Wall Street Journal June 16, 1998 p. A1. US books teach too many
topics over and over. Only 40% of 2nd grade, 30% of some 8th grade
books have any "new" content. Grouping by ability dropped in the 70s,
but math tracks kids into what they are sure to pass, not what they
"need". TIMSS show 4th grade arithmetic is OK. The College Board
Equity 2000 program has signed up Milwaukee and 8 other cities,
requiring them to teach algebra to all 9th and geometry to all 10th
graders. Seniors must pass algebra and math proficiency test to pass,
but nearly half, 90 of 200 seniors are retaking the tests for the 3rd
time.  Lack of algebra is blamed for 100 point SAT difference, five
years ago fewer than 1/4 of Blacks and Hispanics took algebra vs.
about 1/2 of whites.  Milwaukee 10th graders are at the 37th
percentile nationally. Low income students who take algebra go to
college at middle class rates. 1/3 of US students missed 20% off of
$1,250 stereo, 1/9 could plot a graph.

MPS REQUIRES PASSING ALGEBRA TEST TO REACH 10TH GRADE, FLUNKS 50%
MPS exaggerates drop out rate to
signal crisis Dennis W. Redovich Greendale WI, Letter from Leon
Todd that MPS is the only district in the nation with such a drastic
standard that Milwaukee requires ALL 9th graders to take algebra. In
the last four years only 54%, 56%, 55% and 53% in 1996-97 passed
Algebra in the 9th grade. " MPS received an award for substituting
algebra, which many failing students in all probability may never
use, for consumer or ecomonic math which employers minimaly need
students to master for most twenty first century employment."
Students that did not pass the exam were held back at the ninth
grade.  "high skill jobs of the future that require algebra and
"high" academic skills simply don't exist for most graduates and
especially for poverty class people of color."

[[SAT


Percentage by race:

 \doc\95\12\sat95bk.wk1
 1995 Scholastic Aptitude Test Breakdown by Ethnicity
 Data from the College Board
 Data Entry and Analysis by Arthur Hu

Figues: Percentage taken, test score gap vs. white, SAT math score.

                White          Black             Hisp             Asian
 Math Coursework     Gap           Gap               Gap              Gap
 Overall               0  498       -110    388        -72   426         40
 538
 Algebra         97    0  498  96   -110    388  97    -73   425  94     37
 535
 Geometry        95    0  504  90   -109    395  94    -73   431  94     36
 540
 Triginometry    55    0  539  43   -106    433  42    -68   471  64     26
 565
 Precalculus     38    0  573  24   -104    469  32    -77   496  54     18
 591
 Calculus        23    0  613  12   -105    508  16    -76   537  40     13
 626
 Computer Math    9            10                10               13

[[US Dept of Education

\doc\web\99\13\muchmath.txt "HELPING
YOUR CHILD LEARN MATH" US DOEd We now believe that by the end of
the eighth grade, students should have mastered the fundamentals of
algebra and geometry to be ready for high school and on track for
college and the workforce.

zip36\clip\99\17\failam.txt \clip\99\17\failam.txt 9/1/99 THE
CONSPIRACY OF IGNORANCE Part 3 of 4 From today's Washington Times.
This is the third of four excerpts from Martin Gross' new book, "The
Conspiracy of Ignorance: The Failure of American Public Schools."

Luther Williams of the National Science Foundation says American schools
are backward in math. "Basic arithmetic [not algebra and geometry] is
still the staple of eighth-grade math," he laments. Almost half of public
high school grads have never taken intermediate algebra and only one in
eight have studied vital trigonometry.



[[Virginia:

http://www.pen.k12.va.us/go/Sols/math.html#GradeEight
8th grade is preparation for algebra, so algebra would be G9

NAEP - grade 8 math is different from algebra, so would be G9

%%Gambill

GAMBILL ALGEBRA METHOD \clip\99\15\gambill.txt
http://www.oregoneducation.org/math/gambill.htm ..signed up
voluntarily to take the 15-county Annual Algebra I Contest at 9:00
morning. The results of the Preliminary are the same as they have
been for the past 7 years, with my students "totally dominating,"
taking 95% of the top places.

%%Neccesary?

Bracey says most people don't
even need to know algebra.

%%Pass rate

Bishop cites high pass rates
100% Wayne Bishop's Daughters 8th grade by Texas exam
 99% Aransas Pass TX (WB)
 30% Texas (WB)
 15% Dallas ISD (WB)

%%Race

Los Angeles Times Wednesday, December 9, 1998 ON LEARNING / RICHARD
LEE COLVIN A Call to Refocus Our Country's High Schools By RICHARD
LEE COLVIN Two-thirds of Latino and African American students have no
understanding of geometry or algebra when they graduate. In fact, the
average Latino or African American 17-year-old is about as skilled
mathematically as the average white 13-year-old.  That means they are
unprepared for college or the workplace.

---------------------------------------------
\clip\97\27\minmath.txt
http://www.pressdemo.com/news/11-20/st005.html Santa Rose Press
Democrat Nov. 20, 1997 Few minorities enrolled in Santa Rosa
accelerated classes By ROBERT DIGITALE Press Democrat staff writer
Enrollments in middle school accelerated classes in Santa Rose:
Slater middle school 15% latino vs. 6% english 3% algebra.
Asians over-represented in 13 of 20 accelerated categories
Blacks under-represented in 17 ot 20 categories.

\doc\web\99\07\solrace.wk1

Virginia SOL Standards of Learning Test Results by Race

Data fromVirginia Department of Education as published in

Washington Post 5/13/99


In Virginia, Asians scored as much as 50% higher in algebra and some
other topics than whites, ev ery other subject was equal or better.
Blacks did more poorly in all subjects, with pass rates as low as 13%
in algebra.  and history, much lower than traditional norm-referenced
tests. Considering the amount of writing required, the impact on
Asians seems to be minimal on this test.

Ranked by Asian - Asians better or equal than whites in all subjects

                                                Index

Subject         White   Black   Asian   HispanicWhite   Black   Asian   Hisp
anic
Algebra II           34%     13%     50%     26%    100%   -262%    147%   -
131%
Algebra I            46%     20%     61%     33%    100%   -230%    133%   -
139%
History from 100     49%     17%     62%     33%    100%   -288%    127%   -
148%
Geometry             59%     25%     67%     47%    100%   -236%    114%   -
126%
History to 1000      68%     38%     77%     52%    100%   -179%    113%   -
131%
US History           36%     12%     39%     19%    100%   -300%    108%   -
189%
Chemistry            60%     31%     62%     41%    100%   -194%    103%   -
146%
English*             77%     55%     78%     64%    100%   -140%    101%   -
120%
Earth Science        69%     31%     68%     51%    100%   -223%   -101%   -
135%
Biology              81%     50%     79%     61%    100%   -162%   -103%   -
133%

\doc\96\04\sjalgebr.wk1

San Jose Unified Algebra Pass W1.00 B-1.23 H-1.30 A1.08 O-1.06
Eastside Union W1.00 B-1.17 H-1.30 A1.10 O-1.32

Percentage of students passing Algebra in two San Jose school districts
by ethnicity
Note that Asians are half as far ahead of whites as Blacks are behind.

 San Jose Unified School District ...
        1991-92         1994-95         Passing
...     Taking  Passing Taking  Passing Index
Asians       262     98%     282     94%    1.08
Whites       649     90%     793     87%    1.00
Others        36     83%      60     82%   -1.06
Total      1,430     87%   1,889     80%   -1.09
Blacks        52     73%      76     71%   -1.23
Hispanic     431     77%     678     67%   -1.30
 Percent taking(     72%             86%

 East Side Union High School District ...
        1993-94         1994-95         Passing
        Taking  Passing Taking  Passing Index
Asians     1,265     94%   1,680     91%    1.10
Whites       702     89%     947     83%    1.00
Total      3,067     86%   4,548     78%   -1.06
Blacks       194     80%     280     71%   -1.17
Hispanic     867     74%   1,595     64%   -1.30
Others        39     77%      46     63%   -1.32
% Taking             56%             80%

Source: San Jose Unified School District, East Side Union High School
District.  based on chart in San Jose Mercury news May 18, 1995
DOWNSIDE OF 'STAND AND DELIVER' MATH PROGRAM S.J. RESULTS: AS
ENROLLMENT EXPANDS, SO DOES PERCENTAGE OF STUDENTS FLUNKING.
Rankings and index by Arthur Hu

doc\94\7\algebrar.wk1 Algebra score by courses taken, 1990 NEAP
taking algebra in Grade 8: W1.0 B-2.57 H-1.80 A2.11
test score taking algebra - W 0 B-36 H-27 A+9
Asians taking G8 math same as black taking Algebra

%%Rate

z45\clip\2000\08\testgap.txt Academe Today Friday, August 25, 2000
Girls Catch Up With Boys in Math, Report Finds, but Overall Student
Gains Have Slowed By JULIANNE BASINGER Thirteen percent of female
17-year-olds taking the test in 1999 had enrolled in pre-calculus or
calculus courses, compared with 4 percent in 1978. More than half the
young women taking the test in 1999 had taken advanced algebra, while
only 37 percent of those in 1978 had done so.

\clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for
Math Problems RICHARD LEE COLVIN (New math, math reform backlash
against "fantasy lunch")
http://www.math.uic.edu/~cpmp/archive9701.html This fall, the
National Assessment of Educational Progress said 17-year-olds are no
stronger in math than 20 years ago. Only six of 10 high school
seniors can compute with decimals, fractions and percentages. Fewer
than one in 10 can use beginning algebra.


%%Required

New reformers say that since algebra is a "gatekeeper" an associated with high performance, then all students should be required to take it. Traditionally, only a small percentage were thought to be capable enough to master it or even need it if they weren't going to college. Some districts and states are setting up standards requiring algebra for all such as Minneapolis. On the plus side, more kids are passing algebra than were even trying before. On the other hand when 50% of kids who take it are failing, they may be driving up dropout rates, and it's pointless to require what kids won't or can't do.

George Cunningham says just because the best students take algebra, it doesn't automatically mean that all students should take it.



ONLY HALF ARE PASSING ALGEBRA, BUT MORE ARE TRYING, GOALS IS 8TH GRADE
2/28/99 Milwaukee Journal Sentinel: Algabra policy alters MPS
dynamics Requirement has affected course passing rates, fueled debate
about its merits By Joe Williams of the Journal Sentinel staff
February 28, 1999

"the requirement has driven up dropout rates because some students
have not been properly prepared to handle the course"

"One statistic, in particular, leaps off the pages of MPS reports:
There are more kids passing algebra now than were even taking the
subject in 1991.. only about half -- 53% -- of the freshmen who are
taking algebra in the district are passing the course. When algebra
was an elective in 1991 -- when the question of requiring the course
first came up -- 74% of algebra students were passing the course."

"believes a majority of the students who are failing algebra now
would have likely failed any math class they were taking.  Those
students have extremely weak backgrounds in math, don't do the
homework or simply miss school so much they are incapable of passing,
many educators said... when students attend algebra class regularly,
about four out of five tend to pass the course...students who had an
"A" or "B" average had an average daily attendance rate of 95% over
the duration of the semester. Students who were failing the course
attended school only 65% of the time. "

"adult critics of the algebra requirement that the subject is not
needed in the real world -- something that drives math teachers crazy"

"by the class of 2004, for example, all MPS students will be required
to demonstrate a proficiency in algebra by the end of eighth grade.
" [Comment currently only the fastest AP calculus tracks require
students to finish algebra in grade 8]


ALASKA STANDARDS TO REQUIRE ALL STUDENTS TO LEARN ALGEBRA

TEXAS TO ADD ALGEBRA TO EXIT EXAM
November 25, 1998, 08:07 p.m.  Proposals would raise TAAS bar Moses
wants to tighten ratings, add math test Moses said he will formally
propose next week that the Algebra I end-of-course exam be added to
the accountability system

MPS REQUIRES PASSING ALGEBRA TEST TO REACH 10TH GRADE, FLUNKS 50% MPS exaggerates drop out rate to signal
crisis Dennis W. Redovich Greendale WI, Letter from Leon Todd:
MPS is the only district in the nation with such a drastic standard
that Milwaukee requires ALL 9th graders to take algebra.

2/11/98 Austin American Statesman Algebra 1 only recently became a
required math course for most students. (Texas)

%%Simple

%%Standards

[[Algebraic expressions

a * 2
2t + 4

G7 Nevada
G8 Mathematics unlimited 1988

[[Evaluate given variable values

compute A = l * w given l=2 w=6

G8 Nevada
G8 Mathematics unlimited 1988

[[Solve for unknown working backwards

G8 Mathematics Unlimited textbook 1988

[[Solve for equation ax + bx = c

G4 www.passthewasl.com flashcards (2 + x) * 3 = 15
G4 Guess and check WASL apples and pears
G8 Algebra 1
G9 Integrated math 1

Traditionally, this sort of problem is taught in algebra 1 in grade
9, maybe grade 8. I have a whole sequence of pre-1990 math textbooks
from G1 to G8, none of them have problems of this type.

Example 1. There are 18 pieces of fruit, twice as many apples as
oranges, half as many pears, how many of each fruit?

Example 2. There are 5 more crows than cows in a farmer's field.
There is a total of 52 legs on all of the animals.  How many crows
and how many cows are in the field?

However, mid 1990s NCTM inspired assesments and textbooks expect
children in G4 and G5 to solve these problems with guess and check! It has also appeared in the 7th
grade test.

G3-5 Massachusetts
    "know and apply algebraic procedures for solving equations and
    inequalities." (yeah, right)
G4  1997 WA WASL 4th grade "how many bicycles", no solution
G5  New Progress in Mathematics, by Rose Anita McDonnell
G7  1999 WA WASL 7th grade "14 fruit", no solution
G8  2007 WA standards draft "solve linear equations"
G8  2001 Singapore "solve linear equations"
G12 Nevada
G9-12 DODDS
G12 New Jersey
    Solve equations and inequalities of varying degrees

Elementary Algebra Part I by Denholm
Dolciani, Cunningham 1970 Houghton Mifflin: tells how to solve
this problem AFTER nearly a whole book of algebra.

WA EALR benchmarks
http://cisl.ospi.wednet.edu/ComSL/MATHBMK.html
G4 solve simple equations using blocks, sticks, beans, pictures, etc.
G7 set up and solve single-variable equations
G10 create and solve equations and inequalities, evaluate and
  simplify expressions

DODDS Introductory Algebra and Geometry
3. Write numerical or algebraic expressions for expressions in words.
4. Solve and check equations involving signed numbers.
5. Use the distributive property to simplify numerical expressions.
6. Write equations to represent real situations.

[[Polynomials

G9 Algebra 1

@@Alebra Textbook Review

\clip\2009\11\Lee-math-textbooks
http://keen-studios.net/files/mathchoice/Lee.pdf
John M. Lee of University of Washington Dept of Mathematics
Reviews Prentice Hall: Algebra 1 and Algebra 2
"These books are solid, well organized, and mathematically sound.
Computational algorithms and formulas are clearly stated and well
motivated by examples and hands-on activities. The use of graphics
to call out important principles is very effective"

Key Curriculum Press: Discovering Algebra
My first impression is that these books have far too much verbiage for
students to read and too little in the way of clearly stated
mathematical principles. Definitions, computational algorithms, and formulas
seem to be stated vaguely when they are stated at all. For example, a relation
is defined as "any relationship between two variables" [a circular definition]

@@Algorithms



@@All
@@All students

END TRACKING
ALGEBRA FOR ALL
NCTM STANDARDS
BREAK DOWN GENDER AND RACE NUMBERS
http://www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma12000.htm
The Goal and Seven Components of The Equity 2000 Districtwide Reform Model
North Central Regional Education Laboratory
* end tracking and raise standards for all students
* requirement that all students complete algebra by the ninth grade
and geometry by the tenth grade, and including reform of the
curriculum to reflect standards set by the National Council of
Teachers of Mathematics and other discipline-based organizations.
# Establishment of ongoing professional development for teachers,
counselors, and principals to increase their professional knowledge
and skills and to raise their expectations for students.
# Improvements in schools' involvement with students' parents and
families to create a consistent climate for learning as well as to
empower parents to be advocates for their children's education.
# Use of student course enrollment and achievement data broken down by
ethnic group and gender to monitor progress toward reform goals

* all members of the school community will need to reexamine their beliefs,
expectations, and cultural sensitivities;
* develop a shared vision of equity and excellence in mathematics education;
* determine their new roles and responsibilities in supporting equitable mathematics education for all student

* All schools involved in reform will have to understand and share the
??democratic vision?? that underlies the Standards and address the issues
of power and practice raised by the Standards.

ALL STUDENTS MEANS ENSURING EQUITY
Ensuring **Equity** and Excellence in Mathematics In Reaching All Students
With Mathematics (Cuevas & Driscoll, 1993b), an NCTM task force gave
special attention to programs that work to ensure equity and ...
www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm

Educators and community members are beginning to recognize that most
students, including a disproportionate number of women, minorities,
and the poor, leave school without the mathematical skills they need
to thrive in an increasingly complex, global economy.

Behind Goals 2000 and the NCTM standards is the conviction that all
students can learn a significant core of mathematics and that the
entire school community must have high expectations for every child's
mathematics education.

foster cultural and linguistic diversity in an effort to increase the
participation and success of underrepresented groups.

OPPOSITION: Some people believe that inherent
differences in ability among males and females, racial and
socioeconomic groups, and individual students make high expectations
for all students unrealistic and ill-conceived. Although research
generally has discredited this view, the debate has been reopened by a
recent book, The Bell Curve: Intelligence and Class Structure in
American Life, by Murray and Herrnstein.

Parents of minority students are concerned about new math standards
and curricula that deemphasize paper-and-pencil computation.
Computation skills often are associated with mathematical competence,
and the lack of mastery of these skills has been used to justify
denying opportunities to minority students. Therefore, these parents
are not convinced that mathematics reform is in the best interests of
their children (Secada, 1994).

Morris KLINE - 1962- On The Mathematics Curriculum of The High School
The mathematics curriculum of the high school should provide for the
needs of **all students**: it should contribute to the cultural background
of the general ...  michel.delord.free.fr/kline62.html

ALL INCLUDES DISABLED USING NCTM CURRICULA
Including All Students in Meaningful Mathematics: The Story of Darrell. Judith Storeygard Cornelia Tierney, TERC. This article tells the story of Darrell, ...
escholarship.bc.edu/education/tecplus/vol1/iss3/art4/
because a few of his teachers knew how to teach mathematics to a range
of learners using NCTM standards-based mathematics curricula and
because he became aware of how he learns mathematics best, Darrell
began to progress towards the end of elementary school. Students with
disabilities, like Darrell, all deserve the chance to participate in
meaningful mathematics.

Science and Mathematics for All Students [Its Just Good Teaching] File
Format: PDF/Adobe Acrobat - View as HTML Mathematics for All Students
are mirrored in its. content and organization. ... adopt to increase
all students’ participa-. tion in mathematics and science. ...
www.nwrel.org/msec/images/resources/justgood/04.97.pdf

Mathematical Proficiency for All Students
Mathematical Proficiency For All Students. Adding It Up: Helping Children Learn Mathematics cover: click for full report Are the nation's schoolchildren ...
www4.nationalacademies.org/onpi/webextra.nsf/web/proficiency?OpenDocument

RAND | Monograph/Reports | Mathematical Proficiency for All ...
Mathematical Proficiency for All Students. Toward a Strategic Research and Development Program in Mathematics Education. Cover: MR-1643 | Mathematical ...
www.rand.org/pubs/monograph_reports/MR1643/index.html

Appendix: Table of Standards - Number and Operation NCTM's visionary
document for teaching mathematics at any level. ... Pre-K–2
Expectations: In prekindergarten through grade 2 **all students** should–
...  standards.nctm.org/document/appendix/numb.htm

http://www.mste.uiuc.edu/courses/ci332fa02/
Elementary Mathematics Instruction
What is mathematical power?
The National Council of Teachers of Mathematics (NCTM) has called for
fostering the mathematical power of ALL students (1989). 

EXPERTS QUESTION ONE MATH TEST FOR ALL
z74\CLIP\2003\10\mathstin.txt
New York Post
STATE'S HS MATH PROGRAM 'STINKS' 
By KENNETH LOVETT and CARL CAMPANILE 
Members of the panel also raise the question of whether it's
educationally sound to require all students - college bound or not -
to pass an identical math-skills test. 
October 8, 2003


@@Angles

%%vertical

Vertical Angles
G5?  Michigan G.GS.05.03 Identify and name angles on a straight line and vertical angles.
     http://www.eup.k12.mi.us/608973121310511/blank/browse.asp?a=383&BMDRN=2000&BCOB=0&c=55564&608973121310511Nav=|734|&NodeID=734
G6   CA  Identify angles as vertical, adjacent, complementary, or supplementary
     http://www.cde.ca.gov/be/st/ss/mthgrade6.asp
G6?  Indiana Identify and draw vertical, adjacent, complementary, and supplementary angles
     and describe these angle relationships. Solve problems involving an unknown angle.
     http://www.indianastandardsresources.org/standard.asp?Language=English&Subject=math&Grade=6&Standard=4
G7   identify vertical angles
     www.mathscore.com/math/free/lessons/California/7th_grade/Identifying_Angles_lesson.html
G7   Maryland Use vertical, adjacent, complementary, or supplementary angles
     http://www.mdk12.org/instruction/curriculum/mathematics/standard2/grade7.html
G8   Virginia relationships between vertical angles
     http://www.knowledge.state.va.us/main/sol/solview.cfm?curriculum_abb=MAT&category_abb=8
G8-12 prove relationships between angles in polygons by using properties
     of complementary, supplementary, vertical, and exterior angles
     http://www.cde.ca.gov/be/st/ss/mthgeometry.asp
G10  Solve problems involving complementary, supplementary, congruent, and vertical angles
     http://intranet.cps.k12.il.us/Standards/CAS/CAS_Mathematics/Math_10th_Grade/10SG9-Math/10sg9-math.html
Geom VA solve practical problems involving complementary, supplementary,
     and congruent angles that include vertical angles
     http://www.knowledge.state.va.us/main/sol/solview.cfm?curriculum_abb=MAT&category_abb=GEO


@@Applications of Mathematics

A key notion of reform is to apply mathematics to the "real world"
instead of studying abstract mathematics and algebra or geometry.
Critics say that introduces a lot of stuff which has nothing to do
with mathematics, and causes skipping a lot that does have to do with
algebra.


"Modern math book offers clue to lack of
student's abilities" Seattle Times Dec 28, 1997 p. B5 Robert
Supino (letters to editor) Much of the book is not algebra, in fact
the algebra is difficult to find.  The emphasis on application makes
it not really a math text but a bad physical science text.


@@Arise

Innovative new math program that claims to teach exclusively
in "real world" settings, but not rated highly by skeptics

Home Page
Project ARISE (Applications Reform In Secondary Education) is a
3-year college-preparatory mathematics program, in which all math is
taught in the context of real-world problems and settings.  Hogan
Senior High School, located in Vallejo, CA, is one of 15 national
pilot sites, and the only one located in California.

ARISE is a comprehensive curriculum development project funded by a
National Science Foundation (NSF) grant to the Consortium for
Mathematics and its Applications (COMAP). It is developing a 9th-
through 11th-grade secondary mathematics core curriculum in which **
applications of mathematics play a primary role. **


ARISE is a core curriculum; it is a program that allows students
"in", not keep them "out". It demonstrates that mathematics doesn't
have to be ability-grouped in order to be effective. It answers the
age-old question, "When am I ever going to have to use this?", so
that students can concentrate on the learning. It simultaneously
prepares students for college and for vocations. It is equally
effective in block schedules and in traditional schedules. It can be
an alternative program, an academy program or the program for a math
department. It is a model of what the NCTM Standards were addressing,
an actual mathematics curriculum, and a source of new teaching
materials on applications of mathematics.

So, here's an honest admission: students won't be exposed to the same
level of algebraic symbol manipulation that they would by taking 2
full years of algebra in high school. There's no way they could!
However, most students who DO take 2 years of algebra in high school
don't really know their algebra. A lot of them have to retake courses
again when they get to college.

Will students be prepared for college by studying ARISE? While it's
too early to quote statistics, my feeling is that "Some will; some
won't!"

 Testing processes are being adjusted to reflect what the NCTM
Standards have charted as the course for math education, and will
align themselves with the Assessment Standards relatively soon (at
least in our lifetime).

Marti Gaydish: Negative Review of Arise math pr
ogram

@@Area

Circle area (2 PI R squared)
G5 Dist of Columbia - pi times radius squared
   http://www.k12.dc.us/dcps/Standards/Grade-level/Grade%205/WS-math-5-ad4.pdf
G6 Connected Mathematics (PI R squared not in student book)
G6 GA
   public.doe.k12.ga.us/DMGetDocument.aspx/6th%20Grade%20Unit%205%20Circles%20and%20Graph%
G6 CT
G6 CA
   www.cde.ca.gov/be/st/ss/mthgrade6.asp


@@Arithmetic


Ability level


%%Addition
--------

Add to sum = 10 by counting
K Lk Wash
G1 Oak Harbor Christian School
G1 Japan

Add to 10 + 10 = 20 by counting
G1 CA 1998
G1 Lk Wash
G2 Oak Harbor Christian School

Add 3 numbers
G1 Scott Forseman

Commit math facts add/sub to 20 to memory
G1 CA 1998
NA WA

Add 2 digit whole numbers on paper with carry
G2 CA 1998
G2 Lk Wash
G2 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm

Add 3 digit whole numbers
G2 CA 1998
G2 Japan
G3 Lk Wash

Add 5 digit whole numbers
G3 CA 1998

Add whole numbers and simple fractions
1 1/2 + 1/2
G3 Los Angeles

Memorize addition table
(equivlant to 2 digit adding?)

Add money amounts (2 digit decimal)
G4 WA Assessment
G4 LkWash
G7 WA Benchmark
G8 Vermont

Add any decimal amount w/o calculator
G4 Addison Wesley 1991
G5 Lk Wash
G7 WA Benchmark
G7 LA Benchmark
G7 Nebraska 1940s
NA Vermont

Add any decimal amount with calculator
G6 Lk Wash

Add scientific notation
G9 LA


%%Subtraction
-----------

Subtract from 10 K->1

Subtract from 20

Subtract 2 digit with borrow
G2 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm

Subtract from 100

Subtract 3 digit
G3 Lk Wash

Compute change from 1 dollar on paper
G4 Lk Wash

Compute change from 1 dollar in head
NA

Subtract multiple digit whole numbers on paper
G4 WA
G4 Vermont

Subtract decimal numbers on paper
NA Vermont

Subtract any amount on calculator
G5-8 Vermont


%%Multiply
--------

Concrete Multiplication
-----------------------
G1 Draw 3 hats, each with 2 feathers and 3 buttons Lk Wash homework
   z39\clipim\99\15\3hats.efx
G2 Lk Wash

Memorize multiplication table
-----------------------------
G2 Japan 1990
G3 California '98
G4 California '97
--- do not memorize multiplication table ---
NA Alaska
NA Massachusetts
NA Minnesota
NA Washington EALR
NA Lake Washington SD


Multiply to 20 x 20
-------------------------
- Not common in US, common in Germany, Japan

Multiply 2-3 by 1 digit whole number
-----------------------------------
G4 WW Assessment
G4 Lk Wash
G4 1998 Mass MCAS test

Multiply 2 by 2 digits by drawing pictures (I'm
not kidding!)
------------------
G4 America's Choice New Performance Standards (NCEE)

Multiply 3 by 2 or 3 digits
G3 Japan
G4 1964 Addison Wesley
G5 British Columbia

http://www.thecrimson.harvard.edu/opinion/article.asp?ref=7818 May
04, 2000 New Battles in the Math Wars By WILFRIED SCHMID 
What is 256 times 98? Can you do the multiplication without using a
calculator? Two thirds of Massachusetts fourth-graders could not when they
were asked this question on the statewide MCAS assessment test last year. 


Multiply 4 by 2 digits
G4 WA Assessment
G5 Lk Wa

Multiply with decimal money w/o calculator
-------------------------------------------
G4 WA Assessment
G5 1964 Addison Wesley
G5 Lk Wa
G7 WA Benchmark
NA Vermont

Multiply with 1 decimal by estimation
G5 Houghton Mifflin  1.3 * 3

Multiply with decimal w/o calculator
G4 WA Assessment
G5 Lk Wa
G6 1964 Addison Wesley
G7 WA benchmark
G7 1940s Nebraska
NA Vermont

Multiply with sign
G7 WA benchmark

Multiply any amount with calculator
G7 WA benchmark
G5-8 Vermont


%%Division
--------

Sharing Division
G1 Scott Forseman

"Concrete" Division
G1 Washingon 10 feet, how many people? Problem solving with no
   instruction in division.
   http://www.utdanacenter.org/wamathrevision/index.php
G2 Lk Wash
G2 1 card = 3 marbles, how many cards for 24 marbles? Dale Seymour

Equal share division
G2 Utah
   www.uen.org/core/txFile.do?courseNum=5020&fname=math2.pdf 

Equal shares with remainder
G2 California
   "Use repeated subtraction, equal sharing, and forming
   equal groups with remainders to do division."
   www.cde.ca.gov/be/st/ss/mthgrade2.asp

Calculator Division
Prek-4 Massachusetts 1996

Divide 2 by 1 digit with remainder
G2 Wash State 2007 share 38 cents among 3. Problem
   solving with no instruction in equal shares with
   remainder
G3 Japan
G4 Lk Wash
G4 British Columbia http://www.est.gov.bc.ca/.curriculum/www/irps/mathk7/_4n
umno. htm
G4 1998 Mass MCAS
NA Massachusetts 1996

Divide 3 by 1 digit
G3 Japan
G3 1970 Holt
G4 1998 Mass MCAS test
G4 1998 CA Standards
G5 British Columbia http://www.est.gov.bc.ca/.curriculum/www/irps/mathk7/_4n
umno. htm
NA Massachusetts 1996

Divide by 10s
G4 1970 Holt
NA Massachusetts 1996

Divide by 2 digit whole number w/o calculator
G4 Japan
G4 Addison Wesley 1991
G4 Vermont
NA Massachusetts 1996


Long division 4 over 2 digits whole numbers

G4 WA Assessment (60 / 12 = 5, estimate 4 dig / 2 digit)
G4 Addison Wesley 1990 Math 4 textbook
G5 Omitted by Investigations/TERC
G5 Lk Wash
G5 '97 CA (Hard) Math Framework http://www.cde.ca.gov/cilbranch/eltdiv/mathf
w.htm#4-7
G5 Kentucky http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.html
G5 Virginia http://www.pen.k12.va.us/go/Sols/math.html
G5 San Marino CA 3 div by 2 digit
     http://www.san-marino.k12.ca.us/~valentine/fifth/fifthcu. html#MATH
G5 North Carolina http://www.dpi.state.nc.us/Curriculum/Mathematics/grade5.h
tm
     Explain the division process with 1 and 2 digit divisors.
NO British Columbia
NO Wisconsin "selecting and applying algorithms* for division"
 http://www.wisgov.state.wi.us/MSMath.htm
NO '97 CA fuzzy math standard, ommitted on purpose
NO Louisiana http://www.doe.state.la.us/os2httpd/public/contents/math97. htm

NO Nebrask State 1997 http://nde4.nde.state.ne.us/IPS/Issu/mathSTAND.html
NO Washington Benchmark "divide whole numbers"
NO Minneapolis
NO Massachusetts "select and use an appropriate method for computing
  from among mental arithmetic, paper-and-pencil, calculator"

Long division is needed to understand
higher concepts like polynomial factoring, rational numbers.
http://www.csun.edu/~hcbio027/standards/conference.html/
Conference on Standards-Based K-12
Education California State University Northridge Transcript of R.
James Milgram (Mathematics Professor, Stanford)

Money division .xx by whole number

Long division with decimal w/o calculator
G5 1970 Holt Exploring Elementary Mathematics
G6 1964 Addison Wesley Elementary School Mathematics
NA Lk Wash
NA Vermont
NA Massachusetts 1996

Divide with sign
NA Massachusetts 1996

Divide any decimal without calculator
G5-8 Vermont
G7 Mathematics unlimited
G7 1940s Nebraska

Fractions
---------

Add with like denominators
G4 Lk Wash

Compare fractions with fraction strips / benchmark fractions
G6 - Connected mathematics (common denominators not covered)

Add, subtract, multiply, divide with unlike denominators
G5 Lk Wash

Add fractions with common (but not lowest) denominator
G6 Connected Mathematics

Add and subtract fractions using factoring to find least common denominators
G7 1997 California framework
G6-G8 Omitted by Connected Mathematics, only common denominators.



@@Asian 

Asians have the highest quantitative and math scores of any race, the
scores of Asians Americans are just as high as those of Korea, Taiwan
or Japan, about 2 years ahead of white Americans. Asians with english
as 1st language score just as high in verbal as well. Yet Asians
emphasize obedience, rank order testing, conformity and rote
learning, not "progressive" learning styles which have been offered
as the antidote for American kids.

At worst, Asians score only slightly worse than average. More
typically, Asians score as well a communities the next level up in
income, no matter how bad the schools are.

See testing
See Asian Textbook
SAT test

%%Not Applicable

Some claim that Asian methods aren't
applicable since they are teaching to the same race, and suicide
rates are high. In fact, Asians have the fewest "role models" but
the best scores, in the US, Whites have the highest youth suicide
rates.


@@Assessment

Below is the address for NWREL's latest assessment model for problem solving
in mathematics.  The site includes a scoring guide, samples of scored
student work and information about the model.  Check it out at:
http://www.nwrel.org/msec/mpm/index.html.
Mathematics and Science Center
Northwest Regional Educational Laboratory
101 SW Main St. Suite 500
Portland, OR 97204
(503)-275-0689
(800) 547-6339 ext.689
(503) 275-9584 FAX
mcintosr@nwrel.org
http://www.nwrel.org/msec


@@Backlash

%%Defence

http://www.mathematicallysane.com/mission.htm Mathematically Sane
Promoting the rational reform of mathematics education For too long,
however, the public has heard primarily from the side of the
traditionalists. MathematicallySane.com has been developed to balance
the equation. 

http://www.mathematicallysane.com/analysis/survival.htm
Z50\clip\2001\07\survive.htm
Surviving the Math Wars:
Reflections From the Front Lines
Submitted by W. Gary Martin 



%%Offence
LA BATTLE TO KILL FUZZY MATH FOR MINORITIES
http://www.latimes.com/CNS_DAYS/990813/t000072042.html
zip36\clip\99\16\fuzzmat.txt
Friday, August 13, 1999 Order to Scrap New Math Texts Rescinded L.A.
Unified: In clash of philosophies, books were approved, then
eliminated and finally reinstated.  By LOUIS SAHAGUN, LA Times Staff
Writer Moving to quell a furor over traditional versus progressive
math instruction, Los Angeles schools Supt. Ruben Zacarias on
Thursday rescinded an order by his top staffers to eliminate
textbooks used in a federally funded enrichment program for poor
minority students.  

PARENTS FIGHT AGAINST CORE PLUS
\clip\98\02\edcli2.txt Detroit Free press 1/19/98 Bloomfield parents
fight for old math They say new method hurts kids BY TRACY VAN
MOORLEHEM Free Press Education Writer

\clip\98\03\reed\reed.htm CA MATH PROFESSORS SPEAK OUT AGAINST CLAIM
OF "CONSENSUS" ON FUZZY MATH.
http://ourworld.compuserve.com:80/homepages/mathman/reed.htm
(Mathematically Correct) For the record, the omission of long
division with 2 or more digit divisors was a conscious decision. I
pointed out in writing and in oral comments before the Commission
that this was missing.

@@Basic Skills

%%Harmful

@@Manual Computation


NEW MATH STANDARDS DEEMPHASIZE PAPER AND PENCIL COMPUTATION
Ensuring **Equity** and Excellence in Mathematics In Reaching All Students
With Mathematics (Cuevas & Driscoll, 1993b), an NCTM task force gave
special attention to programs that work to ensure equity and ...
www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm

Parents of minority students are concerned about new math standards
and curricula that deemphasize paper-and-pencil computation.
Computation skills often are associated with mathematical competence,
and the lack of mastery of these skills has been used to justify
denying opportunities to minority students. Therefore, these parents
are not convinced that mathematics reform is in the best interests of
their children (Secada, 1994).

TEACHING HOW TO MULTIPLY AND DIVIDE IS DANGEROUS
z39\clip\2000\01\leiwand.txt It's Time To Abandon Computational
Algorithms By Steven Leinwand (2/9/94)/Education Week It's time to
recognize that, for many students, real mathematical power, on the
one hand, and facility with multidigit, pencil-and-paper
computational algorithms, on the other, are mutually exclusive. In
fact, it's time to acknowledge that continuing to teach these skills
to our students is not only unnecessary, but counterproductive and
downright dangerous.

ORIGINAL CONTENTS OF PDF ARTICLE
http://my.nctm.org/ebusiness/productcatalog/Temp_Images/666_contents.pdf
17. The Harmful Effects of Algorithms in Grades 1– 4 . . . . . . . . . . . . . . 130
CONSTANCE KAMII
University of Alabama at Birmingham, Birmingham, Alabama
ANN DOMINICK
South Shades Crest Elementary School, Hoover, Alabama

http://members.aol.com/vlorbik/amstalk.html
Some Contradictions of Education Reform:
Constructivism, High-Tech, and Multi-Culti
Owen Thomas 
Constructivism.
EXHIBIT A: Quotes taken from "The Harmful Effects of Algorithms in
Grades 1--4", by Constance Kamii & Ann Dominick in The Teaching and
Learning of Algorithms in School Mathematics (NCTM Yearbook, 1998).

    "The teaching of algorithms is based on the erroneous assumption
that mathematics is a cultural heritage that must be transmitted to
the next generation." (p.132)

    "Some leaders in mathematics education also began to say that we
must stop teaching algorithms because they make no sense to most
children and discourage logical thinking." (p.141) 

I only wish these quotations could be allowed to speak for themselves.
But apparently some people don't not find them as outrageous as I do;
these ideas are taken seriously by the NCTM, after all. (The National
Council of Teachers of Mathematics needs no introduction to the
audience of my talk -- suffice it to say here that they're the
professional organization most aligned with Math Ed "reform").

Basic Skills Versus Conceptual Understanding/ H. Wu
http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf This
view echoes one that is held by many educators, among them Constance
Kamii. Kamii is generally acknowledged to be a leading advocate of
this point of view. A much quoted recent article co-authored by Kamii
and Ann Dominick is provocatively entitled

“The Harmful Effects of Algorithms in Grades 1-4.”7 Its main thesis is
this: Algorithms not only are not helpful in learning aritha metic,
but also hinder children’s development of numerical reasoning....

We have two reasons for saying that algorithms are harmful: (1) They
encourage children to give up their own thinking, and (2) they
“unteach” place value, thereby preventing children from developing
number sense....

The persisting difficulty [with standard algorithms] lay in the
column-by-column, single-digit approach that prevents children from
thinking about multidigit numbers.

This then brings us to an impasse, according to Kamii and Dominick:
Children can have conceptual understanding of numbers without learning
algorithms, or they become mathematical error-prone robots. Which do
we prefer? Invoking Piaget’s constructivism [sic],

Kamii and Dominick recommend that

Children in the primary grades should be able to invent their own
arithmetic without the instruction th are now receiving from textbooks
and workbooks.

 AMERICAN EDUCATOR/AMERICAN FEDERATION OF TEACHERS FALL 1999


http://www.eiu.edu/~scienced/5660/gotta/G-4_R-1.html
  the harmful effects of algorithms . . . in primary arithmetic
constance kamii ( she wrote the autonomy article ) and barbara a. lewis
teaching k8 --- january 1993
Two educators argue the case for "constructivism" as opposed to "traditional math"

http://www.ericdigests.org/2004-3/math.html
ERIC Identifier:  ED482725
Publication Date: 2003
Author: Roh, Kyeong Ha
Source: ERIC Clearinghouse for Science Mathematics and Environmental Education

Problem-Based Learning in Mathematics. ERIC Digest.
Kamii and Dominick(1998), and Baek (1998) have shown, though, that the
standard arithmetic algorithms would not benefit elementary students
learning arithmetic. Rather, students who had learned the standard
addition algorithm seemed to make more computational errors than
students who never learned the standard addition algorithm, but
instead created their own algorithm.

http://www.learner.org/channel/workshops/lala/resources.html#kamii
(has picture)
Constance Kamii
University of Alabama at Birmingham

Professor of Early Childhood Education at the University of Alabama at
Birmingham, Constance Kamii studied under Jean Piaget for a dozen
years, first as a postdoctoral research fellow and later as an adjunct
professor at the University of Geneva. She developed a preschool
curriculum based on Piaget's theory, especially in science,
mathematics, and the sociomoral realm, and is now developing an
elementary math program based on his theory. Kamii is the author of
Young Children Reinvent Arithmetic; Young Children Continue to
Reinvent Arithmetic, 2nd Grade; and Young Children Continue to
Reinvent Arithmetic, 3rd Grade.

Further Readings by Constance Kamii

Kamii, C. 1984. Young children reinvent arithmetic. New York: Teachers
College Press.

Kamii, C., and DeVries, R. 1980. Group games in early education.
Washington, DC: National Association for the Education of Young
Children.

Kamii, C., and Dominick, A. 1997. "To teach or not to teach
algorithms." Journal of Mathematical Behavior. 16(1): 51-61.

Kamii, C., and Ewing, J. K. 1996. "Basing teaching on Piaget's
constructivism." Childhood Education. 72: 260-264.

Kamii, C., Lewis, B. A., and Livingston, S. J. 1993. "Primary
arithmetic: Children inventing their own procedures." Arithmetic
Teacher. 41(4): 200-203.

INVENTED MATH ENDORSED IN AUSTRALIA
www.aare.edu.au/02pap/mci02517.htm
DEVELOPING INFORMAL WRITTEN COMPUTATION
Alistair J. McIntosh
University of Tasmania 
Paper presented at the Annual Conference of the Australian Association
for Research in Education, University of Queensland, Brisbane,
December 2002

There is a related change in approach to written computation advocated
and described, though less clearly, in official documents. For example
the National Statement on School Mathematics (Australian Education
Council, 1991, p. 109) states that:

The development of flexible computational skills can be inhibited by
emphasising the practice of standard paper-and-pencil methods to the
exclusion of all other methods.

It is far more realistic to use a
combination of mental and informal written methods most of the time,
with paper-and-pencil recording seen as providing memory
support...Consequently less emphasis should be given to standard
paper-and-pencil algorithms and, to the extent that they continue to
be taught, they should be taught at later stages in schooling.'

Some researchers in the UK, the USA and the Netherlands (Kamii &
Dominick, 1989; Hiebert et al, 1997; Carroll& Porter, 1998, Thompson,
1999) have made valuable contributions in this field, but to date
there has been little research undertaken to assist teachers in moving
forward in this area

http://www.math.umd.edu/~jnd/The-Math-Wars.html

Similarly, in their much quoted 1998 article, "The Harmful Effects of
Algorithms in Grades 1-4", Constance Kamii and Ann Dominick wrote:
"Algorithms not only are not helpful in learning arithmetic, but also
hinder children's development of numerical reasoning ..."

Invoking Piaget's constructivism, Kamii and Dominick wrote: "Children
in the Primary grades should be able to invent their own arithmetic
without the instruction they are receiving from textbooks and
workbooks."


www.aare.edu.au/00pap/hei00259.htm
Mental computation: Is it more than mental architecture?
Ann Heirdsfield
Centre for Mathematics and Science Education
Queensland University of Technology
Victoria Park Road,
Kelvin Grove 4059
Presented at the Annual Meeting of the Australian Association for Research in Education
Sydney

Literature at national and international levels argues the importance
of including mental computation in a mathematics curriculum that
promotes number sense (e.g., Klein & Beishuizen, 1994; McIntosh, 1998;
Reys, Reys, Nohda, & Emori, 1995; Sowder, 1992; Verschaffel & De
Corte, 1996; Willis, 1992). It has been posited that when children are
encouraged to formulate their own mental computation strategies, they
learn how numbers work, gain a richer experience in dealing with
numbers, develop number sense, and develop confidence in their ability
to make sense of number operations (Kamii & Dominick, 1998; Reys &
Barger, 1994; Sowder, 1990).

Carroll (1997) and Kamii, Lewis, and Livingston (1993) documented the
mental and written computational procedures invented by children who
are active in their learning. They showed that children could produce
a wide variety of efficient strategies that exhibited sound number
understanding even though there was little direct teaching of
algorithms. They also found that the active development of knowledge
encouraged children to participate in the construction of problems and
the explanation of solution strategies.

In Queensland, there are few reform classrooms and the traditional pen
and paper algorithms are still taught out of context and in situations
where children have little or no input into constructing problems and
explaining solutions. As Cooper, Heirdsfield and Irons (1995 & 1996)
reported, this has resulted in a tendency for Queensland children to
use strategies for mental computation that reflect the procedures
underlying the pen and paper algorithms regardless of their knowledge
and ability to use more efficient strategies.

File Format: Microsoft Word - View as HTML
Some experts in the United States provide evidence that the teaching of standard formal written algorithms is counter-productive (Kamii & Dominick, 1997). ...
www.ltag.education.tas.gov.au/focus/beingnumerate/ApproachingComputation.doc

International advice and practice is still evolving, with research on
the development of non-standard but formal algorithms being developed
particularly in the Netherlands. Some experts in the United States
provide evidence that the teaching of standard formal written
algorithms is counter-productive (Kamii & Dominick, 1997). However the
Australian and Tasmanian documents all take the same basic stance:
Young children should be encouraged to explore and invent informal
paper-and-pencil methods to supplement mental and calculator methods
(National Statement, p. 111).  They [Band B students] should devise a
variety of paper-and-pencil computational strategies, record the
results of their thinking in their own way, and progress towards
efficient, though not necessarily standard, procedures (National
Statement, p. 117).  At Level 2, a student: 2.16 Uses a variety of
strategies, including regrouping, to assist in adding and subtracting
whole numbers when unable to compute mentally (National Profiles, p. 42

GUIDELINES FOR PAPERS SUBMITTED TO THE NINTH DOSME, SHBIE, UBD ...
File Format: Microsoft Word - View as HTML
Firstly, there has been a growing swell of criticism directed towards
the teaching of algorithms in the early primary years (Kamii &
Dominick, 1998; ...
math.ecnu.edu.cn/earcome3/TSG2/07_RegICMIwhite05%5BFinal%5DAllan_EDITED%5B1%5D.doc


@@Bellevue

http://www.jt-actuary.com/Library/hnrsmath.doc
.html
Where is Math Going in Bellevue? John Tupper
CMP math really sucks, what the hell are you guys thinking??


@@Benchmarks by keyword

Links to math grade level benchmarks, by task, survey of different
national and state standards and assessments.




%%States

\clip\98\02\statest.txt Education Week 1/98: States Set To Examine
How To Make Testing Nationally Comparable By Millicent Lawton (states
worried about tests too easy, not too hard) The meeting is the first
event organized by Achieve, the Cambridge, Mass.-based independent
resource center for governors and business leaders on academic
standards and assessments.

@@Birthday Paradox

1993 8th grade text, teacher ed
The following problem appears the Teacher's Edition of "Mathematics in
Action" (1993) published by Macmillan/McGraw-Hill, an 8th grade text.

How many people would you have to ask for there to be a better than
50% probability that two of them will have the same birthday?
 
 You may be surprised to find out that the answer is just 24 people, even
 though there are 366 possible birthdays. 

 Maryland 8th grade assessment
problem with incorrect solution.

 Solution


@@Brain

%%Gender Differences

MATH, NAVIGATION DIFFERENCES IN BRAIN - RATS TOO
z56\clip\2002\05\sexbrain.txt z56\clipim\2002\05\20\sexbrain\sexbrain.htm
http://www.sciam.com/2002/0602mind/0602kimura.html
SEX DIFFERENCES IN THE BRAIN
Men and women display patterns of behavioral and cognitive differences
that reflect varying hormonal influences on brain development by
Doreen Kimura
Men better at 1) 3D rotation, predicting paper folding outcome 2)
aiming projectiles 3) mathematical reasoning
Women better at 1) rapidly identify matching objects 2) recall from
reading or list of words 3) fine motor coordination - placing pegs 4)
mathematical calculation
Note - these are precisely the tasks on the WASL test.

Male and female rodents have also been found to solve problems
differently. Christina L. Williams of Duke University has shown that
female rats have a greater tendency to use landmarks in spatial
learning tasks, as it appears women do. In Williams's experiment,
female rats used landmark cues, such as pictures on the wall, in
preference to geometric cues: angles and the shape of the room, for
instance

%%General

z50\clip\2001\08\mathbrai.txt
The Times  (London)
TUESDAY AUGUST 28 2001
Problems with maths linked to early birth
BY DAVID CHARTER, HEALTH CORRESPONDENT
Neuro-imaging showed that there was a specific area in the left parietal
lobe where children with normal calculation ability had more grey matter
than those with a specific learning deficit in this ability.

@@Burrill

Gail Burrill, president of the NTCM, vice-chair of Clinton math assessment c
ommittee


@@Calculators

Reform math believes that with the advent of the calculator, no one
will have to be taught or know arithmetic. Reaction is to ban use of
calculators in lower grades.


%%Cheating

zip38\clip\99\19\calc.txt
GRAPHING CALCULATORS TOOLS FOR LEARNING AND CHEATING Calculators with
an attitude Legitimate tools for high school math students, or
weapons for lazy cheaters? By JENNIFER LEE New York Times Fri, 08 Oct
1999 Students figure out assembly language, devise cheating programs
and games for calculators.


%%Controversy

http://dallasnews.com/metro/51545_TEACHERS19.html Math teachers
adding technology to help students' skills multiply 03/19/2000 By Ian
McCann / The Dallas Morning News Ann Brooks, a teacher at Richardson
West Junior High School, has used graphing calculators in her
geometry classes since she started teaching three years ago.  "They
help the kids learn the concepts," Ms. Brooks said.

RDYARROW GATHERS ANTI-CALCULATOR
ARTICLES Kids only learn to copy from the display, they don't
understand the underlying math, contrary to the claim that
calculators lead to understanding beyond the calculation of the
answer.

PARENTS FORCE ORE TO PUT NO-CALCULATOR QUESTIONS BACK ON EXAMS
Educators are divided on use of calculators in early grades Scott
Learn Newhouse News Service. Seattle Times 2/21/99
\clipim\99\02\26\calc.tif Math questions without calculators added to
Oregon state math tests after parents ask how to check if children
know manual calculation. Last year half of Ore 5th graders used
calculators in class, all by 10th grade according to NAEP surveys.
NCTM advocated their use in every grade in 1990s.

%%Race 
%%Disadvantaged

BLACKS, POOR MORE LIKELY TO USE CALCULATORS, WORSE OUTCOMES
z49\clip\2000\12\calcrace.txt Calculators May Be the Wrong Answer As
a 'Digital Divide' Widens in Schools By DANIEL GOLDEN Staff Reporter
of THE WALL STREET JOURNAL
http://interactive.wsj.com/archive/retrieve.cgi?id=SB976838326811281152.djm

The Brookings Institution found:
% using calculators every day
50% black
44% Hispanic
27% White

45% subsidized lunch
29% non lunch

42% parents not finished high school
28% college graduate parents

2.0 Public school relative to
1.0 Private school

Kentucky statewide math test 
43% fifth graders in Jefferson County, 30% black
33% statewide 10% black

Pennsylvania 5th graders taking state math test using 
calculators almost every day
5%   overall 
9%   black
8.5% Hispanic
4.4% White
4.1% Asian

Not meeting standards in Maine math test
47%  everyday calculator use
23%  2 or 3 times per month

Analyzing data from the National Assessment of Educational Progress,
every_day calculator users scored lower than less_frequent users,
both overall and within each racial group. 

John S. Bradley, a program manager with the National Science
Foundation, maintains that calculators generally improve student
scores Lee V. Stiff, president of the math_teachers council, contends
that more than 100 studies __ based on testing students with and
without calculators, as well as classroom observation __ show that
calculators can improve student achievement, problem_solving, and
understanding of mathematical ideas.

%%Testing

z41\clip\2000\05\montalg.txt From the Washington Times, Metropolitan
Section, C1, Monday, May 8, 2000 Maryland: Algebra funds OK’d ~
Montgomery seeks $$$ to improve scores By Gerald Mizejewski ­ The
Washington Times. Just 36 percent of county ninthgraders passed final
exams in Algebra 1 in January, the first time educators have used
standardized grading scales.  Grades among minorities are even worse.

Montgomery County Public Schools
have high SAT averages, yet their algebra tests have huge failure rates.

Fri, 15 Oct 1999 From: cassidy@pacifier.com
You can find the restrictions on calculator use in any SAT booklet --
Here are the types NOT allowed:

Calculators with QWERTY keypads (TI92, HP95, etc.)
Calculators with paper tape
Calculators that make noise or "talk"
Calculators that require an electrical outlet
Pocket organizers
Hand held laptop computers
Electronic writing pads and pen-input devices

%%United Kingdom

\clip\98\03\edclip2.txt Christian Science Monitor 1/28/98 Trash the
Calculator, It's Back to Basics in Britain Calculators for children
under 8, for example, have been banned.



@@Calculus

dx/dy, differentials, integrals, and all that. Usually college level,
but taught to upper small percentage of high school students,
sometimes for AP credit. The Efficacy Institute believes that ALL
students are capable of mastering AP Calculus. Also see
testing: AP Calculus

%%All

physics and calculus should be included in all high school curricula.



%%Rates

>>\doc\95\14\mathtake.wk1
Source: SAT scores from The College Board, special compilation
SAT Took Calculus W23%(1.0) B12%(-1.9) H16%(-1.5) A40%(2.0)
Increase 1990-95  W21% B33% H23% A5%

Nearly half of Asian SAT takers have taken Calculus, twice the rate
of whites, who are two times the rate of Blacks. However minorities show
the most improvement.

>>\doc\96\01\hedsmith.txt "America Not Competitive" NW Asian Weekly
July 15, 1995 Hedrick Smith in "Rethinking America" points out 6% of
US, vs. 40% of German and 94% of Japanese students in high school
study calculus. filed under asian.education.calculus

\priv\95\12\blakcalc.txt - San Jose Mercury June 25, 1992 "Keys to the
Scientific Kingdom" Minorities in calculus workshop (article text)

%%All

Even though it hasn't been proven that all students can master
arithmetic or algebra, some insist that nearly all can master
calculus by end of high school. It's still a freshman topic at MIT.

long time homeschooler and scientist Art Robinson: Most children are
capable of finishing calculus between ages 14 and 17.

Bellevue Superintendent Paul Riley: I believe everyone should be
taking calculus in high school, but we're not set up for that yet.

The Efficacy Institute believes that ALL
students are capable of mastering AP Calculus.


%%Bosangue's Calculus Study

BLACKS BEAT ASIANS????? IN CALCULUS??? NAAAAAH!
Blacks and Hispanics who took a calculus workshop got better grades than Asians or Whites. asian.education.math Long-Term Effectiveness of the Calculus Workshop Model Martin Vaern Bosangue et al, Mt San Antonio Community College Study of California Calculus College Students 1990-91 compared to minorities who participated in a Calculus workshop. Black/Latino WShop NonWS Filip Asian White All Study Hours 8.23 6.88 4.00 5.77 6.76 6.20 Group Hours 4.09 1.83 0.56 1.15 0.62 1.13 Involve 8.51 7.54 5.67 6.07 7.08 6.58 HS GPA 3.35 3.29 3.34 3.38 3.37 3.35 SAT Verbal 408 383 461 373 469 411 SAT Math 517 491 555 569 589 557 Parent Ed 2.12 2.08 3.00 2.57 3.19 2.72 Course Grade 2.43 1.47 1.18 1.60 1.68 1.58 Index W1.00 BH1.44(1.14) A-1.05 Note that Black and Latino who took the course had better grades than Asians or Whites with higher SAT Math scores, though non-workshop minorities got worse grades, and Blacks and Hispanics generally score worse in most math courses than Whites or Asians. Blacks in the workshop spent much more time on homework than Whites or Asians, but started out with lower math test scores and grades. Date sent: Thu, 08 Jan 1998 23:02:05 -0800 From: Bruce Crawford Arthur, The Drew book I read was "Aptitude Revisited: Rethinking Math and Science Education for America's Next Century." The Johns Hopkins Press, 1996. ISBN 0-8018-5143-2. I can't remember the price, but it was fairly expensive for its length, about 225 pages. Bosangue is a colleague of Drew's. He also did studies with Hispanics and got similar results. It's truely amazing what a difference good study habits close-coupled with effort makes. %%Links http://integrals.wolfram.com/ Mathematica On-line integral calculator http://www.sicyon.com/ Integral/roots calculator @@Charts Bar Charts K - cut out pictures, paste bar chart, pick highest Pie Charts K - draw pie charts in Georgia Reform math gets kids drawing pie, bar, and line charts as early as kindergarten in format most adults never had to learn in high school. Life is going to be one big Powerpoint presentation in the 21st Century. Pie Charts introduced in Kindergarten?? @@Chinese American Psychological Association VOLUME 29 , NUMBER 6 -June 1998 Dipping math scores heat up debate over math teaching psychologists differ over the merits of teaching children ‘whole math.’ By Bridget Murray Monitor staff http://www.apa.org/monitor/jun98/math.html Students need directed instruction because they aren’t naturally motivated to learn, as the constructivists believe, he says. In a recent study of 372 Chinese and American sixth-graders, 12th-graders and older adults, Geary found that Chinese children outperformed American children on computational and reasoning measures. However, Chinese and American older adults performed much the same, and IQ scores in the two countries were also similar. The study appeared last year in the Psychonomic Bulletin & Review (Vol. 4, No. 3, p. 425–430). According to Geary, America’s math performance sags because our country lacks a rigorous, sequenced national math curriculum like China’s. US MATH REFORM MAY BE MISGUIDED: AMERICANS ALREADY OUTPERFORM ASIANS IN FUZZY PROBLEM SOLVING MATH, LAG IN SYSTEMATIC FORMAL INSTRUCTION http://www.aera.net/uploadedFiles/Publications/Journals/Educational_Researcher/3405/03%20Wang.pdf Educational Researcher Vol 34 No. 5 pp. 3-13 Comparitive Studies on U.S. and Chinese Mathematics Learning and the Implications for Standards-Based Mathematics Teaching Reform. by Jian Wang and Emily Lin Chinese students often outperform US students. Chinese Americans also outperform Caucasian and other Asian American students, even before formal schooling, overall. This is cited as the reason for pushing radical new tranformational reforms in mathematics education as "standards based education", often criticized by many for deliberate omission of the teaching of systematic arithmetic methods in favor of open problem solving. However, test details show that Chinese students do not perform better at tasks such as graphing, and open ended problem solving that is such a priority for American reformers, and that the advantage of Chinese may be due to structered and systematic instruction by their parents. @@City %%Los Angeles z48\clip\2001\02\lamath.txt http://www.newtimesla.com/issues/2001-02-22/stewart.html 02/22/2001 Math War A rumble over an essential math text was one of four events that, taken together, show how hard L.A. Mummified reformers must work. By Jill Stewart @@CMSP Comprehensive Math and Science Program funded by NSF brought Pasadena HS from 26 to 57th percentile at algebra level math (successful fuzzy math program?) @@College Headlines are common that it's ridiculous so many college students need remedial math, but nobody's asking if it's ridiculous to require college students to take college level math beyond intermediate algebra, since it's not even required on the SAT, or for high school graduation. %%Remedial COLLEGE LEVEL MATH REQUIREMENT = INT ALGEBRA IS EXCESSIVE AT CC'S z55\clip\2002\04\mathcoll.txt http://www.sunspot.net/news/local/bal-md.math15apr15.story?coll=bal%2Dlocal%2Dheadlines Unequal equation between college, math, study shows High standards contribute to low graduation rate at BCCC, Abell reports; Requirements seen as roadblock By Alec MacGillis Sun Staff Originally published April 15, 2002 "Of the 1,350 first-time students who entered BCCC in the fall of 1997, 12 had graduated four years later; almost all of its students need remediation in math or English. " "95 percent of entering students last year needed remedial math" "test questions: "Find the equation of the circle at (-4,-4) and radius of 3" and "In how many different ways can three spades be drawn from a standard deck of cards?" Embry notes the SAT does not test intermediate algebra, and many top private colleges no longer require math courses for graduation. " @@Combinations and @@Permutations How many different ways can you order N items? If the order matters, it's a permutation. If it doesn't matter, it's called a combination. Most schools introduce this at middle or high school level. Every college math department includes this in a probability course. But NCTM based tests try to introduce this at elementary level. Here's a good definition from the The University of Saskatchewan http://www.usask.ca/education/ideas/tplan/mathlp/a2.htm Permutation - an arrangement of objects in which order is important There are 6 Permutations of ABC ABC ACB BAC BCA CAB CBA Find the number of permutations of the letters p, q, r, and s. Solution 4 x 3 x 2 x 1 = 24 ways 1*2*3 or n! (factorial) Another variation is how many ways can you combine 3 breads with 3 spreads to make different sandwiches. http://www.usask.ca/education/ideas/tplan/mathlp/a6.htm Combination - a selection in which the order is not important (groupings) How many groups of three letters are there if choosing from the letters A, B , C, D, E? Solution There are 5P3 = 5! / (5-3)! = 60 ways to arrange 3 letters. But for each arrangement of three letters, 6 arrangements are the same group. For example, arrangements using the letters Grade Level Spectrum -------------------------- G4 1998 MA MCAS test 2! problems ---- appropriate ---- G6 1998 CA Standards G7 Katy Junior High G7 Tucson Az District G8 Nevada 1998 G8-12 G8-12 Kings County CA G11-12 Instructional Television G11-12 Minnesota Standards Coll Most Colleges include it in probability courses Permutation G12 Nevada G4 1998 MA MCAS Prob 27 - list different ways to arrange 3 stations Prob 32 - how many numbers can you create with digits 1,5,8 Katy Texas Junior High http://www.katy.isd.tenet.edu/kjh/mathematkjh.htm G7 7th Grade - Math 7 includes ... permutations and combinations in application problems. G7 Benchmarks-Mathematics-Middle School (Tucson Az) http://instech.tusd.k12.az.us/esmsmath-b.htm G8 Orange County Framework Orange County Frameworks for Higher Achievement 1998 http://www.ocps.k12.fl.us/framework/ma/resource/links/241.htm G8 investigates combinations and permutations. http://kings.k12.ca.us/math/lessons/teamwins.htm G8-12 Kings County CA HS Minnesota 9-12 Mathematics (achieve) http://www.achieve.org/a_dir/achieve/achieve.nsf/25827e48252eaa2e85256443005 20ee4/43eed95af0cc74ac852565470072356c?OpenDocument Understand the following concepts related to uncertainty: a. randomness b. permutations c. combinations HS Instructional Television Parade of Programs Combinatorics Grades: 11-12 http://llwisc.wecb.org/ITV/Mathematics/Combinatorics/2._Fundamental_Counting _Prin.html The Fundamental Counting Principle is introduced with the question, "What are the chances of rolling two ones and a two with three dice?" The total number of outcomes are shown and counted. This leads to the development of the general formula of the total number of possible arrangements. Finally the program defines a permutation as an ordered arrangement of things drawn from a given number. HS PRECALCULUS TEXTBOOK http://www.thomson.com/brookscole/math/book_tours/stewart_pre/toc.html Precalculus: Mathematics for Calculus, 3/e by James Stewart, Lothar Redlin, and Saleem Watson 11. Counting and Probability 11.2 Permutations and Combinations HS Permutations and combinations North Quincy High School Mathematics Department Curriculum Guide DISCRETE MATHEMATICS http://ci.quincy.ma.us/qps/nqhs/math/dismath.htm (Now if every 4th grader is supposed to know how to count and compute combinations, why does every college include it in probability?) CCO Northern Virginia Community College http://www.nv.cc.va.us/home/jhorn/MTH182.5OU.htm The student will learn to use elementary counting techniques and will learn to distinguish between permutations and combinations and compute both. CO Purdue School of Engineering and Technology http://www.engr.iupui.edu/~orr/webpages/cpt122/syllab.htm College CPT 122 Finite Mathematics - Syllabus CO AMAT3403 E --- Probability 3E - Australian Defence Force Academy, University College Handbook - UNSW Laws of probability, permutations and combinations. @@Communication A big part of math reform is "math communication" or writing a big essay on how you solved a problem, even though most math is simply working out the numbers, not a research paper. @@Common Denominators (See Fractions) G6 1998 CA standard http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G6 1998 CA Common denominators are used to compare fractions and to solve other problems arising from proportions. %%omitted http://www.wgquirk.com/NCTM2000.html The phrase "common denominator" is not found in PSSM. NCTM 2000 @@Community College www.cascadia.ctc.edu Cascadia Community College From printed 2000 guide: Math for Life 3 unit price, cost, hourly wages, proportional scaling Math for Life 4 fractions, decimals, American metric, money, portioning Math for Life 5 (GED) begin prep use formulas, percents in word problems credit finance, simple geometry, calculators Math for Life 6 (GED) finish prep solve problems with formulas, bar circle graphs, ratio, proportion. (grade 6/7) Prealgebra algebraic geometric notation, abstract representations from arithmetic. Integrated Math 1 "introduces linear algebraic thnking and brings in related concepts from geometry and triginometry. Learners will develop study skills and habits, team skills , and the ability to express math in many forms while work with both abstract and real world applications. Int Math 2 mostly algebra, right triangle trig, probability, number theory Int Math 3 log, exponentials, geometry, trig, probabioity, modeling techniques @@congruent Triangle G1 - Saxon video G2 - NCTM check congruence by moving one geoboard shape to cover another. http://standards.nctm.org/document/eexamples/chap4/4.2/index.htm G2 - CA 2.2 two congruent right triangles can be arranged to form a rectangle http://www.cde.ca.gov/be/st/ss/mthgrade2.asp G3 - Kansas 3.1.K4 parts of congruent triangles find angle measures http://www.kerc-ks.org/Benchmark_ind_list.aspx?stan_con_grade_id=13605&con_id=2&grade_no=08&stan_id=3596 G5 - Indiana identify congruent triangles using equilateral, isosceles, acute, and obtuse http://209.85.173.104/search?q=cache:QaqkGhCc8vQJ:www.doe.state.in.us/standards/docs-Math/2006-Math-Grade05.doc+congruent+triangle+grade+standard&hl=en&ct=clnk&cd=19&gl=us G7 - Identify corresponding parts of congruent triangles www.emsc.nysed.gov/3-8/module5.doc G8-12 CA Students prove that triangles are congruent or similar http://score.kings.k12.ca.us/standards/geometry.html @@Connected Mathematics @@CMP Popular NSF funded math program developed at Michigan State University. Generates controversy. Middle school version of Seymour Investigations Asks students to write about a "number you especially like". Students compare fractions with folded paper strips, common denominators are not even mentioned in the book although parents letter, website, and spokeswoman say students are expected to learn how to use common denominators. Students are asked to develop their own way to add, subtract, multiply and divide mixed fractions but no complete method is explained or presented. Revolt in Plano Texas and New York city. Home page: http://www.math.msu.edu/cmp/Overview/Glance.htm "Research results consistently show that CMP students outperform other students on tests of problem-solving ability, conceptual understanding, and proportional reasoning. And CMP students do as well as, or better than, other students on tests of basic skills. " CHANGES GUIDE http://www.phschool.com/sales_support/Tours/Prentice_Hall/CM2/CMP2_Changes_At_a_Glance%201%20.pdf Adds mean, dividing by fraction but still has no instruction on any complete method, only asks students to devise one. Only parent's letter mentions standard fraction methods despite claim that students are expected to use common denominators to add fractions. geoncyn: Tue, 27 Apr 2004 10:20:56 EDT Bits and Pieces II p. 22 I think have that "textbook" around here somewhere - is that the bright pink one with roller-skates/puppy on the front cover? It looks like an early elementary book at first glance. It's insane. NO instruction whatsoever. The worst of the worst. PIE CHARTS, ASK YOUR PARENTS TO TEACH YOU WHAT'S NOT IN THE BOOK, NO INSTRUCTIONS AGAIN sample Connected Mathematics Grade 6: My kid's section on pie charts is "based on what you know, create a pie chart from this data" No instruction whatsoever. CONNECTED MATHEMATICS: CHOOSE A NUMBER THAT YOU ESPECIALLY LIKE CUT OUT FRACTION STRIPS, NOT COMMON DENOMINATORS http://www.massnews.com/past_issues/2000/10_Oct/1000math.htm z45\clip\2000\09\invest.txt Boston Spends $4M to Avoid Math Basics. Massachusetts News Published: Oct,2000 Author: Paul Moreno Boston Schools: these programs help students "develop their own algorithms," parents ...petitioned against "Connected Math" when they found that it gave sixth-graders assignments like this: "Choose a whole number between 10 and 100 that you especially like" .. in New York rebelled when they found out that it asked sixth-graders to add fractions by folding paper strips instead of by converting to common denominators," says The New York Times. CONNECTED MATH HAS NO INSTRUCTION IN PERCENT, OR FRACTION MATH article Adding fractions: You in a group will devise at least one and preferably two methods to add fractions. Here are examples to try it on. CMP2 gives more examples, and calls it an "algorithm" evidently in response to the complaint that the standard algorithm is not taught, but there is still no description of a complete, correct method. 1st 71 page 1 month booklet uses fraction strips and benchmark fractions to compare fractions, but NOT lowest or any common denominator. One exercise works with least common multiple, but it is not formally introduced as a correct method. From Elizabeth Phillips of CMP Bits and Pieces 1 develops understanding of equivalence, ordering, and comparing fractions. The focus is on the act of partitioning into equal-size pieces, and then repartitioning and renaming smaller and smaller parts. In addition, the units focus on the various meaning of fractions: fractions as parts of whole, fractions as measures or quantities, fractions as indicated divisions, fractions as decimals and fractions as percents. Various representations are used with an emphasis on fraction strips and number line. Least common denominator is not discussed in Bits and Pieces I since the students do not need it to compare fractions. The students are encouraged to compare fractions in a variety ways through the various problems that the explore. One method which I did not expect is that some students found it easier to compare fractions by finding common numerators and then comparing denominators. Some look at how far fractions are from one or some other whole number. The same student will use different methods depending on the problem and context. They use the one that makes sense and is efficient to do within the context. If these student strategies are shared and discussed by the class, it enriches all students' understanding of fractions and in particular, equivalent fractions. You can look at some interesting student work on comparing fractions in the attachment that I am sending. See pp. 66-67. If you can not open this attachment, you can view it at our website at: http://www.connectedmath.msu.edu/rnd/past.html While we do not focus on LCD we do however, emphasize common denominators, particularly in Bits and Pieces II and Bits and Pieces III which develop the algorithms for fractions and decimals. It seems to me that requiring LCD just adds an unnecessary layer to the problem-common denominators are just as efficient. Elizabeth Phillips ephillip @math.msu.edu Hu - The back of the parent's letter states that the students should understand how to use common denominators to add, multiply numerators and denominators to multiply and use reciprocals to invert and multiply to divide, but none of this is in the student textbook which like the first version asks students to devise their own "algorithm" when you look up the page in the index for addition algorithm, etc. There is NOTHING in the books that gives a complete, correct method to any of the 4 functions with fractions. Their web SOME KIDS LIKE CONNECTED MATH, LOTS OF SUPPLEMENT NEEDED z75\clip\2003\10\cmp.txt Providence Journal Julia Steiny: Slater kids connect with math Sunday, October 26, 2003 "I'm good at this math, but I wasn't good at the other math. Actually, I was so bad at the other math that I got held back and I had to change schools. But this math . . . I don't get it all the time at first, but after awhile, I always get it. I like it." %%Algebra http://connectedmath.msu.edu/mathcontent/algebra.html In Variables and Patterns (Grade 7), students solve linear equations using a variety of methods including graph and tables. As students move through the curriculum, these informal equation- solving experiences prepare them for the formal symbolic methods, which are developed in Moving Straight Ahead (Grade 7), and revisited throughout the five remaining algebra units in eighth grade. Solve 2x + 3 = 9, x + 3 = 9 / 2, Use properties of equality and numbers to solve each equation for x: 6x + 3 = 4x + 9 %%Review http://www.pearsoned.com/RESRPTS_FOR_POSTING/MATH_RESEARCH_STUDIES/M15.%20CMP_Final_Report.pdf Most teachers like the program, but the few criticisms are scathing "STUDENTS DO NOT HAVE THE SKILLS NECESSARY TO SUCCEED IN POST HIGH SCHOOL MATH CLASSES! Unless the curriculum is heavy supplemented, students have no mastery of math facts, fractions, decimals, percents, and integers. Students at our school have used Investigation/Connected Math for the past 6 years. 3 years ago after many complaints by parents, parent/students were given a choice of Core Plus or Alg/Geometry. We currently have 13 classes of Alg and 1 class of Core Plus. Student are very poorly prepare to take Algebra. The decision to change to this reform curricula was made by administrators against the recommendation of all but one secondary math teacher." ""It teaches nothing. It does not help parents. Discovery is for science not math. Students do not know simple mult. tables, can 't read, but we are expected to have students excel????" %%Plano Texas Plano Unofficial CMP Math page \clip\99\17\conmath.txt CONNECTED MATH UNDER FIRE IN TEXAS 9/7/99 By Andrea Billups THE WASHINGTON TIMES In Texas, six families from Plano filed a class-action lawsuit late last month claiming their children were not learning in the connected math program, and were not given the option of a more traditional math course -- a violation, they say, of the Texas Education Code. The "connected math" program taught in the Plano Independent School District and used in several school districts around the nation has been criticized by parents, including several in Montgomery County, Md PLANO PARENTS SUE OVER CONNECTED / INVENTED MATH zip36\clip\99\16\planoma.txt The Plano Star Courier. Publication date - Wednesday, August 25, 1999 Parents to file lawsuit today against PISD Organizers claim the district ignored their right to offer input into their children's education By JONATHAN M. BELL Staff writer Parents of Plano students will file a class action lawsuit today claiming the Plano Independent School District ignored their fundamental right to have direct input in the education of their children. The lawsuit stems from a year-long struggle over connected math, a new middle school math curriculum. TEA finds CMP is not compliant with state standards PLANO PARENTS SUE FOR ALTERNATIVE TO HATED "CONNECTED" MATH \doc\web\99\10\planrit.txt The Plano ISD has now adopted the Addison-Wesley (Dale Seymour) Connected Math Program districtwide. In the process of doing so, they ignored, pushed aside and derided the concerned parents who noted a number of problems with the curriculum. At "informational" seminars scheduled throughout the district, officials directed that parents be forbidden from even handing out written materials regarding the program. PLANO PRODUCES DISTRICT RESPONSE TO MATH PROTESTS \doc\web\99\07\conmath.txt For those of you following our effort to rid our school district of Connected Math, here is an update. We direct mailed a petition to about 5000 families of future 6th, 7th and 8th graders and have managed to collect 500, so far, asking for an alternative math class. \clip\99\planmath.txt Parents asking state agency to look into math program School board to vote on textbook Tuesday 03/16/99 By Sandy Louey / The Dallas Morning News Plano district officials said the math curriculum in the schools need to move away from memorization and toward problem-solving and understanding Plano parents against connected math, says that 6 out of 1000 adopting is already failure for nsf math. Articles on Plano protests Letter shows how NSF funded math has sparked protest. In Plano, parental concern over neglected skills have provoked demands that the school provide alternative traditional curriculum ("School district should scrap Connected math experiment," Plano Star Courier, August 12, 1998). The administration of Plano Independent School District implemented Connected Mathematics without review or approval of the Plano School Board %%National WASHINGTON DC CMP rejected in DC suburb and Singapore Math Textbooks Piloted NORTH PENN GETS RID OF CMP z75\priv\2003\11\npenn.txt Reds1122 aol.com was instrumental in killing CMP http://www.phillyburbs.com/intelligencerrecord/news/news%5Fintell/1625921.htm Board subtracts new math program By John Anastasi http://www.zwire.com/site/news.cfm?newsid=4789671&BRD=2275&PAG=461&dept_id=466404&rfi=6 New math gets scaled back http://www.zwire.com/site/news.cfm?newsid=4800668&BRD=2275&PAG=461&dept_id=466401&rfi=6 No final answer‚ but new math is on way out http://www.philly.com/mld/inquirer/news/local/states/pennsylvania/counties/montgomery_county/3459656.htm The inquirer (a strong Merlino supporter) Their report was bias and full of incorrect data. The professors found the Ridley numbers incorrect and other incorrect info. http://209.164.32.120/smni/002/bwFamily-720x300-v01.html the letters to the editorial. I will not deal with the Inquirer because of their bias article. I wonder how they felt when we won. But the letters will give you an idea of what the opposition will try to present. http://www.thereporteronline.com/site/news.cfm?newsid=4862383&BRD=2275&PAG=461&dept_id=466404&rfi=8 Merlino's comments about NP pulling out. http://www.thereporteronline.com/site/news.cfm?newsid=4974105&BRD=2275&PAG=461&dept_id=466404&rfi=8 http://www.phillyburbs.com/couriertimes/library/2001news/863233.htm BRISTOL TOWNSHIP 'Core Plus' a plus or minus for students? A PA suburban school chooses a math program http://www.phillyburbs.com/couriertimes/news/news/0607math.htm A look at the history of these math education. http://www.csmonitor.com/sections/learning/mathmelt/p-2story052300.html LANDSDALE PA z56\clip\2002\07\mathfail.txt http://www.zwire.com/site/news.cfm?brd=2275&Nav_Sec=58218 New math gets scaled back ICHAEL ROCCO , Staff Writer 07/19/2002 The Reporter Lansdale, PA 19446 LANSDALE – New math nearly became extinct math at the North Penn School Board meeting Thursday night after a recommendation by North Penn School District Superintendent Bob Hassler on the much-debated Connected Mathematics .... was used in seventh grade last year‚ but numerous parents have complained that their children are not learning math basics... will use traditional textbooks as the foundation and base of the math program next year %%Review ================================================================== James Milgram reviews CMP Finds alleged study of CMP "evidence" is bogus. Says appears to be remedial in nature, and is confusing even to teachers. No definition of "mean". PARENTS WANT TO DISCONNECT FROM THIS MATH PROGRAM http://cmpinpisd.freeservers.com/ Connected Mathematics Disconnected Parents http://cmpinpisd.freeservers.com/page42.htm When these textbooks were reviewed for compliance to the Texas Essential Knowledge and Skills elements by the Texas Education Agency, they failed to address an average of 43.3% of those elements at each individual grade level. The teaching of Connected Math is characterized by group discovery of mathematical concepts with an emphasis on problem solving, communication, reasoning and connections (the National Council of Teachers of Mathematics goals). Due to the time consuming nature of the program, some classes only completed 4 of the 7 modules scheduled to be covered at a given grade level ================================================================ Mathematically Correct Review Grade 7 - GETS FAILING GRADE http://www.mathematicallycorrect.com/books7a.htm Mathematical Depth [1.7] There is very little mathematical content in this book. Students leaving this course will have no background in or facility with analytic or pre-algebra skills. The introduction to Part 1 says "Connected Mathematics was developed with the belief that calculators should be available and that students should decide when to use them." In one of the great understatements, the Guide to the Connected Mathematics Curriculum states, "Students may not do as well on standardized tests assessing computational skills as students in classes that spend" time practicing these skills. =================================================================== SINGAPORE MATH STINKS EXCEPT FOR MATH SKILLS AND PROCEDURES U Washington Dept of Applied Mathematics http://www.amath.washington.edu/~adams/comparisons.html Middle School Mathematics Comparisons for Singapore Mathematics, Connected Mathematics Program, and Mathematics in Context (Including Comparisons with the NCTM Principles and Standards 2000) Submitted to the National Science Foundation by the Dept of Applied Mathematics Univ. Washington Loyce M. Adams, K.K. Tun, Virginia Warfield Co-Principal Investigator, NSF projects: creating a Community of Mathematical Learners. ... Nov 2, 2000 http://www.amath.washington.edu/~adams/full.pdf Full report - How does Singapore compare since they come out at the top of international comparisons? Mathematics in context: Because MIC is so fixated on conceptual underpinnings, computational methods and efficiency are slighted. Formal algorithms for, say dividing fractions are neither taught nor discovered by the students. we feels a return to some middle ground is warranted. Students should have and understanding of equivalent fractions, decimals and percents before the middle grades. z58\clipim\2002\09\12\cmp.appendix.pdf (Connected Mathematics) CMP summary: We feel that CMP's overwhelming emphasis on conceptual development neglects standard computational methods and techniques. .. there is a danger here of producing students with conceptual understanding but limited computational skills. CMP admits that "because the curriculum does not emphasize arithmetic computations by hand, some CMP students may not do as well on parts of standardized tests assessing compuational skills as students .. that spend most of their time practicing such skills....implies we have still not achieved a balance. Singapore: http://www.amath.washington.edu/~adams/sing.appendix.pdf z58\clipim\2002\09\12\sing.appendix.pdf ..provide some unneccessarily sterotypical depictions of men and women..Does not recognize that some students learn better through guided discovery than a direct presentation... seems to be based on the view that the teacher is the primary disseminator of information. Objectives are not well aligned with those in the NTCM standards. Does an excellent job of helping students acquire mathematical facts and procedures through the many worked out examples and large number of practice problems in its textbooks. However, NCTM has identified other goals, most notably reasoning, communication, and connections (a larger conception of mathematics as a coherent whole that interacts with our world) ================================================================== GLOWING STUDIES OF RESULTS CREATED BY NSF MATH PROMOTERS http://www.csmonitor.com/sections/learning/mathmelt/p-3story052300.html TUESDAY, MAY 23, 2000 Flaws in the evaluation process Mark Clayton (claytonm@csps.com) The Department of Education's expert panel, assembled to find the best math programs in the United States, had a key problem, critics say. It relied heavily on studies of student achievement that were authored or co-authored by the directors of the programs themselves - Yet during his stint as an evaluator, Mr. Hoover also worked and studied at Michigan State, the same university that received the Connected Math project grants of more than $7.7 million. This institutional affiliation violates common standards for independent evaluation, ethicists say. ====================================================================== PORTLAND ORE FIXES KNOW FLAWS, OK WITH HATED SEYMOUR MATH \clip\99\19\conmath.txt From: cassidy@pacifier.com http://www.oregonlive.com/news/99/10/st101006.html New math settles in smoothly Portland allows modifications and adaptations, and the reception is an exception to what happens elsewhere Oregonian Sunday, October 10, 1999 By Betsy Hammond of The Oregonian staff A new way to teach math that asks students to discover concepts and probe deeply rather than memorize formulas and perform drills has generated protests in almost every large school district that has tried to make the switch. MONTGOMERY PROTESTS \clip\99\19\conmath.txt Divided on Connected Math For Some Parents and Experts, Curriculum Doesn't Add Up By Brigid Schulte Washington Post Staff Writer Sunday, October 17, 1999; Page A01 Fun? Math? Koutsos and his class at Montgomery County's Col. E. Brooke Lee Middle School are part of an experiment. Lee is one of five county schools testing a new way of teaching math. What is going on in Koutsos's classroom is at the heart of a passionate, often vitriolic debate that has shot through school districts nationwide and has now reached Montgomery. Arthur Hu Reviews: My experience: He's spending 3 hours generating some stupid chart of every possible move in a "factor game", Arthur, if your son was a homeschooler, hence a high level thinker, he would be programming his Factor Game in Logo. Dale From my free_for_a_whistle Logo1.doc: http://fehps.une.edu.au/f/s/curric/gClark/h.html Garry Clark.Information Technology and Mathematics Australia http://www.northnet.com.au/~mathsactivities/mathact.htm Mathematical Activities is a CD of 109 activities designed to reveal the level of mathematical thinking of young users and to improve their computing skills. http://www.northnet.com.au/~mathsactivities/stratgames.htm Factor Game Players, in turn, choose a number from the board and score that many points. The opponent obtains the sum of the factors of the number chosen that are available on the board. 70 PAGES BUT _NO_ INSTRUCTION ON HOW TO COMPUTE AVERAGE WITHOUT BLOCKS Text z75\clipim\2003\10\28\conmath.efx, .jpg 70 pages but the most important item in statistics, how to compute an average ISN'T THERE!!! By comparison, Saxon spends just 2 pages and spells out exactly how to compute an average. They waste no space or time on "line plots" (frequency histograms) or "steam and leaf" plots. Just ONE item on homework takes a math whiz 10 minutes out of target 30 minute homework time. %%Research ?? http://connectedmath.com/Book%20series.htm GRADE SIX Prime Time Number theory, including factors, multiples, primes and composites Data About Us Statistics, formulating questions, organizing, analyzing data. Shapes and Designs Polygons, angles, measuring two dimensional geometry. Bits and Pieces I Understanding fractions, decimals, percents, all the rational numbers. Covering and Surrounding Area and perimeter of polygons and circles. How Likely Is It? Probability: likely and unlikely. Making sense of the uncertainty of things. Bits and Pieces II Using the rational numbers (B&P I) with +,-,x,%, and division problems. Ruins of Montarek Spatial Visualization: Architectural and isometric representations. http://ra.terc.edu/publications/Alliance_Access/Vol3-No3/math-curriculum.html Choosing a Mathematics Curriculum Debbie Bird, who teaches sixth grade at Fort Fairfield, reports that the selection committee spent almost a full year reviewing mathematics curricula before selecting Connected Mathematics Program (CMP). She says it was time well spent. factor game: She realized that while her students were having fun playing the game, they were also encountering some complex mathematical concepts. " We played the factor game and then analyzed game strategies and this lead to a discussion of prime numbers, an advanced concept for my students." This hands-on experience with Connected Mathematics convinced Debbie that the program would work in her classroom. http://www.pearsonatschool.com/k12/teacher/cat Connected Mathematics , 2002: Data About Us Student Edition Extensively field tested middle school program that features an investigative approach to teaching statistics. For each investigation students do hands-on activities to discover key math concepts....SEE MORE $5.97 Grades: 6 http://www.math.msu.edu/cmp/RREvaluation/Achievement.htm#Mass Quantitative Research or Data The quantitative results consistently show that CMP students do as well as or better than other students on tests of basic skills. And CMP students outperform other students on tests of problem-solving ability (including multi-step problems), conceptual understanding, and proportional reasoning. NO HARM DONE TO 5TH GRADERS, SOLVING, BLACKS DO MUCH BETTER Lapan, R.T., Reys, B.J., Barnes, D.E., Reys, R.E. (1998). Standards-Based Middle Grade Mathematics Curricula: Impact on Student Achievement. Paper presented at the Annual Meeting of American Education Research Association in San Diego, California in April, 1998. Standardized measures of traditional mathematics achievement and mathematics problem solving were administered at the end of fifth grade for base line data and at the end of sixth grade after one full year of implementation. "No significant differences were found between the groups with respect to traditional mathematics achievement. However, students in the two standards-based curricula significantly outperformed the control group in mathematics problem solving. No gender differences in traditional mathematics achievement or mathematics problem solving were found. Mathematics problem solving scores for African American students in the two standards-based curricula were significantly higher than scores for African American students in the control group" (Lapan et al. 2). http://www.phschool.com/product_information/math/middle_grades/connected_math.html Student Materials Connected Mathematics is organized by grade level, with eight units for each grade level. 8 X 70 = 560 @@Connecting Math Concepts :) From: Keta Tom Prof. Bishop likes Saxon and Connecting Math Concepts, a Direct Instruction series published by SRA. @@Coordinate Grid %%Read points 1st quadrant (x,y positive) 3-5 Lk Wash 4 Addison Wesley Math 1991 4th WA Assessment 4 MCAS 1997 MA assessment -------------------------------- 5 Nevada 1998 7th WA Benchmark %%Plot points all 4 quadrants 6 Nevada 1998 WA 4th Grade Assessment - tell which 3 points will connect a straight line given x,y pairs. WA 4th Grade Benchmark - describe relative positions on a grid WA 7th Grade Benchmark describe location of objects on coordinate grids http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html @@Constructing Figures %%Closed Area with fixed perimeter G4 1998 MA MCAS test Construct 4 different closed areas with 2 sections of fence %%Math Problem G4 1998 MA MCAS test ---- appropriate ---- G4 1998 MA MCAS test Write 3 clues for another number game and number your clues. The game must have only one correct answer %%Parallel Perpendicular G4 1998 MA MCAS test (street, trapezoid) NA MA standards G4 1998 MA MCAS test Draw streets that are parallel, perpendicular, and intersection but _not_ perpendicular. Draw figure with four sides with 2 sides parallel and 2 sides not. %%Symmetric Figure G4 1997 WA WASL test G7 1997 WA Benchmarks @@Core Plus New NSF funded integrated math curriculum used in Michigan, perhaps least harmful of new systems, opposed by parents in many districts as too difficult for even A grade students or parents. First page of matrix chapter is all about ... the shoe business, with a one sentence mention that a matrix has rows and columns. "If Joe has an IQ of 75, Is Joe mildly mentally retarded?" Cover many topics traditionally covered in college linear algebra, or not at all, such as network theory. Does not teach basic high school solving algebra equations. Andover students who did well only got 1-5 percentile on college math placement, most had to take remedial math, were not even prepared well enough for college algebra. Study shows that Andover students who were 75th percentile in verbal were only 50 in math, while the other school with traditional math was 75th in math as well. %%abandon MARYSVILLE DUMPED CORE PLUS http://community.seattletimes.nwsource.com/reader_feedback/public/display.php?source_name=mbase&source_id=2010995832 Dorboln Marysville, WA February 9, 2010 at 9:26 AM Well said post. Discovering defintley did a lot of good in addressing many of the issues with Pure reform texts such as Core Plus as much as people are against the Core Plus series (and I am one of them), it did do a very good job of connecting equations to their graph, far better than what happens with traditional texts, which tend to just assume the student will put them together. Also, the CP approach to the quadratic formula is very good. Even though we have dumped Core Plus here, several of us still use several of the activites/investigations to augment the newer and more traditional texts. tkcris 9/23/2009 The East Valley district (Spokane) is abandoning CorePlus. Unfortunately they are phasing it out as the kids that have already started in it years past will finish in it. The curriculum will re-embrace the Glencoe traditional texts that were in storage. %Notes MILLIONS DANGLED TO SWITCH TO COREPLUS IF YOU THOUGHT THE OLD MATH WAS HARD.... z58\ahu\clip\2002\09\coreplus.txt mcall.com - Parents fear new math doesn't add up The Morning Call -- September 15, 2002 ... had received a five-year, $2.6 million grant from the National Science Foundation... to help school districts switch to standards-based math, ... Mathematics Project should find out this month if it will receive a $35 million federal grant to bring reformed math to school districts throughout the Lehigh Valley "All I see is poor grades, a lot of frustration and complaints that he hates math.''" "understanding how to solve for ''x'' in 2x + y = z doesn't do much good in Core-Plus, where one problem can require knowledge of algebra, statistics and geometry." SF CHRONICLE COVERS FAILURE OF NSF FUNDED REFORM MATH IN MICHIGAN \clip\99\08\labrat.txt High School Students And Lab Rats Debra J. Saunders Friday, March 12, 1999 San Francisco Chronicle http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/1999/03/ 12/ED101990.DTL MELISSA LYNN was shocked when she discovered that she placed in the bottom 1 percent of the University of Michigan math placement test. She had graduated from the affluent high-achieving Andover High School in Bloomfield Hills, Mich., with a 3.97 grade point average and A's in math. Full report on how Core Plus flunked out elite Andover students: ftp://math.stanford.edu/pub/papers/milgram/andover-report.htm \doc\web\99\02\pkmath.txt Backtalk Phi Delta Kappan February 10, 1999 The cover story, The Mathematical Miseducation of America’s Youth, by Michael Battista endorses the position the industry pushes..deep in the article, concedes advanced algebra students scored significantly better on paper-and-pencil algebraic procedures. see, "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later", by R. James Milgram, Department of Mathematics, Stanford University: ftp://math.stanford.edu/pub/papers/milgram/andoverreport.htm txt: \clip\99\06\coreplus.txt htm: \clipim\99\04\coreplus\coreplus.htm Andover had, at that time, a group of accelerated students who finished their high school education with calculus, because, currently, all students at Andover take Core Plus. Core Plus was phased in over a four year period. the results are not encouraging. ..almost all the Andover students were severely critical of the program, many bluntly blaming it for their difficulties in university level courses. .. by every measure such as ACT scores, SAT Math scores, grades in college math courses, core plus students fell short of Lahser students. [... even when compared with students who did not even take pre-calculus] useless for real life? the two Core Plus students at Andover who reported entering the work force directly after high school. The first of them says "The math program was good and bad. It tried to apply math to real life - but it didn't make a great attempt. I live on my own in [....], use math in all my taxes and bank account things, and I learned all that outside of the math program." other "I am currently working and feel that I cannot even do basic math calculations. I am missing too many fundamentals." "I feel that the preparation I received in H.S. with Core Plus was hardly adequate enough for college Algebra. The students were quite emphatic about where they felt Core Plus failed them. .. they did not feel it adequately prepared them for college mathematics classes. .. their basic math skills were too weak, three others felt that all they had learned from four years of Core Plus was how to use a TI 82 calculator. Median Percentile SAT-MATH SAT-VERBAL Andover, Core Plus 49 74 Lahser, Group 1 76 79 [two groups are comparable in verbal, but not in math] ANDOVER HIGH SCORES 1-5 PCT WITH CORE PLUS \doc\web\index\corefail.htm The Detroit News Metro Section June 17, 1998 Math debate heats up Professor won't give up controversial data on Core-Plus program in Bloomfield Hills By Rusty Hoover / The Detroit News BLOOMFIELD HILLS -- A math program at Andover High School that students say has cheated them out of a solid math education is now causing a second round of controversy. Detroit Free Press \clip\98\03\coreplus.txt http://www.freep.com/news/education/qmside19.htm Calculators do most of work in new math January 19, 1998 Core-Plus math is a curriculum developed at Western Michigan University. Since 1993, it been tested in 23 Michigan school districts. PARENTS FIGHT AGAINST CORE PLUS \clip\98\02\edcli2.txt Detroit Free press 1/19/98 Bloomfield parents fight for old math They say new method hurts kids BY TRACY VAN MOORLEHEM Free Press Education Writer Calculators do most of work in new math January 19, 1998 Core-Plus math is a curriculum developed at Western Michigan University. Since 1993, it been tested in 23 Michigan school districts. Instead of offering algebra, geometry and calculus as separate courses, Core-Plus integrates the major math disciplines into one four-year course, [lets students discover math rather being lectured to and memorizing] Escondiso flunks CPM, IMP, keeps core plus. Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski "Students in new math at Orange Glen, for example, scored an average of 477 on the SAT, while those in traditional classes at the same campus had average scores of 502. " "No data is available that indicates that the integrated math is a success," he said." %%review http://www.sbe.wa.gov/documents/1-15-09SBEHighSchoolMathematicsInitialrecs.pdf Rank: 1 Holt Mathematics traditional 2 Discovering traditional 5/6 Core PLus Math Integrated M1-3 @@Counting -------- Count to 10 Preschool->K age 2 - India Little Angels Kindergarten NYT 1/2/2008 K Lk Wash Count to 20 Preschool->K K Lk Wash Count to 100 Preschool->G1 G1 Lk Wash G1 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm Count to 1000 G2 CA 1993 G3 Lk Wash Count to 1,000,000 G4 Addison Wesley Math 1991 G4 Lk Wash G4 Vermont Count to 1,000,000,000 G5 Lk Wash %%Language Some "primitive" cultures don't even have words to count up to ten. But the people are capable of learning mathematics. Henry Harpening says the Northern Bushmen have words for 1-4, an expression "kills fingers for five", above that, nothing. abcdThe Naro only have words for 1, 2, 3. Francis Galton explored this area and reported how hard it was to ask Herero's for measures of distance or time as they had no words for numbers. They apparently counted to five with words one, two, three, many, and many-many. %%Monkeys MONKEYS CAN COUNT, HUMANS CAN AT 3 \clip\98\15\monkey.txt Count Monkeys Among the Numerate Study Finds Monkeys Can Count By Rick Weiss Washington Post Staff Writer Friday, October 23, 1998; Page A01 Monkeys have an innate ability to conceptualize numbers and can be taught to count at least to the number nine, according to a series of groundbreaking experiments that promise new insights into the evolution of intelligence. @@courses Even taking into consideration the high participation rate of Asians, Asians take a very high percentage (40%) of Calculus and Honors math courses, and get the best grades. Even when Blacks take the best math courses, they score more poorly than White and Asians who have taken much less math, though the White / Asian gap narrows by 75% when both take calculus. Blacks with the most math still scored lower than Asians with less than 1/2 year of high school math study. \doc\95\14\mathtake.wk1 Source: SAT scores from The College Board, special compilation SAT Took Calculus W23%(1.0) B12%(-1.9) H16%(-1.5) A40%(2.0) Increase 1990-95 W21% B33% H23% A5% Nearly half of Asian SAT takers have taken Calculus, twice the rate of whites, who are two times the rate of Blacks. However minorities show the most improvement. \doc\95\12\sat95bk.xls 1995 Scholastic Aptitude Test Breakdown by Ethnicity Data from the College Board Data Entry and Analysis by Arthur Hu White Black Hisp Asian SAT Math Coursework pct Gap math pct Gap math pct Gap math pct Gap math Overall 0 498 -110 388 -72 426 40 538 Algebra 97 0 498 96 -110 388 97 -73 425 94 37 535 Geometry 95 0 504 90 -109 395 94 -73 431 94 36 540 Triginometry 55 0 539 43 -106 433 42 -68 471 64 26 565 Precalculus 38 0 573 24 -104 469 32 -77 496 54 18 591 Calculus 23 0 613 12 -105 508 16 -76 537 40 13 626 Computer Math 9 10 10 13 Black Calculus is equal to Whites who took Geometry, Asian Algebra, or Hispanic precalculus Asians advantage falls to 13 points with Calculus vs. 40 overall Nearly half of Asians took Calculus, 2X rate of Whites, 4X rate of Blacks White Black Hisp Asian Years of Study pct verb math pct verbal math pct verbal math pct verbal math 4 70 521 62 406 62 451 77 558 3 27 450 33 361 35 390 20 469 2 3 402 4 332 4 356 3 449 1 0 395 0 319 0 329 0 428 1/2 or less 0 435 0 330 0 372 0 434 honors 29 597 18 487 25 518 42 619 42% (nearly half) of Asians took honors math courses compared to 29% White, 18% Black Black 4 year = White 2 year, Hisp 3 Year, Asian 1/2 year or less Blacks who took honors courses (487) still less than Whites overall (498) Asian honors is highest, even higher than Asian $70,000+ income @@CPM (College Preparatory Math / Integrated Math) CPM is an "integrated" math curriculum which does not require students to master and complete learning of basic concepts before going on to more advanced topics. Tigard-Tualatin (OR) school board voted to abandon the program in 2009 http://www.tigardtimes.com/news/story.php?story_id=124231554279260600 CPM a casualty of TTSD math war In a split vote, the school board sides with Parents for Math Choice and decides to return to a more traditional math program By Christina Cooke The Times, May 14, 2009 ...Parents for Math Choice, who said the CPM curriculum was not working for their children. “Given the level of unrest this adoption has caused in our community and even among our teaching staff, I’d prefer to take a step back to a more conservative approach,” “I don’t think it’s fair to throw out CPM when we haven’t used it for a year because it has a few gaps" teacher ... "“We see them understanding concepts more easily and much more deeply.” %%Against Mathematical ly Correct Escondiso flunks CPM, IMP Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski Effectiveness of CPM vs Traditional Math by a Robert W. Haswell, a high school teacher Traditional students trounce those taught algebra with CPM SECOND SEMESTER ALGEBRA FINAL EXAM SCORES GRADES TRADITIONAL CPM A 29.1% 4.5% B 25.5% 6.7% C 14.5% 9.0% D 18.2% 16.9% F 12.7% 62.9% Median 42 27 These figures show that 54.6% of the traditional students earned A or B grades on the multiple-choice portion of the final exam, while 11.2% of the CPM students earned A or B grades. This is almost FIVE TIMES as many A's and B's earned by the traditional students as the CPM students. It can also be seen that 79.8% of the CPM students earned D or F grades, while 30.9% of the traditional students earned D or F grades. Where's the Math http://www.intres.com/math/_disc2/0000004f.htm New Math From: High School Teacher Date: 30 Jan 1997 I only wish we had more parents in Ca. that would check out the new math that is being forced on many of us that teach math. I thank you for speaking up . I teach CPM1 and Trig at Xxxxxxx in Xxxxxx, Ca.I feel that mathland at the lower level anddrop from the group, indicate this in a message to the group and I will contact our postmaster requesting the change. %%For http://www.cit.state.vt.us/educ/alliance/programs.htm Included on a listing of successful programs self-identified by schools on the 1996 Vermont Alliance Survey. http://www.service.com/PAW/morgue/news/1996_May_29.MATH.html Palo Alto Weekly Wednesday May 29, 1996 SCHOOLS: Math program nears adoption Board to choose between two courses Thursday. Creative Publications' "MathLand," a popular and innovative, hands-on approach to math which has no textbook; Everyday Math has no text, but includes a journal which can be used as a workbook and a textbook and integrates basic concepts with newer approaches. KENT JUSTIFIES AND EXPLAINS EVERYDAY MATHEMATICS Philosophy Statement "What is Everyday Mathematics© and why are we involoved with it?" We have also heard about how poorly our students score in mathematics compared to other countries. Everyday Mathematics© attempts to remedy this problem by giving your child a wide range of mathematical experiences and ideas. We achieve this by integrating mathematics instruction into other curricular areas, like science, social studies, and the language of mathematics. @@Democratic vision EPAA Vol. 9 No. 11 Cochran-Smith: Constructing Outcomes in Teacher ... ... researchers, and policy makers committed to a democratic vision of society and to the vital ... Relationships between research and the NCTM standards. ... epaa.asu.edu/epaa/v9n11.htm http://www.ingentaconnect.com/content/routledg/ueee/2004/00000037/00000004/art00007 Review of the Year's Publications for 2003: Social Justice Education Authors: Susan Allen; Marcella Runell; Rani Varghese; Tanya Williams; Maurianne Adams; Elaine Whitlock Source: Equity & Excellence in Education, Volume 37, Number 4, December 2004, pp. 360-376(17) Publisher: Routledge, part of the Taylor & Francis Group [RTF] Theoretical Perspectives for Developmental Education File Format: Rich Text Format - View as HTML ... the significance of difference to a democratic vision of the future. ... the National Council of Teachers of Mathematics (NCTM) articulated a set of ... www.gen.umn.edu/research/crdeul/rtf/monograph/1-theoretical.RTF [PDF] 174 Wednesday Morning, April 13, 2005 File Format: PDF/Adobe Acrobat - View as HTML Achievement and NCTM Standards in Algebra I Classrooms. Belinda Gimbert, Pennsylvania State ... Mapping Diversity of Democratic Vision/Imagination for ... www.aera.net/uploadedFiles/Meetings_and_Events/2005_Annual_Meeting/Program/174-201%20Wednesday%20Morning.pdf Powell's Books - Education A collection of insights into what a democratic vision of literacy looks ... Dozens of ready-to-go activities to develop the NCTM's essential math skills. ... www.powells.com/usedbooks/Education.30.html Ensuring Equity and Excellence in Mathematics Behind Goals 2000 and the NCTM standards is the conviction that all students ... understand and share the democratic vision that underlies the Standards and ... www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm NCTM: News & Media: Past President's Messages NCTM and Democratic Principles In its long history, NCTM has rarely been ... Six important points to know about the vision of mathematics education set ... www.nctm.org/news/pastpresident/ http://www.nctm.org/news/pastpresident/2003-01president.htm NCTM once published some very useful yearbooks. Not only did NCTM once publish some very useful yearbooks, but it still does. Consider the most recent titles in the yearbook series: * 2002: Fractions and Rational Numbers * 2001: The Roles of Representation in School Mathematics * 2000: Learning Mathematics for a New Century * 1999: Developing Mathematical Reasoning in Grades K–12 * 1998: The (NOT) Teaching and Learning of Algorithms in School Mathematics * 1997: Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity I could go on with titles, but only the last one might be incorrectly construed as a "politically correct" publication as opposed to a "useful" book about mathematics. In each of the yearbooks, including the latter, NCTM has taken the stand that (1) all students can learn mathematics; (2) all students are valued in the process; and (3) not all students learn in the same way, so a teacher should know different ways to teach mathematics. These stands are simply restatements of basic principles stated in Principles and Standards for School Mathematics. If these stands represent "political correctness," then the Council should never waver. @@Dilation G8 WA 2007 Draft standard G7 NYS preserved and not preserved under a reflection, rotation, translation, and dilation ... www.emsc.nysed.gov/3-8/module8.doc G8 SC KCSD Curriculum Resources Apply dilation to a square, rectangle, or right triangle www.kershaw.k12.sc.us/district/curriculum/pacing_guides/pacing_math/grade8_math-curriculum_map.doc @@Discovering Algebra Discovering algebra and geometry by key curriculum press Seattle Math presentation http://www.seattleschools.org/area/board/08-09agendas/040809agenda/mathpresentation.pdf 2009-3-8 WA HS Curriculum StudyFile Format: PDF/Adobe Acrobat - View as HTML mathematics is by leaving important mathematics undefined and assumed. Parabolas are one case in point. In Algebra, on page 447, students are given the ... www.math.jhu.edu/~wsw/ED/SThs.pdf "Besides the flaws shared by all the programs, Discovering and Glencoe are mathematically unacceptable for additional reasons. Discovering places more emphasis on the study of graphs rather than the study of quadratic functions. Glencoe presents many unexplained, unjustified rules and procedures related to algebraic skills. Neither program helps students build an understanding of the structure of algebra." Only textbook graded as "unacceptable" OSPI Final Composite Score2 ST Mathematical Soundness Rating Holt 0.838 Meets minimum standard Discovering 0.835 Unacceptable Glencoe 0.826 Approaches minimum standard Prentice Hall 0.820 Unknown McDougal Littell0.783 Unknown CorePlus 0.780 Approaches minimum standard Condemned by Wheres The Math, nearing adoption by Seattle in 2009 Discovering Algebra Everett Parent complains about fuzzy Algebra http://www.youtube.com/watch?v=n340ROI8uYc&feature=channel_page @@Drill vs @@Deep Understanding PARROTS VS DEEP UNDERSTANDING 1960S AND NOW z74\clip\2003\10\mathdrill.txt http://www.newswithviews.com/Erica/Carle9.htm THE MATH WARS - 1960's REVISITED Erica Carle October 13, 2003 NewsWithViews.com @@Equity MULTICULTURAL AND GENDER EQUITY http://www.nctm.org/news/pastpresident/2003-01president.htm NCTM once published some very useful yearbooks. Not only did NCTM once publish some very useful yearbooks, but it still does. Consider the most recent titles in the yearbook series: * 1997: Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity See equity and excellence Ensuring Equity and Excellence in Mathematics Behind Goals 2000 and the NCTM standards is the conviction that all students ... understand and share the democratic vision that underlies the Standards and ... www.ncrel.org/sdrs/areas/issues/content/cntareas/math/ma100.htm @@Everyday Mathematics A Review of Everyday Math, by Tsewei Wang, Ph.D. (Department of Chemical Engineering) and J. Douglas Birdwell, Ph.D. (Department of Electrical and Computer Engineering)University of Tennessee http://www.lit.net/orschools/A_Review_of_Everyday_Math.pdf z75\clipim\2004\01\22\A_Review_of_Everyday_Math.pdf A summary overview: "Constructivist Mathematics in the Oak Ridge Schools" (Updated April 10, 2001) iposted at: http://www.lit.net/orschools/ z75\clip\2003\11\angrydiv.txt http://www.nypost.com/news/regionalnews/10120.htm New York Post ANGRY DIVIDE By CARL CAMPANILE November 6, 2003 -- A war over the city's new math curriculum erupted yesterday, with parents complaining they're befuddled by the new ways of teaching math - and so are their kids. ""We are starting to get a trickle of complaints from parents that are having trouble understanding parts of Everyday Mathematics and Impact Mathematics. Providing forums for parents to meet to get information and ask questions will alleviate many concerns,"" @@Factors G4 CA 1998 G4 MCAS 1998 prob 15 (convert class of 36 to 1/2, 1/3/ 1/6) G5-8 Mass Framework 1996 G4 CA 1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm The Standards require that students know the definition of prime numbers and know that many whole numbers decompose in different ways. G5-8 Mass Framework 1996 http://www.doe.mass.edu/doedocs/frameworks/Mathnumsense.html Grades 5-8 Learning Standards @@Federal EXPERTS ATTACK MATH TEACHING PROGRAMS \clip\99\20\nomath.txt http://www.latimes.com/news/learning/19991118/t000105076.html Los Angeles Times September 17, 1999 page A3 Education: Top mathematicians and scientists urge U.S. to withdraw endorsement of methods that leave out basic skills. Federal official says change is unlikely. By RICHARD LEE COLVIN, Times Education Writer Nearly 200 top mathematicians and scientists, including four Nobel laureates, are urging U.S. Secretary of Education Richard W. Riley to withdraw the government's endorsement of math programs that experiment with nontraditional teaching methods. SAUNDERS SKEWERS DeptED PUSHING FAILED FUZZY MATH TEXTBOOKS \clip\99\19\whermath.txt Where's the Math? San Francisco Chronicle DEBRA J. SAUNDERS Sunday, October 17, 1999 THIS MONTH, the U.S. Department of Education came out with a list of 10 ``exemplary'' or ``promising'' math education programs. Kings County fourth-grade teacher Doug Swords was shocked at the department's bad choices. Some three years ago, his school district adopted MathLand, a math curriculum that prefers not to give lessons with ``predetermined numerical results.'' The department of Educrats, oops, I mean, Education, rated MathLand as ``promising.'' DofEd BLESSES INVENTED MATH PROGRAMS October 6, 1999 Ed. Dept. To Release List Of Recommended Math Programs By Debra Viadero set this week to confer its seal of approval on 10 programs for teaching mathematics to students in kindergarten through 12th grade. [Every one reflects the under-fire NCTM standards which have drawn fire] ZIP37\clip\99\18\badmath.txt For More Information "Exemplary and Promising Mathematics Programs" is scheduled to be available online at www.enc.org/. Print copies are also available by calling (877) 4ED-PUBS. Connected Mathematics, designed for students in grades 6-8 Core-Plus Mathematics Project, an integrated high school program Interactive Mathematics Program, an integrated, problem-based high school curriculum Pact Algebra, a full-year, technology-based course for students in grades 7-12 Programs recommended for "promising'' status: Everyday Mathematics, a program for grades K-6 Mathland, also for grades K-6 Middle School Mathematics Through Application Project Number Power, a supplemental program for grades K-6 University of Chicago School Mathematics Project, a six-course curriculum for grades 7-12 SOURCE: U.S. Department of Education @@Fractions Grade level comparisons learn about fractions G1 Indiana www.doe.state.in.us/standards/docs-Math/2006-Math-Grade01.doc compare fractions with models G3 numbernut http://www.numbernut.com/standards_3.html G3 CA Compare fractions by drawings or concrete materials www.cde.ca.gov/be/st/ss/mthgrade3.asp G4 Ohio Use models and points of reference to compare commonly used fractions http://www.ohiorc.org/standards/ohio/grade/mathematics/grade4.aspx compare fractions with like denominators G3 Mathematically Correct http://www.mathematicallycorrect.com/kprea.htm compare fractions with common denominators compare fractions using common denominators 12 or less G4 Mathematically Correct http://www.mathematicallycorrect.com/kprea.htm G5 NY State Compare and order fractions including unlike denominators http://www.emsc.nysed.gov/ciai/mst/mathstandards/revisedg5.html G6 VA SOL compare and order 141.104.22.210/go/Sols/math6.doc NO G6 Connected mathematics %%Against \CLIP\2007\12\NOFRACT.TXT FRACTIONS SHOULD NOT BE TAUGHT UNTIL AFTER CALCULUS Educators divided by fractions debate http://www.delawareonline.com/apps/pbcs.dll/article?AID=/20071226/NEWS03/712260337/1006/NEWS Penn prof's book aims to ignite math ideas By MAUREEN MILFORD, The News Journal Posted Wednesday, December 26, 2007 "Our kids ... want to know why they are forced to do complicated and difficult calculations," said Dennis DeTurck, dean of the college of arts and sciences at the University of Pennsylvania. (Buy photo) Special to The News Journal/EMILY VARISCO Dennis DeTurck argues that as mathematics has evolved, so must the teaching of mathematics. PHILADELPHIA -- A few years ago, Dennis DeTurck, an award-winning professor of mathematics at the University of Pennsylvania, stood at an outdoor podium on campus and proclaimed "Down with fractions!" "Fractions have had their day, being useful for by-hand calculation," DeTurck said as part of a 60-second lecture series. "But in this digital age, they're as obsolete as Roman numerals are." "He believes fractions are important for high-level mathematics and scientific research. But it could be that the study of fractions should be delayed until it can be understood, perhaps after a student learns calculus, he said. Long division has its uses, too, but maybe it doesn't need to be taught as intensely." %%1/N One of N equal pieces G2 CA http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm %%M/N Is division of M into N equal pieces G4 CA G5 Minnesota sample test (which pie is 3/5) CA standard 1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm The fraction m/n represents the equal division of m into n equal pieces. %%Unlike denominator Adding / Compare / Subtract or decimal 4th 2000 CA STAR assessment 4th Addison Wesley 1991 4th MA MCAS assessment ------------------------ G5 1998 CA Standards (vs assessment) G6 1998 Nevada G6 1940s Nebraska Ommitted NO CMP2 G6 compare fractions, no instruction for +,-,*,/ NO TERC G5 add, subtract, compare fractions http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm The fourth-grade Standards do not require any arithmetic with fractions; however, practice with addition and subtraction of fractions (like denominator) must be continued in this grade, because they become very important in fifth grade. G5: Adding fractions with unlike denominators and multiplying and dividing fractions. %%Part of Whole to Fraction G4 1997 MA Assessment 6 out of 36 students convert to pie slice G5 1998 MN Assessment (10+5+3+2 votes to pie slices) %%Reducing Fraction G4 1998 MA MCAS test (convert 18 out of 36 to 1/2) G4 1998 MN Assessment (convert 10/20 to 1/2) ---- appropriate ---- G6 1998 CA standard G6 1998 CA standard When reducing a fraction, the greatest common divisor of the numerator and denominator can be used as the common factor. %%Multiply set by fraction %%N/M fraction of whole number Traditionally covered at middle school, moved down as low as G4 Not G2 1998, 2005 CA Mathematics Framework www.erusd.k12.ca.us/ProjectALPHAweb/index_files/CA_MF/GLC&AoE_2.pdf "Students should not be expected to solve "2/3 of 15" numerically in second grade, because doing so requires them to multiply fractions and convert an improper fraction to a whole number." -------------------------------------- G4 1998 Scott Forseman math G4 1997 MA Assessment 1/2 x 250 G4 1997 WA Assessment 2/3 x 30 G5 1998 CA standard G5 Minnesota Assessment 5/6 x 24 G7 1980 Mathematics Unlimited G8 %%Convert Fraction to Decimal G4 MA 1998 Assessment (number line) ---- appropriate ---- G4 CA 1998 Teaching G6 Nevada standard 1998 G4 CA Teaching of the conversion of fractions to decimals http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm %%Multiply Large Number by Fraction G4 1998 MCAS Problem 15 (convert 6/12/18 out of 36 to 1/6-3-2) G4 WASL sample (mowing lawn) ---- appropriate ---- G6 CA 1998 standard There are 24 students in our class. two thirds of them passed the test. How many students passed the test?" %%Compare, Order Compare with same denominator 4th Core Knowledge 4th CA Math Framework WA 4th Grade framework identify, compare, and order whole numbers and simple fractions http://cisl.ospi.wednet.edu/ComSL/MATHBMK1.html Compare with different denominators Performance based assessments routinely test for this in 4th grade but most standards based benchmarks leave this to grade 7. Some tough standards like CA mention this in G5, but no standards mention this in grade 4. CA '98 4th Grade MA 4th Grade Assessment - compare 3/4 and 5/7 WA 4th Grade Assessment - compare probability based on fractions with different denominators, or dilution with different denominators. CA G5 11/1998 WA 7th Grade Benchmark - compare and order whole numbers, fractions, and dec imals http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm 11/1998 Students can use fraction equivalence skills in order to compare fractions 5/1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm#k-3 Understand the values of fractions with denominators to 12, including ordering or comparing fractions and mixed numbers with unlike denominators and the equivalence of decimals and fractions in simple cases %%Convert Fraction to Decimal and Percent G5 CA 1998 http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G5 CA 1998 Fractions can be represented as decimals and as percents. @@Fundamental Changes California Mathematics Council May 1, 1993 Dear CMC Members: Last year the State of California issued a new Mathematics Framework for California Public Schools that recommends **fundamental changes in** the way we teach math. @@Gambling Slot machine has 3 items, but I can't find the odds on a typical machine of a jack pot. How many items per reel? @@Gender GENDER MATH GAP SMALLER IN ASIANS, BUT OBSERVERD FOR ALL CULTURES from http://www.mugu.com/cgi-bin/Upstream/Resources/misc.html upstream website "Among....mathematically gifted 13-year olds, [sex] differences favour males in mathematical reasoning ability, but not in verbal reasoning, where there are no [sex] differences. Our gifted males score approximately one half of a standard deviation higher than females on the SAT-M, our measure of mathematical reasoning. Males' SAT-M scores are also more dispersed {yielding an upwardly shifted distribution of male scores (Benbow, 1988, Behav.& Brain Sci.11}. The resulting proportion of males and females at age 13 at various cut-off scores on SAT-M is approximately as follows: > 500 (average score of college-bound 12th-grade [18-year-old] males): 2 : 1; > 600 : 4 : 1; > 700 (top 1 in 10,000 for 7th graders [13-year-olds] :13 : 1. These ratios have remained relatively stable over the past 20 years, and have now been observed among mathematically gifted students in the 3rd grade (8-year-olds), and cross-culturally (though they are smaller in Asian populations)." Camilla P. BENBOW & D.LUBINSKI, 1993, in Ciba Foundation Symposium 178, The Origins and Development of High Ability. Chichester : Wiley-Interscience. MALES SAT ADVANTAGE DOES NOT SHOW UP IN GENERAL POPULATION \clip\2002\01\gendtrail.txt Girls barely trail boys in mathematics http://www.eurekalert.org/pub_releases/2002-01/uonc-nsg011002.php Public release date: 11-Jan-2002 Contact: David Williamson david_williamson@unc.edu 919-962-8596 University of North Carolina at Chapel Hill New study: Girls barely trail boys in mathematics (SAT) About four times as many boys scored above 600 as girls did, and about 13 times as many boys scored above 700, she said. A male advantage was also evident among college-bound high school seniors. ... Among the findings were that girls had higher average math scores than boys until about age 11 and higher reasoning scores at ages 11 to 13. BOYS ONLY 1.5% BETTER AT MATH THAN GIRLS? z54\clip\2002\01\mathgend.txt http://www.suntimes.com/output/news/cst-nws-math13.html Boys may not be better at math after all January 13, 2002 BY TRISH WILSON investigators at the University of North Carolina at Chapel Hill published a report... They found that girls had higher average math scores than boys until about age 11 and higher reasoning scores at ages 11 to 13. Boys did tend to progress faster, and by the end of high school that learning edge resulted in a 1.5 percent advantage over girls, which is very small, Leahey said. \clip\98\19\gendmath.txt Kianian, Amin M., Gender and mathematics achievement parity: evidence from post-secondary education.., Vol. 116, Education, 06-01-1996, pp 586(7). (electric library) With respect to different aspects of mathematics achievement, the general consensus seems to indicate that females tend to perform better than males in computation, and males tend to perform better than females in problem solving (Hyde et al., 1990). Better verbal ability for girls and spatial ability for boys is also frequent finding (Maccoby and Jacklin, 1974; Werdelin, 1985; Kaur, 1992). A meta-analysis of the studies that have been done during the period of 1974-1987 on mathematics and gender has produced two general conclusions. First, the average gender gap is very small and statically insignificant. Second, the gender differences have declined over the years (Friedman, 1989). \clip\98\04\edbrief1.txt Ruth Schubert, "Boys develop an edge in math very early" Seattle Post-Intelligencer, February 3, 1998, B1 According to a University of Washington study of 276 mathematically precocious children, even before they reach first grade, more boys than girls are exceptionally talented in math. @@Geometry %%Congruent G2 Texas Core Curriculum http://www.trinity.edu/departments/education/TCKC/2math97.htm G3 California G3 Virginia G4 Addison Wesley Mathematics 1991 G4 Wisconsin %%3D Shapes Pyramid G4 Addison Wesley Mathematics 1991 G4 TAAS test G4 WA Assessment G3-5 Lk Wash G10 WA Benchmark @@Parallel %%Parallel Lines Lines or line segments which are in the same direction and will not meet. Grade Spectrum G1 A.G Bell 1999 1st/2nd grade class G4 Exploring Elementary Mathematics 1970 Holt Rheinhart Winston G4 MCAS G4 Core Knowledge G4 Addison Wesley Mathematics 1991 G4 Wisconsin G4 California http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G4 Washington Assessment G5-8 Colorado 1998 Standard %%Perpendicular G2 Texas Core Knowledge http://www.trinity.edu/departments/education/TCKC/2math97.htm G4 Mass MCAS G4 Core Knowledge G4 Addison Wesley Mathematics 1991 G4 California http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G4 1970 Holt Exploring Elementary Mathematics G5-8 Colorado 1998 Standard NA 1964 Addison Wesley %%Radius, Diameter G3 Japan G4 California G4 Wisconsin G5 Virginia G7 Washington %%Right Angle G4 Core Knowledge %%Similar Triangles, Proportionality 4 WA Asssessment (no 4th grade curriculums cover this) 7 VA Standards 7 WA Benchmark 8 NAEP Assessment Standards 8 Wisconsin Standards 9 British Columbia Standards Virginia Standards http://www.pen.k12.va.us/go/Sols/math.html The seventh-grade standards place emphasis on solving problems involving consumer applications and proportional reasoning. Wisconsin Standards Mathematics: http://www.wisgov.state.wi.us/MSMath.htm 8th grade: ratios and proportions (e.g., rates, scale drawings*, similarity* ) BC Standards http://www.est.gov.bc.ca/curriculum/curric/inmath11.htm http://www.est.gov.bc.ca/curriculum/curric/apag9.htm NAEP Standard G8 http://www.projmath.caltech.edu/index.htm Project Mathematics video series is for high school students. BC standards G9, G11 solve problems using the concept that, in similar triangles, corresponding sides are proportional WA G4 = use similar triangles to determine height of flagpole from fire hydrant shadow. WA Benchmark http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html understand the concepts of ratio and direct proportion @@Grade 1 Long time homeschooler and scientist Art Robinson: Our curriculum requires that, during the first year of school, the student learn to read well and also learn the addition, subtraction, multiplication, and division tables through 12s by instant, rote memory. http://www.robinsoncurriculum.com/ negative review: http://eho.org/features/robrev.htm @@Grade 2 z39\clipim\99\12\05\catfish.efx 2nd grade Catfish Soup My 2nd grader got this "Get Your Hands on Problem Solving Grade 2" - requires adding 3+6+9+12+15+18 = 63! Carla Cat sold catfish soup in her cafe this week. Carla sold 3 bowls. On Tuesday she sold 6 bowls. On Wednesday she sold 9 bowls. On Thursday she sold 12 bowls. If the pattern continued, how many bowls of catfish soup did Carla sell on Saturday. Bonus: How much soup did she make all week. Make up a price, how much money did she make? Comment - pattern is OK, but it is not appropriate to add up 7 2 digit numbers manually without instruction, 2nd grade is generally adding 2, maybe 3 number with carry. Multiplication was also not covered in this class. @@Grade 8 ONLY 1/3 OF 8TH GRADERS TAKING PRE- OR ALGEBRA, HALF OF ASIANS The 1990 NAEP Trial State Assessment California: 59% 8th grade math vs 36% pre-algebra or algebra, pre/algebra white 43% black 27% Hispanic 23% Asian 55% 30 min homework Nation 62% / 34%, 15-30 min homework @@Grade Level G=Grade level Multiply 3 x 2 digit G4-G5 323 x 45 Multiply money G5-G6 3.23 x 12 Multiply by decimal G5-G6 1.23 x 1.23 Divide 2 dig by 1 dig G3-G4 12 / 2 Div by 10s G4 120 / 20 Long Divide 3 dig by 1 dig G3-G5 124 / 2 Long Divide 3 dig by 2 dig G3-G6 122 / 12 Money division G4-G5 1.24 / 2 Long Divide 3 decimal by 3 decimal G5-G7 1.234 / 2.345 * many states no longer require teaching long division Probability G4-G7 (coin = 1 in 2, 1 marble out of 6) * pre-1970 textbooks do not cover probability in elementary school Pi, circumference G5-G6 Algebra - 8th to 9th grade (about half of Americans don't take algebra at all)

Graph

@@Graph graph y = 3x G4 CA 2000 STAR sample test
@@Great Mathematicians MATHEMATICS LIBRARY AT COLUMBIA U HAS PC MATHEMATICIAN PICS from h-bd 4/2002 John wrote: On the wall in the main room of the Mathematics Library at Columbia University are four huge pictures of mathematicians. Left to right, they are: Henri Poincaré, Sofia Kovalevskaya, Carl Friedrich Gauss and Emmy Noether. Male, female, male, female. .. A personal (but not particularly unfair) ranking of these 4 people by the magnitude of their mathematical talent, among all the mathematicians of history, would be something like: 8, 253, 1, 179

@@Guess and Check Tables

Grade Level Spectrum -------------------- G2 Eric AG Bell 2000 G4 Scott Forseman Math G4 WA WASL 4th grade sample problem (no solution given) G5 New Progress in Mathematics homework (no solution given) --- inappropriate ---- G7 Passport to Algebra and Geometry New assessments and textbooks expect 4th and 5th graders to solve unknowns such as 2x + 3 (x + 3) = 59 5x + 9 = 59 5x = 50 x = 10 which will be solved in minutes by algebra by constructing a table or making a drawing of all possible outcomes based on an initial,guess x=5 x+3=8 * ... x=9 12 56 x=10 13 59 Considering that any job that requies this skill will require algebra, this is a total waste of time better sprnt on teaching arithmetic.
Parent says his gifted son was able to guess and check a solution too. No algebra required?? Eric in 2nd grade AG Bell 2000: Guess and check: 63 cents of pennies, nickels and dimes same dimes as pennies, 3 more nickels than dimes how many (algebra problem!) 5th graders expected to solve for unknowns by constructing guess and check table instead of using algebra taught at grade 9. This is problem solving?? Passport to Algebra and Geometry (7th or 8th grade pre-algebra) tells how to solve a problem like this, and also shows how to use a table to solve the problem. source: http://project2061.aaas.org/newsinfo/press/attach_c.pdf \clip\99\03\attach_c.pdf @@Higher Standards Why does everyone have to be rocket scientist in the 21st century? Answer: this IS no reason other than as an excuse to spend more money on useless reforms. The Mystique of Math and Science in American Education and The Big Con in Education By Dennis W. Redovich What is the rationale for high stakes testing in mathematics and science for promotion and graduation in public elementary and secondary schools? @@Hispanic Achievement \clip\98\08\latmath.txt http://www.edweek.org/ew/current/31nctm.h17 Education Week 4/15/98 Latino Students' Math Scores Climb While Family Income Drops Washington [oh no, a study that shows that you don't have to wait for middle class equality with whites to achieve better] The math achievement of Latinos improved from the early 1970s to the early 1990s nationwide despite the simultaneous shrinkage in the family income for that group and the rise in Latino child poverty, a study by a California researcher shows. ...conflict with earlier research and challenge what the author argues is a widely held assumption among educators that the math achievement of students from lower income levels improves only as their socioeconomic condition improves. @@History MATH CONTENT BALLOONS FROM BASICS IN 1900S http://www.freepress.com/news/education/qmath30.htm zip36\clip\99\17\mathhist.txt Math topics multiply through years Texts add lessons as technology alters educational goals August 30, 1999 BY TRACY VAN MOORLEHEM Detroit FREE PRESS EDUCATION WRITER "The slim books [from the 1900s] are, in many cases, half as tall as their modern counterparts and a third as thick...In the last century, dozens of topics have been added to math curricula. The only topic that has fallen away, Ball said, is some of the bookkeeping arithmetic that was included in the early 1900s...It fueled a movement, which continues today, to make algebra more universal. More and more districts, including Detroit Public Schools, have an algebra requirement in middle or early high school. At the same time, mathematicians began to see the importance of adding statistics -- the study of the collection and analysis of data. " @@Holt Mathematics %%Review @@Homeschool http://www.oaknorton.com/SLTrib-grip.cfm Alpine in grip of 'math wars' Some parents reject the move from traditional teaching By Celia Baker The Salt Lake Tribune Disgruntlement over a math program that emphasizes conceptual understanding and downplays rote learning caused parents there to pull children out of neighborhood schools in favor of charter, private and home schools; circulate a petition calling for abolishment of "fuzzy" math curricula; and threaten to use a newly enacted law to form their own school district. z47\clip\2000\12\math1.doc Dale Reed's homeschool notes, recommends http://www.robinsoncurriculum.com/ mostly negative review at http://eho.org/features/robrev.htm and Saxon. @@Homework A big complaint about new-new math is homework the parents can't understand DON'T EVER GIVE US AN ASSIGNMENT LIKE THIS AGAIN OR LOSE RECESS I found out that the reason it was undone was because they did not understand HOW to do the work. I sat down and took a look at it. You (the paper) have got to be kidding!!! TEARFUL HOMEWORK HOUR Juanita Doyon 5/2001: The problem with the wonderful new curriculum is that it totally discounts the power of numbers in ones head and the power of studying for understanding rather than sweeping past and catching the crumbs. Trouble is, when kids catch nothing but crumbs at school for whatever reason, and are then sent home with work their parents can't comprehend, they don't even get table droppings of math, much less "higher level thinking skills." All they get is tearful homework hour and parents tearing their hair out! @@How http://www.amazon.com/gp/reader/0805831053/ref=sib_dp_pt/105-7617436-0319658#reader-link Fostering Children's Mathematical Power: An Investigative Approach To K-8 Mathematics Instruction Arthur J. Baroody, Ronald T. Coslick $77.13 (How do do math with TERC, EM, Mathland, etc.) "You probably have no difficulty determining the answer to 1/2 + 1/89. More than likely you would invert the divisor 1/8 and multiply. The point is that you have probably mastered the mechanics of elementary arithmetic -- you know how to add with renaming (carrying or borrowing), how to multiply with decimals, how to divide with fractions, and so forth ... but most teachers do not understand why these procedures work".. "why is it important for you to develop proficiency with such mathmematical processes as problem-solving, reasoning, conjecture-making and -testing and communicating? ... you may have had little or no experience in solving challenging mathematical problems @@Injury and @@Intrusive Survey DALE SEYMOUR G5 INTRUSIVE SURVEY INVESTIGATION | image http://www.arthurhu.com/2004/07/injury.txt Arthur Hu 7/25/2004 Investigation 5 * Session 1 --------------------------- Data: Kids, Cats, and Ads [And serious injuries???] "I felt nervous. I was nervous becuse its' hard to answer your problems and injuries in front of another person. " @@Issaquah 2003: The elementary grades have Trailblazers. the middle school has MaTHEmatics. The high school is in their second year of CPM (College Prepatory Math). @@Important Reformers say that the basics aren't important anymore, we need charts, statistics, higher order reasoning skills ACT: COLLEGE PROFS THINK BASIC MATH, NOT STATISTICS IS IMPORTANT A http://www.act.org/news/index.html May 9, 2000 Most basics: addition, subtraction, multiplication division, ratios, percentages algebraic equations statistics Least Z42\clipim\2000\06\23\actmath\actmath.htm similar pattern followed in teaching students to compute probability. Seventy-two percent of college teachers thought it not important while 41 percent of high school teachers thought it very important. The educators were in agreement, however, about teaching the basics: addition, subtraction, multiplication, division, ratios and percentages. College faculty chose addition, subtraction, multiplication and division as the most important skills to have, while high school teachers chose them as second most important, behind performing very simple algebraic equations. [Most state math assessments put most emphasis on statistics, not arithmetic] @@improvement SAT MATH ABOVE 650 DOUBLES FROM 1981 TO 1995 Bracey says SAT math scores are up Here are the relevant numbers: 1981 1995 # Above 650 70,307 132,898 % Above 650 7.1 12.4 # Taking SAT 993,672 1,067,993 \priv\96\16\educcruc.txt Education Week Volume 15, Issue 33, May 8, 1996 "Education Crucial in Modern Economy By Jeff ArcherThe report acknowledges some gains by the public schools, such as the doubling from 1982 to 1992 in the proportion of high school graduates who took advanced algebra, geometry, and trigonometry. \priv\95\10\betmath.txt - US students have improved by about one year of study in math tests from 1982 to 1992, and are taking more math courses. Reading and writing have not improved as much @@Integrated Schedule In an integrated schedule, one school's plan only spends 15 minutes per day on math.

G1-3 Schedule = 15 min math @@Integrated Math Courses (IMP, McDougall Littell) The NSF funded several integrated high school math programs, most of which have gotten terrible reviews from people who make a living with mathematics. Old: Spend one entire class learning how to solve y = mx + b. New: Spend class on 50 topics covering college level statistics, precalculus and linear algebra, and 1 page on solving y = mx + b. %%Critic (http://www.atmos.washington.edu/~cliff/Mathematics.ppt) \doc\web\2006\04 Excellent presentation on Integrated Mathematics by Professor Cliff F. Mass. %%General NEW CA STANDARDS PROPOSES INTEGRATED GEOMETRY ADDED TO ALGEBRA IN 8TH GRADE \clip\97\25\edclip11.txt Nov 5, 1997 "The fact that [the standards for] 8th grade changed from an algebra class to a mathematics class incorporating algebra and geometry is very consistent with what most other countries in TIMSS do," Mr. Schmidt wrote in a September letter to the commission. [mostly Asian countries]..He also objects to the introduction of geometry in the 8th grade, noting that many teachers at that level are not trained in the subject, and the integration of Algebra 1, geometry, and Algebra 2 throughout the high school grades. "The basic problem is that they spread all this material all over hill and dale," Mr. Evers said. "Overall, I don't think that if you have requirements, you should experiment with a whole state population of children. You should have only a proven, research-based curriculum. , rather than algebra, trigonometry, and geometry. It's just a minor detail that colleges have specific math entrance requirements, which the integrated math courses fail to meet. @@Interactive Mathematics Program (IMP) @@IMP A popular integrated college prep math program that emphasizes problem solving skills. Home Page Discussion Listserver< /a> Mathematical ly Correct IMP DELAYS QUADRATIC FORMULA UNTIL G12 ZIP37\clip\99\18\lamath.txt From: "Mike McKeown" Home Page The Interactive Mathematics Program (IMP) is a growing collaboration of mathematicians, teacher-educators, and teachers who have been working together since 1989. This group has created both an exciting full four-year secondary mathematics curriculum and a rich professional development program for secondary mathematics teachers. This new curriculum meets college entrance requirements and prepares students to use problem-solving skills in further education and on the job. "The IMP curriculum integrates traditional material with additional topics recommended by the NCTM Standards, such as statistics, probability, curve fitting, and matrix algebra. IMP units are generally structured around a complex central problem. " "Dr. Webb has found that IMP students do as well as students in traditional mathematics classes on standardized tests such as the SAT. This is especially significant because IMP students spend about 25 percent of their time studying topics that are not covered on these tests. To measure IMP students achievement in these other areas, Dr. Webb conducted three separate studies involving students at different grade levels and in different locations. The three tests used in these studies involved statistics, quantitative reasoning, and general problem solving. In all three cases, the IMP students outperformed their counterparts in traditional programs by a statistically significant margin, even though the two groups began with equivalent scores on eighth grade standardized tests." A Problem-Based Mathematics Curriculum IMP is designed to replace the four-course sequence typical of most high school mathematics programs with an integrated course. While the traditional Algebra I-Geometry-Algebra II/Trigonometry-Precalculus structure emphasizes rote learning of mathematical skills and concepts, the IMP curriculum is problem-based, consisting of four-to-eight-week units that are each organized around a central problem or theme. The "interactive" aspect of IMP refers, in part, to the program's emphasis on students interacting with each other by working in groups. Together, students tackle problems that usually are too challenging to be solved by any one individual %%Failure %%Failure Escondiso flunks CPM, IMP Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski "Students in new math at Orange Glen, for example, scored an average of 477 on the SAT, while those in traditional classes at the same campus had average scores of 502. " ""No data is available that indicates that the integrated math is a success," he said. " Whitney Young Teacher wonders if IMP is math for dummies. Students want real algebra and fear they will get stomped by traditional algebra students. http://www.math.uic.edu/~cpmp/archive9701.html The Interactive Mathematics Program Listserver \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN (New math, math reform backlash against "fantasy lunch") http://www.math.uic.edu/~cpmp/archive9701.html School offers students a choice, only 1/4 chooses reform math. " In trials across the country, IMP students have done no worse--but no better--on college entrance exams than students taught traditionally. Still, Martinez believes weaker students stick with math longer because they enjoy the unconventional approach." %%Anti FEATURED HORROR STORY BY WEEKLY STANDARD The Weekly Standard August 4, 1997 EXAM SCAM The Latest Education Disaster: Whole Math By Lynne V. Cheney Senior Fellow, American Enterprise Institute my file: \clip\97\20\examscam.htm "They lied to me, says Madalyn McDaniel of Atascadero, California. They completely betrayed me..." Received $9 million in federal funds for development. %%General Key Curriculum Press IMP Home Page Check out this exciting mathematics curriculum! The Interactive Mathematics Program is being heralded across the country as one of the freshest breaths of air in today's 9-12 mathematics classrooms. @@Intersect G3-4 New Jersey G4 Mass MCAS G4 Big Horn County Co too low ------------ G6 North Rockland New York ------------ appropriate G6 North Rockland Central School District N.Y http://norock.lhric.org/curric/curric.htm Math Curriculum http://norock.lhric.org/curric/mathgr6.htm G4 Big Horn County School District Wyoming http://w3.trib.com/~rmhs/district/currelemmath.html#fourth Identify how lines, rays, and segments are related to one another (perpendic ular, parallel, intersect). Standard 7 - Geometry and Spatial Sense - Grades 3-4 New Jersey Mathematics Curriculum Framework http://dimacs.rutgers.edu/nj_math_coalition/framework/ch07/ch07_03-04.html They recognize the concepts of point, line, line segment, ray, plane, intersecting lines, radius, diameter, inside, outside, and on a figure. @@Invented Math If you're leery of invented spelling, you'll love invented math. It is harmful to teach standard methods, so you must rely on kids to invent their own methods, so the research says. NCTM STANDARDS 2000 - INVENT MORE THAN ONE METHOD http://standards.nctm.org/protoFINAL/chapter5/number.html In the past, common school practice has been to present a single algorithm for each operation. However, more than one efficient and accurate computational algorithm exists for each arithmetic operation. In addition, if given the opportunity, students naturally invent methods to compute that make sense to them (Fuson forthcoming; Madell 1985). The conventional algorithms for multiplication and division should be investigated in grades 3–5 as one efficient way to calculate. Regardless of the particular algorithm used, students should be able to explain their method and should understand that many methods exist. 728/34: One was conventional, but she "didn't understand". Henry used an offbeat useless method, but he understood. Twenty 34s plus one more is 21. I knew I was pretty close. I didn't think I could add any more 34s, so I subtracted 714 from 728 and got 14. Then I had 21 remainder 14." http://standards.nctm.org/protoFINAL/chapter4/number.html In some cases, their strategies for computing will be close to conventional algorithms; in other cases, they will be quite different. Many times, students' invented approaches are based on a sound understanding of numbers and operations, and they can often be used efficiently and accurately. Some sense of the diversity of approaches students use can be seen in figure 4.3, which shows the ways several students in the same second-grade class computed 25 + 37 Moreover, students who used invented strategies before they learned standard algorithms demonstrated a better knowledge of base-ten concepts and could better extend their knowledge to new situations, such as finding how much of $4.00 would be left after a purchase of $1.86 MANIFESTO FOR INVENTED MATHEMATICS \clipim\99\05\08\nctm\nctm.html \clip\99\10\nctm.txt http://www.nctm.org/jrme/abstracts/volume_30/vol30-01-hiebert.html Journal for Research in Mathematics Education January 1999, Vol. 30, No. 1, Page 3-19 Relationships Between Research and the NCTM Standards James Hiebert, University of Delaware If ability to invent procedures to solve new problems is emphasized in the standards, then the research on students' creative problem solving is of great interest. Standards increasingly emphasize young students' inventions of arithmetic procedures because, in part, we know they are capable of such inventions. Mathematical inventions by students are not included in the Standards simply because students are capable of inventing; they are included because an additional value judgment has been made--that invention is an important mathematical process. EVERYDAY: TEACHING STANDARD ALGORITHMS FAILS - STUDENTS SHARE INVENTED MATH http://www.chattanoogafax.com/email .htm WEEK OF November 17, 1999 \clipim\99\20\evmath.txt California Rejects It After Reviews that Basic Methods Aren't Emphasized "They are free to choose their own method" he writes and then quotes from the curriculum's 3rd Grade Resource Book: "Drill tends to become tedious and gradually loses its effectiveness.....Everyday Mathematics believes in children sharing their own invented algorithms rather than teachers continuing to teach the standard paper-and-pencil algorithms as such....Research shows that teaching the standard algorithms fails with large numbers of children." @@Japan Standards Mathematics Program in Japan (Kindergarten to Upper Secondary School) Japan Society of Mathematical Education January, 1990. $4.75 Reprint by US Dept of Education, US Govt Bookstore ORAD 97-1029 Kindergarten - 4 hrs per day, 39 weeks per year - "children feel interested in numbers, quantities, and geometrical figures" 1st Grade - 2 digit numbers - add, subtract 1 digit - apply 1 digit to simple 2 digit add/sub - counting - comparing - sum / difference - direct measurement - read clock - +, -, =, ones, tens 2nd Grade - 4 digit numbers - add / subtract 3 digit numbers carry borrow - multiplication table 1x1 digit number - = > < not equal - measure in metric meter, liter - triangles, quadrilaterals, right triangles - tables and graphs 3rd Grade - ten thousands - 10 times, 100 times , 1/10 - multiply 2 or 3 by 1 or 2 digit numbers, - multiply in column form - division - divide in column form by 1 digit - decimal fraction, common fraction - abacus / soroban adding, subtracting - gram, kilogram, kilometer - compute time - isosceles equilateral triangles - angles - center, diameter, radius of circle - bar graph - numerator, denominator, second, equal, not equal, divide 4th Grade - measure angle - measure area of geometric figure - hundred million, trillion, billion - rounding - divide by 2 digit number - add sub fractions with common denominator - add decimals - multiply and divide whole numbers - measure area of squares and rectangles - degrees, half-rotation, full arc - parallel, perpendicular - parallelogram, trapezoid, rhombus - cube, rectangular paralleopiped - position of object in space - draw graph from table - fill in variable quantities in frames (square) - plane, proper fractino, improper fraction, quotient, 5th Grade - percent - read pie chart - Investigations: consruct pie chart with 1/10 tics - multiply and divide decimals - compare fractions - least common denominator - add and subtract different denominator fractions - area of triangle, parallelograms, trapezoid - area of polygon by triangle - area of circle - volume of cube and parallelopiped - per unit concept - speed - congruence - pi = ratio of circumference to circle to diameter - use letter x instead of square frame - circle graph, tape graph - common denominator, greatest common divisor, sector, central angle, per cent 6th Grade - divide = multiply by reciprocal - multiply and division as fraction - volume of pyramid, cylinder, circular cone, surface area - proportional relationships - line and point symmetry - scale drawings - ratio - direct proportion - inverse proportion - use table and graph in frequency distribution @@Japan Style The Japanese are said to have implemented US style reforms in their math, but this really isn't true. STEVENSON DOWN ON NCTM STANDARDS NCTM are fuzzy standards that aren't helpful to most students or teachers, and aren't what the Chinese and Japanese do. I met and talked with the author of this article Wayne Bishop this past weekend in California. Incidentally he was the Math teacher of Jamie Escalante of "Stand and Deliver". He has Japanese books, materials, and lessons that were translated to english, along with the TIMSS study, to prove his point. Wayne is an exciting man with extensive knowledge and background. It was a pleasure talking with him. Dr. William Pfeifer http://ourworld.compuserve.com/homepages/mathman/wbishop.htm Math Lessons from Japan The TIMSS and the Truth For the Record - LA Times page A3, 1/15/97 Math teaching--A Jan. 5 article in The Times on math instruction stated incorrectly that a Reform curriculum called the Interactive Mathematics Program is widely used in Japan. It is not. [The Japanese drill very hard on basics, the teacher is definitely in charge, and there is a right answer, and a best way to solve a problem.] @@Job http://www.kiva.net/~pdkintl/kappan/kbra9810.htm The Eighth Bracey Report on the Condition of Public Education By Gerald W. Bracey .. our obsession with math and science, which has led us to overstate the number of people who need high skills in these fields. Borrowing from the study by Anthony Carnevale and Stephen Rose (discussed in "The Statistics from Thin Air Award"), Samuelson concludes that scientists, computer scientists, engineers, accountants, programmers, and business financial officers -- people who need advanced math or science skills -- account for 4% of the work force. @@Kindergarten Usually - count to 10 - colors - shapes Sphere - California, WA draft 2007 Multiplication - WA draft 2007 Grandma went to visit her three grandchildren and discovered they each had holes in every finger of their gloves. She will sew up their gloves. How many glove fingers need to be fixed? %%India \priv\2008\01\indiaschool.txt http://www.nytimes.com/2008/01/02/business/worldbusiness/02japan.html?_r=2&ref=education&oref=slogin&oref=slogin India’s more demanding education standards are apparent at the Little Angels Kindergarten, and are its main selling point. Its 2-year-old pupils are taught to count to 20, 3-year-olds are introduced to computers, and 5-year-olds learn to multiply, solve math word problems and write one-page essays in English, tasks most Japanese schools do not teach until at least second grade. @@Kumon Math Centers Popular math tutor program Some links: http://www.kumon.com/home/ Kumon.com http://family.go.com/Features/family_1997_10/dony/dony107cramschools/dony107 cramschools2.html http://www.ncneuropsych.com/links.htm This is strange! The link to KUMON Math & Reading on a "psych" page! http://www.mcs.net/~shs/schools/math_howtorespond.html Down on the page toward the bottom is the ref to Kumon http://www2.gol.com/users/milkat/alternative.html A Japanese Home-Schooling resource site. http://www.socialresearch.nu/bellpedr.html "all-purpose" good site! It has info on much! @@Least Common Denominator Dale Seymour Investigations Grade 5 does NOT teach least common denominator to compare fractions, but uses fraction lines and a bunch of other ridiculous ways. LCM CAUSES FEAR OF FRACTIONS http://www.delawareonline.com/apps/pbcs.dll/article?AID=/20071226/NEWS03/712260337/1006/NEWS Posted by: Jerome Dancis- Thu Dec 27, 2007 12:17 pm 1. Striking fear in students while teaching fractions. A popular method for teaching addition of fractions (using the LCM) “has struck fear in students for many generations” warns the Mathematics Framework for California Public Schools Chapter 3 Page 154. And, in Appendix A Page 274, it warns: “Many students find these concepts (LCM and GCF) confusing” and advises against teaching the two concepts (LCM and GCF) in “succession”. But books do teach them in “succession” (and at least one book may double the confusion by teaching them in the same lesson.) There is more on “fear of fractions” and “things that terrorize … students” on Page 152. 2. Good ways to teach fractions. @@Least Common Multiple The least common multiple of 10 hot dogs and 8 bugs is union of prime factors: 2 x 5 union 2 x 2 x 2 = 2 x 2 x 2 x 5 = 40 Silly no-brainer method - contructs a guess and check table. Grade Level Ranking 4 WA Assessment (there are NO 4th grade curriculums which teach this!) 5 San Marino School Dist 5 Tatnall School 5 Bill Evers K12 standard ---- appropriate ---- 6 Nevada 1998 6 Ping Wang 6 Prince William County 6 Learn Online 6 CA 1998 standard 6-8 Lk Wash ---- too low ---- 7 VA Standards 7 WA Benchmark 7 Ontario Activities 8 Wisconsin 8 NAEP 8 Kentucky Core Content http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.h tml http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm Least common multiple Wisconsin G8 http://www.wisgov.state.wi.us/MSMath.htm B.8.6 Model* and solve problems involving number-theory concepts such as least common multiples NAEP Use factors and multiples to model and solve problems http://www.nagb.org/pubs/math/mchap3.html San Marino School District 5th grade http://www.san-marino.k12.ca.us/~valentine/fifth/fifthcu.html Ontario Ministry of Education and Training http://www.edu.gov.on.ca/eng/document/curricul/activity/day1/ d1-g7-me.html Mathematics: Grade 7 TOPIC: Multiples FOCUS OF ACTIVITIES: common multiples least common multiples Learn Online http://www.learnonline.com/aec_mathematics_mathematics6.htm Mathematics Content Standards for grades K-12 Submitted by Bill Evers, Commissioner http://www.rahul.net/dehnbase/hold/platinum-standards/alt5. html Grade 5 2.10 Students determine the least common multiple and the greatest common divisor of whole numbers. Novi Meadows School http://itc.novi.k12.mi.us/nmtech/objectives6.html 1609 Find least common multiple given I and 2 digit numerals. The Tatnall School 1501 Barley Mill Road Wilmington Delaware 19807 http://www.ravenet.com/tatnall/MScurric/MS5curr.html The fifth grade students completed their unit on number theory by learning h ow to find the greatest common factor and least common multiple of pairs of numbers. WA Assessment - determine least number of packages need to match up buns (10) and hot dogs (8) WA Benchmark 7th grade http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html understand the concepts of prime and composite numbers, factors and multiples, and divisibility rules http://204.122.127.80/MATH/GRADE6.HTM Prince William County Schools standards VA Standards 7th grade http://www.pen.k12.va.us/go/Sols/math.html#Grade Four 7.2 The student will find common multiples and factors, including least common multiple and greatest common factor. Ping Wang's Home Page http://juliet.stfx.ca/people/fac/pwang/mathpage/grade6.html @@Level Education Week Quality Counts "Race and Demography" Lynn Olson http://www.edweek.com/qc/intros/race.htm 1/98 Nationally, roughly 55 out of every 100 white and Asian students complete Algebra 2 and geometry. Only 35% of African-American and American Indian seniors take this math. Although one in four white seniors takes physics, only one in six black seniors and one in seven Hispanic seniors completes this course. \clip\97\24\edclip1.txt 10/26/97 Sacramento Bee Proposed math standards divide state's educators By Deborah Anderluh Bee Staff Writer The proposed standards call for every student to learn algebra, geometry and most of advanced algebra between grades eight and 10. Source: California State Department of Education Students who complete: 44% algebra 25% geometry 14% advanced algebra 6% trigonometry and calculus ONLY 7% OF NAEP 17 YR OLDS DEMONSTRATED BEGINNING ALGEBRA Shockingly few students perform at the top competency level (above 350). To reach that score on the math portion of the NAEP students need only demonstrate "the use of beginning algebra." Yet in 1996 only 7 per cent of 17- year-olds scored in this category. NATIONAL REVIEW, October 27, 1997 Right Data, Ed Rubenstein Riley Hauls Out Less-Than-Fresh Math Findings in Education Blitz By Millicent Lawton \clip\97\25\edclip5.txt The Education Department reports one in four 8th graders took algebra in 1996, according to data collected as part of the National Assessment of Educational Progress, vs 1 in five in 1992. @@Marxist Is this from Mao's China or the NCTM standards?? "Hungry Ghosts" by Jasper Becker (The Free Press, 1996, ISBN 0-684-83457-X.) True scientists were peasants filled with intuitive knowledge and led by Party members driven by revolutionary fervor...we reject the fetishism of figures which holds us in thrall...We reject the multiplication table as the basis for policy.'" "The People's Daily reported how students in one faculty of science and mathematics showed their disdain for basic theory by putting decimal points in the wrong place while others deliberately made mistakes when calculating square roots." @@Mastery Learning z87\clip\2005\04\mymathlab.txt http://www.mymathlab.com/ Our proposed solution to the problem is to change the system for teaching entry level math courses at DeVry to a mastery learning approach, supported by Pearson Education's MyMathLab software. Mastery learning is an educational philosophy, theory, and instructional strategy developed by Benjamin Bloom of the University of Chicago in the mid-1960s. In essence, mastery learning uses feedback and correctives to bring increasing numbers of students to a predetermined mastery criterion. It has been used successfully in thousands of classrooms @@Mathematical power PENCIL AND PAPER HINDERS REAL MATHEMATICAL POWER z39\clip\2000\01\leiwand.txt It's Time To Abandon Computational Algorithms By Steven Leinwand (2/9/94)/Education Week It's time to recognize that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it's time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous. GOOGLE FINDS ONLY ONE MATCH "WHAT IS MATHEMATICAL POWER" http://www.mste.uiuc.edu/courses/ci332fa02/ Elementary Mathematics Instruction What is mathematical power? The National Council of Teachers of Mathematics (NCTM) has called for fostering the mathematical power of ALL students (1989). In its most recent articulation of Principles and Standards for School Mathematics (2000), NCTM has reinforced this call with a clear vision for school mathematics. Mathematical power involves * a positive disposition toward mathematics (e.g., the interest and confidence to learn and to use mathematics), * the skills to conduct mathematical inquiry (e.g., problem solving and reasoning skills), and * understanding (well-connected knowledge). This course considers how K-8 instruction can foster each of these components of mathematical power. MATH POWER PART OF NEW CALIFORNIA FRAMEWORK, BUT NOT DEFINED did Richard Lee Colvin blow the whistle on this pseudo-educational junk when it was first promulgated? Dom Rosa California Mathematics Council May 1, 1993 Dear CMC Members: Last year the State of California issued a new Mathematics Framework for California Public Schools that recommends fundamental changes in the way we teach mathematics. In this packet, you will find a general summary of this Framework, titled, "They're Counting On Us: Mathematics for Your Children's Future" and seven inserts for teachers that elaborate on topics such as curriculum and assessment. Although these inserts can be read in any order, we suggest the following sequence: What is Mathematical Power? Moving Beyond Exercises Assessing Mathematical Power http://math.coe.uga.edu/tme/issues/v10n1/3davis.pdf DF] What Seems to be Happening in Mathematics Lessons? Findings from ... File Format: PDF/Adobe Acrobat - View as HTML The 1998 NCTM Yearbook on algorithms notwith-. standing, we note that the last NCTM Yearbook ad-. dressing classroom issues, such as the role of practice, ... The Standards of the National Council of Teachers of Mathematics (NCTM, 1989) referenced by Forgione call for a balance of procedural and conceptual knowledge so that students gain mathematical power. Mathematics Curriculum Framework: Achieving Mathematical Power ... The core concept of this Massachusetts Mathematics Framework is that students develop mathematical power through problem solving, communication, reasoning, ... www.doe.mass.edu/frameworks/math/1996/content.html - 31k Fostering the mathematical power of children with behavioral ... 'Fostering the mathematical power of children with behavioral difficulties: the case of Carter. from Teaching Children Mathematics in Reference & Education ... www.findarticles.com/p/articles/mi_hb3451/is_200104/ai_n8218343 Amazon.com: Mathematical Power: Lessons from a Classroom: Books ... Amazon.com: Mathematical Power: Lessons from a Classroom: Books: Ruth E. Parker by Ruth E. Parker. www.amazon.com/Mathematical-Power-Lessons-a-Classroom/dp/0435083392 Children’s Mathematical Power It seems to me to be appropriate, for the purposes of initiating this discussion on Developing Children’s Mathematical Power , that an example of a child ... www.nku.edu/~sheffield/edgellpbyd2.html [PDF] MATHEMATICAL POWER FOR ALL STUDENTS K-12 File Format: PDF/Adobe Acrobat - View as HTML mathematics to express. mathematical ideas. precisely. Build a connection from. everyday, familiar language to. the power and precision of ... fcit.usf.edu/math/resource/mathpower/fullpowr.pdf (FACT standards) C&I 332: An Investigative Approach to Elementary Mathematics ... What is mathematical power? The National Council of Teachers of Mathematics (NCTM) has called for fostering the mathematical power of ALL students (1989). ... www.mste.uiuc.edu/courses/ci332fa02/ - 14k - Cached - Similar pages Date: Mar 27, 2000 3:40 PM Author: Domenico Rosa Subject ... What is Mathematical Power? Moving Beyond Exercises Assessing Mathematical Power Getting Started What is a Unit? Growth Patters: An example of a Unit ... mathforum.org/kb/plaintext.jspa?messageID=715845 - 6k - Supplemental Result - Cached - Similar pages TEACH MATHEMATICS FOR SOCIAL JUSTICE oslund home What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? ... www.msu.edu/~oslund/ - 14k - Supplemental Result - Cached - Similar pages TE 803: Professional Roles and Teaching Practice--Elementary Mathematics What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? In the upcoming semester, Joy, along with 18 interns in MSU's teacher certification program, will grapple with these big ideas while navigtating the day-to-day experiences of the internship. @@Linear Algebra @@Matrix Arithmetic Grade Level ------------------ Matrix addition, subtraction, scalar multiplication G8-9 Virginia Algebra I (achieve) G9-12 Utah (all) G11-12 Algebra 3 DODDS G9-12 Michigan (all) Matrix multiplication Matrix inversion NA WA NA Virginia G10 McDougall Little Integrated Math 2 Matrix solve systems of equations ----------------------------------- G12 Oregon CAM G9-12 New Mexico Use matrices to solve linear systems. @@Line Segment (line AB segment CD) G2 Texas Core curriculum http://www.trinity.edu/departments/education/TCKC/2math97.htm @@Logo Seymour Papert's turtle based programming language is a favorite of constructivists and people who advocate use of technology. Was a fad in New Zealand. Dale Seymour devotes an entire book to Logo in the third grade even though it admits most schools don't have an adequate number of Mac computers to use the unit. z50\clip\2001\07\logo.txt EducationNews.org Date 06-Jul-2001 Headline Improving numeracy: It is time to revisit logo! Logo was once heralded as the touchstone for raising educational standards through computer use. However, like so many things in our educational systems all over the globe, it was something of a passing fad. @@Long Division The toughest calculation on paper method is long division (dividing by numbers more than 1 digit), some believe that it has been made obsolete by the calculator, but others believe it should still be taught and assessed. TERC not only omits long division but claims mathematicans no longer use long division notation. Spectrum ------------------- 4th WA Assessment 5th Lake Washington NO New-New math CA '97 Standard \clip\98\03\reed\reed.htm PROPOSED NEW-NEW MATH CA STANDARD WOULD DROP LONG DIVISION http://ourworld.compuserve.com:80/homepages/mathman/reed.htm (Mathematically Correct) For the record, the omission of long division with 2 or more digit divisors was a conscious decision. I pointed out in writing and in oral comments before the Commission that this was missing. Undoubtedly some thought long division obsolete; others probably thought teachers would teach long division and that it need not be specifically mentioned. The problem with this latter view is that since long division was not an explicit expectation under the Commission's standards, teachers and testmakers could and would in good conscience omit it. Since it would not have appeared on a state standards-based test (had one been created under the Commission's standards), it would have widely been dropped from textbooks and curricula used around the state. Bill Evers Commissioner, Academic Standards Commission @@Mathematically Correct %%Against MATHEMATICALLY CORRECT ATTACKED AS ARM OF CONSERVATIVE RIGHT \clip\99\06\mathco.txt Are the traditionalists mathematically right? Columnist Rick Casey, San Antonio Express News Feb. 22, 1999 Our friends at the conservative Texas Public Policy Foundation have taken on another task. They want to teach your children math. Mathematically Correct named themselves, apparently with no sense of irony. They have several things in common with the left- wing politically correct. Both include intelligent, well- intentioned people. Both are ideologically based. Both are intolerant of those who think differently. And while the politically correct have an idealized view of the future, Mathematically Correct has an idealized view of the past. Improvement among Texas fourth- and eighth-grade students on another standardized test, the National Assessment of Educational Progress, has been among the best in the nation since 1990. @@Mathland Mathland is a complete K - 6 (OBE) Math program from Creative Publications. They say they are rigorous, but it is another OBE all students can learn, but we won't drill them on basics, let's let them spend a week talking about our dream house project math system. It features cutting out a "fantasy lunch" and writing about or doing plays about why 1+3=4. It has no textbook. Mathematical ly Correct MATHLAND REFUSES TO TEACH KIDS HOW TO MULTIPLY TWO NUMBERS! ZIP37\clip\99\18\lamath.txt From: "Mike McKeown" Mathematically Correct Links z46\doc\web\2000\11\mathland.txt http://www.southcountyjournal.com/sited/retr_story.pl/33642 SUMNER SCHOOLS Math program lacking Shortly after the beginning of the 2000/2001 school year, I began to question the recent adoption by the Sumner School District of Mathland in Grades K-6. SANTA ROSE FLUNKS MATHLAND SR board frowns on MathLand program Oct. 15, 1998 By ROBERT DIGITALE Press Democrat Staff Writer Santa Rosa school board members voiced strong displeasure Wednesday night with the results of the MathLand math program and directed their staff to work immediately to help students improve basic computation skills. \clip\98\14\mathland.txt DRAW AND KILL Diary of a Mad Math Teacher While lovers of new-new math trash the old math as Drill and Kill, they've sadly replaced it with Draw and Kill. Many children must be bored out of their skulls with all the drawing, cutting and pasting and writing about why 3+1=4. Leona notes that her students are itching for more equations. Indeed, on more than one occasion, they have said to her, ``Can we do some real math now?'' MATHLAND BLAME FOR SCORE DECLINE IN SF Thursday, Aug. 15, 1996 · Page A 4 San Francisco Examiner Mixed math test results leading S.F. district to rethink methods Students in City's elementary, high schools lose ground on basic skills test; superintendent cites new curriculum Venise Wagner "Superintendent Bill Rojas partly attributes the lesser elementary school performance to the district's year-old math curriculum. Called Mathland, it emphasizes concepts and problem-solving rather than rote drills. Rojas speculated that because 40 percent of the district's primary school children entered without preschool experience, many were not ready for such a conceptual approach. " http://www.sfgate.com/programs/srch_archive/srch_archive_ wrap?unregistered= true&WAISdocFile=/WAISlink/examiner/ archive/1996/08/15/NEWS16113.dtl&WAISdb Name=/doc_root/wais/ examiner/1996&WAISaction=retrieve&WAISdocID=5387710402+ 2+0+0& WAISheadline=Mixed+math+ MATHLAND IS _NOT_ RIGOROUS MATH, BASED ON OBE ASSUMPTION THAT ALL STUDENTS ARE CAPABLE LEARNERS (Tennisons from Oregon) DOD PARENTS RISE UP AGAINST MATHLAND From: "Michael L. Bledsoe" Date: 1997/05/14 Message-ID: <3379B4C5.4001@msw0.attnet.or.jp> Newsgroups: alt.internet.yokota.general (math correcct) This site is about Mathland and the other "fuzzy math" programs that the bureaucrats in the DoD schools, as well as those in the states, are using to replace quality education. About a year or so ago, Stars and Stripes printed a number of letters from concerned parents about these programs. The controversy was strong enough that here in Misawa there were even meetings with parents to show us that Mathland wasn't as bad as we had heard. Test Your Kid's Math Ability From: "Richard C. Webb" Date: 1997/06/20 Message-ID: <33AAD076.3E2@webblabs.com> Newsgroups: wi.general,milw.general Here is a link to the math placement test given to 12 year olds in Japan: http://www.japanese-online.com/math/index.htm Test your high school sons and daughters. Your middle-schoolers will likely fail miserably. If they do, demand a written explanation from your school's superintendent. Many schools in Wisconsin are using math curricula proven to result in failure to learn math. A few of these boondoggles are: Algebra: Themes, Concepts, Tools; Creative Publication Quest 2000 (Addison-Wesley) Quasar Everday Math (UCSMP) Mathland (Creative Publications) From someone whose boys have successfully dodged the New-New Math, best of luck to all of you in avoiding these abusive curricula. Richard C. Webb Hartland %%For Subject: Re: Just what is Mathland From: Central School Date: 1996/10/01 Message-ID: <32506332.7937@bc.cybernex.net> Newsgroups: k12.ed.math I am a fifth grade teacher in a district in northern NJ that adopted MathLand last year. We are beginning our second year with this program from Creative Publications. We are generally happy with the program. The children are asked to analyze their thinking as they complete math projects. In addition to practice with computation in context, they are encouraged to estimate, consider alternative solutions (when appropriate) or alternative methods, and communicate their findings. http://www.cit.state.vt.us/educ/alliance/programs.htm Included on a a listing of successful programs self-identified by schools on the 1996 Vermont Alliance Survey. http://www.service.com/PAW/morgue/news/1996_May_29.MATH.html Palo Alto Weekly Wednesday May 29, 1996 SCHOOLS: Math program nears adoption Board to choose between two courses Thursday. Creative Publications' "MathLand," a popular and innovative, hands-on approach to math which has no textbook; Everyday Math has no text, but includes a journal which can be used as a workbook and a textbook and integrates basic concepts with newer approaches. @@Math Central Math Central seems extremely dumbed down, covers 1-10 numbers in 2nd grade. Houghton Mifflin. Poor review of math central. Principal tells parents to hire tutors and supplement at home. @@Math Expressions - Replaced TERC in Bellevue - Preferred by teachers and students over TERC - Math Expressions does not have a student textbook(?) - Invented methods means it is still not truly traditional %%adopt http://www.wheresthemath.com/2008/03/09/bellevue-school-board-to-vote-on-new-elementary-math-curriculum/ http://www.wheresthemath.com/local-groups/bellevue-school-district/ Bellevue adopts math expressions to replace TERC investigations in 2008 "I can't believe how awful [TERC] it is in comparison to Math Expressions." "Math Expressions is the best the teacher has ever seen." "thrilled that he actually had a book that he brought home" %%algoritms. Mercer Island Math Fair 2009: "the actual teaching in grades 3-5 is having the students try out what they like and personally adopt their favorite. Many of these ME invented algorithms are 2 pass algorithms suitable for mental arithmetic but not well suited for paper. Like left to right subtraction." D. Myerson @@Math Power New buzzword thrown about by 90's reform math, used by CA reformers and Houghton Mifflin. @@Math Trailblazers MATH TRAILBLAZERS ANOTHER CONSTRUCTIVIST NIGHTMARE http://www.illinoisloop.org/mathtrail.html A review of Kendall/Hunt’s Math Trailblazers Second Grade, Unit 11: "Ways of Subtracting with Larger Numbers" By Rebecca P., April 2002 Any way but the standard way is OK. z55\clip\2002\04\mathtrail.htm @@ASVAB Military Entrance Exam ASVAB REQUIRES MANUAL ARITHMETIC Our senior high son just came back from taking the Military ASVAB Entrance Exam. No calculators are allowed to be used on the test. Students are to compute all calculations by hand. This included calculating square roots, long division which contained 3 digits in the divisors-- into decimals, complex multiplication, and various other tedious math computations. My son thanked me for reteaching long division to him 2 summers ago. I would have added calculation of square roots by hand if I had known. I guess the military wants their recruits to be strongly competent and efficient in classical math. Colleen F. Kennewick Here's one question with square roots: The value of the sq. root of 164 to the nearest integer is: A. 18 B. 108 C. 42 D. 13 @@Average @@Mean, Median, Mode, Range Most Likely Value 4th Grade New Standards (given raisins in 12 boxes, what is most likely value) 4th KIRIS released (given candy in 12 bags, organize, what is most likely value Average - informal splitting 2nd Exemplars Mean = Average = sum / number 4th MCAS assesment 4th Vermont (begin simple concepts) 4th Addison Wesley 1991 --------- assessment appropriate ------- 5th Ommitted by Investigations / TERC 5th Addison Wesley 1964 5th Holt 1970 5-8 Vermont - appropriately use 6th Connected Mathematics V2 (ommitted from V1) Median/Mode/Range 4th Kentucky KIRIS Assessment 4th WA Assessment 4th Wisconsin 4th New Standards 5th Kentucky Core Content Standards 5th Nevada 6-8 Lk Washington 7th BC Standard 7th WA Benchmark (4th = rough centrality) 13 Not on SAT test HOMEWORK - EVERYTHING _BUT_ AVERAGE zip63\clipim\2003\01\07\mathhome.efx Homegrown homework sheet has frequency histogram, range, median, mode, but NOT average. COLLEGE LEVEL SAT DOES NOT REQUIRE MEDIAN OR MODE z60\doc\web\2002\09\meanmode.txt Deanna M. De'Liberto 2002 As someone who was an assistant examiner at ETS and assembled forms of the SAT I...we do not expect students to know the terminology for mean, median, and mode. ..we asked the average or arithmetic mean Distribution with most below a value 4th WA Assesment (frequency histogram of battery life) 8th Voluntary National Test Kentucky KIRIS Open-Response Item Scoring Worksheets 1995-96 http://www.kde.state.ky.us/blrs/ocaa/dcad/97/M4/M4Q5.PDF Expects students to pick from the mode or median from a sample of bags. WA 4th grade assessment: pick frequency histogram chart with battery most likely to last at least 8 hours (pick the one with most values below a value) Wisc 4th grade: min, max, range, mode (most frequent value) median (middle value) New Standards Test: "predict" next value based on frequency histogram of 11 boxes of raisins. (kid has to make a wild guess within the range, pick the median, or compute a mean???) Mean BC Standards 4th grade - possible, impossible, certain, or uncertain compare outcomes using the terms equally likely, more likely, or less likely design and conduct experiments to answer their own questions 6th grade - compute experimental and theoretical probability, probability of dice. 7th grade = mode median mean determine measures of the distribution of a set of data: range extremes, gaps, and clusters quartiles WA 4th grade benchmark - use different measures of central tendency such as "most often" and "middle" in describing a set of data understand the difference between certain and uncertain events know how to list all possible outcomes of simple experiments (does NOT include precise computation of probability) 1997 version says mean, median and mode %%Exemplars Exemplars Task expects kids to know how to divide up whole numbers into parts, and then parts again. Correct answer - line up equal whole numbers. Then cut remaining pieces into parts, and distribute the parts. (???!) @@Measurement %%Appropriate Size 4th WA Assessment 4th NAEP Guidelines (estimate size) 8th NAEP Guidelines (picking unit) WA - the size of a notebook paper is approximately 20 mm, cm, or meters? NAEP - determine appropriate size of unit in problem situation. Do not assess at 4th, OK at 8th. estimate the size of an object - 4th grade OK. %%Conversion of Units 4th Virginia Standards 4th WA Assessment 5th Houghton Mifflin Math 1998 5-8 SC Standards 7th WA Benchmark 8th NAEP Guidelines 5th Houghton Mifflin Math 1998 Compare speed of animals measured in miles per hour vs inches per minute. 5-8 South Carolina Convert units within and, given appropriate conversion factors, between systems. http://www.achieve.org/ WA 4th grade asessment - bird feeder requires conversion from 60 inches to 5 feet, test does not give conversion table, rubric does not mention that conversion is neccesary. WA 7th grade standard understand the relationship among units within both the U.S. and metric syst ems http://cisl.ospi.wednet.edu/NAVIG/INFORM.html Virginia standards http://www.pen.k12.va.us/go/Sols/math.html http://cisl.ospi.wednet.edu/ComSL/MATHBMK1.html WA G4: Perimeter, Area, Volume NAEP Convert from one measurement system to another within the same system: Do not assess at 4th, OK at 8th. %%Area = Length Times Width 4th Core Knowldge 4th WA Assessment 4th Addison Wesley Mathematics 1991 5-8 LA Standard 7th WA Benchmark 8th KY Standard 8th NAEP Measure area by multiplying length and width NAEP http://www.nagb.org/pubs/math/mchap3.html Solve problems involving perimeter and area (e.g., triangles, quadrilaterals, other polygons, circles, and combined forms) # = very simple at 4th grade CT 4th Grade Assessment Estimate lengths and areas CT 6th Grade Assessment Compute area LA 5-8th Grade Standard Mapplying the concepts of length, area, surface area, volume, capacity, weight, mass, money, time, temperature, and rate to real-world experiences WA 4th Grade Assessment Sample: Which pizza is the best value, gives pictures of 4 rectangles with 2 digit sides. WA 7th Grade Standard http://cisl.ospi.wednet.edu/ComSL/MATHBMK2.html measure objects and events directly or using indirect methods such as finding the area of a rectangle given its length and width http://www.kde.state.ky.us/blrs/ocaa/dcad/CCA/CCM2.html KY 8th Grade Standard: use formulas to find measurements of two-dimensional shapes, how two or more measurements are related (perimeter and area, time and distance, height and weight, etc.) http://www.pen.k12.va.us/go/Sols/math.html Virginia standards VA 2nd Grade - count squares for area VA 6th Grade - measure area %%Perimeter G2 Texas Core Curriculum %%Rate Ranking: 4th WA Assessment 7th WA Benchmark 8th NAEP WA 4th - Use ruler and stack of cards to determine how many cards a box will hold WA 7th - understand the concept of rate and how to calculate rates and determine units 8th NAEP Apply the concept of rate to measurment situations - do not assess at 4th, 8th OK. @@Mental math z47\clip\2000\12\mentmath.txt straits times 28 December Singapore Maths whiz uses parts of brain others cannot reach A team headed by Ms Nathalie Tzourio-Mazoyer of France's National Centre for Scientific Research (CNRS), working with neuropsychologists from Louvain University in Belgium, carried out PET brain scans on a noted German maths prodigy, Mr Rudiger Gamm, while he was doing [extreme mental] calculations. [like using hard drive for long term storage] that most people don't use. @@Metric JOKE - METRIC COMMONLY USED IN THE 'HOOD z47\clip\2001\01\metric.txt z47\clipim\2001\01\31\metric\metric.htm http://www.theonion.com/onion3703/metric_system_thriving.html [warning, a bit of 'hood stereotyping here] Department of Education: Metric System Thriving in Nation's Inner Cities "While the typical teen has only a vague notion of what a kilogram is, teens in the Cabrini Green housing projects in Chicago and the Watts neighborhood of Los Angeles were thoroughly familiar with this unit of metric measurement," @@Mexico Mexican schools are more run down, but have higher standards than new US schools! @@Middle School \clip\99\16\achmath.txt www.achieve.org Achieve and Ten States Form Partnership Tying Middle School Math Teaching and Testing to Common, Internationally Challenging Standards New Materials, Training, and Exam Based on Third International Math & Science Study Will Add More Algebra, Geometry to States' Offerings @@Money %%Coins 2nd graders are expected to do math aned distinguish between coins on the basis of black and white pictures of the heads on the coins, which do not say their value on the ITBS test. Some tests ask students how many different combinations of coins they can use, but do not specify if rarely used half dollars or dollar coins may be used. Some textbooks do use pictures of coins with the number of cents on them. Most children and many adults have no idea who the heads on the coins are. NOTES ON US COINS cents name color face says 1 penny copper Lincoln "one cent" 5 nickle silver Jefferson 10 dime silver FDR Roosevelt "one dime" 25 quarter dollar silver Washington "quarter dollar" 50 half dollar silver Kennedy The canadian penny I have gives the name of the head (Elizabeth II), and the number of cents (1)! Comments on coin problem and history ITBS notes @@More Than One Way to Get an Answer Another popular reform slogan. @@Mountain Math Mountain Math is a brand of Math software developed by: http://www.mtnmath.com/mtnmath.html It is used in Tennessee(at least): http://www.acorns.k12.tn.us/curricu/cu01001.htm http://guaraldi.cs.colostate.edu:2000/form @@Multiply @@Multiplication Introduction K - Little Angels India Kindergarten %%Colored pencils TERC asks students to use different colored pencils on a 10,000 grid to show decimal addition. TERC does not show conventional addition as it does not even cover regrouping in 2nd grade %%Repeated addition http://wgquirk.com/NCEE.html#good a total of 38 math-related "examples", with 19 at the 4th grade level in Volume 1, 12 at the 8th grade level in Volume 2, and 7 at the 10th grade level in Volume 3. ** 3 equally inefficient ways to multiply ** Task 3: Demonstrate multiple ways to multiply 62 x 85. Method 2: The student "added 85, 62 times." Method 3: "The student showed how the problem could be solved by making 62 circles with 85 stars in each circle." @@NCEE America's Choice Performance Standards z48\clip\2001\03\nceemath.htm http://wgquirk.com/NCEE.html#good a total of 38 math-related "examples", with 19 at the 4th grade level in Volume 1, 12 at the 8th grade level in Volume 2, and 7 at the 10th grade level in Volume 3. these standards have been benchmarked to the expectations of those countries with the highest student performance in the world." They say the ACPS have been reviewed by researchers and recognized experts in several other countries, including Germany, Japan, and Singapore, and "No reviewer identified a case of significant omission," and "None of the reviewers identified standards for which the expectations expressed in the standards were less demanding than those for students in other countries." ** 3 equally inefficient ways to multiply ** Task 3: Demonstrate multiple ways to multiply 62 x 85. Method 2: The student "added 85, 62 times." Method 3: "The student showed how the problem could be solved by making 62 circles with 85 stars in each circle." @@Negative Numbers G2 - Dale Seymour uses negative numbers, but not borrow/regroup! G4 - California Nevada Covina Valley Nebraska G6 - Washington State G6-8 Florida G8 Texas G8 Ohio Math Standard: Grade 4: Number & Number Relationships MATH CONTENT STANDARDS. GRADE: 4. ... including the use of standard and expanded form. Identify ... Use concepts of negative numbers (eg, on a number line, in counting ... www.cvusd.k12.ca.us/covina-valley/Tech_Plan/K-5Math/grade04_nos.htm - 10k - Texas G7 (A) compare and order non-negative rational numbers; G8 (A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals; Japan Nebraska G4. By the end of fourth grade, students will identify and demonstrate positive and negative numbers and zero. Vermont G3-5 b. Begin to use simple concepts of negative numbers, properties of numbers (e.g., prime, square, composite), three-digit and larger multipliers and divisors, rates, and the relationship among fractions, decimals, and percents; G7 (1) To help students deepen their understanding of the concept of numbers, through the enlarging of the scope of numbers to include positive and negative numbers. Ohio G8 - negative with color chips Nevada 4.1.4 By the end of fourth grade, students will identify and demonstrate positive and negative numbers and zero. Washington state EALR G6 understands negative numbers www.seattleschools.org/area/acastan/full/math.pdf California G4 1. Students understand place value of whole numbers and decimals to two decimal places, how these relate to simple fractions, and use concepts of negative numbers. www.achieve.org @@New Math Introduced in 1957 in response to Sputnik, it added a lot of set theory, abstractions, rigor, but it was a disaster. Nobody understood it. Only the top 10% got any benefit, the rest were swamped by abstract mathematics. Funding was pulled by the feds in 1972 after it was widely regarded as a failure. Some blamed it on mathematicians, but more likely it came from the educators. Forerunner to the new wave of failing "fuzzy" math. NEW MATH 1958-1972 WAS A DISASTER z49\clip\2001\04\newmath.txt New York Post LET'S SEE: 2,001-1,957 IS . . . By CARL CAMPANILE April 17, 2001 Educators first introduced what was called "the New Math" in 1957 There was more logic, more abstractions and more proofs," said Richard Raim, a math professor at the University of Rochester. "But it was a disaster. Nobody understood it. Some of the commercial textbooks were inferior - and wrong." Raim said only elite students - the top 10 percent - benefited from the New Math while the rest of America's kids were numb with numbers. The federal government stopped funding the New Math in 1972, after it was widely considered a flop. z49\clipim\2001\05\09\newmath\newmath.htm New Math 1960's parody by Tom Lehrer Hooray for New Math, New-oo-oo-Math, It won't do you a bit of good to review math. It's so simple, So very simple, That only a child can do it! SPUTNIK, NSF BEGAT NEW MATH http://www.math.rochester.edu:8080/u/rarm/smsg.html z40\clip\2000\03\whatmath.txt Ralph A. Raimi 22 October 1995 Whatever Happened to the New Math? (Sputnik) The year 1958 therefore kicked off the largest and best financed single reform effort ever seen in mathematics education, the School Mathematics Study Group (SMSG), upon which the National Science Foundation (NSF) spent millions of dollars over its twelve-year lifetime. The result, after twelve years, was total failure. By any reasonable measure, and measures were taken, school mathematics was worse off in 1975 than it had been in 1955. The idiocies of the older curriculum had in most places been removed, but often to be replaced with new ones. "Gerald W. Bracey" Yeah, well John, the last time people listened to mathematicians, we got The New Math. It was an absolute disaster (see the section on post-Sputnik reforms in either my book, Final Exam, or Charles Silberman's 1970 tome, Crisis in the Classroom). I do not come to this from a distance: I spent the summer of 1963 with the School Math Study Group (SMSG: Some Math, Some Garbage to us disrespectful graduate students) at Stanford helping mathematicians rewrite their New Math texts so that teachers, not to mention kids, could understand them. My experiences with mathematicians is that they can barely communicate with college students and are clueless when trying to cope with teachers and k-12 students. I suggest you go dig up the Post-Sputnik literature about what it means to know mathematics. It was the mathematicians who decided that third graders had to know what "null set" and "empty set" and "commutativity" and "associativity" and the "distribution law" meant. Really. Third grade. No joke. Wish I had kept the textbooks. \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN (New math, math reform backlash against "fantasy lunch") http://www.math.uic.edu/~cpmp/archive9701.html New math was a reaction to Sputnik. "Instead of starting out by 'borrowing' and 'carrying,' we want children to understand what they're doing." ". Children were drilled on fancy concepts like spelling "commutive property", which is simply 2 + 3 = 3 + 2, concern was that children were not picking up basic skills. "By 1966, the movement was unraveling amid concerns that students were not learning basic skills. Over the next decade, New Math was satirized as "hopelessly abstract, elitist, confusing and impractical,"" @@New Standards NEW STANDARDS RESULTS IN LOW MATH CAT PERCENTILES IN VERMONT Sixth grade test CAT California Achievement Test scores: Median National Percentile (MDNP) 1990 1996 Math Computation: 71.6 48.6 Math Concepts and Appl. 89.5 87.4 Total Math: 86.0 70.3 @@Newsgroup http://www.thinkspot.net/k12math/charter.html Charter for k12.ed.math

@@NCTM Standards

The National Committee on Teaching Mathematics created an influential new document on teaching mathetmatics in 1989 which unfortunately legitimized the movement to stop teaching arithmetic. Really. It focused not on raising math standards, but moving towards "fuzzy" math which seeks "natural learning styles", discourages drilling and paper and pencil tasks, and "performance-based" tasks based on "real life" instead of concentrating on mastering the basics, and proving that there is never just "one correct answer". Proponents say that not all students are good at memorization, and that all students should be exposed to all math, but this turns a class that teaches students how to be good at algebra with lots of practice into an "integrated class" which turns into algebra "apprececiation" - you can be a listener of Beethoven, but not a piano player than can perform it. Critics say that the NCTM standards are responsible for dumbing down math education, and are something to run away from. This is all really the application of political correctness to mathematics. It's all about destroying "eurocentric male dominated", and math for women, minorities and losers. It promises algebra and calculus for all, yet relies on assessing students before they've been taught anything. ORIGINAL VISIONARY DOCUMENT Appendix: Table of Standards - Number and Operation NCTM's visionary document for teaching mathematics at any level. ... Pre-K–2 Expectations: In prekindergarten through grade 2 all students should– standards.nctm.org/document/appendix/numb.htm %%Assessment DAS KAPITAL FOR MATH MATH POWER, MATH FOR WOMEN, MINORITIES AND LOSERS, ALL CHILDREN MUST LEARN ALGEBRA, CALCULUS, STATISTICS, NUMBER THEORY INTEGRATED INTO ELEMENTARY AND MIDDLE SCHOOL. ASSESS STUDENTS _BEFORE_ YOU TEACH THEM HOW TO DO IT z43\clipim\2000\06\26\nctm.efx z43\clipim\2000\06\26\nctm.txt Assessment Standards for School Mathematics Working Draft October 1993 (Joanne Mccann copy) For all students to achieve mathematical power, they need to be mathematical problem solvers, to value mathematics, to reason and communicate mathematically, and to be confident in using mathematics to make sense of rael-worls problem situations. The mathematics curriculum, instructional methods and the strategies used to assess student performance must be congruent with this notion of mathematical power There has been too much reliance on brief problems that can be quickly solved (multiple choice or closed, constructed-response items.. creates equity problem.. different curricular experiences to different social classes p14 judged in terms of several levels of performance from less to more rather than incorrect so students can demonstrate what they know and are able to do. p10 all students need to develop personal and robust understandings of algebra, geometry, triginometry, statistics, probability, discrete mathematics, and even calculus. Furthermore, many of these understandings can, and must be initially developed in elementary and middle school. balanced variety that reflect cultural diversity must be in the basic elements of reform p66 it took 8 perpl rods (invented spelling k-4) p85 and is intended to be used holistically, not point by point P31 must allow for studens use of alternative approaches.. to distinguish from an elegant solution from one that is merely brief requires mathematical knowledge and sophistication. Sample is 6 wk statistics unit about how many Hispanics and blacks are put into jail. 13 has defined every child as follows - students denied access to opportunity students who are black, hispanic, AmIndian, other minorities female as well as male who have not been successful as well as successful 22 the group of afam girls wanted to investigate racism in the school, but their work was sloppy and incomplete.. was worried they claim racism if i gave them low marks Foreign exams usually small number of probs 2-6 eith parts take 10-16 min, American 50 tasks 1-2min %%Documents http://www.nctm.org/standards2000/download.html \clipim\98\11\PSSMDRFT.pdf Draft of 1998 NCTM Standards 2000 Electronic Standards Featuring invented mathematics. z42\clipim\2000\05\23\mathskill\mathskill.htm Here are the new M ath Standards National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 1989.(Eisenhower National Clearinghouse for Mathematics and Science Education> %%Critic http://mathematicallycorrect.com/frankallen.htm

More Nctm Standards links

Mathematics Education

Uiuc Site

Misc. Commercial Sites

Misc. Educational Institution Sites

Misc. Internet Provider Sites

Misc. Non-Profit Sites

%%Against NCTM: WE WERE ONLY KIDDING ABOUT THROWING OUT ARITHMETIC z40\clip\2000\04\backmath.txt www.nytimes.com/library/041300math-test.edu.html New York Times April 13, 2000 Math Teachers Back Return of Education in Basic Skills By ANEMONA HARTOCOLLIS In an important about-face, the nation's most influential group of mathematics teachers announced yesterday that it was recommending, in essence, that the arithmetic be put back into mathematics, urging teachers to emphasize the fundamentals of computation rather than focus on concepts and reasoning. Lee V. Stiff, president elect of the mathematics teachers' council, insisted that despite the protests of parents, the old standards had not done any harm. NOW NCTM SAYS THEY NEVER WANTED TO BAN TEACHING MANUAL ARITHMETIC z40\clipim\2000\04\10\nctm\nctm.htm http://www.edweek.org/ew/ewstory.cfm?slug=31nctm.h19 April 12, 2000 Math Revisions Add Emphasis on Basic Skills By David J. Hoff NCTM BACKPEDALS FROM 89 STANDARDS, EMPHASIZES BASICS Education Week http://www.edweek.org/ew/current/10nctm.h18 \clip\98\16\nctmnew.txt [November 4, 1998] [Education Week on the Web] Math Council Again Mulling Its Standards By David J. Hoff Note - Washington state EALR standards and WASL assessments are based on the NCTM standards which are being revised because they were just plain silly. NTCM STANDARDS ARE TO BLAME FOR PROMOTING FUZZY MATH Investors Business Daily 'Standards' To Blame For Rise Of 'Fuzzy Math' Date: 4/3/98 Math Correct Cease Fire Terms and why the NCTM standards have been harmful to math teaching. %%Problems THEY'RE TAKING NOTES AND WORKING ON TEXTBOOK PROBLEMS INSTEAD OF PLAYING WITH MANIPULATIVES AND COMPUTERS \clip\98\08\latmath.txt http://www.edweek.org/ew/current/31nctm.h17 First-year teachers have a hard time putting the voluntary national standards for mathematics into practice in their classrooms, a small study by Illinois teacher-educators has found. (Takes too much time to play with manipulatives, not enough computers) half or more of the respondents to the questionnaire--all teaching in secondary schools--said they "seldom" or "never" used hand-on materials, or so-called manipulatives, and seldom or never used computers or had their students write about math. Half or more of the dozen respondents said their students engaged in the more traditional activities of working on problems from textbooks or taking notes during teacher presentations. %%Research Constructivist wonders if there is any research to back up constructivism? %%review AMS Report on NCTM Standards Date: 3/4/98 The American Mathematical Society committee to comment on the NCTM Standards and possible revisions to the standards has released its first and second reports. These are available on line at http://www.ams.org/government/nctm2000.html %%Revision z40\clip\2000\02\apmath.txt http://seattletimes.com/news/nation-world/html98/math13_20000413.html Thursday, April 13, 2000 New math guidelines 'set higher standards' for students by Nicole Ziegler Dizon The Associated Press %%Support CA STATE SUP AND NSF SUPPORT NTCM STANDARDS Date sent: Thu, 22 Jan 1998 17:11:45 -0700 (PDT) From: Charles L Hagopian Anyone can access California's reading and math standards at www.csbe.ca.gov. The standards that match NCTM standards were recommended by our standards commission and rejected by our state board. Our state superintendent has recommended that districts follow the commission standards instead of the board's standards. NSF has threatened to withhold funding if a district uses the state board's standards. %%Videotape study "Are the Japanese using progressive education?" Of course not, as the TIMSS videos and James Stigler's writings about them demonstrate so clearly. Here's a couple of sources that show that what the Japanese do is excellent instruction, not ed school panacea. http://mathematicallycorrect.com/wbishop.htm (Interview with Stigler on TIMSS) "Understanding and Improving Classroom Mathematics Instruction: An Overview of the TIMSS Video Study", by James W.Stigler and James Hiebert, Sept '97 Phi Delta Kappan: http://www.pdkintl.org/kappan/kstg9709.htm Wayne Bishop NCTM SAYS NEW STANDARDS ALREADY BEING IMPLEMENTED BY JAPANESE http://www.thonline.com/th/news/1996/th1121/stories/35200.htm \clip\97\28\ustud.htm November 21, 1996 U.S. students aren't at the top of the class Associated Press . Average: American teens score low in math, but better in science WASHINGTON (AP) - American eighth graders ranked 28th in math tests given to students in 41 nations, far behind Asian countries at the top of the list. The U.S. students made it into the top half in science, ranking 17th. The National Council of Teachers of Mathematics has a videotape study that shows Japanese teachers already were doing a better job implementing the kind of reforms the council advocates. In the United States and Germany, students are taught procedures for solving practice math problems, said Jim Stigler, who directed the classroom videotape study. In Japan, the goal is conceptual understanding, he said. Explore Math Lessons in Germany, Japan, and the United States http://nces.ed.gov/timss/video/jimvid1.htm %%Critical STEVENSON DOWN ON NCTM STANDARDS Dr. Harold Stevenson, author of THE LEARNING GAP and University of Michigan researcher who has for 15 years analyzed math education in Eastern Asia and the United States, wrote the following as a response to the previous posting about the NCTM standards: NCTM are fuzzy standards that aren't helpful to most students or teachers, and aren't what the Chinese and Japanese do. SAXON HATES THE NEW STANDARDS We do not need guidelines that recommend leaving students ill-prepared for chemistry and physics, and that ridicule preparation for calculus. NCTM STANDARDS CHANGES Word Problems and the NCTM Standards

Math Forum

The math reform movement is based on constructivism, and against drilling. It seeks to concentrate on "problem solving" skills, and relate math to real life like cooking. The NTCM standards and several new math text series funded by the National Science Foundation have done the most to promote the "new new" or "fuzzy" math. Most states have adopted "performance-based" assesments which promote reform math philsophy

Critics say it has resulted in plunging test scores which have provoked parent revolts in cities across the nation. Problem solving inevitably ends up asking 4th graders how to solve what traditionally were 7th grade ratio and proportion and 9th grade algebra problems by "figuring it out" rather than teaching the skills, or waiting until they are taught. They say that students learn more about how to write about answers than getting the right answer, indeed, one of the most important principals is that there isn't such as a thing as "one right answer", and students are encouraged or required to "construct" their own methods of computation rather than being shown how it has been done for the past 5 thousand years. Traditionalists call for a return to contents based teaching and drill based programs like that of John Saxon for students who are failing in math.

Protest Pages


z49\clip\2001\04\badnews.txt Date: Tue, 17 Apr 2001 BAD NEWS FOR
CHILDREN, GOOD NEWS FOR TUTORS By CARL CAMPANILE Parents can't help
their kids with homework because the new math is "unrecognizable" to
what they learned in school.  Students who aren't fluent in English
are particularly handicapped with constructivist math because so much
is based on reading passages and writing answers regarding math
problems.

z49\clip\2001\04\crewmath.txt
From: "Elizabeth Carson" 
Apr 17, 2001 SCHOOLS' ‘NEW MATH' = TROUBLE FOR CITY KIDS By CARL
CAMPANILE "The movement - initiated by District 2 in Manhattan and
pushed by former Schools Chancellor Rudy Crew - continues, even
though mathematicians at the city's elite high schools are against
it.  "

NSF $3.5M grant to implement math reform in NYC
z48\clip\2001\04\addup.htm New York Post: SCHOOL'S MATHEMATICS DON'T
ADD UP Sunday,April 8,2001 By ROD DREHER 'IWALKED out of there, and I
tell you, my head was spinning," the distressed caller told me. "It
was like a cult. It was like they were selling Amway or something."
It has also been ground zero for a local movement of parents
desperately worried that their children are being harmed by this fad.
Carson and others have long tried, and failed, to get the district to
agree to a public forum to discuss the pros and cons of
constructivist math.  Raimi discovered that the National Science
Foundation had authorized a $3.5 million grant to implement and study
math "reform" in District 2 schools, along constructivist lines. 

WSJ ED ON NEWNEW MATH: WE HAD TO DESTROY IT TO SAVE IT...
\clip\99\21\wsjmath.txt Wall Street Journal Lead Editorial January 4,
2000 Page A22 MATH WARS The reason for the New New Math, as for many
other curriculum reforms, is that teachers, school administrators and
their unions are tired of being blamed for statistical declines and
poor student performances.  So with math, as in their campaign to
dumb down the SAT, such educators work to destroy or reject the
standards that brought them trouble in the first place.  Children are
different nowadays, goes the line, and cannot be measured by old
benchmarks.

 Have
Math Fundamentals Gone Fuzzy?  by Betsy Van Dorn  Family Education

Issues against
- results in falling test scores from 90 to 61 (Palo Alto, U Chicago)
- based on reading, weak readers can't do it.
- often no textbooks
- relies on discovery learning, some hit right answer right away,
   others never get it
- takes lots of prep and time to assess 25 free response questions.
- few exercises, little practice



%%Activism

PARENTS SUCCEED IN NEARLY KILLING CONNECTED MATH
z56\clip\2002\07\mathfail.txt
http://www.zwire.com/site/news.cfm?brd=2275&Nav_Sec=58218
New math gets scaled back 
ICHAEL ROCCO , Staff Writer  07/19/2002 
The Reporter Lansdale, PA 19446
...Although scaled back considerably‚ parents against Connected Math
want it gone completely.  Trish Gallagher of Montgomery Township said
final exam test sores of students show Connected Math has failed. The
board’s action proves the point‚ she said.

z49\clip\2001\04\fightmat.txt
Front Page Headline: BIG FAT MINUS PARENTS & TEACHERS: 'NEW MATH' DOING A
NUMBER ON KIDS
Inside Headline: SCHOOLS' 'NEW MATH' = TROUBLE FOR CITY KIDS
SUM-THING IS WRONG: PARENTS AND TEACHERS, Carl Campanile
LET'S SEE: 2,001-1,957 IS . . , Carl Campanile
BAD NEWS FOR CHILDREN, GOOD NEWS FOR TUTORS , Carl Campanile

GET MAD, THEN GO AFTER THE BUREAUCRATS By ROD DREHER April 17, 2001
-- HERE'S how you become angry: Read up on what many New York public
schools are doing to math education, and how permanently crippled our
kids will be because of this "constructivist" fad.

%%Bush Initiative

BUSH FUNDS MATH BASICS STUDY
z60\clip\2002\11\bushmath.txt
http://edweek.org/ew/ewstory.cfm?slug=12math.h22
November 20, 2002 
Bush to Push for Math 
and Science Upgrade
By David J. Hoff
Washington
[of three...] Mr. Milgram helped rewrite the California math standards
that had reflected the NCTM's influence.

%%Civil Rights

NEW NEW MATH IS A CIVIL RIGHTS ISSUE
Z56\doc\web\2002\05\mathgood.txt
http://www.aera.net/pubs/er/pdf/vol31_01/AERA310104.pdf
Making Mathematics Work for All Children:
Issues of Standards,Testing, and Equity
by Alan H. Schoenfeld
“Mathematics Education is a civil rights issue,” says civil rights
leader Robert Moses The data have been clear for decades: poor
children and children of color are consistently shortchanged when it
comes to mathematics.

%%critical

*** EXCELLENT 2 PG SUMMARY OF FUZZY MATH BOMBING IN CANADA ****
z49\clip\2001\05\canmath.txt canmath.doc
http://www.globeandmail.com/gam/Education/20010505/COWENT05.html Go
figure, Ashley can't MARGARET WENTE Saturday, May 5, 2001 Caitlin
Kirby's only in Grade 4, but already she has hit the math wall.
Sometimes she lays her head down on her math homework and cries. "I'm
stupid!" she tells her mother Tressa.  "It's time to acknowledge that
continuing to teach these skills to our students is not only
unnecessary, but counterproductive and downright dangerous."  The new
curriculum also introduces kids to complicated concepts they don't
yet have the tools to master, such as geometry and probability
statistics.

z45\clip\2000\08\silber.txt Boston Herald:
http://www.bostonherald.com/news/columnists/silber08212000.htm `Old
math' fans should go forth and multiply by John Silber Monday, August
21, 2000 The Massachusetts Board of Education recently adopted a new
set of guidelines for teaching mathematics. A Boston math teacher was
quoted as saying, ``The new framework means going back to the way our
grandparents did it, which was a terrible way to do math.'' 

z41\clip\2000\05\flexmath.txt FUZZY ANSWERS / A SPECIAL REPORT The
New, Flexible Math Meets Parental Rebellion By ANEMONA HARTOCOLLIS
Three years ago, one of New York City's most adventurous school
districts set out to tackle a nagging problem: the math phobia that
afflicts many students, and the disparity between the test scores of
white middle-class students and their poorer black and Hispanic
counterparts.

DEPT OF ED MATH PROGRAMS OMIT TRADITIONAL MATH ON PURPOSE
z40\clip\2000\03\mathadd.txt
http://www.mathematicallycorrect.com/usnoadd.htm American School
Board Journal April 2000 MATH PROBLEMS: Why the U.S. Department of
Education's recommended math programs don't add up By David Klein The
standard algorithms for arithmetic (that is, the standard procedures
for addition, subtraction, multiplication, and division of numbers)
are missing or abridged in ED's recommended elementary school
curricula.  Steven Leinwand of the Connecticut Department of
Education was a member of the expert panel that made final decisions
on ED's "exemplary".. In a Feb. 9, 1994, article in Education Week,
he wrote: continuing to teach these [manual math] skills to our
students is not only unnecessary, but counterproductive and downright
dangerous."
There is a unifying ideology behind "whole math." It is advertised as
math for all students, as opposed to only white males. But the word
all is a code for minority students and women

z40\clip\2000\03\innum.txt
Politically Correct Math=Innumerate Children
by Wendy McElroy 
Saturday, March 18, 2000 
"A. If math were a color, it would be __, because __. 
B. If it were a food, it would be __, because __. 
C. If it were weather, it would be __, because __." 
grade school children discover the rules of multiplication and
subtraction by themselves without the tyranny of "teacher-imposed
rules." 


SAN GABRIEL PASAENA PAPERS FLUNK OUT MATHLAND, QUEST 2000
zip37\clip\99\18\fuzmath.txt 
San Gabriel Valley Newspapers
Group/Pasadena Star News FUZZY MATH FLUNKS OUT October 5, 1999 In
closing, we say dump the fuzzy math. Dump a curriculum called
MathLand.  Dump Quest 2000, which is used at Rowland Unified School
District. One analysis says this will leave students by the time they
reach 6th grade well behind the state standard.

THANKS TO ACTIVISTS MOST TEXAS DISTRICTS REJECT NSF-FUNDED FUZZY MATH TEXTS
html
\doc\web\99\07\nofuzzy.txt
Texas School Districts Reject "Fuzzy Math"
Textbooks -- Major Defeat for Statewide Systemic Initiative Texas
school districts have overwhelmingly rejected the latest fad in math
instruction. Sometimes called "fuzzy math," "whole math," and "new
new math," textbooks based on this pedagogical approach received only
4% of the textbook orders for second grade math, 2% for fifth grade
math, and 5.6% for seventh grade math. Ironically, those promoting
this approach refer to it as "standards-based math." 
[including' Everyday Mathematics published by Everyday Learning
Corporation; and Investigations in Number, Data and Space published
by Addison Wesley Longman; (fifth grade books) Everyday Mathematics;
and Investigations in Number, Data and Space; (seventh grade books)
Math Thematics published by McDougal Littell; and Connected
Mathematics

\clipim\98\03\newmath.tif New Math Misses Mark The Washington Times
Marion Kester Coombs Tuesday June 17, 1997 The National Science
Foundation funded development of MathLand, Interactive Math and Math
in Context.  Prodded by "A Nation at Risk", the NCTM in 1986
appointed a commision to come up with new standards - verbalization.
Everyday real world.  Guess and check. Manipulatives. Calculators and
computers.  Understanding vs. memorization. Teamwork. Repetition of
topics rather than sequential.

%%Deceptive

z55\clip\2002\04\mathref.txt
Math is a gatekeeper for success
Compass
Anchorage Daily News 
By P.T. Chang
Published: April 10, 2002)
Ed Reform Buzzwords
- Carnegie Foundation Math Teacher of the Year ED INDUSTRY
- Teachers must become facilitators of learning PROGRESSIVE
- The right answer does not indicate MASTERY of a subject OBE
- Math seems to be a high-anxiety subject #1 REASON FOR FUZZY MATH
- International community WORLD CLASS STANDARDS
- Success ALL MUST SUCCEED, BELOW HIGH STANDARDS IS A WORTHLESS FAILURE
Looks like even Asian American math teachers aren't immune
from fuzzy math standards.

%%Defence


FUZZY MATH WORKS WHEN TEACHERS RE-EDUCATED??
Z49\CLIP\2001\04\FUZZBETT.TXT  NY POST Wednesday,
April 18, 2001 DON'T ALLOW 'NEW MATH' TO MULTIPLY, REGENT SAYS By
KENNETH LOVETT, CARL CAMPANILE and IKIMULISA SOCKWELL-MASON
Professors at City College and the Freudenthal Institute in the
Netherlands retrained more than 400 teachers in Districts 2 through 6
in Manhattan.  Their analysis shows that students taught the New Math
scored better on city and state standardized tests in 1999.  In
grades 4 and 5, students in constructivist math scored at least 10
points higher. 


http://showmecenter.missouri.edu/showme/keynote1full.html
Standards Under Fire: Issues and Options in the Math Wars
Summary of Keynote Session by
James Fey, Professor, University of Maryland-College Park 
Show-Me Project Curriculum Showcase, May 21-23, 1999
For almost 30 years, evidence from international comparative studies,
our own National Assessment of Educational Progress, and the SAT/ACT
college admission testing programs has suggested that, in relation to
other countries that are our intellectual and economic competitors, 
• Our curricula do not challenge students to learn important topics
in depth; 
• Our teaching traditions encourage students to acquire routine
procedural skills through a passive classroom routine of listening
and practicing; 
• Our assessment of student knowledge emphasizes multiple choice and
short answer responses to low-level tasks. 




PARROT MATH WINS - REPEATED SUBTRACTION SAME AS LONG DIVISION??
http://www.pdkintl.org/kappan/kbec0003.htm
z40\clipim\2000\03\22\math\math.htm
The Politics of California School Mathematics: The Anti-Reform of 1997-99, 
by Jerry P. Becker and Bill Jacob
. His criticisms are revealing, including, for example, that
"students are never required to use the standard long division
algorithm" as required by California's grade 5 standards. Inspection
of Everyday Mathematics reveals that students do indeed study a minor variant
of the standard division algorithm that illustrates that repeated
subtraction enables one to calculate a long division. And even though
many students understand this process far better than the
conventional approach, it is now unacceptable for California's
students. Parrot math has scored a significant victory.

Latino Educator in LA Vows to Go on
Hunger Strike Over an LAUSD Board Claims LA district data shows
more minorities completing college prep math, school with high math
scores have reform math texts.
1) There has been an increased of 73% in the number of African
American students that complete, with a C or higher, the first
mathematics college-prep course. 

Wayne bishop says:
At this link is the real LA and CA data regarding integrated math of the genre
supported by Mr. Mendieta.  Essentially, every way you slice the data -
disadvantaged or not, LEP or not , male or female, SAT-9 or the standards-based
STAR augmentation, LA Unified (where this protest is to happen, tomorrow night
on my own campus) or California as a whole - the integrated programs which are,
Allah be praised, coded into the database (but not by specific program,
unfortunately) come in 5-15% below traditional programs.  The idea is that, if
you do enough project oriented math experiences and use enough group grading,
even empty chairs get college preparatory credit in math.  Ah... Reform!! 
Don't educate underrepresented minorities.  Lie to them.
      http://mathematicallycorrect.com/la.htm

REFORM MATH GIVES HIGHER, GENDER BALANCED TEST SCORES ON UK EXIT
EXAMS?  
\clip\99\12\mathnew.txt Mathematics for the Moment, Or the
Millennium?  By Jo Boaler Education Week March 1999
http://www.edweek.org/ search: standards and assessments

"On the national examination, three times as many students from the
heterogeneous groups in the project school as those in the tracked
groups in the textbook school attained the highest possible grade.
The project approach was also more equitable, with girls and boys
attaining the different grades in equal proportions.  "

Comment - I'd like to see the actual study, I don't believe this, 
most US projects show reform students don't master methods and score
LOWER on the SAT, not higher.


> Two articles from the last issue of the Phi Delta Kappan that
> gave significant attention to mathematics reform in the U.S. are
> now available on the Phi Delta Kappan website.
 Here are the articles and locations:
 "The Mathematical Miseducation Of America's Youth"
 By Michael T. Battista
 http://www.pdkintl.org/kappan/kbat9902.htm
\clip\99\03\25\mathmis\mathmis.htm

"Parrot Math" By Thomas C. O'Brien
http://www.pdkintl.org/kappan/kobr9902.htm
\clipim\99\03\25\parrot\parrot.htm d:\clip\99\10\parrot.txt

%%Falling Test Scores

Despite the claim that Reform math does not result in lower math performance, history is riddled with failures in affluent communities which have resulted in falling math scores, and high school seniors who find themselves graded for remedial math instead of calculus.



[[Andover

Andover High School Bloomfield Hills School District in Michigan
"Outcomes Analysis for Core Plus Students at Andover High
School: One Year Later", by R. James Milgram, Department of
Mathematics, Stanford University:
ftp://math.stanford.edu/pub/papers/milgram/andover-report.htm
txt: \clip\99\06\coreplus.txt
htm: \clipim\99\04\coreplus\coreplus.htm

almost all the Andover students were severely critical of the
program, many bluntly blaming it for their difficulties in university
level courses. .. by every measure such as ACT scores, SAT Math
scores, grades in college math courses, core plus students fell short
of Lahser students. [... even when compared with students who did not
even take pre-calculus]


[[Norwich, Vermont

\doc\web\99\03\vtfail.txt From: Nanny714@aol.com In our financially
well heeled community of Norwich, Vermont which has a close
affiliation with Dartmouth College, we pioneered mathematics reforms
in our state. Our mathematics test scores as measured by the
California Achievement Test dropped dramatically consistent with our
pioneering effort.

\doc\web\98\06\vermath.txt The following is an excerpt from a Valley
News [Vermont] article dated May 6, 1997 titled "Norwich Voices
Concern Over Low Scores On Test" by Kristina Eddy "The median score
for the sixth grade in math computation dropped from 72 in 1990 (it
was 67 in 1989) to 41 in 1991, and stayed between 44 and 50 for the
next five years (55 in 1997). " [New Standards curriculum]


[[California

\clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for
Math Problems RICHARD LEE COLVIN (New math, math reform backlash
against "fantasy lunch")
http://www.math.uic.edu/~cpmp/archive9701.html Performance in
elementary grades is shaky as well. Last year, after many California
schools began using Reform lesson plans, test scores immediately
plunged in Santa Barbara, San Francisco and elsewhere--stirring
parent revolts.


[[ Chicago University of Chicago

Child with 135-140 IQ Math falls
from 99.5% to only 29-52% in only 3 years of reform math in wealthy
Chicago suburb.


[[ Palo Alto

PALO ALTO MATH TEST SCORES FALL FROM 91 IN '92 TO 58 IN '94
http://www.sfgate.com/cgi-bin/chronicle/article.cgi?ED26421. DTL:/chronicle/
archive/1995/03/10
\clip\98\01\newnew.txt Friday, March 10, 1995 · Page A23 1998 San
Francisco Chronicle Problems of New-New Math "However, the
dissatisfied parents note the drop in the Stanford test's math
computation scores for that grade -- which plummeted from the 91st in
1992 to 58th in 1994." "Problem of the week:" ``There is no
solution,'' concluded Wayne Bishop of California State University at
Los Angeles' department of mathematics and computer science.

NEW NEW MATH DESTROYS PALO ALTO MATH SUPERIORITY Wednesday, February
22, 1995 · Page A20 ©1998 San Francisco Chronicle Palo Alto Parents
Upset by the Even Newer Math John Wildermuth, Chronicle Peninsula
Bureau
http://www.sfgate.com/cgi-bin/chronicle/article.cgi?MN51592. DTL:/chronicle/
archive/1995/02/22
The average eighth-grade scores in number concepts and math
applications have stayed around the 90th percentile, but computation
scores skidded from 91st percentile in 1992 to 79th in 1993 and 58th
in 1994. `I cannot believe that the parents of children in the
high-tech Silicon Valley will put up with this `there's no correct
answer' math,'' said Evers.


[[Lake Washington

One parent reports his daughter was getting only 50th percentile math
scores until he sent his daughter to a Christian school, and it
bounced up to 90%. Bruce Poehlman of Lake Wash SD.


[[Plano Texas

\clip\99\17\conmath.txt CONNECTED MATH UNDER FIRE IN TEXAS 9/7/99 By
Andrea Billups THE WASHINGTON TIMES The "connected math" program
taught in the Plano Independent School District and used in several
school districts around the nation has been criticized by parents,
Celia J. Chiu, pulled her son out of the Plano public schools last
year after his once-stellar math grades declined.

%%Homework (or lack of)

Subject:      Re: Just what is Mathland?
From:         righteye@interaccess.com (The Other One)
Date:         1996/09/29
Message-ID:   
Newsgroups:   k12.ed.math
I work for a new math curriculum called Math Trailblazers, written at
the University of Illinois at Chicago One of the hardest things for
parents of a child using a math reform curriculum is that there are
no (or few) pages of drill and practice coming home.  The empahasis
is usually on giving students meaningful problems to solve.  Many
times the students are encouraged to come up with their own stratgies
for solving the problems, they are given manipulatives to use to work
out their ideas, and they work in groups to communicate their
strategies.  This is why there is less work coming home, so I feel
parents and teachers have to communicate more themselves.

%%Failure

PROBLEMS WITH NEW NEW MATH
Date sent:        Tue, 3 Mar 1998 08:14:09 -0500
From:             Nancy Torborg 
Subject:          Re: Got any U of Chicago Math Results?

Dear Diane,
I've used "Math in Stride" (Addison Wessley) and "Mathland"; my daughter is
currently using "Quest 2000" (new to our district).

Your principal is right; it will take several years for students to
cultivate the "habits of mind" that these programs try to develop. These
programs do not directly teach algorithims; they rely on student discovery.
There are several problems with this approach.

1) What do you do with the student who makes the "discovery" early? Keep
them in a holding pattern? This would mean in order to keep things flowing,
you need to run an individual program for each child, according to their
progress.
2) I will tell you from experience that some kids NEVER make the
"discovery"; they need the direct instruction
3) These math programs are reading-based; if you have kids with
reading/language/learning problems, they are at a real disadvantage
4) The programs downplay memorization of basic math facts, which are an
inescapable part of the real-world
5) These math programs take an INCREDIBLE amount of teacher-prep and
evaluation time; any school district that's bought into these programs
never had to sit and "evaluate" 25+ "free responses" on a daily basis! I
ended up sacrificing other subject areas just to try to get through the
program.

As in everything in life, moderation is the key. While I think the
problem solving aspect of these programs is admirable, I think direct
instruction is still appropriate and needed for some topics.  Nancy
Torborg Amherst NH mailto:nancy@torborg.com
http://www.torborg.com/nancy


\clip\98\04\flunktes.txt San Francisco Chronicle, Sunday, February
15, 1998 FLUNKING THE TESTS by DEBRA J. SAUNDERS "trendy math --
write about math, but you don't have to be right about math"

LOTS OF CONCEPTS, BUT NO MASTERY
I discovered the results of this trend
in that while she understood lowest common denominators and greatest
common factors, it took her forever to figure out the problems
because she had never been taught her multiplication facts.

%%Justification

CPM cites professors
students should learn beyond the basics to solve problems when
calculators do the basic functions.  (\doc\web\98\01\cmp.txt)

%%Netherlands

NO-ALGORITHM MATH SUCCESSFUL IN NETHERLANDS FOR 30 YEARS?
z62\clip\2002\12\realmath.txt
http://educationupdate.com/archives/2002/dec02/issue/spot_mathtorrence.html
New York City December 2002
Realistic Math Makes Sense for Student
By Eve Torrence
I am a mathematician. I am a college professor. I am a mother ..at his
Dutch school.. they were not taught the carrying and borrowing
algorithms. This approach has been used successfully in Holland for
almost thirty years.. Realistic Mathematics Education (RME)...The
teacher uses the method of guided reinvention,

Realistic Mathematics Education
http://www.fi.ruu.nl/en/projects/realme.html
Since 1971, the Freudenthal Institute has developed a theoretical
approach towards the learning and teaching of mathematics known as
'Realistic Mathematics Education'. ... students should not be
considered as passive recipients of ready-made mathematics, but rather
that education should guide the students towards using opportunities
to reinvent mathematics by doing it themselves. 


%%New Articles

\clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for
Math Problems RICHARD LEE COLVIN (New math, math reform backlash
against "fantasy lunch")
http://www.math.uic.edu/~cpmp/archive9701.html Why can't math be for
everyone? Turn new math upside down by letting students discover
concepts in groups, the process of finding an answer was more
important than using a complex formula to get the right answer. CA
adopted a "mathematically powerful" math instruction framework.
"Education journals highlight ways to teach "African American math."
Conferences attracting 5,000 teachers suggest downplaying the
difficulty of classwork by basing problems on fairy tales."

Friday, December 19, 1997 · Page A31 © 1997 San Francisco Chronicle
DEBRA J. SAUNDERS -- Man of Science Has a Problem With Real Math
http://www.sfgate.com/cgi-bin/chronicle/article.cgi?file= ED67991.DTL&direct
ory=/chronicle/archive/1997/12/19
California's commitment to ``deep, balanced mathematical learning''
-- aka new-new math -- has resulted in computational deficiencies, as
well as general arithmetical idiocy. For some years, trendy
California educators have focused on students writing about math,
repeatedly explaining how equations work and exploring their feelings
about math... credit for wrong answers.  The result: In the last
National Assessment of Educational Progress math test, California
fourth-graders scored behind students from every state but
Mississippi and Louisiana. Only 13 percent were rated proficient.

DISTRICTS ALREADY COMMITED TO WHOLE MATH "HIGHER" STANDARDS
\clip\97\29\baytep.txt Saturday, Dec. 13, 1997 · Page A 1 ©1997 San
Francisco Examiner Bay tepid to math standards Educators question
sense of the state's new guidelines Julian Guthrie OF THE EXAMINER
STAFF [state needs to revise textbook, curriculum, asessment]

/images/972/112197/p23.gif Numbers Racket: 'Standards' Math is
Creating a Big Division in Education Circles Wall Street Journal Nov
5, 1997 [generally sympathetic to new math movement, but cites
vehement opposition]

 MATH TALK IN WSU PULLMAN

KID CAN'T DO CHANGE IN HIS HEAD
http://washingtonpost.com:80/wp-srv/WPlate/1997-11/02/164l- 110297-idx.html
11/2/97 Washington Post Math Teachers' Modern Ways Don't Add Up for
Everyone By Victoria Benning Washington Post Staff Writer

NCTM - WHY REFORM?
\doc\web\97\08\need4.txt
http://www.enc.org/reform/journals/ENC2280/nf_28015.htm#need

CHILDREN NEED TIME TO "DEVELOP", "The notion of a developmentally
appropriate curriculum is an important one.  ..encourages the
exploration of a wide variety of mathematical ideas in such a way
that children retain their enjoyment of, and curiosity about,
mathematics. It incorporates real-world contexts, children's
experiences, and children's language in developing ideas.  It looks
beyond what children appear to know to determine how they think about
ideas.

WORKSHEETS, COMPUTATIONAL RULES DO NOT FIT "NATURAL LEARNING
PATTERNS" Programs that provide limited developmental work, that
emphasize symbol manipulation and computational rules, and that rely
heavily on paper-and-pencil worksheets do not fit the natural
learning patterns of children and do not contribute to important
aspects of children's mathematical development.  "

HOW MANY SKILLS THEY ACQUIRE IS "NOT AS IMPORTANT" "Thus, how well
children come to understand mathematical ideas is far more important
than how many skills they acquire"

REASONING AND PROBLEM SOLVING "Developing these characteristics in
children requires that schools build appropriate reasoning and
problem-solving experiences into the curriculum from the outset."

Child with 135-140 IQ flunks out
in math because of new math program that wastes 3 weeks on a group
project on my the Romand Empire fell.

 The Second Great Math Rebellion By
Tom Loveless Few truisms exist in the politics of education, but
you can usually count on two things. When reformers seize control of
the policy agenda, whether at the local, state, or national level,
they almost always go too far in jettisoning what they don't like and
too far in embracing the new, unproven practices they favor.

How many coins... Another silly
hard math problem that doesn't teach anything.

\doc\web\97\08\uchimath.txt U of Chicago math program puts "higher level thinking" ahead of basics so most students are just lost. PALO ALTO PARENTS MOBILIZE AGAINST FUZZY MATH http://www.rahul.net/dehnbase/hold/ Are you concerned about: the de-emphasis on basic math skills? the lack of textbooks and standard student materials? the hours that your child spends writing and illustrating a Problem of the Week (P.O.W.) that took him/her fifteen minutes to solve? the fact that 8th grade standardized test scores in computation have plummeted from the 90th to the 58th percentile in the past two years? the level to which your child is challenged in math? the ability of teachers to meet all children's needs in a heterogeneous (mixed ability) class? the failure of PAUSD to communicate with parents before changing the entire direction of a successful math program? the fact that PAUSD seems to have a different view of mathematics than you do? http://www.ait.net/catalog/catpages/c223.htm It Figures Problem Solving in Basic Mathematics for Grade 4 Encourage students to apply mathematics skills, ideas, and problem-solving strategies to real-life problems. Fourth-grade students become effective problem solvers by understanding that the process of reaching a correct answer is as important as the answer itself. It Figures, Math Works, and Solve It correlate to 4th-, 5th-, and 6th-grade student editions of Addison Wesley "Mathematics" (1987) and "Mathematics K-8" (1985); Harcourt Brace Jovanovich "Mathematics Today" (1985, 1987); Heath "Mathematics" (1985, 1987); Holt, Rinehart and Winston "Mathematics Unlimited" (1987) and Holt Mathematics (1985); Houghton Mifflin "Mathematics" (1987) and "Mathematics K-8" (1985); Macmillan "Mathematics" (1987); and Scott, Foresman "Invitation to Mathematics" (1985) and "Mathematics K-8" (1983). REFORM MATH HITS TEXTBOOKS http://hepg.awl.com/AWBookCatalog/Search/results.asp? TERTIARY_ID=88 A Problem Solving Approach to Mathematics for Elementary School Teachers , Sixth Edition, Rick Billstein, Shlomo Libeskind, Johnny W. Lott, 0-201-56649-4 BLL focuses on math skills (in contrast to teaching methods) for the teacher education market with a hallmark problem-solving emphasis, critical thinking techniques and selected major math reform trends (such as group work, writing and increased technology) that leave students at the end of the course with a clear understanding of the type of content outlines, challenges and situations they will face in the elementary education math classroom.... NEW MATH TESTS ARE SUBJECTIVE, AMBIGUOUS, GRADED ON WORDING MORE THAN CORRECT ANSWER REFORM MATH IS BOGUS - IS MEMORIZATION AND FACTS GOOD OR BAD? \clip\97\20\newmath.txt Please go to the following web site and read what a Ph.D. mathematics professor at Dartmouth has to say about math education. http://www.wgquirk.com/wgquirk/ Read the following document. http://www.wgquirk.com/wgquirk/#Documents Memorize Multiplication Facts? Cheney - Yes, Romberg - Abstained WHOLE MATH IS THE NEW DISASTER The Weekly Standard August 4, 1997 EXAM SCAM The Latest Education Disaster: Whole Math By Lynne V. Cheney Senior Fellow, American Enterprise Institute my file: \clip\97\20\examscam.htm "They lied to me, says Madalyn McDaniel of Atascadero, California. They completely betrayed me..." REFORM MATH IS A MULTICULTURAL BUST LIKE WHOLE READING \clip\97\13\fuzzmath.txt http://www.usnews.com/usnews/issue/970526/26john.htm ON SOCIETY BY JOHN LEO That so-called Pythagoras "Deep Thoughts" started as Jack Handy's running joke on TV's Saturday Night Live--a series of mock-inspirational messages about life that make no sense at all. Now "Deep Thoughts" are available on greeting cards, including one that pokes fun at the fuzzy new math in the schools. MATH DRILL RAISES SCORES, BUT SPURNED BY REFORMERS. REFORM MATH FAD IS FAILING US STUDENTS, VALUE FEELING GOOD OVER TEST SCORES \clip\97\01\refmath.txt http://www.seattletimes.com/extra/browse/html97/math_010597. html Copyright © 1997 The Seattle Times Company Jan. 5, 1997 Math-teaching fads failing U.S. students by Richard Lee Colvin Los Angeles Times Now the "reform" movement rules, it puts more value on feeling good about math than high test scores. It includes "fantasy lunch", cutting out paper shapes which has more to do with art than math, students confused about trying to "discover" 1000 years of math concepts on their own in groups, banning textbooks with "too many" formulas, and relating to fairy tales. US Ed Secretary urged not "abandoning" the reform method, critics say that drill on addition and subtraction is what builds up the mind for harder tasks. (comment, this has got to be the dumbest way to teach math I've ever heard of, it almost guarantees Asian supremacy in math, they never stand for this silliness.) %%higher scores DISTRICTS ALREADY COMMITED TO WHOLE MATH "HIGHER" STANDARDS \clip\97\29\baytep.txt Saturday, Dec. 13, 1997 · Page A 1 ©1997 San Francisco Examiner Bay tepid to math standards Educators question sense of the state's new guidelines Julian Guthrie OF THE EXAMINER STAFF [state needs to revise textbook, curriculum, asessment] For Redwood City superintendent Ron Crates, the new math standards couldn't have come at a worse time. Five years ago, at a cost of nearly $700,000, the district adopted content performance standards that he says have resulted in higher test scores. The district also spent $2.5 million to retrain teachers to teach under the more rigorous standards. %%TQM Blomstom says that Seattle teachers were told to support the reform math textbooks @@Remedial Math Colleges find many college students aren't ready for college level math or english and require students to take remedial courses in algebra or english. \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN http://www.math.uic.edu/~cpmp/archive9701.html Math professors shake their heads at the skills of freshmen--54% in the CSU system have to take remedial math. "Things the average students would know backward and forward 12 years ago, these students don't know at all," said Jerry Rosen of Cal State Northridge, lamenting how students now use calculators to add single-digit numbers. z45\clip\2000\08\remedma.txt Cal State Puts Remediation on an 'Or Else' Basis University system combines a tough approach with efforts to help high-school students prepare By JEFFREY SELINGO Long Beach, Calif. Chronicle of Higher Ed August 4, 2000 http://chronicle.com/free/v46/i48/48a02701.htm Last fall, 74 percent of black freshmen and 65 percent of Hispanic freshmen in the university system needed remediation in math, com pared with 40 percent of white freshmen. In English, 64 percent of black freshmen and 62 percent of Hispanic freshmen needed remediation, compared with 29 percent of white freshmen. @@Rhomberg, Thomas University of Wisconsin education professor who lead development of the NTCM standards, dismisses value of basic skills tests like the TIMSS where US 8th graders did relatively poorly. Author of "Math in Context" published by Encyclopedia Brittanica, received $1,702,780 from the National Science Foundation to develoop it. Weekly Standard Aug 4, 1997. @@Rhombus Parallelogram with all sides equal Grade Spectrum G1 A.G Bell 1999 1st/2nd grade class G4 Exploring Elementary Mathematics 1970 Holt Rheinhart Winston @@SAT Scores asian.education.math doc\95\01\sat93us.xlw 1993 SAT Scores Ranked by Race and Gender (unpublished special tabulations, College Board) 559 Asian male 518 White male 512 Asian female (only 6 points below WM) 472 White female 451 Hispanic male 408 Hispanic female 400 Black male @@Saxon John Harold Saxon is a leading proponent of a system empasizing rote drill reputed to be a remedy for fuzzy new new reform math. Founded a publisher dedicated to mastery of phonics and math skills / facts. Hated by educator reformers who insist on avoiding learing detailed phonics or math exercises, especially so because evidence seems to show that Saxon's methods work extremely well, and there is little evidence that show that conventional reforms result in improved performance. Now the company is run by his first employee, Frank Wang, who was a 16 yr old high school junior looking for a summer job. There are many success stories, often in inner city or rural settings, but it is shunned by the mainstream which embraces "standards based" (or fuzzy) mathematics. Saxon Publishers Home Page Article B ibliography %%Anti VERY GOOD AT PROCEDURAL ACCURACY BUT ONLY ONLY LEARN A BUNCH OF TECHNIQUES Prof. Hung-Hsi Wu raps Saxon for falling short of California standards, rejected by CA board It is extremely good at promoting procedural accuracy. And what David says about building everything up in small increments, that's correct, but the great pedagogy is devoted, is used, to serve only one purpose, which is to make sure that the procedures get memorized, get used correctly. .hundreds of thousands of students thinking that mathematics is basically a collection of techniques. %%General LOS ANGELES NIXES SAXON DESPITE SUCCESS WITH MINORITIES z50\clip\2001\06\saxon.txt Not on the Same Page Some Educators Say Saxon Math Books Are Great Teaching Tools, but Many School Systems Refuse to Use Them By Jay Mathews Washington Post Staff Writer Tuesday, June 19, 2001; Page A09 MAYWOOD, Calif. Last year's state tests showed that the school's first-graders had climbed from the 28th to the 44th percentile using Saxon. Second-graders had jumped from 24th to 42nd. z43\clip\2000\07\saxon.txt Subject: Saxon math: practice, practice Gail Russell Chaddock (chaddockg@csps.com) Staff writer of The Christian Science Monitor 5.30.00 BACK TO BASICS Saxon math: practice, practice - We don't lecture about internal combustion engines, we take you for a drive around the block. link For details on Saxon's story, go to http://www.winonanet.com/taa/NOTABLE/saxon.html Texas Commissioner refuses to allow Saxon Texts despite high performance. School board rejects Saxon math despite high scores \clip\98\08\saxmath.txt Denver Post Jeffco schools subtract Saxon math By Janet Bingham Denver Post Education Writer May 8 1998 - JEFFERSON COUNTY - A group of parents Thursday lost their battle to keep the Saxon math textbooks as a central part of the curriculum at three Jefferson County elementary schools. doc\web\97\08\saxon.txt Parent says saxon fixed harm caused by U Chicago Everyday Math http://www.seattletimes.com/sbin/iarecord?NS-search-set=/ 3353b/aaaa006YQ53b e0f&NS-doc-offset=0& \clip\97\11\saxon.txt Seattle Times Local News : Feb. 9, 1997 Math + memory, math + memory . . . by E.J. Gong Jr. "The approach is simple: repetition with frequent quizzes and review exercises. Some educators swear by it, while many others just swear at it. " John Saxon, now deceased has a popular math drill program for students failing in math. %%Sequence G2 venn diagram line of symmetry deg far mult add sub 2 digit color 3 3/4 squares bar chart estimate pounds horizontal (diagonal) oblique parallel line survey with chart perimeter < > = adding coins math54 roman numeral 1/4 + 1/8 450 / 15 75% of 100 div by 2 digit int multi > 2 dig adding exponents 5^2 + 2^3 meter kilometer reading scales tic marks adding with regrouping tally (||||/) sales tax (given as .20, not computed as %) area = rows x columns (but not height x width) mixed num improper fraction adding decimal adding like denom fraction estimate area by counting grids mult 3 x 2 digit sphere pyramid cylinder sphere cone math65 parentheses multiplication table long division practice read unlabeled tics reading clock time hands parallel perpendicular intersecting right acute obtuse angle ruler to 1/4 inch short division long 1 4 +------- 4 | 5 6 4 1 6 vs 1 4 --------- 4 | 5 (1)6 perimeter circumference radius (but not c=2 pi r) length unit conersion meter cm yard ft inch eq fractions percent to name part of group mult by decimal prob as fraction area = row x col draw count squares div decimal change a @@Scale Drawings %%Read 4th WA Assessment (bird feeder) 4th New Standards (with help of professional carpenter) --------- too early ------- 6th Nevada 6th Japan 1990 8th NAEP 5-8 Vermont - make scale drawings 8th 2001 Singapore math 10th WA Benchmark %%Construct 7th Nevada 1998 Create scale drawings New Standards - 4th grade "applied learning project" is to create plans for a bike trailer "with the help of a professional carpenter" over a period of months, with several views. NAEP Make and read scale drawings - do not assess at 4, ok at 8th grade. WA 4th Grade Assessment - read drawing for bird feeder, it has a top view, and orthogonal 3D view to give dimensions from arrows. WA 10 Grade Benchmark http://cisl.ospi.wednet.edu/ComSL/MATHBMK3.html construct geometric models and scale drawings using tools as appropriate, for example, designing a house plan or building a model of a bridge @@Scientific Notation G6 Utah G6-8 Florida @@Scott Forseman Addison Wesley Math http://www.illinoisloop.org/sf.html#conclusion z68\clipim\2003\06\03\sfaw\safaw.htm Illinois loop says it's not as bad as some off the deep end books, but still insists on 4th grade stem and leaf plots, distracting sidebars which give parents ADD, and still does the "solve it 3 different ways", but at least the traditional way is ONE of the correct ways, unlike Dale Seymour which says death to arithmetic as we know it. @@Sequence %%Traditional "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later", by R. James Milgram, Department of Mathematics, Stanford University: ftp://math.stanford.edu/pub/papers/milgram/andover-report.html txt: \clip\99\06\coreplus.txt "Traditional" Calculus = College 1 ----------------------------------- G1-G6 Elementary K : counting to 20 G1: add sub to 10 G2: add sub to 20, mult G3: add sub to 100 mult divide G4: add sub to 1000, money, average, compare like fractions G5: add sub, mult, div to 2 decimals, percent, ratio? G6: add sub, mult div decimals, neg integers, ratio, proportion G7-G8 Middle School 1-3 G7: decimal math, exponents, sci notation, exact probability, total of products, compare fraction unlike denonominator, unit conversion, percent interest, discount, mult by fraction, volume = l x w x h, neg integers, probability as ratio, percent, fraction, similar triangles. G8: decimal math, pythagorean theorem, algebraic expressions, triginometry, solve 5x + 24 = 300, rotation scatter chart, prime factorization, divisibility, permutation, frequency table flagpole proportionality? 1980s ------------------------- G9: Algebra I (solve ax + bx = c) G10: Geometry (obtuse angle) G11: Algebra II G12: Pre-Calculus (Trigonometry and Topics in Advanced Algebra) College: Calculus 1960s --------------------- G9: Algebra I G10: Algebra II G11: Geometry G12: Triginometry (thanks to Lauren Scheffers) "in my generation we had six subject hours (55 minutes) per day. I had 4 years of math (algebra I & II, geometry, and trigonometry), 4 years of English with an elective of rhetoric (in the "missing" science year that follows), 3(?) years of science (chemistry, biology, physics), 2 years of history (U.S. and world), 2 years of a foreign language, 4 years of gym, and 1 "elective" hour. People tended to use that for study hall, home ec, shop, or in my case, orchestra for 4 years." Accelerated ------------ G8 Algebra I G9 Geometry G10 Algebra II G11 Pre-Calculus (Trigonometry and Topics in Advanced Algebra) G12 Calculus http://www.arthurhu.com/images/99/09/07/highmath.gif Renton High District 403 High School Registration Booklet Graduating class of 1998 & beyond This chart give an excellent view of different levels of traditional math, as compared to "integrated math" and the notion that all students must master algebra and geometry by the 8th grade. Accelerated->Calculus ----------------- G8 Algebra 1,2 G9 Geometry(2) 1,2 G10 Algebra 3,4 G11 Math Anal/Trig G12 Calculus College Prep Normal->Math Anal -------------------- G8 65 percentile Algebra Aptitude or 80% Math Placement G9 Algebra 1,2 G10 Geometry 1,2 G11 Algebra 3,4 G12 Math Anal / Trig Slow Algebra->Algebra 3,4 --------------------- G8 36-64 Algebra prep, 60% Math Placement G9 Algebra 1A, 1B G10 Algebra 2A, 2B G11 Geometry 1,2 G12 Algebra 3,4 Minimum ----------------------- G8 0-35 Algebra test, < 60 math place G9 none G10 Math 1,2 G11 Math Maintenance Math Applications G12 Consumer Math 1,2 %%Reform "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later", by R. James Milgram, Department of Mathematics, Stanford University: ftp://math.stanford.edu/pub/papers/milgram/andover-report.html txt: \clip\99\06\coreplus.txt Integrated Math G1-G5 Elementary G6-G8 Middle School 1-3 G10-12 Integrated Math 1-4 College Remedial->Algebra->Calculus @@Singapore Math Textbook http://www.rockymountainnews.com/drmn/opinion_columnists/article/0,2777,DRMN_23972_4987887,00.html Back to basics Vincent Carroll, editor of the editorial pages, Yes, Singapore - whose structured approach gives many progressive educators the fits. Perhaps mastery of the facts is not so mindless after all. US STINKS IN BASIC MATH, BUT GOOD AT 21ST CENTURY FUZZY APPLICATIONS z87\clip\2005\02\airstudy.htm AMERICAN INSTITUTES FOR RESEARCH® What the United States Can Learn From Singapore’s World-Class Mathematics System AIR Report in pdf at: http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf American Institutes for Research (AIR) February 7, 2005 New AIR Study Compares the Quality of U.S. Math Instruction with Singapore, a Recognized World Leader U.S. Trails, But Both Nations Could Learn from Each Other Although the U.S. mathematics program is weaker than Singapore’s in most respects, the U.S. system is stronger than Singapore’s in some areas. The U.S. frameworks give greater emphasis than Singapore’s to developing important 21st century mathematical skills such as representation, reasoning, making connections, and communication. The frameworks and textbooks also place greater emphasis on applied mathematics, including statistics and probability "Because topics are mapped out in such a general way, the NCTM requirements risk exposing students to unrealistically advanced mathematics content in the early grades. NCTM’s Pre-K–2 algebra topics, shown in Appendix: Exhibit B3–2, indicate that students should understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various contexts, all in the very early grades. Students are exposed to these complicated mathematical topics in kindergarten and first grade at the same time they are learning basic addition and subtraction. Singapore, in contrast, considers algebraic concepts to be advanced rather than introductory mathematics, so algebra is not introduced until the sixth grade. Overall, NCTM’s grade-band structure lacks the specificity needed to serve as a solid national content benchmark. The specificity and logic in Singapore’s spiral approach offer a more effective, bettersequenced framework for a mathematical curriculum." The California mathematics framework is modeled on Singaporean and Japanese frameworks. It is similar to the Singapore framework in that it is organized around a varying set of mathematical topics appropriate to the grades in which they are taught. "this approach means that Singapore relies on early high-stakes testing [but for sorting, not all pass at the same level], but it also holds teachers responsible for the success of all children and ensures that teachers devote more attention, rather than less, to students with greater academic needs." BOTH CHINESE AND MALAY SCORE 83/96 ABOVE AVERAGE, US BLACK AT 25 PCT "1999 TIMSS scores for its Malay and Chinese populations (Ministry of Education Singapore, 2000b). Although 96 percent of Chinese students performed better than the international eighth-grade mathematics average, Malaysian Singaporeans also did very well, with 83 percent scoring above the international average. Scores for Singapore’s Indian minority population were not available, but typically, students of Indian background outperform their Malaysian peers by a small margin. By comparison, in the United States, half of black eighth-grade students achieved no better than the bottom quarter of all international test takers (NCES, 2000)." "We first looked at the Singapore textbooks and workbooks, the Scott-Foresman student texts, and the Everyday Mathematics student journals to get an overall sense of how they address mathematical topics." "Singapore students are expected to complete about one thorough lesson focused on a single topic per week, while U.S. students are expected to complete about one lesson on a narrowly focused topic each day." "the Scott-Foresman textbooks cover the geometric properties of plane shapes, 3-D solid figures, symmetry, congruence, and transformations in all six elementary grades. The Singapore textbooks, in contrast, do not introduce 3-D solid figures and symmetry until grade 4." "The only statistics content in the Singapore grade 5 textbooks and workbooks is a single lesson on line graphs. The lesson consists of one line graph made by using a table of data on attendance at a swimming pool over a 5-month period." "Despite the generally poor showing of both U.S. textbooks in terms of teaching mathematical concepts, the nontraditional U.S. textbook, Everyday Mathematics, does do one thing much better than the Singaporean texts do. It poses interesting real-world problems and uses illustrations that demonstrate the practical application of mathematical topics," z84\clip\2004\06\singpore.txt Schools import Singapore math style Diagrams, models used to aid comprehension By Susan Ware, Boston Globe Correspondent | June 10, 2004 The students at the Varnum Brook Elementary School in Pepperell groaned in unison when teacher Karin Pillion announced they would do the next set of problems out loud -- without pencil, paper, or calculators. "What is 6 times .04?" Pillion began. @@Slope Intercept G8 WA 2007 Draft math standard "interpret meaning of graph's slope" @@Standards Posted Northshore Schools (Seattle Suburb) http://wo1.nsd.org/Apps/WebObjects/Standards.woa/1/wo/O91vLCwJWgxc2g4Ni9C1Hq9XogU/0.12 @@Social Justice TEACH MATHEMATICS FOR SOCIAL JUSTICE oslund home What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? ... www.msu.edu/~oslund/ - 14k - Supplemental Result - Cached - Similar pages TE 803: Professional Roles and Teaching Practice--Elementary Mathematics What is mathematical power? What does it mean to teach mathematics for social justice? Why should all students learn mathematics, anyway? In the upcoming semester, Joy, along with 18 interns in MSU's teacher certification program, will grapple with these big ideas while navigtating the day-to-day experiences of the internship. @@Standards Wars CA MATH STANDARDS WARS 12/97 "...school systems that embark on a course that substitutes computational proficiencies for a commitment to deep, balanced, mathematical learning." US "WORLD CLASS MATH STANDARDS" AREN'T WORLD CLASS AT ALL! z57\doc\web\2002\08\mathstan.txt z47\clipim\2002\08\06\mathstan.pdf http://www.aft.org/american_educator/summer2002/curriculum.pdf A Coherent Curriculum The Case of Mathematics By William Schmidt, Richard Houang, and Leland Cogan American Educator (AFT) Summer 2002 Note - the scattershot state standards are partly BECAUSE of reform efforts such as NCTM which deliberately call for putting high level math and algebra into grades as low as kindergarten. These were never aligned with standards of other nations. Ironically, Schmidt is one of the people calling for NCTM "higher order thinking" constructivist math, but this call for sane standards is a step forward. E. D. Hirsch, Mr. Core Curriculum also writes inside this article. State standards contrast to international standards - * "For instance, even more demanding topics such as geometric transformations, measurement error, three-dimensional geometry, and functions are intro-duced as early as first grade." * Prerequisite knowledge doesn’t come first. For example, the distributive property is intended to be covered in first grade, vs. grade four (and not earlier than grade three) in the top-achieving countries. * Stuff is taught in every grade instead of few topics over only 2 or 3 years. @@Statistics %%Frequency Table / Histogram Many new assessments include very complex frequency histograms or distribution tables as early as the 4th grade. In addition the WA test expects students to pick out the distrbution with the most items LESS than an amount. G2 Eric's 2nd Grade G4 Scott Forseman Math 1998 (called a line plot) G4 New Standards Assessment (raisins) G4 WA Assessment (battery) G4 KIRIS sample ---- appropriate ---- G6 Japan 1990 G7 WA Benchmark (freq table) G8 Nevada 1998 (frequency distribution) G9-12 VT %%Effective MAY 2004: ALL FUZZY MATH PROGRAMS ARE ACTUALLY UNPROVEN TO BE EFFECTIVE http://www.nap.edu/books/0309092426/html/ A report just released from the National Academies reveals all 13 National Science Foundation (NSF) funded mathematics programs lack adequate scientifically valid evidence of effectiveness. Among the programs deemed to be still experimental are NYC's universal elementary program Everyday Math, as well as several others used in some waivered K-12 schools. National Academies announcement: "Evaluations of mathematics curricula provide important information for educators, parents, students and curriculum developers, but those conducted to date on 19 specific curricula fall short of the scientific standards necessary to gauge overall effectiveness, says a new report from the National Academies' Mathematical Sciences Education Board." - Latest News From the National Academies, May 18, 2004 http://www.nas.edu/ %%Eric's 2nd grade graph2.gif Scott Forseman Addison Wesley p. 45 "Critical Thinking" Each * stands for 10 children More than 2 miles ****** 2 miles **** 1 mile ***** less than 1 mile *** How far do most students live from school? () 2 miles or more () 1 mile or less How many students live less than a mile from school () 50 () 30 The children who live more than 1 mile from school ride the bus. How many children ride the bus? () 100 () 50 How many children must get to school in other ways? () 30 () 80 This form of a chart is equivalent to a frequency histogram, this form of analysis is beyond the 7th grade EALRs since it involves evaluating distributions other than the central value. To determine where most students live involves either a) figuring out the half-way median point out of 18 students, or b) figure that 2 miles or more consists of the the first two sets, and 1 mile or less is the last two sets, and that the the first set is larger than the 2nd set. Either way is way beyond basic 2nd grade math skills which is basically addition and subtraction facts to 100 with regrouping, very simple fractions and very simple multiply divide. @@Square G5 GA Pi r squared http://www.glc.k12.ga.us/BuilderV03/LPTools/LPShared/lpdisplay.asp?Session_Stamp=&LPID=15155 G5 Everyday Math exponential notation for squared numbers is introduced http://www.mathematicallycorrect.com/books5h.htm G6 squared means second power www.achievementtech.com/files/OH_MathI.pdf @@Square Roots and Power Use square root to solve for radius given area of circle G6 Connected Mathematics teacher solution Not covered in student book until G8. G6 square roots that are whole numbers http://www.arlingtonschools.org/Curriculum/math6.html Estimate square root of non-square number G7 CA "find the two integers between which its square root lies" www.cde.ca.gov/be/st/ss/mthgrade7.asp G8 OH "estimate the square root of non-perfect" www.ode.state.oh.us/GD/DocumentManagement/DocumentDownload.aspx?DocumentID=14972 G8 WA 2007 math draft "explain why such a root is not a rational number" Basic Skill - Square root of (x) is number that multiplied by itself will result in x. G5 DODDS demonstrate square root G6-8 Lake Wash G7 California 1998 G8 DODDS graph square root (achieve) G8 Connected Mathematics Looking for Squares "introduces the term square root " http://mmmproject.org/cmp.htm Looking for Pythagoras Understand how to find the square root of a number http://schools.mukilteo.wednet.edu/staff/lapinskiij/math/level_5_math_syllabus.htm G8 Oregon recognize square root G9 Japan Japan http://www.achieve.org/achieve/ search for square root http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm @@Stem and Leaf Plot Grade level ----------- G4 Scott Foresman G5 Hougton Mifflin From Scott Foresman / Addison Wesley Math 4th grade: Create a table using place value to organize data into a histogram --------- 2 0 20 3 3 33 4 5 0 0 8 50,50,8 6 5 2 0 65,62,0 7 8 2 82 @@Story Problems 8-11 (stage 2) http://www.nrich.maths.org.uk/primary/current_month/penta.htm#5081 Train Timetable Three trains travel from City Station to Farmland Station on the same morning. The Express leaves City 10 minutes after the All Stations train, but arrives at Farmland 10 minutes before it. The All Stations takes 50 minutes to reach Farmland and arrives at 10:30. The Goods train leaves 20 minutes before the All Stations and arrives at Farmland 20 minutes after the Express. Work out the timetable. That is; what time does each train leave City Station and what time does each train arrive at Farmland Station? "Train Tunnel" comes from Teacher Tactics for Problem Solving by K. Stacey & B. Southwell. @@Sum of Products Most G4 textbooks do not teach kids how to construct totals of products such as total price of a number of repeated items. I have yet to find a single curriculum standard that specifies this ,even though grade 4 tests often have such problems. G4 1997 WASL WA test (bird feeder) G4 1998 MCAS MA test (prob 4 scores) @@Symmetry Also translation, rotation, reflection G2 Dale Seymour (construct symmetric figure) G2 Texas Core Curriculum (recognize line of symmetry) http://www.trinity.edu/departments/education/TCKC/2math97.htm G4 Washington EALRS (recognize) --------------------------------------------------- G5 Nevada - G5-8 Vermont rotational and bilateral in 2/3D G6 Japan standard 1990 G7 Washington EALRS (construct figure) @@Systems of linear equations G7 MarcoPolo NY - Lesson DetailCoordinate Geometry, (A.G.7) Graph and solve systems of linear equations www.nyiteez.org/MarcoPoloNY/ProgramDetail.php?CourseID=IL039791 G8 WA Math Draft 2007 "identify graphical solutions to systems of linear equations" @@Tally ||||/ ||||/ || = 12 Groups of 4 and slash for 5 G1 Scott Forseman 1998 @@Teacher %%China z57\clip\2002\08\chinmath.txt Creativity lacking in Chinese schools Seattle Post Intelligencer August 29, 2002 MADHU NARAYANAN UNIVERSITY STUDENT we saw rigorous math proofs and college-level physics. The nationalized curriculum packs an amazing amount of material into 12 years, and students emerge with a set of skills that would seem to put the average American high school graduate to shame. "American students aren't afraid to make mistakes, but our students are too worried about finding the one right answer." CHINESE TEACHERS LESS EDUCATED BUT BETTER AT MATH \clip\99\20\techchin.txt Rocky Mountain News November 14, 1999 http://InsideDenver.com/seebach/1114seeba.shtml Linda Seebach An American nightmare: mathematics education Only nine of the 23 US teachers got the right answer to 1 3/4 divided by 1/2 Chinese teachers usually have less formal education than Americans -- two or three years of normal school training after ninth grade -- yet all of the Chinese teachers got the correct answer to the division calculation. Ma also tested a group of Chinese ninth-graders. They did better than the American teachers too. Several confessed they had to look up the formulas for perimeter and area of a rectangle. Notices of the American Mathematical Society, which is available at www.ams.org/notices/199908/rev-howe.pdf online. ONLY 50% OF AMERICAN VS 100% OF CHINESE MATH TEACHERS SOLVE FRACTION PROBLEM http://www.arthurhu.com/99/07/asmath.txt From: "Mark J.K. Penzkover" Liping Ma has written a new book, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, Lawrence Erlbaum Associates. 50% of American but 100% of Chinese math teachers could solve moderately complex fraction problem. %%general WE NEED $5 BILLION / YR TO IMPROVE MATH z45\clip\2000\09\nsta.txt National Science Teachers Association: Legislative Update September 27, 2000 **Glenn Commission Issues Final Report on Science and Mathematics Teaching for the 21st Century** "We as a nation must take immediate action to improve the quality of math and science teaching in every classroom in the country. If we delay, we put at risk our continued economic growth and future scientific discovery," said Senator Glenn. The Commission estimates the action strategies for achieving the three goals will cost more than $5 billion annually. http://www.ed.gov/americacounts/glenn/ has .pdf, it promotes "discovery" math, discounts rote learning, calls for "high standards" It's building a "systems" approach to the math and science curriculum. Everything from certification to accreditation, training to curriculum development, standards to assessments, will all be leveraged toward the predetermined "international" outcomes. This guarantees that the curriculum and assessments will be dictated by UNESCO, regardless of local/state interests or control (what a joke!). TEACHERS MUST RELEARN CONSTRUCTIVIST MATH Canda paper EQAO has sponsored a second research paper "Varieties of Assessment: Issues >of Validity and Reliability" (June 1999) by Anthony Barley (Lakehead) and Alexandra Lawson (OISE). "From this perspective, teachers need to spend time relearning mathematics in a constructivist or problem-based manner in order to be able to teach in this fashion. Genuine mathematical reform of teachers' practices, the type of reform that might result in children understanding more about mathematics, is highly challenging." TRAINING TRADITIONAL OR INVENTED MATH? delay textbooks to meet new traditoinal CA standards \clip\99\15\mathte.txt Los Angeles Times July 23, 1999 http//www.latimes.com/HOME/NEWS/STATE/topstory.html Classes for Teachers Return to Basics, Especially Math SchoolsDistricts focus on notion that one can't teach what one doesn't know. Often that includes fundamentals. By RICHARD LEE COLVIN, Times Education Writer In the Los Angeles Unified School District, one in five math teachers are working under emergency permits, meaning they are not fully trained. But there's little evidence, researchers now say, that the billions of dollars spent on pushing such generic teaching techniques have had much, if any, impact on student achievement. MATH SCIENCE TEACHERS WITH "EMERGENCY" CREDENTIALS JUST AS GOOD, HAVE BETTER TEST SCORES \clip\99\14\teaccred.txt The Washington Post Effectiveness Of Teacher Certification Questioned By Kenneth J. Cooper and Jay Mathews Washington Post Staff Writers Thursday, July 15, 1999; Page A14 ... high school students whose teachers have emergency teaching certificates perform about as well in mathematics and science as students whose teachers hold regular teaching credentials. ... based on the test scores of a national sample of high school seniors and sophomores, runs contrary to the assumptions of a Clinton administration proposal to require states to stop issuing emergency teaching certificates as a condition for receiving federal education aid.... students whose teachers have college degrees in math or have been specifically certified to teach math score significantly higher on standardized tests than students whose teachers did not specialize.

@@Test Scores

Traditional math ends up with better test scores every time, or at best, equal. The claims is that there is NO evidence that NTCM methods result in lower scores, but this is almost always the case. %%Equal There are no programs at any level that share the core instructional features, have been implemented as intended for reasonable lengths of time, and show that students perform more poorly than their traditionally taught peers http://www.nctm.org/jrme/abstracts/volume_30/vol30-01-hiebert.html Journal for Research in Mathematics Education January 1999, Vol. 30, No. 1, Page 3-19 Relationships Between Research and the NCTM Standards James Hiebert, University of Delaware [yet cites controversy over poor Algebra performance in Riverside] Home Page The Interactive Mathematics Program (IMP) Dr. Webb has found that IMP students do as well as students in traditional mathematics classes on standardized tests such as the SAT. \clip\98\01\mathform.txt LOS ANGELES TIMES Jan. 5, 1996 Formulas for Math Problems RICHARD LEE COLVIN (New math, math reform backlash against "fantasy lunch") http://www.math.uic.edu/~cpmp/archive9701.html School offers students a choice, only 1/4 chooses reform math. " In trials across the country, IMP students have done no worse--but no better--on college entrance exams than students taught traditionally. Still, Martinez believes weaker students stick with math longer because they enjoy the unconventional approach." %%Higher Scores There are _no_ studies that show higher math scores for new integrated math programs. %%Lower Block scheduling also results in lower SAT scores. MATHLAND BLAME FOR SCORE DECLINE IN SF Thursday, Aug. 15, 1996 · Page A 4 San Francisco Examiner Mixed math test results leading S.F. district to rethink methods Students in City's elementary, high schools lose ground on basic skills test; superintendent cites new curriculum Venise Wagner San Francisco students scored 50.3 in reading and 53.7 in math vs. national 50 Elementary math scores fell to 50.5 this year from 50.8 in 1995. High school scores dropped to 57.1 from 57.7. African Americans scored 36.7, down from 38.6 in 1995; Filipinos scored 50.7, down from 52. Nearly 50 percent of African American students were at the bottom 25 percent in math. About 57 percent of African American second-graders were at the bottom 25 percent. In the fifth grade the percentage was 52.8. VERMONT SHOWS MASSIVE FALL IN COMPUTATION SCORES Vermont pioneered NCEE program We pioneered the math. What they haven't told you is that the computation scores on our California Achievement Tests plummented during the time we were involved in this so-called "project" with no gains in the area of "concepts and applications." Our involvement began in 1990 and our children are tested in the fall of each year. Here are the math computation percentile score summaries for 6th grade on the CAT: FALL IN PERCENTILE FROM 72% TO 59% 1989: 67%; 1990: 72%; 1991: 41%; 1992: 50%; 1993: 49%; 1994: 44%; 1995: 49%; 1996: 49% RISE IN FAILURE FROM 9% TO 28% Here is the percent of kids scoring in the lowest quartile: 1989: 9%; 1990: **; 1991: 25%; 1992: 24%; 1993: 31%; 1994: 27%; 1995: 28%; 1996: 28% Finally, here's the difference between the scores on the "Total Battery" and the "math computation" scores: 1989: -10%; 1990: -13%; 1991: -34%; 1992: -32%; 1993: -32%; 1994: -32%; 1995: -29%; 1996: -30%] April 26, 1998 edition of the Riverside Press-Enterprise newspaper High failure rates and concerns that students are not learning the math skills they need has prompted a third of Inland high schools trying a new college-prep program to drop it. Riverside's Poly High School discontinued College Prepatory Mathematics [CPM] in June after only 27 percent of the Algebra I students earned a C or better. One semester after scrapping the program, the passing rate went up to 42 percent (Sharma, 1998) DOD STUDY SHOWS MINORITES HAVE LARGER GAP WITH REFORM MATH http://www.tppf.org/ecot.html \clip\99\02\ecot.htm SCHOOL DISTRICT ALERT FOR MATHEMATICS TEXTBOOK SELECTION Texas policy foundation. NSF funded books are ranked as unsuitable for algebra by 8th grade In 1995 the Department of Defense introduced two "standards" math programs ...standardized testing of the 81,140 students enrolled in "Mathland" (elementary school) and "Interactive Math" (middle school). The CTBS indicated that scores in computation had significantly dropped (9 points for grade 3, 12 points for grade 4, 11 points for grade 5, 10 points for grades 6 and 7, and 4 points for grade 8). Data generated by this study can be accessed on the Internet at http://206.86.183.194/math/McArthurText.htm. ANDOVER HIGH SCORES 1-5 PCT WITH CORE PLUS \doc\web\index\corefail.htm The Detroit News Metro Section June 17, 1998 Math debate heats up Professor won't give up controversial data on Core-Plus program in Bloomfield Hills By Rusty Hoover / The Detroit News BLOOMFIELD HILLS -- A math program at Andover High School that students say has cheated them out of a solid math education is now causing a second round of controversy. Escondiso flunks CPM, IMP Traditional math has best SAT scores. San Diego Union 1/21/98 A step back for the new math Trustees act to end it at one high school Susan Gembrowski "Students in new math at Orange Glen, for example, scored an average of 477 on the SAT, while those in traditional classes at the same campus had average scores of 502. " ""No data is available that indicates that the integrated math is a success," he said. " @@Testosterone Testosterone levels may have something to do with male/female differences in math and verbal performance. zip37\clipim\99\09\06\test.efx Seattle Times June 16, 1996 Testosterone may have links to skills in English, math John Hopkins University found 11 men with low testosterone levels did worse in math but better in verbal tasks without treatment. @@Textbook %%AAAS middle school Major warning flags! [[Project 2061 Project 2061 promotes NSF funded math like connected mathematics Reform: Project 2061, the long-term math and science education reform initiative of the American Association for the Advancement of Science (AAAS) has made a major contribution to education reform efforts with this standards-based textbook analysis," Funded by the source of funding of worst math textbooks: The benchmarks-based approach to evaluation was developed with funding from the National Science Foundation. Funding for the middle school math book evaluation was provided by the Carnegie Corporation of New York Based on dreaded NCTM standards: he analysts evaluated textbooks on how likely they are to help students achieve six key learning goals from Project 2061 landmark Benchmarks for Science Literacy. These benchmarks are consistent with the widely accepted standards developed by the National Council of Teachers of Mathematics. The AAAS math reviews are available on line as .pdf files in the press relea se at \clip\99\03\aaas.htm http://project2061.aaas.org/newsinfo/press/rl012299.htm The entire document is 4 pages long (the total of 3 files). ratings \clip\99\03\attach_a.pdf http://project2061.aaas.org/newsinfo/press/attach_a.pdf benchmarks attach_b.pdf http://project2061.aaas.org/newsinfo/press/attach_b.pdf good/bad example http://project2061.aaas.org/newsinfo/press/attach_c.pdf \clip\99\03\attach_c.pdf Best: Dale Seymour, Mathscape, Math Thematics McDougal Littell Worst: Saxon, Scott Forseman, Passport McDougall Littell %%Addison Wesley Focus on Algebra "Rainforest Algebra" Rainforest Algebra 800 pages of junk vs. 200 page japanese book that just teaches algebra, links to other bad reviews. %%Asian %%Japanese %%Singapore @@singapore The claim is that the fuzzy math texts are just like the Asian books but you can be darned sure they don't leave out carry and borrow but put in sheet music to Bingo!. http://www1.moe.edu.sg/syllabuses/default.asp Link to pdf Prim, HS standards z48\clipim\2001\03\29\maths_pri.pdf 2001 Singapore Math Standards Maths_LowSec.def lower secondary school. Singapore fuzzy math: Mathematics education aims to enable pupils to: • acquire and apply the skills and knowledge relating to number, measure and space in mathematical situations that they will meet in life. • acquire mathematical concepts and skills necessary for a further study in mathematics or other disciplines. • develop the ability to make logical deduction and induction as well as to explicate their thinking and reasoning skills through the solving of mathematical problems. • use mathematical language to communicate mathematical ideas and arguments precisely, concisely and logically. • develop positive attitudes towards mathematics including confidence, enjoyment and perseverance. • appreciate the power and structure of mathematics, including patterns and relationships, and to enhance their intellectual curiosity. key features of the syllabus: • mental calculation • mathematical communication • practical uses of mathematics • investigative work • problem solving • critical thinking • creative work • use of information technology Continual Assessment It is important to carry out assessment on a continual basis. Teachers should use continual assessment to: • obtain information about pupils’ learning, suitability of teaching methods and materials and effectiveness of the teaching programme • identify any learning difficulties that pupils may encounter or misconceptions that they may have so as to plan effective remedial help • provide prompt feedback to pupils on their progress and attainment • promote pupils’ confidence in doing mathematics by focusing on what they can achieve rather than what they cannot NSF Report faults Connected mathematics for shorting basics, but knocks Singapore math for "higher order thinking" even though Singapore students scored higher in math ability. SINGAPORE FOLLOWED VERMONT MATH ADVICE April 2001: Representatives from Singapore visited Vermont for two years studying the Vermont's standards and assessment system....Marge Petite, Acting Commissioner of Education at the time, spoke to the Business Round Table extolling the visitations and how Vt. had been selected by Singapore. In her address she stated that she advised the Singapore delegations that it was necessary to reduce existing math content by 30%. Looks like they followed instructions! Fran Rice How to get actual Japanese or Singapore math texts for $20 a book Japanese grade 7-9 textbooks are available from the University of Chicago School Math Project at 773-702-9770 or e-mail ucsmp@cicero.uchicago.edu . Individual books cost $19. %%California z47\clip\2001\01\camath.txt Dec. 15, 2000 Curriculum Commission overrules advisors on math texts Traditional emphasis continues as commission recommends only algebra books for eighth grade By Colleen Flannery The Curriculum Development and Supplemental Materials Commission only approved traditional algebra texts over the objections of ... Instructional Materials Advisory Panel (IMAP), composed of K-12 teachers and math education experts, reviews each book carefully, noting corrections that should be made and where each book deviates from state standards. A Content Review Panel (CRP) made up of university math professors, some of whom helped write current state standards, also reviews the materials. %%Comprehensive Curriculum z62\clipim\2002\12\02\comp4.jpg 4th grade workbook: 287x43 _____ 3)368 ____r 2)271 add fraction, same denom 2/5 + 1/5 = 3/5 reducing fractions 1/2 = 2/4 = 4/8 5/15 = 1/3 10/15 = 2/3 add/sub mixed numbers: 9 1/3 + 3 1/3 = 12 2/3 7 3/8 - 4 2/8 = 3 1/8 add/sub decimals 6.4 + 5.3 93.6 - 79.8 %%Open Source Wikipedia-like project (some content from the wikipedia) online free alternative to textbooks. http://flexbooks-wiki.ck12.org/index.php/Frequently_Asked_Questions has reader reviwer ... I've looked at their 6th grade and Algebra "flexbooks" and find nothing alarming. The standard algorithms are presented in all their glory. %%Scott Forseman http://bg016.k12.sd.us/math.htm Grade 5 Math Links %%Singapore ARTICLE HAS SAMPLE PROBLEMS - NOT BEYOND STANDARD TRADITIONAL MATH z43\clipim\2000\06\26\muslim.txt Muslims worry about compulsory education By JAMIE TARABAY Associated Press Writer G3 - what is cost of 4 books @ $5 each G8 - what is probability of pulling 2 cards that add up to 11 http://www.singaporemath.com/. Books come in one semester sets. Each year uses two sets, for example grade 4 is 3B and 4A (for slightly lower level students) or 4A and 4B (for slightly higher level students). Each set contains th e text book and two work books for $18.50. z40\clip\2000\04\sing2.txt Subject: US education chief praises S'pore way MATHS AND SCIENCE By TRACYQUEK The Straits Times US education chief praises S'pore way MATHS AND SCIENCE By TRACY QUEK MATHEMATICS and science textbooks used in Singapore's schools provide students here with a firm grasp of these subjects. It is no wonder Singapore students outperform their peers around the world in international mathematics and science tests, said US Education Secretary Richard Riley yesterday. Mr Riley Singapore The Singapore Math books are for sale through a family business in Oregon, whose website is http://www.singaporemath.com/ A Washington Post columnist has an article about them, posted at http://washingtonpost.com/wp-srv/WPlate/2000-02/17/059l-021700-idx.html SOME ADOPTING ASIAN DRILL, SEQUENCE APPROACHES KUMON, SINGAPORE z40\clip\2000\03\ormath.txt http://www.washingtonpost.com/wp-srv/WPlate/2000-03/21/076l-032100-idx.html Looking East for Math Techniques Approach Initiated In Japan, Singapore Guides U.S. Pupils By Valerie Strauss Washington Post Staff Writer Tuesday, March 21, 2000; Page A11 if students learn solid, basic math, they should be able to pass any standardized test. Students in Taiwan, for example, were given the MSPAP math and science exams in 1998 and outscored Maryland children--even though the Taiwanese instructors didn't teach to that test. The aim of Kumon, like that of Singapore math, is to ensure mastery over basic skills so that the student will have a foundation for creative thinking. From: Gerald W. Bracey Sent: Monday, May 15, 2000 He should be reminded that the Singapore Minister of Education was here a couple of years ago looking for ways to make his kids more like ours. Someone asked him why, since he had the #1 test scores in the world. He said "That's all they can do--take tests." %%Basic College Mathematics z47\clip\2000\12\collmath.txt http://www.bluestockingpress.com/pages/frameset.html Mathematics The reason Bluestocking Press distributes Basic College Mathematics is because the mathematical explanations behind the problem solving are excellent. we believe that most seventh graders can comfortably use this book. [teachers can use as an aid] %%Homeschool Dale Reed reviews math books, has reservations about Saxon books which are very expensive. %%Math Central Houghton Mifflin Math Central is terrible fuzzy math that does not teach basics, yet given credit for raising math scores %%Mathematically Correct Review Algebra z42\clip\2000\06\algebra\*.htm http://www.mathematicallycorrect.com/algebra.htm 1/1999 http://www.mathematicallycorrect.com/books.htm 2nd Grade http://www.mathematicallycorrect.com/books2f.htm Addition and Subtraction "In their adamance that facts and algorithms have no place in modern math classes, the authors accept that some children, at the end of second grade, will still add and subtract by drawing pictures and counting, or by counting back and forth on a "100 chart." So much emphasis is placed on personal strategies that an entire activity is devoted to adding 29 + 12 (book 5 page 7)." There is no formal instruction in telling time. An entire book (number 6) is dedicated to measurement, yet no real world measuring device appears. There are no rulers, no measuring cups, no thermometers, no balances There is little or no mathematics of consequence in this book. This program is totally dedicated to discovery learning and away from mastery, depth, or any skill or understanding necessary to succeed in any mathematics based profession. The program claims to want to "ensure that all students are included in significant mathematics learning." They succeed part way, all students, living or dead, can participate. The second part, "significant mathematics learning," is missing. "There is nothing to recommend about this program. The use of this program in our public schools is a strong argument for vouchers." 5th grade 4.1 A- SRA/McGraw-Hill SRA Math: Explorations and Applications The second group contains two programs that might be reasonably effective and contain a fair degree of mathematical depth, but fall short of the expectations of this review. There are substantial differences between these programs, but both have the potential for success. However, achievement to the level expected in the review would require supplementation. 3.8 B+ Saxon Publishers Math 65: An Incremental Development 3.5 B Silver Burdett Ginn Mathematics - Texas Edition The third group contains three programs with ratings overall that are below the expectations of this review. All three are lacking an adequate introduction to negative numbers, for example. Achievement with these programs would be expected to be limited to modest levels without more substantial supplementation. 3.2 B- Scott Foresman Addison Wesley Math - Texas Edition 3.1 B- Harcourt Brace Math Advantage 3.0 B- McGraw-Hill Math in My World Finally, the last group contains the two programs that are not recommended f or fifth grade use. 2.3 C- Everyday Learning Corporation Everyday Mathematics 1.3 F Dale Seymour Publications Investigations in Number, Data, and Spa ce Seymour G2 book does not even tell how to add 2 digit numbers Seymour G5 book does not teach how to multiply 2 digit numbers, discourages the use of standard division method, no decimal multiplication or division The emphasis on having students to devise their own methods leaves open the possibility that the students will not achieve any regular and reliable approaches. This risk is aggravated by a limited number and range of practice items. 7th grade Overall Ratings Please read the individual reviews to determine if a particular book is likely to meet the needs of a particular school or district. As noted below, not all books with the same grade are equivalent in presentation or organization. A - Well suited to pre-Algebra. These books may be considered 8th grade texts in some areas, but should be considered for seventh grade students where possible, and were evaluated based on seventh grade criteria. 4.8 A Glencoe/McGraw-Hill Pre-Algebra, an Integrated Transition to Alge bra and Geometry 4.6 A McDougal Littell Passport to Algebra and Geometry 4.3 A Saxon Publishers Algebra 1/2 B - Possibly suited to pre-Algebra. Definitely suited to pre-pre-Algebra. A true pre-Algebra book in the same series would probably rate at the A level 3.8 B+ Scott Foresman/Addison Wesley Middle School Math Course 2 3.6 B Glencoe/McGraw-Hill Mathematics: Applications and Connections, Co urse 2 3.5 B Harcourt Brace Math Advantage Middle School II Preparation for Al gebra 3.5 B Prentice Hall Middle Grades Math: Tools for Success Course 2 C - Not suited to pre-Algebra. May do well in certain pre-pre-algebra situat ions 2.8 C+ Saxon Publishers Math 87 2.7 C McDougal Littell Passport to Mathematics, Book 2 D - Not suitable 2.2 D+ McDougal Littell Math Thematics F - Not suitable 1.7 F Dale Seymour Publications Connected Mathematics Progrma \clip\98\07\badtext.txt From the San Antonio Express-News http://www.expressnews.com/pantheon/news-bus/education/ 2401agta.shtml Group denounces algebra textbook By Anastasia Cisneros-Lunsford Express-News Staff Writer " ''The Texas Public Policy Foundation, I've never heard of them. I also have never heard of Mathematically Correct . . . I have questions that are unanswered,'' Rhume said. " ''Addison- Wesley Secondary Math: Focus on Algebra,'' which received a D-plus from the math advocates. The 843- page textbook is published by Scott Foresman/Addison-Wesley Publishing Co. The company also publishes the only A-rated textbook, written by Alamo Heights High School teacher Paul Foerster, called ''Algebra I: Expressions, Equations and Applications.'' The high school also uses Foerster's book. %%High School %%Houghton Mifflin Initial impressions of Houghton Mifflin K12 text Down on H-M math Houghton Mifflin's new math program, Math Central , is math power. With Math Central students develop a strong foundation in skills and concepts, and learn to investigate, reason, and explain. %%McDougall Littel Integrated Mathematics Issaquah 2003 considers dropping integrated math in favor of traditional sequence. Integrated Math spends very little time on traditional algebra story problems found on WASL. No guess and check strategy either. MCDOUGAL LITTELL INTEGRATED MATHEMATICS McDougal Littell series is Integrated Mathematics 1, 2, Rubenstein, Craine, and Butts NCTM inspired book. Adopted by Lake Washington SD, Issaquah MATHEMATICALLY CORRECT SLAMS MCDOUGALL LITTELL TEXT http://mathematicallycorrect.com/integrat.htm "I do know that after some familiarity with probably fifty secondary mathematics texts in more than three decades, this is the only one which has ever made me ill." claim that students can learn more mathematics than before and can have better retention of what they've learned. I couldn't use a standardized test this year: there are too many topics on it we've not covered. And retention is way down: Product page http://www.mcdougallittell.com/product/mathcat/intmath.htm http://www.winonanet.com/taa/NOTABLE/rubenstein.html Math author It was an ambitious objective -- to bring a wider range of mathematics to a wider range of students," we worked from NCTM's original recommendations and the syllabi in the core curriculum addenda book," Rheta Rubenstein's goal in writing the Texty-winning textbook series, Integrated Mathematics, was to provide quality math in a form that is accessible to all high school students The title of our McDougal Littell series is Integrated Mathematics 1, 2, and senior authors are Rubenstein, Craine, and Butts. Rubenstein, Craine, Butts All areas of mathmatics woven into an integrated three-year course [Issaquah, Lake Washington] The course summary is amazing in that it's supposed to replace the algebra 1 - geometry - algebra 2 sequence. Traditionally, you spent the entire year learning to be able to solve ax + bx = c by the end of the year. This textbook appears to have NO traditional algebra story problems, and only 5-6 pages devoted to solving equations. Now, solving ax + bx = c is 5% of the the 1st year content, and you get to learn a lot of "other" topics like graphs, statisics, linear algebra, not to mention "unit projects". They use require students to have $100 graphical TI-82 calculators which can invert matrices, solve systems of equations. It's like setting your M16 to full auto and letting these kids have it. There's no way kids are going to retain this stuff. Teacher comments the sharp kids who can pick it up instantly will love it, but the other kids? Some districts are giving this to 7th graders rather than 9th grade normal start. "You can learn more with Integrated Mathematics because the mathematics topics are integrated. Over a three-year period, this program teaches all the essential topics in a contemporary Algebra 1/Geometry/Algebra 2 sequence, plus many other interesting topics.. Algebra and Geometry are taught all 3 years, Topics from Logical Reasoning, Measurement, Probability, Statistics, Discrete Mathematics and Functions are interwoven throughout". Course goals: This new program has been written to prepare you for success in college, careers and in daily life in the 21st century. Explore and solve mathematical problems. Think critically. Work cooperatively with others. Communicate ideas clearly. Advantages: develops clear understanding of topics and strong problem solving skills by giving you opportunities to: get actively involved in learning - study meaningful mathematics - see connections among different branches - try a wide variety of problems , real-world and long-term projects - use calculators and computers http://www.mcdougallittell.com/product/mathcat/mcdmath.htm %%Middle school 2 middle school text series Mathematics in Our World (c) 1978, 1981 Addison Wesley Middle School Textbook , evidently Grade 7 Mathematics Unlimited (evidently G8 math, 2nd of two books) %%Modern Curriculum Press Mathematics Popular inexpensive math series for homeschooling, books are thin, but comprehensive, tear out sheets can be figured out without the teacher book. I rate it A or A-. Compare this 1/3 inch thick book to Dale Seymour's NCTM "Investigations" which is literally 2 feet of books but little or no actual math instruction on borrow, carry, or fractions. G1 and G2 have simple tear-out sheets http://mcschool.com/html/math.html $21.50 for teacher $12.95 for student %%New Progress in Mathematics Progress in Mathematics: K-6 Balances a traditional teaching approach with the NCTM Standards. by Rose Anita McDonnell, published by Sadlier-Oxford 1995 Home Page 5th grade workbook has problems with ratio, solving for algebra unknowns using tables which appears in middle school texts. %%Reform http://www.tppf.org/ecot.html \clip\99\02\ecot.htm SCHOOL DISTRICT ALERT FOR MATHEMATICS TEXTBOOK SELECTION Texas policy foundation. NSF funded books are ranked as unsuitable for algebra by 8th grade "Modern math book offers clue to lack of student's abilities" Seattle Times Dec 28, 1997 p. B5 Robert Supino (letters to editor) "The old algebra text I bought has nine chapters and 320 pages. There are only two colors gblack and red. The red is used to emphasize important points. There are no pictures, cartoons, or diversions. It is clear what each chapter in the book is covering and it all pertains to algebra. It was written by two authors, Lial and Miller, working together to make a new text" Modern text has five authors, and 10 "conceptualizers", nine chapters and 690 pages. Much of the book is not algebra, in fact the algebra is difficult to find. The emphasis on application makes it not really a math text but a bad physical science text. %%Review Arthur Hu Review 3/11/99 of McDougall Littel Integrated Math, Scott Forseman elementary math %%Saxon %%Scott Forseman Claims to be #1 math text publisher http://www.scottforesman.com Home page The KnowZone - http://www.scottforesman.com/kz/kzsite/index.htm Sample test questions Arthur Hu Review of G4 Negative review of Grade 4th grade math @@Investigations / Connected Mathematics %%Seymour, Dale @@Dale Seymour %%Dale Seymour @@TERC %%General http://archives.seattletimes.nwsource.com/cgi-bin/texis.cgi/web/vortex/display?slug=study24e&date=20040324&query=us%2Bexpert%2Bassesses%2Bdistrict%2Bcurriculum http://www.bsd405.org/TIMSS.html A Summary Profile of Mathematics and Science Education in the Bellevue School District Wednesday, April 07, 2004 The $300,000 study was funded by one anonymous parent donor, and was the result of parent concerns with TERC, CMP and Core-Plus. The programs were brought into the district in staggered implementation beginning 5 years ago. The purpose of this report, funded by the Bellevue Schools Foundation is to provide information to facilitate Bellevue's mission to achieve K-16 alignment for every student. This assessment of the current state of mathematics and science education in Bellevue is an essential benchmark against which future efforts towards the goal may be measured. z75\doc\web\2004\04\let-seattle-terc-030122.html http://www.math.nyu.edu/mfdd/braams/nychold/let-seattle-terc-030122.html Jodi Gable and Erin Johnson Bellevue WA While aspects of the review are highly technical, the following substantial and notable omissions from the TERC program include: Carrying algorithms for addition Borrowing algorithms for subtraction Multiplication algorithm of "complex" values (i.e., 3247 x 348) Long division Multiplication and division of decimals Addition, subtraction, and multiplication of complex fractions Division of fractions Calculating an average Area and perimeter formulas for rectangles and triangles A commie wacko NSF funded constructivist thematic multicultural inclusive math curriculum with lots of cutting pasting, singing, clapping, card games and god knows what else. TERC stands for Technical Education Research Centers. Investigations in Number, Data, and Space was developed by TERC and is published by Dale Seymour Publications, an imprint of Addison Wesley Longman, Inc. More information about Investigations can be found at: http://www2.lab.brown.edu/investigations/ Wisdom from TERC: -------------------------------- - Don't teach carry or borrow __4_r 2 - Don't teach 7)30 or long multiplication (WASL) - Don't teach common denominators to add fractions - Don't teach mean = sum of items / number of items - Don't teach volume = l x w x h - Don't teach any standard algorithms Steinbock bio of seymour The 6th grade version is connected mathematics. %%Against For those interested in the basic TERC Investigations program without the supplements written specifically for Washington State: http://www.math.jhu.edu/~wsw/ED/wswmathreviewterc.pdf (There is insufficient time for students to learn efficient standard method, lots of time spent on unusual strategies) vs Math Expressions (much better) "The primary problem with whole number multiplication in TERC Investigations is the lack of opportunity to develop fluency with the standard algorithm." "As an historical note, what they call the U.S. algorithm is in the first printed arithmetic book, printed in 1478, somewhat before the discovery of America." "teacher-class dialogue on page 146 of Unit 7. In it we have: This U.S. algorithm was created when all calculation was done by hand. There were no calculators and no computers, so people invented algorithms that had as few steps as possible and that they hoped would be accurate and efficient." TERC Hands-On Math: The Truth is in the Details An Analysis of Investigations in Number, Data, and Space by Bill Quirk "You are likely to have students who suggest the arithmetic mean, or as they may call it, the average. They may know how to find it with the "add-'em-all-up-and-divide-by-the-number" technique. Although this algorithm is often taught in elementary school, research has shown that it is often not understood, even by older students and adults. At this point, it is better to stay away from the mean and the confusion it may introduce." U9, Page 6 " "In the Investigations curriculum, standard algorithms are not taught because they interfere with a child's growing number sense and fluency with the number system." BA, Page 74 5th Grade card game comparing fractions without instruction in common denominators or conversion to decimals. z60\clip\2002\11\desmath.txt http://deseretnews.com/dn/view/1,1249,450014357,00.html Math war heats up in Alpine By Jeffrey P. Haney (Utah) Deseret News staff writer Hundreds of parents, teachers and students on both sides of the ideological battlefield packed district headquarters Tuesday to voice both support and displeasure for the math programs, called "Investigations of Space and Data" for grade schools and "Connected Math" for higher grades. NO INSTRUCTION IN MULTIPLICATION OR DIVISION IN LAKE WASH 3RD GRADE Link Hu looks over 3rd grade book. Turtle Logo is worse than useless without 10 Mac computers, the only mention of long division or multiplication is to NOT do it, the only method for volume that is not approved is V = L x W x H! 2+2=5: Fuzzy Math Invades Wisconsin Schools Leah Vukmir Wisconsin Interest http://www.wpri.org/WIInterest/Vol10No1/Vukmir10.1.pdf by Leah Vukmir z48\clipim\2001\02\22\wiscmath.pdf Has example of singing happy birthday, counting on 2 hands, adding 3 ways including calculator. SING HAPPY BIRTHDAY IN MANY LANGUAGES FOR 3RD GRADE MATH z45\clip\2000\09\invest.txt Boston Spends $4M to Avoid Math Basics. Massachusetts News Published: Oct,2000 Author: Paul Moreno Posted on 10/04/2000 09:08:40 PDT Investigations is also fashionably multicultural. "Sing 'Happy Birthday' and encourage students to sing along with you. Ask for volunteers to sing the song in their native languages. Connected Mathematics review http://project2061.aaas.org/matheval/toc.htm DALE SEYMOUR: MATH FOR DUMMIES THAT LOOKS LIKE ME zip37\doc\web\99\14\mathall.txt zip37\clipim\99\09\23\mathall1.tif zip37\clipim\99\09\23\mathall2.tif Dale Seymour's Investigations: Teaching Mathmatics to _All_ Students [Or Math for Dummies of Color and Gender] ....The curriculum was designed so every student can find himself or herself reflected in it at various places Lots of Papers by Authors: http://www.terc.edu/investigations/relevant/html/relevantarticles-map.html#Z STUDY SHOWS INVESTIGATIONS MAKES GAINS, DOES NO HARM Full Year Pilot Grades 3 and 4 Investigations in Number, Data, and Space® December, 1994 Jan Mokros, Mary Berle-Carman, Andee Rubin, Tracey Wright TERC, Cambridge, MA http://www.terc.edu/investigations/impact/html/eval-3-4.html the z49\clipim\2001\05\07\pilot34\pilot34.htm Investigations group made substantially greater gains than students in the comparison group, particularly for items involving understanding of number and geometry. On the written test, both comparison and Investigations students made substantial gains. We conclude that the Investigations curriculum has the potential to substantially deepen students' mathematical understanding. At the same time, it does not seem to stand in the way of performance on traditional tests of computation skills. For example, in the Elephant Problem (fourth grade) students figure out how many 60 pound dogs would weigh the same as a 3000 pound elephant. We found that some students knew that they should choose an operation and perform it, but didn't know which operation to use. On the other hand, students who were developing good number strategies approached the task by building up chunks of 60's in order to find out how many 60's would equal 3000 http://www.lab.brown.edu/investigations/resources/studresults/iccuwno.html Study 1: Learning Number Operations in Second Grade The Comparison classrooms used a curriculum that emphasized both invented procedures and traditional algorithms. Both groups were from suburban Boston schools, with the Comparison students having a smaller class size and being from a somewhat more affluent community z49\clipim\2001\05\07\mismath.htm The Mathematical Miseducation Of America's Youth By Michael T. Battista http://www.pdkintl.org/kappan/kbat9902.htm Phi Delta Kappan Feb 1999 RECENT NEWSPAPER and newsmagazine articles, ... have aimed a great deal of criticism at the current "reform movement" in mathematics education. ... they attempt to seize control of school mathematics programs and return them to traditional teaching -- that is, to the "basics." As they cite isolated examples of alleged failures of mathematics reform, they ignore the countless failures of traditional curricula These curricula focus on the basic skills of today, not those of 40 years ago. Problem solving, reasoning, justifying ideas, making sense of complex situations, and learning new ideas independently -- not paper-and-pencil computation -- are now critical skills for all Americans. Scientific constructivism is a well-developed scientific theory that has proved invaluable in understanding empirical research on students' learning of mathematics In the mathematics curricula recommended by NCTM and all other professional organizations that deal with mathematics education, the exclusive emphasis that traditional teaching places on paper-and-pencil computation has been __moderated__. INCREDIBLE CLAIMS THAT INVENTED MATH IS _BETTER_ THAN TRADITIONAL MATH in 2nd Grade http://www.terc.edu/investigations/impact/html/eval-2.goodrow.html adding subtraction better without regrouping?? This has to be completely bogus. The traditional kids think that 9 + 4 = 12 yet the 2nd grade constructivist kids somehow understand that 3 x 50 = 150 (3rd grade) and that 8 - 9 is negative 1 (4th grade). This proves that the constructivist group is well beyond grade level in math ability. DON'T CARRY, COUNT WITH BLOCKS OR FINGERS z41\clip\2000\05\flexmath.txt FUZZY ANSWERS / A SPECIAL REPORT The New, Flexible Math Meets Parental Rebellion By ANEMONA HARTOCOLLIS When she started second grade last fall, Sabina knew how to carry tens and add two-digit numbers, Mr. Schmid said. Sabina's teacher, who is well-intentioned but too inexperienced to deviate from the program, Mr. Schmid said, told the child that she was not allowed to use this method; she had to demonstrate her work with blocks or by counting on her fingers. http://www.nwrel.org/scpd/natspec/catalog/connected.htm cmp participants outperformed comparison students on problem solving and proportional reasoning John Hall hates it too the LK WA standards requires teaching regrouping which is not in this book Lake Washington to adopt Dale Seymour WARNING! Notes about radical footnotes, long class prep, Bingo (from Barney preschool song) Portland OR adopts invented math over objections. \clip\99\10\oremath.txt http://oregonlive.com/news/99/05/st051101.html New math programs get board approval Portland elementary and middle schools will change the way math is taught, making the district one of the nation's largest to do so Tuesday May 11, 1999 By Betsy Hammond of The Oregonian staff "The district has estimated it will cost $3 million to buy any new math series and the needed calculators and hands-on math tools for the district's 56,000 students. District officials also have said they would have to spend about $700,000 on training for teachers if the new series is to succeed. " Investigations is rated unacceptable by Mathematically Correct %%Research http://investigations.terc.edu/impact/impact-studies/modesofteaching.cfm R's work: 1 2\8\ 18 - 9 --- 1 9 I: How did you think about that one? R: Cause you can't take nine from eight, so you cross it out and get um, you cross it out, you cross the two out and make a 1 and take that one and put it with the 8, and the 8 has 2 numbers and then 9 plus 9 equals 18. (Looks to me they didn't teach the kid how to do regrouping properly) Figure 6: Standard subtraction algorithm in the Traditional group. N's work: 28 -9 __ 19 N: 28 minus 9 I: Now this one's tricky I: How come it is 19? Tell me what you think? N: Wait. um I: That's right. Why is it right? N: Because 9 minus 8 is -1. I: 9 minus 8? N: No, I don't want to start with that. Let's see Hmmm. I have to start with ath. 9 minus 8 equals negative 1 and negative 1 minus 20. That's 20 minus 1. Equals 19. @@Time %%Time conversions 24 hr = 1 day 60 min = 1 hr 60 sec = 1 min G2 Students will need to review time equivalencies, e.g., 1 minute equals 6 0 seconds http://www.cde.ca.gov/cilbranch/eltdiv/mathfw.htm G5 Nevada %%Days of Week K Nevada %%Months, Calendar G1 Nevada %%Calendar Arithmetic G5 Houghton Mifflin - use a calendar to count days between july 10 and aug 22. %%Read Time to Half Hour, AM PM G1 Nevada G1 Lk Wash %%Read Time to Quarter Hour G2 Lk Wash G2 Nevada %%Read Time to 5 minutes G2 CA 1998 %%Read Time to minute G3 Nevada G4 Addison Wesley Math 1991 %%Elapsed Time (Identify) G3 Nevada G4 Massachusetts %%Add Time within even hour %%Add Time over even hour No standards specify time arithmetic going beyond hours or AM/PM. G4 1998 MA MCAS test G4 1998 MN assessment ---- appropriate ---- %%Add Time over 12 hours G5 Minnesota 1997 assessment (take medicine every 4 and 6 hrs, when same time?) (trip starting at 9PM) %%Elapsed Time within same Hour G4 Addison Wesley Math 1991 G4 TX TAAS %%Elapsed Time within different hours G1 Scott Forseman 3 to 4:30 G4 Scott Forseman Math (no minute regrouping) G4 WA Assessment G5 Houghton Mifflin math (minute regrouping) ---- appropriate ---- %%Divide Time, Result in minutes G4 1998 MA MCAS test ---- appropriate ---- Timelines ----------- G3-5 Lk Wash @@Too Hard TEACHING MATH THAT IS TOO HARD KILLS MASTERY OF BASICS MATRIX INVERSIONS VS BASIC ALGEBRA AND ARITHMETIC http://www.baltimoresun.com/news/opinion/oped/bal-op.math02nov02,0,1068320.story Teaching too-hard math concepts does students no favors By Joseph Ganem November 2, 2009 We are in the midst of a paradox in math education. As more states strive to improve math curricula and raise standardized test scores, more students show up to college unprepared for college-level math... In many cases, incoming college students cannot do basic arithmetic, even after passing all high school math tests. ... I've seen how little understanding is conveyed by the grade-school math curricula. For example, the problems assigned to my children have become progressively more difficult through the years, to the point of absurdity. My eighth-grade daughter asked me one evening how to perform matrix inversions, a technique I teach in my sophomore-level college course on mathematical methods for physics majors. ... My other daughter struggled through a high-school trigonometry course filled with problems I might assign to upper-class physics majors. goodoc: Teaching too-hard math concepts @@Tracking Traditionalists like tracking when possible, but progressives say mixed grouping is best when all are held to one "high standard". UK RESEARCH SAYS MIXED-GROUPS BEST, TRACKING CAUSES LOW MATH OUTCOMES(?) z48\clip\2001\02\uktrack.txt http://www.independent.co.uk/news/UK/Education/2001-02/pupils190201.shtml Grouping by ability disadvantages bright pupils By Judith Judd, Education Editor 19 February 2001 "research suggests that countries where pupils are taught in mixed-ability groups tend to be more successful than others. Setting, it suggests, could be "the single most important cause of the low levels of achievement in mathematics in the UK". " @@Traditional The proof that we need reform math is the "research" and "ancedotal" evidence that most adults don't think they are good at math. Yet reform math doesn't even try to teach math like carry or paper multiply or divide at all. WHERE IS THE EVIDENCE THAT TRADITIONAL MATH DOES NOT WORK? z39\clip\2000\01\mamath.txt Teachers object to plan to alter math standards By Andreae Downs, Globe Correspondent, 2/6/2000 Sandra Stotsky, the state's deputy commissioner for academic affairs [proposes to throw out 1995 NCTM math standards] ''we have a significant database that these `traditional' methods haven't worked,'' said Susan Jo Russell of Technical Education Research Centers, who develops council-based curricula in urban schools. ''The last time we had research mathematicians write K-through-12 math curricula, we got New Math,'' said Kendall. [Nope that's when we let the educators do it] ''The traditional way in which math was taught - and for all intents and purposes that's what we've had for the last 30 to 40 years - was fairly ineffective for most kids,'' said Mary Eich, kindergarten-through-eighth-grade mathematics coordinator in the Newton Public Schools. ''We know this anecdotally by the number of adults who feel they are not good at math.'' @@Trailblazers DO NOT TEACH STANDARD METHOD UNLESS NO STUDENTS INVENT IT http://www.illinoisloop.org/mathtrail.html "Later in grade 2, systematic work begins on paper-and-pencil methods for subtracting two-digit numbers. Students are asked to solve two-digit subtraction problems using their own methods and to record their solution on paper. The class examines and discusses the various procedures that students devise. At this time, if no student introduces the standard subtraction algorithm, then the teacher does so, explaining that it is a subtraction method that many people use. The standard method is examined and discussed, just as the invented methods were. Students who do not have an effective method of their own are urged to adopt the standard method." Appendix D: Constance Kamii "The teaching of algorithms is based on the erroneous assumption that mathematics is a cultural heritage that must be transmitted to the next generation." Constance Kamii is a professor of education at the University of Alabama. She studied under Piaget, @@Triginometry Only about half of college bound students take triginometry in high school, compared to nearly all taking algebra. G8 - Singapore 2001 G10 - integrated high school math G11 - standard high school sequence %%SAT Percentage taking by race: \doc\95\12\sat95bk.wk1 1995 Scholastic Aptitude Test Breakdown by Ethnicity Data from the College Board Data Entry and Analysis by Arthur Hu White Black Hisp Asian Math Coursework Gap Gap Gap Gap Triginometry 55 0 539 43 -106 433 42 -68 471 64 26 565 @@United Kingdom New New Math in UK an obsessive preoccupation with things like networks, 'clock arithmetic', Venn diagrams, different bases for counting, matrices, transformations and a whole new vocabulary to describe things with which we had previously become familiar without needing to attach names to them. @@University TRADITIONAL UNIVERSITY CALLS FOR 4 YRS OF MATH STARTING WITH ALGEBRA z62\clip\2002\12\ncpath.txt http://www.rethinkingschools.org/archive/17_02/IBM172.shtml 'McDonald's or IBM' In North Carolina, eighth graders are forced to make decisions that will impact the rest of their lives Winter 2002/2003 "U-track: Algebra I and II, then Geometry and a higher-level math. Peacock acknowledges that students not placed in Algebra I in their freshman year will have a hard time getting into a four-year institution since they'll have to complete four math courses in a three-year period." @@University of Chicago http://www.enc.org/professional/federalresources/exemplary/promising/document.shtm?input=CDS-000496-496_31 The University of Chicago School Mathematics Project (UCSMP) has been designated a Promising mathematics program. (by the Dept of Ed) UCSMP is designed to revitalize the traditional mathematics curriculum, improve student achievement, and increase the number of students who take mathematics beyond algebra and geometry. UCSMP provides a variety of exercises for students. These are challenging and inviting to students including lower level students, students with language barriers, and accelerated students. mean score of percent correct of test items for the UCSMP classes on the HSST was 1.2 percentage points higher than comparison classes. Similar results were found in a 1987-88 evaluation of the Advanced Algebra component; UCSMP students scored 15.6% higher than comparison students on a test using 50 multiple choice and four open-ended questions. Statistically significant positive differences favoring UCSMP students were found in three areas: reading, applications, and technology The program has clear, challenging learning goals consistent with NCTM standards. The content is well aligned with those goals and is carefully developed from problem situations to real-world experiences. The goals emphasize skill development and application. @@Venn Diagram Venn Diagrams (union, intersection of sets) are generally not introduced until after the 4th grade, but some places introduce them as early as the 1st grade. Traditionally, most adults were not introduced until college. My son got Venn Diagrams as a READING exercise in 2nd grade (2000) Grade Level Ranking ------------------ 1st Bill Evers 2nd Bridlemile Elementary School Portland, Oregon 2nd AG Bell (reading) 3rd Ohio 4th WA Assessment 4th Maine 6th Our Lady of Peace 8th Virgina (after algebra) 9-12 Missisippi 12th Wisconsin Standards NA WA Benchmark NA Nevada NA Massachusetts NA California College - Traditional Gerald Bracey Consider a recent Washington Post article. While the focus of the piece was the math wars as they are being played out in Maryland, the article used a sixth grade classroom as its center. The story mentioned in passing that the teacher was using Venn diagrams in his instruction. Venn diagrams!?!?!? I encountered Venn diagrams for the first time in a logic course I took as a junior in college. Another Post reporter affirmed that he, too, had not seen them until well into college. Yesterday I heard the same thing from teachers in Los Angeles they had not used Venn's before college but were now, as early as third grade. from Date sent: Wed, 22 Mar 2000 22:41:19 -0500 The use of Venn diagrams would be worth looking into for someone, wish I had the time. I first encountered them in college; a recent Washington Post article matter of factly described their use in 6th grade math. I mentioned this in LA and was told that they show up as early as second grade. My audience was a group of math and science teachers. I have since heard of them in various English classes. If anyone has time to explore, I'd love to know what's up. AG Bell 2000 Eric in 2nd grade was asked to draw a venn diagram of what was different and common between the tortoise and hare as a reading exercise! z42\clipim\2000\05\12\eric2.efx AG Bell - given Venn diagram without name - likes peaches, likes peaches and grapes, likes grapes. Ohio G3 http://www.achieve.org/ 4.make and use a Venn diagram to collect and sort information. Mississippi 9-12th grade http://www.achieve.org/ draw a Venn diagram, create a flow chart http://www.pen.k12.va.us/go/Sols/math.html#Grade Four Virginia standards - Venn diagrams are presented in Geometry (after algebra, grade 8/ 9 http://oaktree.dpi.state.nc.us/Curriculum/Mathematics/Mth. LssnPlns/Mth.2.3. 2 Strategies for Instruction in Mathematics Instructional Services North Carolina Department of Public Instruction Grade 2 http://www.achieve.org/clearinghouse/main.html Maine 4th Grade ELEMENTARY GRADES 3-4 1.Create and use organized lists, tree diagrams, Venn diagrams, and networks. http://www.wisgov.state.wi.us/MSMath.htm Wisconsin G12 B.12.1 Use complex counting procedures such as union and intersection of sets and arrangements (permutations* and combinations*) to solve problems Alternative California Math Standards http://www.rahul.net/dehnbase/hold/platinum-standards/alt1. html Data Analysis - Grade 1 1. Students collect, organize, represent and compare categorical data on simple graphs and charts, and Venn diagrams. Mathematics Content Standards for grades K-12 Submitted by Bill Evers, Commissioner September 15, 1997 6th Grade Highlights Sixth grade mathematics scholars begin to write numerals using exponents, and divide with two and three digit divisors, dividends and quotients. Set study introduces the children to the Venn diagram. Our Lady of Peace School \clip\97\26\lady.txt http://www.mcps.k12.md.us/schools/damascuses/mediacenter.html The concept of using a Venn diagram, to compare and contrast information, is featured in our first grade classrooms. Damascus Elementary School Media Center Program Montgomery County Public Schools, Maryland Bridlemile Elementary School Portland, Oregon USA Second Grade Enrichment Activities By Month http://www.icon.portland.or.us/education/elem/bridlemile/St_ projs/2nd_grd/E r_mon.htm Math Create a Venn Diagram. Label and illustrate it. Explain your diagram to someone. The Saginaw Intermediate School District LEVEL: FIRST GRADE Compare and contrast using a Venn diagram. http://isd.saginaw.k12.mi.us/curriculum/k-12/first.html VENN DIAGRAM IS PROBABLY A LOT TO ASK FOR STATE ESSENTIAL 4TH GRADE STANDARD \doc\web\97\09\venn2.txt "Finally, if I understood your question correctly, I'm inclined to agree that it's a bit early to require that knowledge as a part of a state standardized test." @@Videotape Study by James W. Stigler comparing math teaching, US, Japan and Germany on CD-ROM. NCTM claims the Japanese are using their reforms, but the EdWeek example shows the Japanese concentrate on one concept, not the "integrated approach" where they introduce themes and topics which have nothing to do with math entirely. http://www.edweek.org/ew/vol-16/28vids1.h16 \clip\97\28\vcr.txt 4/9/97 Education Week From VCR to CD-ROM: A New Way of Viewing Los Angeles "This has enabled them to learn, for example, that 8th grade teachers in Japan give a coherent lesson tightly focused on one mathematical concept, while their U.S. counterparts tend to introduce many topics at a time. " http://nces.ed.gov/timss/97198-6.html To overcome this lack, and to understand how U.S. classroom teaching compares to that of other countries, NCES added an innovative new research methodology to the TIMSS project- videotaping and quantitative coding of a national sample of eighth-grade mathematics classes in Germany, Japan, and the U.S. Explore Math Lessons in Germany, Japan, and the United States http://nces.ed.gov/timss/video/jimvid1.htm @@Volume Lots of new standards calls for knowing complicated formulas for volumes of cylinders, spheres and truncated frustrums, which we all need in everyday life, right? %%Cone Some states require knowing the volume of a cone as early as grade 7 G7 2007 WA State Math Standards draft develop (not just use) formula for volume of pyramids and cones G8 McREL INSTITUTE MATHEMATICS STANDARDS AND BENCHMARKS GRADE 8 Use appropriate formula: volume of cone www.dpi.state.nd.us/title1/benchmrk/math/math8.pdf G8 Newark NJ teachers union http://www.ntuaft.com/njcccs/Webpage/contents/STANDARD%204.2%20grade%208.htm volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height (e.g., use rice to compare volumes of figures with same base and height G8 Grade 8 Measurement Kent, Ohio volume should be calculated for spheres and cones kent.k12.oh.us/boe/Meas_8.htm G11 2007 IMAGE Sample Book Mathematics Volume of a cone = pr. 2. h. www.isbe.state.il.us/assessment/pdfs/2007_IMAGE_Math_Sample_Gr11.pdf %%Cylinder G8 WASL expects students to tell which dimension to increase to double capacity of can, but G10 gives the formula for the volume of a cylinder. G7 2007 WA State Math Standards draft justify volume formulas for right circular cylinders G8 2001 Singapore math G10 WASL gives sheet with formula for volume G11 PA Math Grade 11 The volume V of a right circular cylinder like the one in the figure is given by the formula V = ... www.pde.state.pa.us/a_and_t/lib/a_and_t/m11.b.2.pdf G12 Ohio Resource Center NAEP Assessment Item, Grade 12: Find the Volume of a Right Circular Cylinder ohiorc.org/standards/ohio/search/mathematics/gli/205.aspx?page=1 %%Sphere G10 New Standards expects students to memorize volume of 1/2 of sphere and "truncated frustrum". @@wars z75\clipim\2003\11\20\mathshift\mathshift.htm Math shift draws unequal reactions Schools like new system, but some parents say it's 'fuzzy' Eric Hübler, Denver Post Education Writer Wednesday, November 12, 2003 - "I've heard about people who sell their homes and move to another town because they don't like our stuff," he said. Holt 1981: Which is a square? triangle? (simple) Everyday: which of these does not belong (one figure is not "regular" - much more difficult task) z75\clip\2003\11\mathbattt.txt http://www.projo.com/education/content/projo_20031116_edwatch16.dbd29.html Edwatch by Julia Steiny: Math-war battle lines are drawn Providence Journal November 16, 2003 "In fact, testing results such as the SATs did drop probably in part because of this airhead math, though the public was considerably less aware then of such tests than they are now." @@Weighted Scores WA Assessment - devise weighted scoring scheme to determine winner in 4 categories WA Benchmark - no such task listed. @@Whole math Case for brain based thinking and "whole mat h" @@Women (Disadvantage) VERBAL UP, MATH DOWN WHEN FEMALE ESTROGEN IS HIGH http://www.genderweb.org/~julie/medical/hormones/ability.html \clip\98\16\hormmath.txt Hormones Linked to Reasoning Ability Los Angeles Times at the annual meeting of the Society for Neuroscience last week in Toronto, psychologists Elizabeth Hampson and Doreen Kimura said tests on three groups of women showed muscular coordination and verbal facility increased by as much as 10 percent during periods of the month when levels of estrogen, the female hormone, were high. At the same time, the women's ability to solve problems involving spatial reasoning fell by a similar amount. [well that explains a lot about why men score higher in math and lower in verbal, doesn't it?] @@Word Problems READING IS OFTEN THE HARDEST PART OF WORD PROBLEMS z43\doc\web\2000\07\ted2.txt To: "Word problems for example generallly demand higher than grade level reading skills and comprehension--math is the least difficult part of word problems." @@workplace 8TH GRADE LEVEL MATH (NON-ALGEBRA) SUFFICIENT FOR MODERN NONPROF WORK Does Higher Tech Require Higher Skills? Gerald Bracey Phi Delta Kappan May 2001 p. 715 John Smith III of Michigan state University concludes that we don't have to be first in the world as in Goals 2000. "Managers and human resource personell corroborate that the equivalent of an 8th grade level of mathematics education [pre-algebra] is an adequate preparation for modern, nonprofessional work." @@world %%Czech Czech students excel at math, science Seattle Times Feb 15, 1998 p. A17 \clipim\98\03\czech.tif TIMSS finds Czech's among world's highest, Americans down the list. no-pain no-gain. US has friendly teacdhers and multiple choice tests. %%general US 4TH GRADERS ABOVE AVERAGE IN MATH AND SCIENCE "Digest of Education Statistics 1999." National Center for Education Statistics, * International Comparisons The results of a 1995 international assessment in math & science show that U.S. 4th & 8th graders compare more favorably with other countries in science than in mathematics. In mathematics, U.S. 8th graders scored below the international average, falling below 20 of the 41 countries tested. Fourth graders performed above the international average of 26 countries tested, scoring below seven countries, including Singapore, Korea, & Japan. Students at both the 4th & 8th grade levels scored above the international average in science. Eighth grade students in the U.S. were outperformed by nine out of 41 countries. Fourth grade students once again compared more favorably with their international counterparts than 8th grade students. Out of 26 countries who participated in the 4th grade assessment, only one country outperformed the U.S. students in science. US Dept of Education National Center for Education Statistics Pursuing Excellence (TIMSS findings report) http://nces.ed.gov/timss/97198-6.html \clip\97\28\teach\teach.htm CHAPTER 3 : TEACHING Says the Japanese have been studying American research into higher level thinking, discovering, etc. and are implenting these ideas. Americans tend to just give out concepts and routine exercises rather than pondering over problems with no obvious solution. Michigan State mathematics professor Bill Schmidt says we should teach fewer topics to mastery, not repeat them every year, hit more advanced math, less basic arithmetic in 5,6,7 JAPAN AND GERMANY HAVE MORE DIFFICULT MATH MATERIAL \doc\web\97\08\mathrept.txt Chancellor's Conference on School Excellence and Accountability Vanderbilt University June 4, 1997 Jeanne Griffith -- Third International Math & Social Studies Report The most enlightening piece of information for me was her discussion of the videotaped math lessons effort. One hundred math lessons were videotaped in each of three countries: Japan, the U.S., and Germany. These lessons were then transcribed and translated, and a panel of college math teachers reviewed them. The were ranked as high, medium, or low quality for math content. For the U.S., 87% were ranked LOW, 13% medium, and NONE HIGH. Germany and Japan both had a much smaller percentage of their lessons in the low category, and a significant percentage for each was in the high category. US DOESN'T TEACH ENOUGH "DEPTH" IN MATH? http://www.washingtonpost.com/wp-srv/WPlate/1997-01/23/104L- 012397-idx.html \CLIP\97\02\MATHPROB.TXT U.S. Struggles To Solve Its Math Problem Time, Teaching Style Appear to Be Factors By Rene Sanchez and Robert O'Harrow Jr. Washington Post Staff Writers Thursday, January 23 1997; Page A01 The Washington Post %%Korea North Carolina State University Libraries: http://library.ncsu.edu/MARION/AJW-3833 Rethinking the mathematics curriculum / edited by Celia Hoyles, Candia Morgan and Geoffrey Woodhouse. Ch. 17. New Goals and Directions for Mathematics Education in Korea / Hee-Chan Lew. Ch. 18 http://203.247.208.20/pro/rhc/nonmun/england3.htm \doc\web\99\01\korea.txt "The new goals and directions of mathematics education of Korea for the next century." Fuzzy math for Koreans. Author of the coument was Hee-chan Lew, Korea National University of Education. The new goals and directions of mathematics education of Korea for the next century "At the outward appearance, mathematics education of Korea seems to make a success. Very recently, Korea was ranked 2nd in the TIMSS and 9th in the IMO. Although this result needs to be analyzed closely, too many problems are being raised from the so called skill- and fact-oriented unflexible curriculum. Most students believe that mathematics is meaningless and only some specific students' possessions." %%Russia observations claims of Russian math superiority - algebra at grade 7, calculus by high school - are exaggerated. %%math US States vs. world on IAEP http://nces.ed.gov/pubs/esn/n25b.html \clip\97\27\iaep\iaep.htm