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.
NYC Hold Math Wars in New York City
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
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
5th Dave Cole's saturday class
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
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. "
AKRON TO DUMP WIMP ALGEBRA 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]
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 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
@@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
@@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
@@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
G2 Lk Wash
G2 1 card = 3 marbles, how many cards for 24 marbles? Dale Seymour
Calculator Division
Prek-4 Massachusetts 1996
Divide 2 by 1 digit 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 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
Add, subtract, multiply, divide with
unlike denominators
G5 Lk Wash
Add and subtract fractions using factoring to find common denominators
G7 1997 California framework
@@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.
- Algebra 8th-9th grade
- Area = LxW 8th
- Coordinate Grid 8th
- Frequency Table/ Histogram
- Probability
- Probability, Independent 10th
- Proportionality 8th
- Percent
- Rate
- Unit Conversion 8th
- Venn Diagrams 1-12
-
%%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
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.
@@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
@@Connected Mathematics
@@CMP
NSF funded math program developed at Michigan State University.
Generates controversy. Middle school version of Seymour Investigations
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. "
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
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.
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."
%%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.
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.
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."
@@Counting
--------
Count to 10 Preschool->K
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.
%%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 TRADITI