http://www.leconsulting.com/arthurhu/99/04/sampwasl.txt
4th GRADE WASHINGTON ASSESSMENT OF STUDENT LEARNING IS A TEST OF
WHAT STUDENTS ARE NOT EXPECTED TO KNOW OR LEARN UNTIL 7TH AND 10TH
GRADE!
this can be found on the web at
http://www.leconsulting.com/arthurhu/99/04/sampwasl.txt
More info on the flaws of ed reform/deform and performance based testing see
http://www.leconsulting.com/arthurhu/index/washtest.htm
Aug 27, 1998 - Feb 23, 1999
Arthur Hu
12422 107th PL NE
Kirkland WA 98034
email: arthurhu@halcyon.com
206-748-5347
Advertisement: The WASL is a test of what 4th graders should know
near the end of 4th grade.
Truth: The WASL is a test of what 4th grades aren't expected to learn
or know until grades 7 and 10 according the the EALR standards
defined by the state.
CONCLUSION: THE CLAIM THAT THE TEST ASSESSES 4TH GRADE ESSENTIAL
ACADEMIC LEARNING REQUIREMENTS IS FRADULENT, IT IS FILLED WITH SKILLS
TAKEN FROM 7TH AND 10TH GRADE LEVELS.
THE COMMISSION NOW CLAIMS THAT INCLUSION OF 7TH AND 10TH GRADE SKILLS
IS INTENTIONAL, BUT THERE IS NO DOCUMENTATION TO SUPPORT THIS. IT IS
CLEAR THE STANDARDS SETTING COMMITTEE HAD NO SAY OVER INCLUSION OF
THESE PROBLEMS. IT IS FAR MORE LIKELY THAT THOSE WHO CREATED THE TEST
CLEARLY NEVER COMPARED ANY OF THESE QUESTIONS WITH THE APPROPRIATE
BENCHMARK SKILLS. UNDER THE ACCOUTABILITY TASK FORCE, MONEY WILL BE
AWARDED AND PENALIZED TO SCHOOLS BASED ON THIS FAULTY TEST.
Besides:
- The test is supposed to be more accurate, and eliminate guessing
skills. In fact, manual scoring is very unreliable, has not been
validated. Many problems have more than one, or no correct solution,
or require guessing.
- Standardized Tests are supposed to be economical. The WASL costs
$25 just to score, not $2. That's not counting development costs, and
takes days, not hours from teaching.
- The results are supposed to be different from the CTBS. In fact,
the best and worst scoring schools are exactly the same as the CTBS.
- It is supposed to set world class standards. In fact, it does not
compare students to other nations or states. It not based on any
other national or state standard. It is not even compliant with our
own EALR standard. Every comparison puts WA above national average,
and the TIMSS puts the US near the top in math in 4th grade.
- It is supposed to be fairer to minorities and abolish the
bell-curve. In fact, nearly all (95%) of blacks and Hispanics failed
to meet the math standard, compared to 30-40% above average on the
CTBS. The difference in average scores is 1 standard deviation, so
the scores are hiding the same "bell-curve" found in IQ and SAT
scores. The 10th grade version is the Certificate of Initial Mastery
(CIM) that will deny diplomas to those who do not meet "standard".
- It is supposed to be validated and created by the community. It was
actually created by a consensus process which is applied to every
other state with a similar test. It produced a test where half of
problems are not compliant with EALR benchmarks, similar to tests in
other states with similar benchmarks. The OSPI CSL is absolutely
non-responsive to community complaints and input outside of closed
meetings, only stating that the process is incapable of error. According
to the draft technical document, judges were invited to place "bookmarks"
on a test already established to be "4th grade level". At no place in
the process was the public invited to evaluate whether or not the
questions which were on the test were 4th grade level compliant in the
first place. Thus, the claim that a "commmittee of experts" has checked
them against the benchmarks is likely false.
Paul Englesberg notes:
> Judges proceeded through the ordered item booklets and specially trained
> table leaders
> encouraged them to observe the increase in the complexity of the items and
> note the increase in knowledge, skills, and abilities required to answer the
> items...."
>
> This document discusses the setting of "bookmarks" for the standards by
> judges, but doesn't seem to directly discuss reference to the 4th grade
> benchmarks. I would certainly expect that the standard-setters would be
> constantly referring to the EALR benchmarks.
Technical Manual description:
http://csl.wednet.edu/Web%20page/3%20Assessment%20System/subdocuments/
Technical%20Manual/E-SettingProc.html
- It is the first phase of Marc-Tucker's "standards-based" reform.
Tucker and his NCEE is largely responsible for the 1209 ed reform
blueprint which is now state law. School-to-work is patterned after
Germany's failing apprenticeship program. Germany has one of the
highest rates of unemployment in the industrialized world. Most
Germans effectively end their education at 10th grade, spending half
time at jobs requiring limited education. (That is why the CIM is
10th and not 12th grade). Half of Germany's unemployed have passed
their "CIM". More German students are choosing to go to university
(which do not accept their CIM) than vocational
education. By contrast, 90% of WA students will complete 12 yrs, and
over 60% will continue to college. WA proposes to require ALL
students to have a "work-experience" and pass a 10th grade exam,
which is a step BACKWARDS when the US leads in education and industry
(Boeing, Microsoft, Intel IBM, Exxon, etc.)
Here is web location of the benchmark document
http://cisl.ospi.wednet.edu/ComSL/MATHBMK.html
-----------------------------------------------------------------------
TEST DRAFT SPECIFICATION IS NOT CONSISTENT WITH BENCHMARKS EITHER
Not only is the sample test not consistent with 4th grade benchmarks,
but the Feb 1998 Draft Test Specifications which specifies which
questions can be placed on the test also is inconsistent. "The
following learning targets are intended to summarize the knowledge or
Essential Academic Learning Requirements (benchmarks or process
examples) as identified in the mathematics section of the Essential
Academic Learning Requirements Technical Manual Feb 26, 1997".
MEAN, MEDIAN, MODE = G7 IN BENCHMARK, = G4 IN DRAFT SPECIFICATION
Draft Specification:
Strand 4: Probability and Statistics PS04 Identify, find and use
defined measures of central tendency (_mean_, _median_, _mode_) and other
characteristics to describe set(s) of data and sample populations (1.4.7)
Technical Document:
G4: use different mesures of central tendency such as "most often"
and "middle" in describing a set of data
G7: calculate and use _mean_, _median_ and _mode_ as appropriate in
describing a set of data.
MONEY DECIMALS = G4 IN DRAFT SPECIFICATION, WHOLE NUMBERS ONLY IN BENCHMARK
Draft Specification:
Strand 1: Number Sense
NS03: Add, subtract, and divide whole numbers
Addition and subtraction of money (decimals) will be required.
Technical Document:
G4: add, subtract and multiply and divide whole numbers
G7: add, subtract multiply, and divide non-negative fractions
and decimals using rules for order of operation.
--------------------------------------------------------------
SKILLS THAT CAN NOT BE ASSESSED AT GRADE 4 BUT ARE IN G4 TEST
These skills can NOT be asssesed at Grade 4, but are contained in 4th
grade examples which have been approved as being representative of
the actual test.
INDIRECT MEASUREMENT OF AREA = HEIGHT X WIDTH = G7
RATIO, UNCOMMON FRACTIONS, FRACTIONS AS DECIMAL = G7
CHOOSE METERS VS MILLIMETERS = G7
CONSTRUCTING SYMMETRIC FIGURES = G7
APPLICATION OF FACTORS AND DIVISIBILITY = G10
INDEPENDENT PROBABILITY = G10
COUNTING OUTCOMES TO DETERMINE PROBABILITY = G4
DECIMAL MATH = G7
UNIT CONVERSION WITHIN SYSTEM = G7
SCALE DRAWING = G10
The CSL is unwilling to remove any of these skills from the
"validated" test pool.
Note, the CSL has evidently voluntarily withdrawn the former web
examples, it had
* the faulty flagpole (application of proportionality) shadow, an
incorrect solution was printed in the Seattle PI = G10
* the battery life that required finding the one with fewest BELOW a
threshhold given 3 frequency histograms = G7
* computing how many cards would fit into
a box based on finding how many would fit in an inch (rate) = G7
* the marble probability problem given below. = G7
It has been replaced by the bird feeder question, which is G7, not
counting workworking skills which are not taught in G4.
NONCOMPLIANT QUESTION EXAMPLES:
##########################################################################
"PIZZA"
INDIRECT MEASURMENT OF AREA = HEIGHT X WIDTH = G7
Problem 37: This week, a pizza restaurant is selling the three sizes
of rectangular pizzas shown below for the same price
A=8 inches by 14 inches
B=9 inches by 12 inches
C=10 inches by 10 inches
Which pizza will give you the most for your money?
------------------------------------------------------------------------
Solution
area of a = 8 x 14 = 112
area of b = 9 x 12 = 108
area of c = 10 x 10 = 100
A has the largest area, if the price and height and composition are
the same, it will have the most pizza at the lowest cost per square
inch.
-------------------------------------------------------------------------
Requires
* knowlege that price per unit is price / quantity = G7
* knowledge that area = height x width = G7
* multiplication by 1 by 2 digit number manually or with calculator = G4
If the pizzas were broken up into squares that could be counted, and
the question was changed to "which pizza is the largest", it would be
compliant.
-------------------------------------------------------------------------
Benchmark 1.2 understand and apply concepts and procedures from
measurement
attributes and dimensions
THIS MEASURES DIRECTLY, NO COMPUTATION. THIS PROBLEM GIVES NO DIRECT
WAY TO MEASURE THE PIZZAS.
G4: use directly measurable attributes such as length, perimeter,
area, volume/capacity, angle, weight/mass, money, and temperature to
describe and compare objects
THIS IS THE ONE THAT MEASURES RECTANGLES INDIRECTLY A = H * W
G7: measure objects and events directly or using indirect methods
such as **finding the area of a rectangle given its length and width**
THIS USES COMPLEX 3D FORMULAS
G10: measure objects and events directly or use indirect methods such
as finding the volume of a cone given its height and diameter
This requires one grade 7 level level and one grade 4 skill.
------------------------------------------------------------------------
RATIO, UNCOMMON FRACTIONS, FRACTIONS AS DECIMAL = G7
Problem 26: Three students are making lemonade by mixing a dry powder
with water. The pictures below show the number of cups of power and
water that each student uses. Which will give the strongest lemonade?
A: 2 powder 1 water
B: 4 powder 3 water
C: 1 powder 2 water
Solution
Compare ratios 2/1 to 4/3 to 1/2
Method A: compute as decimal 2.0 vs. 1.25 vs. 0.5 on calculator
Method B: create common denominator 12/6, 8/6, 3/6
A is the greatest.
Requires
* State concentration as a ratio = G7
* Compare fractions with uncommon denominator = G7
* Compute value of fraction as a decimal = G7
No question that involves ratios or comparing fractions is
compliant with the benchmarks.
-----------------------------------------------------------------
Benchmark 1.1 understand and apply concepts and procedures from
number sense
number and numeration
NOTHING
G4: blank
RATIO IS GRADE 7
G7: understand the concepts of ratio and direct proportion
COMPLEX APPLICATION OF RATIO IS GRADE 10
G10: understand and apply the concepts of ratio and both direct and
indirect proportion
The answer is that expressing a ratio (such as parts per cup) is up
to 3 grade 7 level skills. 4th graders are barely learning to do
simple division at this age.
Compliant version:
- ratio cannot be assessed within these benchmarks.
- Perhaps a vesion that compared 1, 2 and 3 packets of powder with
equal water would be fair.
------------------------------------------------------------------
"PENCIL"
METERS VS MILLIMETERS = G7
Problem 19:
Which of the following is closest to the distance
around the middle of an unsharpened pencil?
A: 25 millimeters
B: 25 centimeters
C: 25 meters
---------------------------------------------------------------
Requires knowing difference between which version of metric
unit for length is appropriate for the size = G7
Most American students never use millimeters or centimeters or meters
outside of a couple of days in math class in a year. A fairer
question would be feet, yards, or inches, but even that skill would
fall under G7.
---------------------------------------------------------------
Benchmark
1.2 understand and apply concepts and procedures from measurement
systems and tools
BASIC USE OF MEASURMENT
G4: use appropriate tools for measuring time, money, length, area,
volume, mass, and temperature
KNOW DIFFERENCE BETWEEN SIZES OF UNIT LIKE METER VS. MILLIMETER
G7: select and use tools that will provide an appropriate degree of
precision, for example, using meters vs. kilometers
G10: select and use tools that will provide an appropriate degree of
precision, for example, using kilometers vs. light years
Compliant Version:
A question that gave a centimeter ruler and asked to measure
an item would be compliant.
-----------------------------------------------------------------------
"PEGBOARD"
CONSTRUCTING SYMMETRIC FIGURES = G7
Problem 20: Look at figures 1, 2, and 3. Each has at least one
line of symmetry.
++ + ++++
++ ++ ++
Draw a different figure on the geoboard that has at least one line
of symmetry. Then draw the line of symmetry.
......
......
......
......
......
-------------------------------------------------------------------
Requires: construct (vs. simply recognize) a symmetric figure = G7
-----------------------------------------------------------------------
Benchmark 1.3 understand and apply concepts and procedures from
geometric sense
shape and dimension
G4: ***understand concepts*** of symmetry, congruence, and similarity
G7: ***construct*** symmetric, congruent, and similar figures
G10: understand and use properties of symmetry, similarity, and
congruence
Remark - some math teachers don't consider a geoboard to be
"construction". Yeah, right.
Compliant Version:
A question which asked which of figures 1,2,3 was symmetric would
comply with the benchmarks.
###################################################################33
"HOT DOGS AND BUNS"
APPLICATION OF FACTORS AND DIVISIBILITY = G10
Problem 21: A refreshment stand buys hot dogs in packages of 10. Hot
dog buns come in packages of 12. What is the least number of hot dogs
and buns that must be bought to have an equal number of each?
A: 120 hot dogs and 120 buns
B: 60 hot dogs and 60 buns
C. 30 hot dogs and 30 buns
Solution A: compute the least common multiple by constructing the
smallest number which contains all factors.
10 = 2 x 5
12 = 2 x 2 x 3
2 x 2 x 3 x 5 = 60
Solution B: check with a calculator for divisibility
A: 120/12 = 10 120/10=10
B: 60/12=5 60/10=6 <= smallest that works
C: 30/12=NO 30/10=3
Requires:
- Least Common Multiple = G7
- Divisibility = G7
- Use processes involving factors and divisibility = G10
Simply asking for the least common multiple would reduce this
to G7.
Asking how many total hot dogs you could sell if you had 5 packages
of buns and 6 packages of hot dogs would be compliant with 4th grade
skills.
Benchmark 1.1 understand and apply concepts and procedures
from number sense
G4: blank
G7: understand the concepts of prime and composite numbers,
***factors and multiples***, and ***divisibility*** rules.
G10: understand concepts of and use processes involving prime and
composite numbers, factors and divisibility.
Compliant Version:
If students were instructed to use repeated addition or trial
multiplication to check which combination would use up all hot dogs
and buns, it might be compliant.
###################################################################
"COIN TOSS"
INDEPENDENT PROBABILITY = G10
COUNTING OUTCOMES TO DETERMINE PROBABILITY = G7
Problem 9: Leon tossed a coin in the air 20 times to see how it
would land. He got heads 12 times. What is the probability of Leon
getting tails on the next toss?
A: 12 out of 20
B: 8 out of 20
C: 1 out of 2
Solution:
Coin tosses with fair coins are independent events. Therefore, the
probability of tails is 1 out of 2 possible outcomes, or (C)
Requires:
- Calculate numerical measure of uncertainty = G7
- Understand the properties of dependent and independent events = G10
---------------------------------
Benchmark 1.4 understand and apply concepts and procedures from
probability and statistics
statistics
G4: understand the difference between certain and uncertain events
G7: know how to calculate numerical measures of uncertainty for simple
events
G10: understand the properties of dependent and ***independent***
events
G4: know how to list all possible outcomes of simple experiments
G7: understand procedures for ***counting outcomes** to determine
probabilities
G10: understand and use appropriate counting procedures to determine
probabilities
Grade 7 Test Draft specification: students should be able to
interpret or express the probability of a given event in the form of
a ratio or percentage.
National NAEP specification: Do NOT assess for independent
probability in 4th grade.
Compliant:
If they asked what is the probability that Leon will get heads
without mentioning previous trials, it would be G7.
If they ask how many possible outcomes are there (2), it would be G4.
###################################################################
"BAG OF MARBLES"
UNCOMMON DENOMINATOR = G7
COUNT OUTCOMES TO DETERMINE PROBABILITY = G7
Math Task 3 (deleted from the web page as of 1998)
You have 3 different bags of marbles. Each bag contains black and
white marbles. Which bag gives you the best chance of picking a
white marble?
A: BB W
B: BBBBB WWW
C: BB WW
Solution:
A is 1/3 or 8/24 or .333
B is 3/8 or 9/24 or .375
C is 2/4 or 12/24 .500
Requires:
- Express probability as a ratio
- Counting outcomes to determine probability
- Comparing fractions with uncommon denominators OR
- Convert fractions to decimal with calculator / long division
Benchmark
This problem requires students to express probability as a ratio (G7)
and compare fractions with unlike denominators (G7)
Benchmark 1.4 understand and apply concepts and procedures from
probability and statistics
EXPRESS PROBABILITY AS A RATIO IS G7
statistics
G4: understand the difference between certain and uncertain events
G7: know how to calculate numerical measures of uncertainty for simple
events
G10: understand the properties of dependent and ***independent***
events
G4: know how to list all possible outcomes of simple experiments
G7: understand procedures for ***counting outcomes** to determine
probabilities
G10: understand and use appropriate counting procedures to determine
probabilities
Grade 7 Test Draft specification: students should be able to
interpret or express the probability of a given event in the form of
a ratio or percentage.
COMPARING FRACTIONS WITH UNLIKE DENOMINATORS = G7
G4: identify, compare, and order whole numbers and simple fractions.
G7: compare and order whole numbers, fractions and decimals.
G10: explain the magnitude of numbers by comparing and ordering real
numbers.
Grade 4 Draft Specification: Operations with fractions will involve
like denominators ONLY.
-----------------------------
Compliant Version:
Count the number of white and black marbles.
###################################################################
"BIRD FEEDER"
DECIMAL MATH = G7
UNIT CONVERSION WITHIN SYSTEM = G7
SCALE DRAWING = G10
COMPUTING PRICE OF LIST OF ITEMS = G7
DRAWING IS INCORRECT
PUBLISHED SOLUTION IS INCORRECT
RATE=G7
Problem #10
Your Project is to build a bird feeder. Explain how you could use
the information given to find the total cost of materials. Use
words, numbers, or pictures
+------+
/ /
/ /
+-------+
# ^
# |
# 60 in.
# |
# v
#
#
~~~ #~~~~~~~
# <--- Bottom of post is set in cement
#
(looks like oblique projection scale drawing)
Top view of square food tray
#==================# ^
# Screws attach # |
# to post # 2 ft
# # |
# +-----+ # |
# | x x | # |
# | x x | # |
# +-----+ # |
# # |
# # |
# # |
#==================# v
^
+ Tray frame made from wooden strips
---------------------------------------------
Item Cost per unit
wooden $2.50 per foot
post
wooden strips $1.00 per foot
for tray frame
tray bottom $6.00
tools, screws, loaned or donated by parents
nails, wood glue,
and cement mix
Solution: The solution given in the version of the test booklet which
HAS a scoring rubric (the one I have does not even give any solution)
neglects to convert 60 inches to 5 feet, which requires either
memorizing 5 ft=60 inches, or a division by 12 which calls for a
calculator according to the draft specifications. The CSL isn't sure
if the solution actually calls for working out an answer, which is
typical of these tests which often have more than one, or no correct
answer. The acknowledged "problems" with this example.
Post 60 in / (12 in per ft) = 5 ft x 2.50 per foot = 12.50
Wooden strips = 4 * 2 ft = 8 ft total (square is equal length on all sides)
* $1.00 per foot = 8.00
Tray bottom = 6.00
All other materials = free, other information is not needed by this
problem.
12.50 + 8 + 6 = 26.50
Requires:
* Know that price = sum of item price * item quantity
* Price per unit is a rate = G7.
* Square has 4 equal sizes = G4.
* Multiply decimal numbers 5 x 2.50 = G7.
* Read scale construction drawing, oblique and top view = G10.
* Read dimension arrows, dashed "hidden" lines = G10.
* Shop / workworking skills = middle school boys
* Convert 60 to 5 ft memorizing conversion factor is divide by 12 in
= 1 ft. = G7.
* 2 digit divide by draft specification requires calculator. = G4
Remarks:
If you asked to compute the cost of one tray, 4 strips, and a pole,
giving the cost of each unit, (add them all up, or multiply strips by
4) that would be compliant, if they left out the scale drawing.
If the bottom of the post is set in cement, the pole is actually
longer than 60 inches if the arrow is measured from the ground and
not the bottom of the pole. So the correct answer actually cannot be
determined, a typical performance based problem which has no correct
answer.
Benchmarks:
This problem requires unit conversion (G7), decimal math (G7)
knowledge of woodworking (middle school shop), knowledge of how to
construct a total cost spreadsheet (not in any 4th grade textbook
I've seen, not in benchmarks, but in 7th grade textbooks), reading a
scale drawing (not mentioned until G10) The benchmarks do not specify
adding a list of repeated items, they do not specify computing the
cost of 5 feet of lumber at $2.50 per foot, this is not even in 7th
grade textbooks.
Textbooks:
Summing of a list of repeated items is not covered until grade 7.
Even grade 7 books I have only cover unit items, they do not include
computation of cost based on cost per unit lenght x length. Grade 4
textbook problems involve only sum or products in isolation.
UNIT CONVERSION
G4: understand appropriate units of measure [no conversion]
G7: understand the relationship among units [conversion within
system] within both the U.S. and metric systems
G10: compare, contrast and use both the U.S. and metric systems
[metric to english conversion]
G7 Math Draft Item Specifications: Conversion factors may be used in
some problems and students may be given a formula for converting from
unit to another, e.g. feet to miles. [this problem does not even tell
how to convert from feet to inches - by contrast the 7th grade
example tells there are 12 inches in a foot! But not 4th grade!]
SCALE DRAWINGS
G4: blank
G7: blank
G10: construct geometric models and scale drawings using tools as
appropriate, for example, designing a house plan or building a model
of a bridge [OR A BIRD FEEDER, NO SEPARATE STANDARD FOR READING SUCH
A DRAWING]
COMPUTATION
G4: add, subtract, multiply and divide ***whole numbers***.
G7: add, subtract, multiply and divide non-negative fractions
and decimals using rules for order of operation.
G10: compute with real numbers, powers and roots
Compliant version:
The bird feeder consists of a pole which costs $4.00
a top which costs $2.00
and requires 4 strips along the edges which cost $1.00 each.
A: How much do the 4 strips cost? (multiplication)
B: If we add the pole and the top, what is the total cost? (addition)
No conversion.
No drawing interpretation.
No computation of cost based on cost per unit.
No need to know how to construct cost total
#############################################################
"FLAGPOLE"
APPPLICATION OF PROPORTIONALITY = G10
(this problem has been removed from the CSL website, it was published
by the Seattle Post Intelligencer with an incorrect answer)
Eddie wants to find the height of the school flagpole below.
The only measuring tool Eddie has is a 12-inch ruler.
Brick wall
###############
############### @
############### |
############### |
############### |
############### |
############### |
############### |
############### |
############### @ |
############### @@@ |
############### @# #@ |
############### # # ###
.............. .. .
......... .. .
...... .
shadows fire hydrant flagpole
Official Answer (as appears in Seattle Post Intelligencer) : This
math question has more than one possible answer, earning varying
points. The most complete answer uses the information provided. Eddie
could use his ruler to measure a single brick, then count the number
of bricks (vertically ) to guage the flag pole's height. This is not
on the actual test
Remarks: This is a classic performance based problem with an
incorrect published solution. You can't accurately measure which
brick is even with the top of the pole, and most flagpoles are taller
than any surrounding building. Even so, it's an application for
scaling and proportionality and rates, which is G7. The fact that
it's an application makes it grade 10. This problem appears in the
7th grade middle school textbook Mathematics in Our World (c) 1978,
1981 Addison Wesley as a proportionality problem. This sample has
was withdrawn from the CSL sample web site in 1998.
It's actually MORE difficult than the sample 7th grade
proportionality sample problems since proportionality isn't even
mentioned or hinted at as the solution. (if I make a slide half the
size, what happens to the length?) The classic solution (it's on
several web sites, and some textbooks) is to use the shadow, which is
not used by the solution above. The ratio of the hydrant height and
its shadow will be the same for the flagpole, assuming that it is
perpendicular to the ground. Measure the height of the flagpole
shadow, and apply the same ratio.
Requires Benchmarks:
* Recognition that this is a proportionality problem (G10)
* Knowledge that similar right triangles are proportional (G7)
* Indirect measurement (G4)
Benchmarks:
This problem violates at least 2 different benchmarks, application of
direct proportion, and indirect measurement.
APPLICATION OF DIRECT PROPORTION IS G10, NOT G7 OR G4
1.1 understand and apply concepts and procedures from number sense
G4: blank
G7: understand the concepts of ratio and direct proportion
G10: understand and apply the concepts of ratio and both direct and
indirect proportion (since the problem does not even hint at the use
of direct proportion, this is an application)
INDIRECT MEASUREMENT IS G7, NOT G4
G4: use directly measurable attributes such as length, perimeter,
area, volume/capacity, angle, weight/mass, money, and temperature to
describe and compare object
* G7: measure objects and events directly or using indirect methods
such as finding the area of a rectangle given its length and width
(this is clearly an indirect measurement of height)
Compliant
You have a tape measure, a ruler, and a string. Which could be used
to measure the height of a flagpole? (No indirect measurement or
proportionality)
--------------------
Bicycle Tricycle algebra story problem:
As presented as sample 4th grade problem by Commision on Student
Learning, Nov 1999 at A.G. Bell Elementary
Suzy counts 18 wheels on a group of bicycles and tricycles. She
notices there is one more tricycle than bicycles. How many bicycles
and tricycles are there?
Benchmarks:
G7: set up and solve single-variable equations
G10: create and solve equations and inequalities
This could only be covered under non-specfic "problem solving" in 4th
grade. Some students can be expected to "construct" ways to solve
this problem, but without prior instruction, most cannot be expected
to master a problem fewer than 50% of adults have ever been taught to
solve. (Typically less than 50% of high school students take algebra
in high school)
Textbooks:
This is demonstrated at the _end_ of an Algebra 1 textbook (normally
takes one full year) after going over commutative and distributed
properites.
This problem does not appear in any pre-1990 K-6 or G7-G8 middle
school textbooks. It does appear in community college catalogs as
"algebra story problems"
An appropirate 4th grade level story problem:
Jack has $6.50 in his pocket. He wants to buy 2 toy cars at $4.00
each. How much additional money does he need to buy these cars.
Appropriate grade level:
This problem is appropriate only after completion of 9th grade
algebra 1, it is not even appropriate as a 10th grade exit exam since
not all students are required to take or pass algebra.
Some new textbooks such as Progress in Mathematics: K-6 Balances a
traditional teaching approach with the NCTM Standards. by Rose Anita
McDonnell, published by Sadlier-Oxford 1995 include such problems in
5th grade workbooks as guess and check problems.
Solution 1: Guess and check
Make a table
Bicycle Tricycle BWheel TWheel Total
1 2 2 6 8
2 3 4 9 13
3 4 6 12 18 <- solution
4 5 8 15 23
3 bicycles, 4 tricycles
Solution 2: Algebra ax + bx = c
x = bicycle
x + 1 = tricycle
x * 2 + (x + 1) * 3 = 18
2x + 3x + 3 = 18
5x + 3 = 18
5x = 18 - 3 = 15
x = 3
3 bicycle
4 tricycle
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WASL 4TH GRADE SORTING PROBLEMS FROM HELL
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How many of your 4th graders can solve this sorting problem? Do you want your 4th
grader held back because he doesn't meet the "standard" of what "he should know and be
able to do"? Do you want your kid's diploma denied because you couldn't pass an equally
hard 10th grade test? This is exactly what states like Texas and New York are threatening
to do, we could be next.
Can you solve it? How long did it take? Is this the sort of problem you want on a test
where you have to finish 30 other problems in one day? Do you want your kids wasting
an entire week trying to solve problems like this when a standardized test only takes a
couple of hours on one day, and costs only $2 not $40 to score?
See the math benchmarks for Washington State's EALR
at http://cisl.ospi.wednet.edu/ComSL/MATHBMK.html
BTW, Terry Bergeson claims somebody HAS done a 2nd review of problems and
pronounce them fully compliant and reasonable within the goal of 80% passing once
everybody starts teaching to the new EALRs. Do YOU agree?
Sorting problems:
problem 17 page 70 "Scales and Blocks" (sorting)
The pictures below show the results when some
boxes are placed on a balance:
1----
T
J
2----
L
X
3----
R
W
4----
J
W
5----
R
L
6----
X
T
7----
T
W
---
Name two boxes that are heavier than Box X.
Write the number of the picture or pictures
you used to find each of your answers
_______________________________
Tell whether box R is lighter or heavier than
Box X. Write the number of the picture or
pictures you used to find your answer
_________________________________
List the 6 boxes in order from heaviest to
lightest:
1. 2. 3. 4. 5. 6.
Comment - there is nothing in the benchmarks that specifies being
able to sort 6 boxes based on 7 inequalities, except "problem
solving". There are likely no textbooks that give a solution to this
problem. Most adults can't do this problem, I doubt more than a few
percent of 4th graders can do this, even after being shown a solution
algorithm. This problem is not even appropriate for most 12th graders
unless that have taken an algorithms course that includes format
sorting algorithms.
4th Benchmark: identify, compare, and order whole numbers and simple
fractions. Nowhere is sorting of a list of numbers or items
mentioned, even at grades 7 or 10
This problem is not just ordering two numbers, it is sorting a list
of unknown values, and asking for a solution as to their order. A
benchmark to match this problem would be to "sort a list of six items
given 7 inequalities between different pairs of items".
Grade level appropriate problem
Block A 100 lb
Block B 75 lb
Block C 200 lb
Block D 115 lb
Arrange these blocks in order of increasing weight.
Appropriate Grade level benchmark: "Sort a list of 4 3 digit
integers".
One Solution, based on insertion sorting algorithm
1. T, J. 6 shows T is heavier than X, 1
shows J is heavier than T, which is also
heavier than X.
2. based on following sort order, R is
lighter than X
3. from heavy to light: W J T X L R
reverse this result: RLXTJW
Letters to sort
JTLWRX-6 blocks total
# is sorting list
* write heavier from left to right
* add a letter to left or right if it is definitely
to the left or right of what we already have.
* try out each letter in sequence
* stop when we have all 6 letters
Look for J
TJ
sequence #TJ
JW, put W at right end
sequence #TJW
done J!T!LW!RX
Look for T
XT put X at left end
sequence #XTJW
done J!T!LW!RX!
Look for W
RW?
R would be in the middle, wait
Look for R
RW
RL
Still in the middle
Look for L, lighter than lightest
LX
Put L at left
sequence #LXTJW
done J!T!L!W!RX!
Next L
RL
Put R at left again
sequence #RLXTJW
done J!T!L!W!R!X!
All letters complete, stop
Problem 35 p.90
In 1991, the five states below had the greatest
number of people visit their state parks and recreation
areas. The states are listed in alphabetical order
Visitors (in thousands)
------------------------
California 70,444
New York 60,744
Ohio 67,222
Oregon 39,479
Washington 46,813
How does washington rank in terms of total number of
visitors?
A. third largest
B. fourth largest
C. fifth largest
Solution
1. Count how many states are greater (3), then add one for
washington's position, answer is fourth.
2. Sort the list, find washington on the list (4 from top) This
involves rewriting the list, or writing numbers beside each line
without getting confused. Note that sorting a list is NOT a 4th grade
required skill.
This problem can figured out by many fourth graders, but it is still
much more complex than simply "ordering whole numbers". The answer is
not directly taught, but must be "figured out", which means that you
cannot expect all children to master this problem unless they are
either "smart" or have been coached on these particular kinds of
problems. Whenever you test for the ability to solve a problem for
which there is no known or taught solution, you are testing for
cognitive ability, or IQ, which cannot be taught or assessed
directly, and the advantage goes to kids with highest IQ and
out-of-school resources and exposure.
---------------------------------------------------------
Final comment - please note that any compliant question should be
simple to answer by any adult with a 6th grade education. That is NOT
true of the current 4th grade test, which would be difficult for any
4th grade teacher, let alone student or parent. This should not be.
Standards should be based on what actual kids and teachers have been
shown to be capable of, not what some consensus committee believes it
should be set to 10 years from now.