A Math Standards Revision is Harder Than College SAT Algebra for 2nd grade

If you hope to have the math standards approved by the

legislature, you really MUST fix these errors in the standard

which you have published on the OSPI site.

Arthur Hu Feb 2, 2008

This is a review of problems with the Charles A. Dana

Center's Washington Mathematics Standards Revision.

While in general many have pointed out the lack of rigor

and low general level of expectations, there are some

shocking inclusions of above grade level math concepts

maquerading as kindergarten, 1st and 2nd grade level

math. Kindergarters are essentially asked to multiply

without using multiplication, 2nd graders are asked to

do what adults would using long division to divide 39

3 ways with a remainder. 2nd graders are also asked to

solve an unknown an unknown in two variables where one

is related to the other - solving a linear Algebra 1

level equation. That is a higher level of skill than

required by the College Board's SAT test.

The inclusion of these expectations reveals a shocking

degree of sloppiness in insuring that grade level

expectations are developmentally appropriate, and do

not simply overlay expectations of what adults can do

onto very young children under the title of "problem

solving". Problem solving needs to be restricted to

appropriate, efficent mathematical tools, not brute

force substitutes for more powerful concepts taught

in later grades such as multiplication, division, and

solving linear equations which are expected of students

at the end of a K12 education.

None of the problems were removed after I had sent

an email commenting on the first draft, and also

stated in person at a PTSA meeting with Terry Bergeson

attending in Federal Way. The 2nd grade algebra problem appeared

in the 2nd revision of the standards.

Project page

http://www.utdanacenter.org/wamathrevision/

Standards documents

http://www.utdanacenter.org/wamathrevision/standards.php

Send feedback to

wastandards@austin.utexas.edu

Summary of problems

* Kindergarten multiplication 2 x 5 x 3

* 1st Grade Division 10 divided by 2

* 2nd Grade Long Division 39 divided by 3 = 12 R 2

* 2nd Grade Long Division 39 divided by 3 = 12 R 2

* Kindergarten multiplication 2 x 5 x 3

Kindergarten

5. Core Processes: Reasoning, problem solving,

and communication

K.5.A Identify questions to be answered when

solving a problem.

K.5.B Solve problems, choosing from a variety of

problem-solving strategies such as drawing

pictures, manipulating objects, using

numbers, or acting out the situation.

K.5.C Determine whether a solution makes sense.

K.5.D Tell what the student did to solve a problem.

Example:

• Grandma went to visit her three grandchildren

and discovered that the gloves they were

each wearing had holes in every finger. She

will fix their gloves. How many glove fingers

need to be fixed?

=== Problem ===

This is a multiplication problem 2 x 5 x 3 = 30, even

if done by modeling.

Addition in kindergarten is only through modeling.

K.2.C Model addition by joining sets of objects

with 10 or fewer total objects when joined;

model subtraction by separating a set of 10

or fewer objects.

Get 4 counting chips. Now get 3 counting chips.

How many counting chips are there altogether?

Multiplication is not introduced until grade 2

2.4.C Model, create, and describe multiplication

situations in which sets of equal size are

joined.

- This pretty much describes this alleged

kindergarten level problem.

This is 2 years ahead of grade level.

==============================================

* 1st Grade Division 10 divided by 2

1.6.B Solve problems, choosing from a variety of

problem-solving strategies such as drawing

pictures, manipulating objects, using

numbers, or acting out the situation

Example:

There are ten feet living in my house. Who

could be living in my house?

Think about how many feet a person has.

How many feet does a cat have? How many

feet does a snail have? How about a fish or a

snake?

Come up with a variety of ways you can have

a total of ten feet living in your house. Use

pictures, words, or numbers to show your

answer.

== Problem ==

This not a problem that has one or even

neccesarily a small number of possible solutions.

It is MORE complicated than a division problem,

since not all creatures may have the same

number of feet.

Division is not introduced until the 3rd grade,

so this is 2 years ahead of grade level.

=================================================

* 2nd Grade Long Division 39 divided by 3 = 12 R 2

2.5.D

Solve problems, choosing from a variety of

problem-solving strategies such as drawing

pictures, manipulating objects, using

numbers, looking for a pattern, or making a

list.

Suzy, Ben, and Pedro have found 1 quarter, 1

dime, and 4 pennies under the sofa. Their

mother has lots of change in her purse, so

they could trade any of these coins for other

coins adding up to the same value. She says

they can keep the money if they can tell her

what coins they need to end up with so they

can share the money equally. How can they

do this?

== Problem ==

This is clearly a division problem, easily solved

by division. Dividing 39 by 3 requires long division

with a remainder which is not in these standards

until grade 5. 4.1.: "division algorithms, including long

division, are developed in fifth grade"

This problem is 3 years ahead of grade level.

=================================================

* 2nd Grade Algebra = X + X + 7 = 20, x = 6.5

2.2.D Solve a variety of addition and subtraction

problems and justify the solutions.

Problems should include those involving takeaway

situations, missing addends, and

comparisons.

Hazel and Kimmy each have stamp

collections. Kimmy’s collection has 7 more

stamps than Hazel’s collection. Kimmy has 20

stamps. How many stamps are in Hazel’s

collection?

A student may justify a solution orally, with

pictures, or in writing. For instance,

20 - 7 = 13

Hazel + xxxxxxx = 20

Kimmy's

=== Problem ===

* This problem is misstated, the solution, by

algebra, is 6.5

x + x + 7 = 20 state problem

2x + 7 = 20 factor x

2x = 13 subtract 7 both sides

x = 6.5 divide both sides by 2

* This cannot be solved by mere addition or

subtraction, the given example gives no hint

of the solution method, and it is incorrect.

If the difference was 6, then 7 would be correct

for X.

This is actually solving for a linear equation

of the form ax + b = c, traditionally taught in

Algebra 1 in grade 8 or grade 9.

The college SAT does NOT require algebra 1, so

the level of this alleged 2nd grade problem is

MORE difficult than required in the SAT.

If Algebra 1 is to be taught at grade 9, then this

is 7 years ahead of grade level, and IT IS NOT

EVEN REQUIRED FOR COLLEGE ENTRANCE for most

majors.

## Friday, February 01, 2008

### 2nd Graders get Algebra 1 Problem not on college SAT test

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## 1 comment:

My first grader can do algebra.

I gave him the following problems, orally. He answered them correctly.

4 times X plus 2 = 10, what is X?

3 times X minus 1 = 8, what is X?

I taught him multiplication when he was in kindergarten.

One day he asked me how wide and long a football field was and then worked through the math to figure out how many yardsticks would be needed to "make" the edges of a field (i.e., the circumferance).

He hates school because it is "too easy." He has a voracious interest in evolution and space, etc.

Is he some kind of genius?

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