## Tuesday, April 8, 2014

### Deconstructing the sample Keystone Exam, continued

I've been mulling over some great comments I received on my most recent post on the sample algebra exam for Pennsylvania's new Keystone tests. As I commented in response, I'm intrigued by the idea that these problems are each intended to measure a particular skill rather than, say, the general skills of setting up word problems algebraically and manipulating the resulting expressions to solve find solutions. It makes sense that the test-designers are attempting to align particular problems to particular Standards, and also that they are trying to ensure that students who failed to master skills from pre-Algebra and below are still able demonstrate that which they can nontheless do.

However, it seems to me that there's a significant overlap in what these 10 problems measure, and that the skills they measure boil down to:

1. passively recognizing the correct set up of an equation
2. correctly plugging in numbers and doing the arithmetic
3. using estimation to rule out unlikely candidates
4. knowledge of ordinal pair conventions
5. understanding of the inequality sign
6. facility with arithmetic

This list, unfortunately, includes few, if any, of the core skills of first year algebra.

I've ended up with a more cynical take on what, at least in part, is going on here. To most people, unless they actually sit down and do the problems, this sample exam looks to be testing much more advanced skills than the 6 I've listed above. It looks like we have word problems that need to be set up; systems of equations to solve algebraically; expression upon expression to manipulate symbolically; possibly complex relationships involving ordered pairs, or vertical and horizontal distances. In other words, it looks like a student's performance on this test is a function of how well he or she mastered first year algebra. Or, using ordered pair notation: (test score, mastery of Algebra I).

This gambit will quickly appease many people will might otherwise worry about what students are learning--or not learning--in today's schools. Enough kids will do OK, and it will look like they're thinking deeply and critically about algebra.

I'm reminded of the few problem sets in Math Investigations that appear at first glance to actually involve complex calculations, and that only on closer inspection clearly involve none. Consider, for example, this one, excerpted from one of my Problems of the Week.

STOP. Don't start yet. Star problems that may have odd answers.

1.
953
× 7

2.
624
×80
3.
53
×46

4.
87
× 65

5.
569
× 37

6.
__
6|428

7.
___
80|646

8.
____
70|5,044

9.
____
31|1,984

10.
_____
49|3,3,43

Auntie Ann said...

"Enough kids will do OK, and it will look like they're thinking deeply and critically about algebra."

And enough kids will have parents who realize there kidz arnt lerning and either teach them themselves or go to Kumon.

Deirdre Mundy said...

Several of the division problems have remainders. So, for instance, is 45 r 4 (not an actual answer from the page--I'm too lazy to click backwards.), odd or even???? Did the writer bother to WORK the problems?

Auntie Ann said...

The entire sheet can be done in a couple of minutes. Who cares if it's odd or even? Just do the math.

(And really, I can't tell you why anyone has to know whether something is odd or even--I suppose it helps you a little bit to check your answer, but not much.)

ChemProf said...

They are just testing a rule: odd x odd is odd, anything else is even. And many teachers would take off points for doing the math, because you aren't following directions.