### Massachusetts teachers' math exam

I was almost ready to comment on this exam, where only about 27% of aspiring aspiring

*elementary school teachers*passed the new math section of the state's licensing exam this year...

Boston.com says about this test, "Education leaders said the high failure rate reflects what they feared, that too many elementary classroom and special education teachers do not have a strong background in math and are in many ways responsible for poor student achievement in the subject, even in middle and high schools."

...and then I noticed I had been looking at the wrong link for the practice test. The real link is this:

Massachusetts Tests for Educator Licensure, Mathematics Subtest, from MTEL Practice Tests website.

I feel that test is pretty good! In fact, I'd recommend that you do some problems from it, if you're teaching any grade from 1-12. If you're teaching middle or high school, you could use some of those problems with your students, and if you're teaching elementary, it's just to check if YOU have the adequate math skills.

The open-response item is particularly interesting, and good, I think. It shows a student response on a particular geometry problem, and asks:

"Use your knowledge of mathematics to create a response in which you analyze the elementary school student's work and provide an alternative solution to the problem. In your response, you should:

- correct any errors or misconceptions evident in the elementary school student's work and explain why the response is not mathematically sound (be sure to provide a correct solution, show your work, and explain your reasoning); and
- solve the problem using an alternative method that could enhance the elementary school student's conceptual understanding of ratios and decimal multiplication in the context of the problem."

## What kind of math would *I* test elementary teachers on

If I made a test for future *elementary*school teachers, I'd ask lots of questions about

*elementary*and middle school math

**INCLUDING "WHY" questions**. If they know that, then they can explain the math to their students as well.

I might ask questions related to common errors and misconceptions kids have. "Sally calculated that 0.5 + 0.12 = 0.17. What concept is Sally not understanding (and it's not decimal addition)? What kind of intervention do you think would help?"

I would ask questions that test their understanding of why long division or long multiplication works.

I'd test their knowledge of middle school level math and some high school level math. I'd test for problem solving abilities.

Elementary teachers should know middle school math well (percents, proportions, equations, geometric constructions, statistical graphs, etc.) so that they know what the elementary math they teach is leading to. For example, they should know square roots and Pythagorean theorem. That way, when they teach multiplication, they can throw in a "teaser" for the best kids in the class, asking, "What number multiplied by itself is 64?" Or, "I say a number, you say what number multiplied by itself gives that number."

So, I might actually ask, "What further mathematical concepts after 3rd grade depend on a good knowledge of multiplication tables?" Or, "Students study prime factorization in 6th grade. Give two examples where the understanding of this concept is needful in further mathematics studies within grades 6-12."

See also what MathMama writes about Tests .... (TIMSS & the MA teacher licensing test)