Massachusetts teachers' math exam

Photo by Made In China

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... 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."
Take a look at the math test.

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)


Anonymous said…
I am a homeschooling mom. I looked at the test and found most of the problems difficult. I know I could've done them many years ago, but my math skills have become rusty. I have a bachelor's degree, but the highest level of math I did was only college algebra.

I would like to be the best teacher I can be for my children, and I feel like I should be able to do a test like this. How can I brush up on my math skills?
Burt said…
Good post. I read the article previously but did not look at the test until your post. It is a nice test. Wouldn’t it be great if all elementary school teachers could pass that test? I looked for a passing score. They did not set a passing score for the practice test. What do you think should be a passing score?
Maria Miller said…
There are many options - the handiest is probably to read books and/or read math material on websites. Such as:

Burt, I saw somewhere that 75% was a passing score on the Massachusetts test.
Sue VanHattum said…
Maria, You might have seen that 75% in my post, but that referred to the high school test. As far as I could tell, they didn't give the cutoff for passing.
Anonymous said…
I went to the bookstore today to find a book about teaching math, or brushing up on old math skills. I found it very telling that while there were scores and scores of books on teaching reading, there were only TWO on teaching math.

Where did our country go wrong in teaching math?? I went to school in the 70s and 80s, when they were doing "new math." Math was always a struggle for me. Although I remember when my dad helped me with my homework, he explained things differently than my teachers, and his way made a lot more sense. But I didn't see him often, so I floundered through math in high school.

For instance, my Algebra 2 teacher had no idea what he was doing. He would go through the sample problems from the textbook, and that was it. If we had any questions, he would just say, "Look at the book." No thanks to him, I failed Algebra 2, and ended up having to take college algebra at a community college to get accepted at university. I had the most awesome professor, and he taught in a totally different way than the teachers at my school. After struggling with math throughout elementary, middle school, and high school, I made a B+ in the class, and an A on the final exam. He even recommended I take more math classes! I couldn't believe it.

How did our country get to where it is? I'm probably over-generalizing, but people of my parents' generation (baby boomers) seem to have had a solid foundation in math. But I've read that the reason people came up with "new math" is that they felt that kids were being taught math by rote, not understanding. But it seems like ever since they came up with new math, and new-new math, things have gotten worse.
Will Thomas said…
As for math materials online, I would recommend a relatively new website, with thousands of helpful videos:

The website teaches K-12 math topics in easy, convenient, 2 to 3 minute videos each. One of the neatest features is the ability to customize the learning to their own personal style. Is one of the videos not getting through? simply click 'show me another way' to see the same topic approached in a different manner.
Jeff Goldstein said…
Thought I'd share.

My post on the Huffington Post about Math education, titled "Let's Ban English in School Except in English Class." They put it in the comedy section.

Lot's more math at Blog on the Universe

Please share!

Jeff Goldstein
Center Director
Nat'l Cntr for Earth & Space Sci Ed
In my teaching classes in college I had to take a math class that focused on the "why" of math, not just the how. I was amazed at how little I understood multiplication and other basic concepts. We had to solve simple problems without using algorithms and it was some of the hardest work I had ever done. I was so grateful for that class when I started teaching. When my students looked at me and said "why" or "I don't get it", I had alternate ways of explaining. It made such a difference, I was soon recruited for teaching the intervention class for kids failing math. And I loved it. If only every teacher could have that kind of in depth training.
David Greenberg said…
In New York, what certification is required to a home-school teacher?
CaptiousNut said…
I don't know what to make of that test.

It seemed *tedious* and *tricky*; I can imagine it was tough for a lot of teachers who, well, don't take a lot of timed tests themselves.
Anonymous said…
I just took this test a few days ago, it was nothing like the practice test, I studied for weeks, even saw a tutor, went online for tutorials, bought the prep book etc. This test is nothing more than the state wanting to make money! You cannot convince me that this test will make me a more competent teacher than those licenced last year or the year before when this test was not required! I am a college educated person who typically does not struggle as a student. This test was a joke. There must be a better way to evaluate teacher knowledge. I passed the Foundations of Reading and the Comm/Literacy on the first try.
Anonymous said…
Working for an online education company and writing about our products, I have found myself watching our own math videos and realizing how much math disappears from our brains as we get older.

I highly recommend anyone who needs a refresher check out our free videos on YouTube:

Or check my blog where I post more.
Often the videos have multiple lectures on them. Our math instructor, Edward Burger, is really great at teaching math!

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