Closing the Teach For America Blogging Gap
Sep 15 2012

NCTM brief: Local Educator adopts clever method which allows kids to do math without understanding

My National Council of Teachers of Mathematics Smart Brief just sent me this article about a role-model math teacher.

These articles are hand picked to bring me the best of math education. I feel like the person choosing them knows nothing about what it means to teach math meaningfully. The teacher in the article had helped students do well on standardized tests and obviously cared about her students. There were probably some great things she was doing in her classroom. However, they highlighted her practice of talking about square roots as a dating game. They quoted her “If you have a couple inside the house then they get to go on a date. If you are alone inside the house you don’t get to go on a date.” I had to guess, because the article didn’t even mention mathematics that they were talking about simplifying perfect squares under radical signs. They even proudly claimed in the article that her classroom doesn’t even sound like a math classroom as if that was a good thing! If the words in a math classroom don’t sound like math, then the kid is probably not actually learning math! They are probably learning to move symbols around with out understanding, which is not what the word math means to me.

I fully believe that kids in that class could learn how to correctly simplify square roots with this method and have no idea what the square root symbol even means. In fact, I tutored a sixth grader the other day who was supposed to be learning what to do with a cube root symbol but had no idea how to find the area of a square or the volume of a cube. In fact, even her textbook worksheet had mathematical errors on it that made it impossible to meaningfully answer the questions about square roots and cube roots. If she was actually thinking about what any of the symbols meant, it became impossible to answer the questions. The “correct” answer according to an example was that the “value” (they meant volume) of a cube was two different numbers. The only way to get the correct answer and understand the problem was to follow the example without thinking about the meaning of cube roots or volume. I had no idea what to tell that sixth grader. I know saying “your teacher gave you a worksheet that is mathematically incoherent” isn’t always the best strategy.

In any case, I wish NCTM, who is supposed to be promoting sense making and reasoning could be a little more careful about sending out articles about people finding cute tricks to help kids get right answers without understanding math. I’m all for fun mnemonics to remember things like the quadratic formula and I’d proudly sing the quadratic formula song. However, it is never okay to think of square roots as “dating” or the quadratic formula as a “song.” They are mathematics with meaning that should be attached to volumes, and gravity, and areas, and all the other ways science uses these concepts to describe the world.

2 Responses

  1. Wess

    I got the same email and didn’t follow the link, but I did suspect that “clever method” really meant “cute trick.”

    I’ve actually heard quite a few dating analogies from algebra teachers, and some of them are as heinous as this one. However, I think some do promote understanding rather than evading it. I wish I could think of some examples… but I think if you’re careful about the analogies you’re making, they’re not always “tricks.”

    There’s a line, though. This is definitely an analogy that to numbers moving around on a page, not one to the real math behind it.

  2. Ms. Math

    I agree that some analogies are great-there are some papers about how kids learn the concepts of limits through metaphors. Eventually their thinking is refined enough that they see that the metaphors are close, but not perfect approximations of the logic.

    I also had some dating stories about math to serve as mnemonic devices for formulas and I use mnemonic devices to speed up formula recall. But I can always really analyze the formula in the end which is what I think the kids would be missing with the snapshot of the teacher’s instruction presented in the article.

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