Tag Archives: mathematics

Why study math?

Posted on April 19, 2012 | 4 comments

As usual, I was the house rabble-rouser at my institution today. Someone sent around a link to an article (subscription required, unfortunately) titled “Why study math?”

Reading the piece from the perspective of my inner middle-schooler, I was unimpressed. It felt to me like a rehashing of the usual vague unsubstantiated claims about transferring problem-solving skills and learning to reason. And also this:

Learning math develops stick-to-it-ness, defined as dogged perseverance or resolute tenacity, and develops perseverance, resilience, persistence, and patience. Students have opportunities to develop their work ethic in my math class by not making excuses, not blaming others, and not giving up easily.

Um, teacher? Do we have even one shred of evidence to support these claims?

So I wrote up my own reasons for studying math. Here they are:

I have two reasons people should study math.

First is that there is a set of very practical quantitative and spatial skills that are necessary for informed participation in society. Access to these skills ought to be both a civil right and an obligation.

The second is that there are many bodies of knowledge that we have agreed as a society are important; to be educated means knowing and having experienced certain things in the arts and sciences. In this way we pass on our culture.

I see these reasons as being quite different from more generalized claims about reasoning and problem-solving skills. An important part of the difference is that my reasons invite conversation and debate about exactly what mathematics we should teach.
If the practical skills are a major reason we impose math on students, we need to inspect the curriculum pretty closely to make sure we’re teaching the right ones. In a technologically advanced society, the long division algorithm for multi-digit decimals is pretty hard to defend from this perspective, for instance (to say nothing of polynomial long division!)

And if passing along mathematical knowledge and ways of thinking are culturally important, we ought to design curricula that give students experiences with mathematical ways of knowing. I would argue that our standard curriculum K-12 and through calculus does a pretty poor job of this.

But if we appeal vaguely to reasoning skills and stick-to-it-iveness, there is no further conversation. We tell students, “Take our word for it-studying this will make you better at that, and you’re gonna need that. So study this now and don’t ask any further questions.”

And while I don’t know everything about how to teach critical thinking, I know that when we talk to students this way-either explicitly or implicitly-we devalue it.

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I concede

Posted on March 1, 2012 | 15 comments

OK world, I concede.

Math really is just a bunch of disconnected rules.

Keywords are a good instructional strategy because getting a right answer now is more important than learning so you can get right answers later on.

This thing has one formula, that thing has a slightly different one; and these have nothing whatsoever to do with each other.

If you’re in situation A, you should do this; unless condition B holds, in which case it’s this other thing.

Oh, and CAUTION! Be sure not to make this error.

If this is bigger than that, treat it this way. If it’s smaller, do the opposite. If they’re equal you don’t have to do anything. Unless they can’t be equal in which case, see the caution above.

These things are equal, while those are congruent. Don’t get these confused.

We can’t take the square root of these things, unless we’re in that class. Not even if you already took that class. But there is no class where we can divide by this. But we can multiply by anything. As long it’s this sort of thing.

Flash cards equal learning.

Memorization is the goal, and the standard by which all should be judged.

Thinking is for losers.

All of the useful ideas in mathematics have already been had by others. We should study those instead of reinventing the wheel.

I concede, world. I concede. You are right.

I give up.

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