Should math class be hard? – Math with Bad Drawings

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A couple of weeks back, I ‘d have considered this concern meaningless. Less a genuine concern than a sort of unclear hand gesture.

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But I simply checked out an excellent book that moved my thinking. [EDIT: I forgot to say which book! It’s The New Math: A Political History, by Christopher Phillips.] Now, instead of an unclear hand gesture, I see the hard/easy concern as a pointed and rather exact gesture. (No, not that gesture.) Particularly, the concern points towards another, larger concern:

What is mathematics class actually about?

One possibility: Is mathematics education for cultivating a basic quality of believed? For developing the capability to factor realistically? For honing the mind into an all-purpose tool?

In that case, it must most likely be as difficult as possible. The mind, like a pencil, requires friction to grow sharper. Not too much friction, or you’ll break the pencil (and the metaphor), however all else being equivalent, an excellent obstacle is a good idea.

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Or, another possibility: is mathematics education for imparting a particular set of helpful abilities? Is it about information literacy, arithmetical knowledge, and algebraic fluency?

In that case, it must be as simple as possible. Simplify into itty-bitty jobs, and practice every one up until you have it cold. Mathematics ed should resemble motorists’ ed: so blindingly basic that any person can obtain these standard, required abilities.

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A streamlined contrast, to be sure. For me, it’s an unexpected inversion of my normal thinking.

I most enjoy the difficulties of mathematics when I’m in “traditionalist” mode, when I feel genuine faith in the abilities and techniques that make up the historic discipline. (This isn’t my normal operating mode, however hey, I take pleasure in the chain guideline as much as anybody.)

But wait. If controling polynomials is really a human excellent, should not I wish to make it simple? Should not Iwant algebraic literacy to end up being like English literacy, with 99% of kids attaining it?

In the minutes when I’m most indulgent of “difficult,” I possibly should be pursuing “simple.”

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Meanwhile, I’m wariest of mathematics sensation too hard when I’m in “progressive” mode, picturing a human-centered mathematics education. On nowadays, I tend to believe that mathematics is not about a particular ability, however broadening our intellectual toolkit and boosting our capability to factor.

But if this is my concern, why should I be troubled if mathematics is agonizing or undesirable? Sure, excessive obstacle will drive my trainees away. If my job is enhancing minds, then aren’t difficult days an excellent thing?

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Of course, “difficult” is not one thing– its meaning differs trainee to trainee, job to job, minute to minute. There’s no “problem” dial I can turn. Still, these ideas leave me with a weird conclusion that I’m having a hard time to soak up.

When mathematics education has to do with the mathematics, I ought to be making every effort to make it simple. And when mathematics education has to do with the education, I should not avoid making it hard.

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