Vito Prosciutto: Teaching community college math on the road to a PhD.

Friday, October 17, 2003

The Mathematical Approach to Life 

Another good Open Source Politics article on math education. It seems a lot of critics of math education are caught up in the idea that math should be about doing computation. This is a silly view of what math is about. After all, few people, even in mathematics, do a lot of computation by hand on a daily basis. Why bother when computers and calculators will do the job much better. What mathematics is really about is a way of thinking. It's a thought provoking article, but doesn't really address the big issue in contemporary mathematics education: That we don't really do a good job of teaching computation or mathematical thinking at the secondary level. Part of that is the testing. We're stuck about a generation behind in how we test mathematical understanding (e.g., when I taught remedial algebra I last year, the first quiz was supposed to be completed without calculators. Why? Is it really essential that students be able to do, e.g., 0.0004/0.2 without a calculator to do well in math? Hell, I can do that, but I'll as often as not whip out a calculator for something like that just to make sure that I don't inadvertently misplace my decimal point. Much of the standardized testing falls into the same trap. If it were up to me, the math sections of standardized tests would be based entirely on finding the underlying formula for word problems (or very close to it).

On a related front, something that I've seen in geometry textbooks which leaves me perplexed are questions along the lines of:

Angles 1 and 2 are supplementary. If angle 1 has measure x and angle 2 has measure 2x + 3, what is the measure of angle 2?
Is there any case outside of a contrived problem like this where this will come up? I have a vague notion that I saw questions like this in one of the ACT prep books that I looked at, but this has no relation to how someone actually works with supplementary angles. It's not a geometry problem, it's an algebra problem, and while students should be able to solve this, the contrived nature of the problem is such that its ex nihilo nature outweighs the benefit of the algebra review, I think.

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