### Why Johnny Can't Integrate, By Parts

In her most recent column (Parade magazine, 13 October 2002), Marilyn vos Savant takes up the question of "why more people don't understand math better than they do." Her tentative answer: "I believe that much of the problem lies in the lack of logic and reasoning skills. Math is just logic with numbers and symbols attached, and success with it requires the ability to reason effectively. But children usually are taught *what* to think, not *how* to think." That's a good partial answer (and I don't think Marilyn intended her answer to be exhaustive), but it should be taken with at least a grain of salt. For many years, the fad in pedagogy has been to emphasize understanding rather than outcomes. As Tom Lehrer once put it, "New Math" was based on the notion that "the important thing is to understand what you're doing, rather than to get the right answer." The problem is, math is a field in which understanding and accuracy are bound up together. You can't have one without the other, and accuracy is one (not to say the only) viable indicator of understanding.In any case, I want to suggest another reason that so many people don't understand math (and this reason is meant as a complement, not a substitute, for Marilyn's). Math is one of those disciplines that builds heavily on itself. If you don't get arithmetic, you won't get algebra; if you don't get algebra, you won't get trig; and so on. Students often learn to hate math because of one really lousy teacher, and after that they never really catch up. If your American history teacher is horrible, that won't cripple your efforts in World history; but if you algebra teacher is horrible, your geometry and trig teachers may never be able to rescue you. The point, then, is that math education is much more sensitive to failure at any point in the learning process.

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