Saturday, April 18, 2009

A Mathematician's Lament

I recently came across this fascinating article about everything that's wrong with math education according to Paul Lockhart. (Click through and read the pdf, I promise, it's worth it.)

He starts with the idea of what music or art classes would be like if taught as math is:
"A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school."
This goes on for a few pages before he gets into the real rant. His main point is that math is actually as creative an endeavor as art or music or history or anything else generally recognized to be interesting and creative, yet we teach it as something to memorize and practice and kill most students' interest in it. I think there are some elements of his argument that could be critiqued, but he does have some valid points.

It certainly appeals to the part of me that never remembered formulas but did remember the principles the formulas were based on, and would re-derive them all on the test because that was more fun than memorization. His "real" description of the standard math courses seems pretty accurate, especially in judging the utter uselessness of Algebra II and PreCalc. (Do you know how many definitions of limits we had to learn? Me either, but it was a lot. Why? We never used them in Calc.) Despite all that, I enjoyed math, because solving a problem is fun, an interesting challenge, and has a definite end-point. This is a much-needed break when you're also writing papers, themes and doing research--there's always more research you could do, more editing you could give that paper. At least, that's how I feel: I'm never done with a writeen assignment until I turn it in, and even then I'm only turning it in because it's due now.

Anyway, I started to write because I could take a lot of his points and apply them to history. As I've mentioned, I don't actually think that the point of learning history is to learn a set of facts. Especially not the set of facts currently contained in the curriculum, which are heavily political history biased, as well as being heavily biased in general. Facts without context are useless. (A problem he has with formulas, heh.)

Context isn't the whole problem though--I don't really want my students to learn history because I think they need to know everything that ever happened, or even certain important events that happened. I want my students to learn to do history: to analyze primary sources, to go digging for information, to construct narrative around a pile of facts, to argue interpretations of said pile of facts, to wrestle with deeper questions of morality and human nature and to think. Lots of thinking. Just as Lockhart wants his students to discover math for themselves, I feel that the most valuable history is that which you discover for yourself.