Saving Mathematics
The despicable state of K-12 mathematics in the US has been summarized in one charming, witty, furious article by Paul Lockhart. That’s Lockhart the mathematician-turned-gradeschool-teacher, not Lockhart the astronaut. He currently teaches at New York’s prestigious Saint Ann’s School. Here’s the article (it’s well worth the 30-minutes it takes to read):
PDF (or alternatively PDF.)
Much of Lockhart’s effort goes into cataloging what we all woefully remember: how math, as taught in most K-12 schools, is ugly and tedious. This is an absurd state of affairs. The practice of mathematicians is both artistic and refreshing. Something’s gone wrong. And Lockhart’s got a some great ideas about how to fix it:
what about the real story? The one about mankind’s struggle with the problem of measuring curves; about Eudoxus and Archimedes and the method of exhaustion; about the transcendence of pi? Which is more interesting— measuring the rough dimensions of a circular piece of graph paper, using a formula that someone handed you without explanation (and made you memorize and practice over and over) or hearing the story of one of the most beautiful, fascinating problems, and one of the most brilliant and powerful ideas in human history? We’re killing people’s interest in circles for god’s sake! (p.9)
It’s always interesting to hear how different math-lovers manage to overcome their arid early math education. In my case, it was a book. My friend Patrick suggested it to me in my first year of college; it was Richard Courant’s classic “What Is Mathematics?” and it was like reading about a completely new subject.
There are many books of this kind. The goal is not to batter you with formalism, but to help you develop the imagination and the curiosity and the discovery that makes mathematics so beautifully enjoyable. I remember my first experience with Courant’s book like a breath of fresh air. And I’ve always wondered: why on earth wasn’t math like that in school?
I think it can be. But as Lockhart laments, it’s much more demanding to teach in this way. On the other hand, he assures us, it’s much more rewarding as well. Here’s hoping Lockhart’s ideas take off.
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The objective of mainstream k-12 education should be to have each graduate owning a little piece of land upon which they have built their own little house — not “to code” but simply the kind of thing pioneer families would have built — and from which they are harvesting most of their food requirements.
The objective of gifted education should be to understand the double slit experiment — to which they should be introduced in kindergarten.