Yesterday DJ Strouse, a student in MIT’s quantum computing summer school, pointed me to A Mathematician’s Lament by Paul Lockhart, the most blistering indictment of K-12 “math” education I’ve ever encountered.
Lockhart says pretty much everything I’ve wanted to say about this subject since the age of twelve, and does so with the thunderous rage of an Old Testament prophet. If you like math, and more so if you think you don’t like math, I implore you to read his essay with every atom of my being.
Which is not to say I don’t have a few quibbles:
1. I think Lockhart gives too much credit to the school system when he portrays the bureaucratization, hollowing-out, and general doofusication of knowledge as unique to math. In my experience, science, literature, and other fields are often butchered with quite as much gusto. Not until grad school, for example, had I sufficiently recovered from eleventh-grade English to give Shakespeare another try (or from Phys Ed do push-ups).
2. Lockhart doesn’t discuss the many ways motivated students can and do end up learning what math is, despite the best efforts of the school system to prevent it. These side-channels include the web, the books of Martin Gardner, recreational programming, and math competitions and camps. Obviously it’s no defense of an execrable system to point out how some people learn in spite of it—but these omissions make the overall picture too depressing even for me (which is really saying something).
3. In describing math purely as a soul-uplifting pursuit of beautiful patterns, Lockhart leaves open the question of why, in that case, it’s been in bed with science and technology throughout its history—not merely for the education bureaucrats but for Archimedes, Newton, and Gauss. (Of course, like most relationships, this one is not without its sniping feuds.) Personally I have no problem with teachers who want to recognize and celebrate that aspect of math, provided the students respond to it. “So you say you want theorems that are not only beautiful, but also inspired by physics or economics or cryptography? Line up then, because here comes a heaping helping of them…”
4. Lockhart doesn’t address an interesting problem that’s arisen in my own teaching over the last few years. Namely, what happens when you try to teach as he advocates—with history and philosophy and challenging puzzles and arguments about the definitions and improvisation and digressions—but the students want more structure and drill and routine? Should you deny it to them? (For myself, I concluded that brains come in different types, and that it would be presumptuous to assume a teaching style that wouldn’t work for me can’t possibly work for anyone else. Still, before beginning a traditional rote drill session, it’s probably a good idea for all parties involved to agree on a safe-word.)
In the end, Lockhart’s lament is subversive, angry, and radical … but if you know anything about math and anything about K-12 “education” (at least in the United States), I defy you to read it and find a single sentence that isn’t permeated, suffused, soaked, and encrusted with truth.