overheard in providence

By way of Scott Aaronson, I recently read a surprisingly inspired essay on the dysfunctional state of math education. Paul Lockhart, the essay’s author, is a serious mathematician. He has a PhD in mathematics, is a former MSRI fellow and a former Brown professor. Since 2000, however, he has chosen to teach math at Saint Ann’s, a K-12 school in Brooklyn. Saint Ann’s is a rather unique institution that gives it’s teachers (and students) significant freedom—I like to think of it as the anti-Stuyvesant (my alma mater)—affording Paul the opportunity to step back from the tyrannical absurdity of standard US math curricula.

Paul’s essay, Lockhart’s Lament, is a little on the long side (24 pages), but the first three pages make his point beautifully (and humorously). Remember back when you were ages 6 – 18 taking 12 years worth of math classes, well it turns out you weren’t learning math. At first you learned some arithmetic (albeit in an extremely dry, monotonous fashion), and after that it was all downhill. Seriously, just read the first 3 pages, it’s a good time (also maybe check out the last two pages for quick drilldown of the standard US math education, plus I really like page 18 onward).

Here’s the big secret about math: It’s an art, not a science. It may look like a science, but that’s just because science has a lot of math in it. Almost all of mathematics, particularly the math you see in school, was not developed to try understand the world. It was developed when smart people made up interesting questions, then thought about how to answer them in interesting ways. As such, no one should attempt to learn math without taking time, a lot of time, to think about those very same questions. Examples of said questions (from Paul’s essay) include: “What is the area of a triangle?” or “Given the sum and difference of two numbers, can you determine what they are?”

With luck, time, and guidance from the teacher, students may actually be able to figure out solutions to these problem (and remember them), but even if they fail, they’ll make progress, and when they are taught the answer (i.e. a formula, an algorithm, a proof) they’ll appreciate why someone is bothering to explain it to them. Also they’ll have gotten a taste for the amount of thought that’s realistically required to understand math (hint: it’s a lot).

Sadly, in your own math classes, you were probably too busy learning to solve “math problems”—and you’ve no doubt forgotten how to solve most of them—to spend any time at all thinking about actual math. When it’s was all over, your big reward was that you went to college, got a job, and then never, ever, solved a “math problem” again. Maybe you use arithmetic, although I seriously doubt you find yourself multiplying 3 digit numbers or carrying out long division, but if you do anything beyond that it’s almost certainly material you saw/revisited in college.

In short, we really get very little in return for 12 long years of math education. Even for someone who likes math (me!) there’s just a ton of wasted time. Most of the skills you learn aren’t at all practical, and the most of the interesting ideas behind them are left out. I could go on (and trust me, I will) but mainly I just wanted to share Paul’s essay because it does a great job of illustrating, to the corrupt masses, what mathematics is actually about. As Paul points out on page three, most people leave high school with absolutely no idea.