Math and science can be hard to learn—and that’s OK. The proper job of a teacher is not to make it easy, but to guide students through the difficulty by getting them to practice and persevere. “Some of the best basketball players on Earth will stand at that foul line and shoot foul shots for hours and be bored out of their minds,” says Williams. Math students, too, need to practice foul shots: adding fractions, factoring polynomials. And whether or not the students are bright, “once they buy into the idea that hard work leads to cool results,” Williams says, you can work with them.
There are plenty of lines to cringe at in Kakaes' article. PJ Karafiol knocks down most of them in a great post that was eventually syndicated by Slate. (Good for Slate. Good for Karafiol.) Mr. Williams' metaphor deserves extra scrutiny, though. Here are just two of its most screwy aspects:
- Drills aren't a basketball player's first, only, or most prominent experience with basketball. Drills come after a student has been sufficiently enticed by the game of basketball — either by watching it or playing it on the playground — to sign up for a more dedicated commitment. If a player's first, only, or most prominent experience with basketball is hours of free-throw and perimeter drills, she'll quit the first day — even if she's six foot two with a twenty-eight inch vertical and enormous potential to excel at and love the game.
- Basketball players aren't bored shooting foul shots. Long before "math teacher" was on my resume, I was a lanky high school basketball player trying to get his foul shooting above 50%. I'd shoot for hours but I wouldn't get bored, as Williams suggests I must have been. That's because I knew my practice had a purpose. I knew where that practice would eventually be situated. I knew it would pay off in a game where I'd be called to the line for a shot that had consequences.
There is a place for drills and explanation in mathematics, as in basketball. But consider what little good they do in either arena if the student isn't first made aware of the larger, more enticing purposes they serve.
BTW. The worked examples literature leans heavily on De Groot's research into chess masters who, it turns out, have memorized an enormous number of board configurations relative to casual players. This is unsurprising in the same way it's unsurprising that professional basketball players practice their free throws much more often than amateurs. But it doesn't necessarily follow from either of those facts that the best way to start inducting new members into either of those groups is to force novice chess players to memorize board configurations for hours or new basketball players to shoot hours of free throws from the line.
BTW. Max Ray articulates a strong framework for technology use in the math classroom at the end of his recent post at the Math Forum.
2012 Jul 11. PJ Karafiol follows up.
Am I the only one who is reminded of The Karate Kid? Mr. Miagi has Daniel do crazy, de-contextualized drills without knowing their purpose. In the end it works (because it’s a movie), but in the meantime Daniel gets extremely frustrated and wants to give up. Perhaps if Mr. Miagi had made it more clear what the “cool results” would be or how he would be “painting the fence” and “sanding the floor” in a tournament, Daniel-san would have been more than happy to wax all his cars.