Blog

by Joshua A. Taton, Ph.D. | November 14, 2023 | 2 min read

My high school track coach used to do something compelling, from an instructional perspective, even if it was somewhat sadistic. His method reminds me of a famous quotation with a dubious history.

In the middle of the season, approaching an important meet, Coach would conclude our workouts with a game that he called "Catch the Rabbit." (And, yes, he often said it while mimicking Elmer Fudd's diabolical voice.)

The game went like this:

We lined up—one following the other—at the starting line. Coach pointed out a mark in the distance: a tree, a cone, whatever. That mark was the turnaround point.

Each of my teammates had to chase the person ahead of us. And the goal was to catch that preceding person before we returned to the starting line. 

We left the starting line, one at a time, on Coach's "go." He would space us out according to relative speed, endurance, and frankly, his own whims.

But if no one caught their predecessor runner, we would all repeat the drill. Over and over. The "game" (i.e., punishment) finished whenever someone was able, successfully, to catch the person ahead of them.

Coach often warned us that, if we weren't successful—if no one caught a preceding runner in any of the rounds—we would just "keep at it," indefinitely, and that he might need to "turn the headlights on" of his car. Just so we could see each other, while we kept on chasing our teammates.

For some reason, we believed Coach. Or at least I did. 

It never dawned on me, not fully, that we could simply have left practice on our own accord. There wasn't much he could do. I also never fully realized that he was manipulating the distances between us, so that one of us would eventually "win" the game.

What does this have to do with math education? Simple.

When teachers demonstrate how to solve math problems for their students, writing on the board...or when teachers tell students how to solve math problems, describing every painstaking step in the process...a process they, themselves, have chosen...

...this would have been the same thing as Coach running in my place (or running on behalf of all of us). 

Sure, he motivated us, and he helped us pursue our own goals. He did so by structuring the exercise. But, of course, he let us run on our own.

He was an excellent track coach.

Excellent teachers, likewise, set up the conditions to have their students think. To think for themselves. And collaborate. And to feed off each other.

Importantly, they DON'T do all the thinking FOR their students. And, in so doing, they would deprive students of the struggle of learning and the joy of the process.

Remembering this story about Coach reminds me of a "fake" quote about teaching: "The best teachers show their students where to look but don't tell them what to see." (This is a "fake" quote, because there is no evidence that the person to whom it is often attributed, Alexandra K. Trenfor, hasn't been definitively shown to be a person who has ever existed—much less ever written or spoken this sentence.)

Despite being an apocryphal quote, I still think the sentiment holds. Of course, I welcome your thoughts!

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