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The tortoise and the hare

Why steady practice beats raw quickness in math, sooner or later.

For everyone

I see this pattern often enough that I think it deserves an essay. Nobody ridicules anybody, as in the fable, but the similarities are striking. Here's how the two characters tend to study math.

The tortoise

Doesn't grasp concepts quickly and finds the material hard. But the tortoise is dedicated. He does the homework, practices a variety of computations over and over, knows he has to work hard, and is willing to do it to get a solid understanding and good grades.

The hare

Quick. Has a better-than-average command of some of the fundamental ideas and can solve many problems in his head. But he doesn't like doing computation, and if he can't simply think his way to the answer, he resists doing the problem at all. He tends to rest on his laurels.

What happens

Sooner or later, material arrives that the hare can't solve in his head. Now he has a problem: he never practiced the computational techniques the problem requires, so he can't keep up. The good news is that the hare is quick and could learn the computation easily, if he put in the effort. His biggest obstacle is himself. Math has always been easy, he wants it to stay that way, and he may stubbornly resist. He either gives in and learns the computation, or he gets left behind.

Meanwhile, the tortoise has been quietly working. He's become proficient and he's ready for the next topic. This is where the tortoise pulls ahead. The point where math gets too involved to do in your head is different for everyone, but it always comes. And the tortoise, who is used to working hard, keeps going through the rest of his math education.

If you recognize yourself in the hare, take heart. You have the ability. You just have to do the work. And if you see yourself in the tortoise: keep going. It pays off.

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