I was talking to my brother about math and teaching the other day, and he mentioned the Karate Kid (the original). It’s a classic story of learning. And in this case, learning happens through repetition.

• Daniel’s Introduction to Karate – wherein he makes a deal to question nothing Mr. Miyagi tells him to do, and begins the monotonous task of washing and waxing all the cars in the lot.
• Lesson 4 – wherein he paints the fence, another monotonous and seemingly pointless task.

These Karate lessons in disguise are a kind of template for a certain perspective on math education. Kids need to know that 3+5 = 8! Kids need to learn their times tables! And they need to know these things deep in their bones! These aren’t things you should have to think about; you know them intimately and instantly. As my advisor once told me when I showed my ignorance of something elementary (to him): “If someone wakes you up in the middle of the night and asks you this, you should know the answer without having to think about it.”

And here’s the thing: I agree! If you’re busy re-remembering your times tables or how to add fractions when you’re trying to learn, say, calculus, it presents a huge impediment to learning. And it takes repetition to get these things feeling deep enough in your body to feel natural and instinctual.

But before we break out our wax and paint and assume we’ve got the perfect recipe for effective instruction, we need to look a little more at the movie. What happens before he signs up to learn karate, and is willing to do hundreds of hours of incredibly boring, repetitive labor? First of all, he’s getting the stuffing kicked out of him by kids who know karate. Then, he’s saved by Mr. Miyagi, who knows karate even better. (I couldn’t find a good video of this scene… but here’s the same basic idea from Karate Kid 3).

So right away we have: motivation and choice of a mentor. And just so we’re clear, this is a pretty serious motivation.

What happens after he’s been working at this incredibly monotonous, repetitious acts that seem to have nothing to do with his original motivation for being there? Daniel questions his teacher, and threatens to leave.

• Lesson 5: Daniel questions, and Mr Miyagi justifies the work.

How would this scene have played out, I wonder, if Mr. Miyagi taught karate like we (usually) teach math?

Daniel (confronting Miyagi): I haven’t learned karate!

Miyagi: You learn plenty.

Daniel: I learned plenty… I learned how to sand your decks maybe, I’ve washed your car, paint your house, paint your fence, I learned plenty, right.

Miyagi: Ah, not everything is as seem.

Daniel: Oh, $%&@ it, I’m going home, man.

Miyagi: Daniel-san. Daniel-san! Come here. Show me… sand floor. (Daniel shows him) You need this for Advanced Sand Floor, coming up in spring. Then in college you ready for Sand Ceiling, much more difficult. Now show me… wax on, wax off. Someday you have own car, need karate to wax it, wash it. Also, big karate entrance exam for University coming up, and you need paint many fences to prepare.

If it isn’t blatantly clear at this point, it isn’t enough just to tell someone why something is useful, and that isn’t what Miyagi does in the movie; In other words, Mr. Miyagi shows Daniel how the practice solves his problem.

So to those who say we should drill math facts into kids, I say fine, but only if you do it in a context where

1. There’s an actual motivation beyond the absolute crap we feed kids (“You need math every day–how else can you make change if your calculator breaks?”)
2. There’s a clear usefulness to the repetitious, possibly boring stuff that helps them address the original motivation.

If you can’t do that, then I don’t want to be in your class, and I don’t know why any kid would want to be in there, either.