Math is a Well-Defined Body of Knowledge

At the end of the day, whether or not they know math comes down to whether or not they can apply techniques within that well-defined body of knowledge to solve problems within that well-defined body of knowledge.

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You can’t have students do a character-building activity in a loosely mathematical setting and then claim that you’re teaching them math.

Math is a well-defined body of knowledge.

Sure, students will need to persevere through challenge to acquire that knowledge.

But at the end of the day, whether or not they know math comes down to whether or not they can apply techniques within that well-defined body of knowledge to solve problems within that well-defined body of knowledge.

If they can’t do that, then they don’t know math.

It doesn’t matter the amount of time they’re willing to fight with the problem before giving up, the degree of clarity with which they can communicate their thoughts about the problem…

These things are not proxies for mathematical knowledge.

“I understand everything, but I just can’t solve the problems”

is the equivalent of

“I am really strong, but I just can’t lift heavy weights.”

You are only as strong as the feats of strength you can pull off.

You only understand as much as you can evidence that understanding, solving problems.

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