I find that lots of students are really good at *how*.

Like, how do you factorize a quadratic? How to you differentiate a cubic? How do you solve a system of simultaneous linear equations? How do you poach an egg?

(Apparently you need a gentle whirlpool to get the egg moving. Whirlpools: the unsung hero of the breakfast table.)

Why are they so skilled at *how*?* *It’s because students like procedures. They like certainty, clarity, the feeling that you know exactly what to do at every moment.

But they struggle with *why*. And – even more basically – they struggle with *what*.

For example…

I find that questions like this elicit one of two responses from students. Either this:

Or this:

These aren’t questions students are accustomed to answering in math class. In history, perhaps, where they have to write IDs of historical figures and events; or even in science, where they have to understand each component’s role in a theory.

But not in math. We math teachers tend to ask lots of *how* questions, and not so many *what* questions.

If you ask me, that’s sort of sad. They’re experts in *how*, and they can’t even tell you what the *how* is for.

And in this case, it turns out, there’s a pretty satisfying answer. Continue reading