Vi Hart‘s good for lots of things mathematical. I thoroughly enjoyed her deviously recursive video called, “How to Make a Video About How to Make a Video…” Even better was her recent video, “They Became What They Beheld:,” in which she discusses who she creates for and why. In it, Vi reads a fantastic quote by Edmund Snow Carpenter that I wanted to share.

“The trouble with knowing what to say and saying it clearly & fully, is that clear speaking is generally obsolete thinking. Clear statement is like an art object: it is the afterlife of the process which called it into being.”

This is why it’s so important to do real mathematics with young people. The process generates thinking. Hearing the foolproof method and mastering the technique is not enough, because it merely replicates the fait accompli. It’s the creation of the algorithm, the invention of the problem, and the mathematical process that need to be replicated, because these habits fuel creative acts. So which is the math? The object or the process?

“The problem with full statement is that it doesn’t involve: it leaves no room for participation: it’s addressed to consumer, not co-producer.”

There it is exactly. If the goal of math class is to get *this* stuff into *those* heads, then who cares about having co-producer? Is anything even to be produced? My job, as I see it, is to turn the math on in the brains of these kids. If I do it right, they come alive. They interact. They create. They control. THAT is participation. And the best part is, it infects your brain. Doing math affects how you see things, what occurs to you, what decisions you make.

See, this is what we work on in school. This is what the students and I co-produce — their minds. In math class, we make new mathematicians.