Wednesday, March 5, 2014

Where Creativity Comes In

Sam Shah, who was there from the start, reflects:
I want to make it so that kids see math as an artistic and creative endeavor... I am now pretty good at coming up with deep and conceptual approaches to mathematical ideas. And I’m okay at promoting mathematical communication. And I’m transitioning to having kids do groupwork all the time, to learn from each other — so I am not the sole mathematical authority in the room.
But all of that said: I don’t think I teach math in a way to shows how it is an art form, how deeply creativity and mathematics are intertwined.
I was just hanging out with some third graders. A kid asked me, "What's 6 times 8"? I said, "Dunno. What's a good problem to start with?"

She decides to start with 5 times 8. Clearly, she's thinking that she'll start by counting 5 eights, and then add one more eight at the end. But -- and this was the really cool part -- she decides instead to count 8 fives. She quickly ends up with 40, and then she returns and adds on an eight and lands on 48.

Isn't that a beautiful bit of thinking?

I don't have an answer to Sam's question -- duh -- but I know that creativity and math can be intertwined when kids learn their operations. What are the conditions for creativity in a math class? Dunno, but I have one trick that works with some reliability: Take some problem that could be solved efficiently and formally and give it to kids that only have inefficient ways to solve it.

E.g. Ask kids to find the area of a trapezoid without a trapezoid formula.
E.g. Ask kids to equally share 13 donuts with 5 people.
E.g. Ask kids to approximate the speed of a car from its distance graph

The gap between inefficient and efficient techniques is the sweet spot for learning, as far as I'm concerned. The hardest areas for me (us?) to teach are the ones that can't be solved by our kids using inefficient techniques, and its a fundamental problem of curriculum to ensure that kids have those tools at each moment of new learning.

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