Yesterday: a student tells me he solved a 3×3 system by letting x, y & z be (3, 1, 1) in the first equation, (2, 2, 1) in the second, and (1, 2, 2) in the third. It’s cool, I say, that he found solutions for each equation, but we’re looking for x, y & z that are the same in all three equations and still work. “That’s the game,” I say, as his eyes widen and he really takes in the nature of the puzzle he’s facing.
Today: the puzzle is to find the equation of a parabola that passes through three given points. The aim is for them to discover a strategy. The minutes tick by. Many students, not knowing how to do this, have given up. I call them together, we go through finding the equation of a line. “So, how are we going to find b?” “Plug in x and y,” says J. “Good. Does that help with our problem?”
I tour the groups. It has not helped. Energy in the room: zero. Less than 10 minutes to go. Call them back together. “Let’s try J’s solution on our problem. If I plug in the first point, what do I get?” Two or three voices chant out: “0 equals a times 1 squared plus b times 1 plus c”. We continue and soon there’s a 3×3 system on the board. How do we solve that? “Like we learned yesterday.” “Ok, go to it.” Energy is still zero – there isn’t a problem anymore. Assiduous students plug away. The rest wait for the bell.
In inquiry classes, what do you do when they stop looking? Leaving them stuck deflates them. Revealing the answer deflates them. What’s the right thing in between, and what do you do if you don’t have it? That’s the game.