This September, I gave my 7th-graders an elegant little problem about a 12-step staircase. You’re climbing from the bottom to the top, using combinations of single and double steps. The question is, how many ways can you do this?
I was stunned when some of my students offered answers almost immediately. “145!” one screamed, as if he had just gotten bingo. “Am I right?”
“Whoa, that was fast!” I said. “Why 145?”
“12 times 12, plus 1!” he announced. “Am I right?”
“But…” I hesitated. “But why 12 times 12? Why plus 1? Are we just doing random computations that sound like fun?”
He listened to my questioning with the same patience you’d give a friend’s mediocre guitar solo. Then he launched right back into his chorus: “So,” he said, “am I right?”
To him, at that moment, “doing math” meant “making a number smoothie.” You take the numbers in front of you, throw them all into the blender, and mash the “pulse” button until you get something.
The funny thing is, in our classes, this often works. You see a thick block of text; you pick out the numbers; you run them through the formula; and voila, you’ve got a solution, no thinking required!