Several months ago, I asked people on Twitter, “You’re about to plan a lesson on concept [x] and you’d like students to find it interesting. What questions do you ask yourself as you plan?”
There were nearly 100 responses and they said a great deal about the theories of learning and motivation that hum beneath everything we do, whether or not we’d call them “theories,” or call them anything at all.
- “How can [x] help them to see math in the world around them?”
- “How can I connect [x] to something they already know?”
- “How can I explain [x] clearly?”
- “What has led up to [x] and where does [x] lead?”
All fine questions and I have one more to add. Here is the most satisfying question I’ve asked about great lessons in the last year. It has led to some bonkers experiences with students and I want more.
- “If [x] is aspirin, then how do I create the headache?”
I’d like you to think of yourself for a moment not as a teacher or as an explainer or a caregiver though you are doubtlessly all of those things. Think of yourself as someone who sells aspirin. And realize that the best customer for your aspirin is someone who is in pain. Not a lot of pain. Not a migraine. Just a little.
Piaget called that pain “disequilibrium.” Neo-Piagetians call it “cognitive conflict.” Guershon Harel calls it “intellectual need.” I’m calling it a headache. I’m obviously not originating this idea but I’d like to advance it some more.
One of the worst things you can do is force people who don’t feel pain to take your aspirin. They may oblige you if you have some particular kind of authority in their lives but that aspirin will feel pointless. It’ll undermine their respect for medicine in general.
Math shouldn’t feel pointless. Math isn’t pointless. It may not have a point in job [y] or [z] but math has a point in math. We invented new math to resolve the limitations of old math. My challenge to all of us here is, before you offer students the new, more powerful math, put them in a place to experience the limitations of the older, less powerful math.
I’m going to explore this idea further in my talk at NCTM on Saturday at 8AM. I’ll offer ideas from K to 12 illustrating how math can feel like pain relief, rather than pain, how math can feel like power, rather than punishment. I hope you’ll join me.