Every teacher should have one of these in their career

This year I teach calculus. For the first time. Never wanted it – less challenging since the kids can already do math. Ugly pressure from yet another standardized test (Advanced Placement). And I kind of liked the electives, and liked the challenge of the younger kids.

But here I am, knee-deep in dy and dx and all that fancy sort of stuff. Since I’m teaching AP, I must be smart? Not particularly. But it is the last math course in my school, the only one I haven’t taught.

About three weeks ago a moment had arrived. We had played with finding the slope of a tangent line to a curve at a point. And with limits. And with all the other little pieces. We were ready to find the derivative of a function, using the definition. More than ready. I had delayed them two or three days.

So there we were, with ten minutes left in a class, finding for the first time the slope of the tangent line not at a particular point, but at any point. I made them give me each step. “Oh, no!” I panicked, each time we hit an obstacle, “We’re stuck!” and each time someone in the class would point out that we had already resolved that situation in a previous lesson, and told me what to do.

“Oh no, there’s only five minutes left!” “Oh no, we’re not close enough to x!” “Oh no! Oh no! Oh no!”

As I pushed faster and further, I got more panicky. “Oh no!” I shouted, again and again. “Oh no! Zero over zero, we’re stuck!” “You can factor” a chorus responded. And as I panicked they found the value of the limit, and an expression popped out. And I rapidly exclaimed: Now we know the slope of the tangent, not at one specific point, but at any point on the graph!

It was a speed drill, with the kids playing along 100%. A clear derivation sat on the board. “Ladies and gentlemen” I gasped “the period is not quite done, but I am” I leaned on the table in front of me, and caught my breath.

And then I heard a sound, something hitting something else. And it repeated, and multiplied.

Better teachers than me have gone through whole careers without getting applause for a lesson. It took me two days to wipe the grin off my face.