I know, I know, teachers are always complaining.
But what’s even more terrible is that we teachers don’t tend to share our success with each other. We do have successes, I swear– even though they tend to come in small numbers and sporadically. Still, we keep them to ourselves.
So in this post, I’m going to brag.
In my calculus class yesterday, my students struggled hardcore with the chain rule. They didn’t quite get substitution for the more involved problems, and I’ve been trying to hone their intuition explicitly — saying I don’t want them to do problems formally. I want them to practice “seeing” the solutions.
Let’s level here: getting an assortment of calculus students to “see” anything is hard. They like rules, procedures, things they know will always work. Telling them to “hone their intuition” frightens them. There’s less certainty. But the reward of finally getting it is so much greater — because you can suddenly attack incredibly complicated problems.
So I waltzed into my classroom filled with students fretting about not “seeing” the solutions, and said: “Screw the homework for now. We’re going to get this!” And I gave them this sheet with 9 problems on it — I worked hard to come up with the idea the night before — specifically designed to “hone their intuition.” And all I can say is that: it worked fabulously. They were doing really complicated chain rule problems in their heads!
The rest of the class was spent capitalizing on this new understanding. At the end of class, one of my students said that calculus class is the first time she’s enjoyed math since 7th grade when she first learned to solve for x. Which means I must be doing something right.
I left glowing.