At the beginning of the summer, I went to a conference at Exeter, and vowed to blog about some of the things I learned from it. Which I haven’t made good on, yet. There were a few gems, and I thought I’d write about ’em briefly in a series on mini-posts.
The first is a simple way to get kids to think about the meaning of a derivative or an integral conceptually, before they’ve formally been introduced to it. It’s a Gedankenexperiment (thought experiment) and the presenter said they actually do it on parent visitation day, so the parents can think too.
You’re in a car with three things: a speedometer, an odometer, and a clock. Everything is going along dandy, until suddenly, your speedometer breaks. Can you tell how fast you’re going? You don’t want to get pulled over by the cops, after all.
That’s it. Can you imagine how fun that conversation would be to listen to, as a proverbial teacher-fly on the wall? And then to get to lead that discussion? Obviously, most students are going to talk about the problem as if you are going at a constant speed. Getting them out of that mindset will be awesome.
Of course, the natural second question is what happens if not the speedometer, but the odometer, breaks. Can you tell how far you’ve gone?
I dig this thought experiment. I mean, it’s so simple I don’t know why I hadn’t thought of doing it to motivate our work. Heck, you can have students talk in groups and present their ideas. Good stuff.