Wednesday, October 17, 2007

Calculus Success

Things went really well in the calculus class today. For some reason they were in a good mood. And the material I was teaching was just the right level of difficulty to make class go smoothly. It was novel enough that they felt compelled to pay attention, but it was simple enough that they could mostly comprehend it in real time. When the material cooperates like that, the students instinctively know that they can optimize their use of time by paying attention. When it's too easy, they can tell that they can do something in addition to calculus (frequently chit-chat); when it's too hard, they know that they'll have to put in a bunch of time at home, so they don't bother to even try to learn the material in class.

Today's topic was anti-derivatives. The text does not start the integration chapter with the Riemann sums. It begins with indefinite integrals (much like the Thomas text that I learned calculus from) and only later brings up those pesky notions of areas. Since this is Calculus Lite, we only work with the most basic of integrals, so my students were able to accept that there is a mandatory constant and to learn the very simple rules for anti-differentiating linear combinations of power functions.

Adding to this, there were a few light spots in the lecture. To prepare them for the idea that anti-derivatives are derivatives done backwards, I put up that quote about how Ginger Rogers did everything that Fred Astaire did but backwards in high heels. When I told the class that we'd be doing derivatives backwards the rest of the semester, a heckler called out "and in high heels!" At which point I took off my shoe (3" heel) and held it up so everyone could see and told them that they all needed to wear shoes like that next class. I also referred to that calculus joke about the waitress (and the +C). One of my slides about the rules of integration poked fun at the rules of Fight Club.

I wish class went that well every day.