I was nervous about classes today because I was EXHAUSTED this week and didn’t have much time for planning. I didn’t really have much of a lesson plan for either class, just a few prompts that I thought weren’t really all that interesting. But then I ended up having great classes today that I could not have predicted. All three were almost completely socratic dialogue mixed with individual practice, i.e. nothing fancy (which is what I’m totally biased towards as defining a “good” class). Most suprising was seeing how excitedly my non-AP students dealt with this simple question: How do these functions compare? f(x)=2, g(x)=(2x)/x, h(x)=(2*x*(x-1))/(x*(x-1)). Then how do they compare to these three functions? f(x)=2, g(x)=2/x, h(x)=2/(x*(x-1)). It just reminded me of how simply letting students explore a mystery can bring light to even the most boring topic.
In AP, I asked how we could find the speed of a ball at a given point if we have good numerical data. Students connected this with the rolly chair activity from the day before, and then we connected both to more abstract versions of the same idea with difference quotients.
Both AP and non-AP, despite starting with limits and derivatives respectively, are about 2 classes away from the limit definition of the derivative. So exciting!