I subscribe to several education sites and a popular theme recently has been teachers sharing their favorite lessons. This got me thinking about whether or not I have a favorite lesson.
A few years ago, it would have been difficult for me to answer this because there would have been several I would have wanted to choose. “Everything You Need to Know about Logarithms in Less Than 45 Minutes” would have made the short list. “Crash Day” near the end of the first half of honors pre-calculus when so much material we have covered up to that point goes into proving e^(iπ)+1=0. Partial fraction decomposition and rotation of conics would have been on the short list as well. I enjoy the material from these lessons, it’s easy to build a story around them, and the kids were able to follow them (for the most part).
However, I’m no longer lecturing, and at this point I would have to say that I don’t have a favorite lesson because I don’t have math lessons in my classroom. Refocusing the course in a Harkness style has meant transferring the class over to a more holistic outlook when it comes to the material. We don’t focus on individual topics. Rather, we focus on how the material they already know coming into the course can be extended, utilized, and synthesized. As such, there aren’t lessons on the individual topics. Instead, we focus on making a little progress every day with a lot of different topics. For example, a “normal” day this term could include working with parametric equations and projectile motion, equations of conics, solving trigonometric equations, and solving triangles, all on the same day. And that’s not an exhaustive list of the material we cover.
So if pressed to give my favorite lesson, it would have to be the one where I help the kids see that math isn’t a bunch of separate topics, but rather is a unified whole. In other words, I get to present my favorite lesson every day.