I taught a good lesson this week. Not considering-the-limitations-of-remote/hybrid-learning good. Just really good.
A lesson where all students hit the checkpoints on schedule. Where small group conversations served their intended purpose with precision. Where the variance of whole class conversation was small enough to keep us focused but large enough to keep it interesting.
The lesson was on the Mean Value Theorem. I’ve taught it many times, and it’s usually very successful. But success is a little harder to come by right now, so it was a welcome surprise to see just how successful this lesson was in remote / hybrid learning.
Early in the lesson every group was able to outline the proof of Rolle’s Theorem via its connection to the Extreme Value Theorem. Later on, every group was able to develop a proof of the Mean Value Theorem based on its connection to Rolle’s Theorem. Our final whole-class discussion of the proof of the MVT was driven by several students who have been fairly quiet in class up to this point, which is always a sign of success.
The success of the lesson wasn’t due to any particular innovation. I simply have a better feel for this kind of teaching now: How to structure tasks, which questions to ask, how long to leave students in small groups, how to organize platforms to serve my instructional goals. And I have a better feel for my students, as well. I know who needs a nudge, and who needs to struggle a little more.
It’s been challenging trying to redevelop my feel for teaching this year. Success has come here and there, in brief moments. But this lesson accomplished exactly what I hoped it would. It feels good to finally be able to say that.
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