Teaching and Improvising

Published by MrHonner on

I was preparing my Area / Volume unit for BC Calculus and I pulled up last year’s lesson on the Shell Method. I started preparing a new remote teaching plan by transferring what I could from the existing face-to-face version. I chuckled when I reached this line in my old lesson.

Provide overview of Shell Method.”

I have what I call a “Problems First” approach to lesson planning. The most important part of my plan is designing the specific problems I want students to engage with. First I need an accessible problem that motivates the big idea at the start of the lesson. Then I need a variety of exercises that highlight a technique’s features and obstacles. Finally, I need extensions that push students to make deeper conceptual connections.

Having these specific problems means I have a solid plan. But designing these problems takes considerable time and effort. When it comes to time, teaching is a zero-sum game, so this means other elements of my plan might be, shall we say, less detailed. Like “Provide overview of Shell Method“.

Now, I love the Shell Method and don’t find it difficult to provide an extemporaneous development of it, as my “plan” suggests. But I’ve discovered that an important part of that improvisation is being in a physical classroom, face to face to with students. In that setting, I can pick up a few markers, jot down a few diagrams, ask a few questions, circulate, and conjure up an interactive derivation of the Shell Method.

I just don’t have the feel for that kind of improvisation in remote teaching yet. I find that I need to have many more logistical details explicitly prepared ahead of time when designing a remote lesson: Not just the problems, but the text that maps out the connections, the slides for the transitions, the multi-stage diagrams. There’s so much more that can go wrong, and one little blunder can turn a lively improvisation into a plodding mess.

I don’t think my teaching suffers from the increased scripting. It’s just one more adaptation I have to make. And I’m still improvising, but just in smaller, more targeted ways. More targeted than “Provide overview of Shell Method, anyway.

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Categories: Teaching


Richard Ngai · February 3, 2021 at 11:56 am

Your in-class presentations have always made the dots connect in AP Calculus in a way no other math teacher I’ve had has done, and I know your virtual class will appreciate the effort as well, even if they don’t say so.

    MrHonner · February 3, 2021 at 7:26 pm

    Thanks for the kind words, Richard. It means a lot that you’ve taken the time to read and respond, and that you remember our class fondly, as I do.

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