Teaching

We just started the Spring semester and I asked students to reflect on the Fall. As usual, I received lots of great feedback, both positive and constructive. And as usual, I was reminded how difficult it can be to think broadly about education.

Here are two comments taken from adjacent rows of my spreadsheet.

“You should use peardeck. It’s really interactive.”

“I would say don’t use interactive slideshows like peardeck”

The responses contained more apparent contradictions. You should require students to have their cameras on in breakout rooms . . . Thank you for not requiring us to have our cameras on . . . One of my teachers created a name wheel to pick on students randomly; please don’t do this . . . You should consider using a name wheel.

I say apparent contradictions because there is no real inconsistency here. These comments are all reasonable, thoughtful, and grounded in truth. It’s just that different students have different truths. Each student experiences education in their own way. What works for one student may not work for another. What works for one teacher may not work for another. What works today may not work tomorrow.

I wrote this last year when I collected feedback at the end of emergency remote learning. This is part of what makes teaching, and thinking about teaching, so difficult. There’s no single problem that you can find the answer to. It’s about dealing with the many different problems and their seemingly contradictory answers every day. But this is also part of what makes teaching such energizing work, even if it’s hard to imagine what you do working at scale.

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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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Last spring was probably the strangest semester of my 20+ year teaching career. Second on that list is this fall semester, which just ended.

This week felt like the end of the term. Stress could be felt everywhere: from students in classes, colleagues in meetings, administrators in emails. It’s always a mad dash at the end of the term, but every struggle is amplified now.

I always try to structure my courses so students don’t have much work due during the final week. I know other teachers are piling it on to make deadlines and cover curriculum, so a normal week in at least one class can be a relief. That seemed especially important this year. An unusual number of students came late to class during finals week, and there were a few extra cameras turned off. I hope it’s the kind of temporary stress that fades quickly.

One of the best parts of the job of teaching is the constant renewal. New years and new semesters mean new starts for everyone. And looking forward to a new start is an appropriate theme for this week, both inside and outside of school.

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To accommodate the different logistical consequences of potential in-person, hybrid, and fully-remote instruction, our school adopted a radically new schedule this year: Classes that meet every other day for periods that are 40% longer, but with an overall reduction of total class time.

The decision made sense from a organizational standpoint, but it made a mess of existing course maps and lessons plans. Trying to reorganize and redistribute content has been an ongoing challenge. It’s no simple thing to break up an existing course and reassemble it in different-sized chunks: You can’t just teach 40% more content because a class is 40% longer. Ideas needs to flow in a sensible way, and some in particular need time to set. Judging how to accomplish this was especially difficult at the start of the year, when it wasn’t even clear how much could be accomplished in a fully remote 55-minute class.

With three months behind me and a much better sense of what I’m doing, I’m feeling more comfortable putting the pieces together. Last week I was struggling to plan a 2-hour block in my trigonometry unit. But after some experimenting, I ended up pulling together material I side-stepped in October (special trigonometric limits), the core material I intended to cover (trigonometric integrals), and wrapped it up by laying the groundwork for some future extensions (Fourier series).

I would never have thought of putting these things together in a normal year. Nor would I have thought of this in September as I mapped out the semester. Back then I wasn’t even sure what would come of special trig limits as I side-stepped them, because it was impossible for me to look ahead.

But with nearly a semester under my belt, it made sense, and it worked. Three months on a steep learning curve can be painful, but it does make a difference.

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