Finding Teaching Skills in Unexpected Places

The other day as I was recording a video (on planes of symmetry and chirality) for my organic chemistry class, I realized that the video wasn’t really about what I thought it was about. While my lips were moving and I was scribbling on the screen, I was busy contemplating a new way to think about chirality, one that had never really crossed my mind before. It was a very interesting moment!

One reason I like recording videos is that it gives me that feeling of being on the hot seat, of playing to an audience surrounded by distractions and burdened with a limited attention span. An interesting structure, logical consistency, and “sticky” take-home ideas are all essential. In a face-to-face environment where a student can meet you halfway and instructor and student engage in dialogue, much of that pressure is off (though dialogue has a completely different set of challenges!). Good questioning and a warm demeanor can draw students into a dialogue, but great videos have to be fundamentally compelling in and of themselves.

While recording this video on chirality, I got thinking about the difficulties some students have in seeing that chiral molecules lack a plane of symmetry. I’ve seen students who gain great facility with identifying planes of symmetry in achiral molecules, but who don’t build enough confidence to assert that such-and-such chiral molecule has no planes of symmetry at all. I ended up having to pause the recording—how do organic chemists see a lack of a plane of symmetry in a chiral molecule? How do we see something that’s not there?

Brute force is one option: we could try reflection through every possible internal mirror plane and verify that none of them leave the appearance of the (chiral) molecule unchanged. Though a computer might be able to approximate this in some reasonable time frame, no human could hope to apply this approach with any success. What we need to really move forward with solving the problem is a set of candidate mirror planes that are the most likely to be planes of symmetry. Given an efficient method to generate a few candidate planes, we can try reflecting through them to come to a good educated guess about whether a molecule is chiral or not (“educated” in the sense that the guess is not rigorous but still correct something like 99% of the time).

Enter the idea of “corresponding structures,” identical portions of a molecule that must either stay put or exchange positions upon reflection through a plane of symmetry. In practice, we use corresponding structures to whittle down the list of candidate planes of symmetry: a huge range of possibilities is cut down to three or four at most. If one of them is a “hit” we call the molecule achiral right then and there; if not, we also know with great confidence that the molecule is chiral (never mind inversion centers).

If a student in conversation had asked me “how do you see something that isn’t there?”, I might have awkwardly fumbled my way to this idea. But recording a video gave me a chance to do it in an artificial environment, which was very cool. I wonder if anyone has studied the development of teaching skills during preparation of digital content?

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