The happy Thursday


From Monday to Wednesday (or actually from Saturday to Wednesday, but this is harder to admit), I was thinking how to teach – how to teach mathematics online.

At normal times I teach in front of a big blackboard, or better in front of several big blackboards, and I present a coherent story from A to Z in each class. Mathematics is just easier to follow when it rolls out bit by bit, symbol by symbol, with natural pauses and hesitations, making blackboards preferable to slides.

Juhan Aru giving a lecture. Photo credit: Juhan Aru.
Juhan Aru giving a lecture. Photo credit: Juhan Aru.

But what about teaching online? It’s annoying to follow someone with bad handwriting on a video for 90 or even 45 minutes in a row! Thus, I have been thinking about whether we could teach mathematics differently when teaching online. After all, by cutting the material into small videos, we are no longer forced to present one coherent story from A to Z, but we can rather have different types of videos either giving a bird’s-eye-view of the content or zooming in on important details of proofs or definitions. Maybe linearity could be present only in the written notes, and videos help to roll out the content bit by bit?

I have no good answers, and this annoys me. Nothing seems quite perfect. There probably even is no one correct answer – for some students, something works, for others something different…

But luckily today is Thursday! I try to keep Thursday and Friday solely for thinking and writing, mainly for my own mathematical research – in the end, this is what feeds my own curiosity and enthusiasm and I have realized that without spending enough time on research, I have no enthusiasm to pass on to the students. To help others discover mathematics, I have to keep on discovering it myself – and I like this discovery very much!

Juhan Aru is a mathematician at EPFL, working on the geometry of random phenomena.

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