Dancing on Stilts
An experienced teacher describes the process of adapting his classroom technique to a virtual environment. He finds places where the face-to-face techniques cannot be applied, but also describes new possibilities afforded by the technology. The classroom
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I thought I knew how to teach. After spending 35 years in classrooms from grades 3 through 12, I could go into a classroom with 15 min notice and deliver a meaningful, if not polished, lesson. I could do it for advanced students, for average learners, and for struggling students. And I could keep inattentive students down to one or two out of thirty. Then came COVID, and I had to learn to teach all over again. I had the intellectual part down, pretty much. I knew where the students were and what they should be guided to next. But I didn’t have eye contact. I didn’t have body language. Worst of all, I didn’t have an expansive chalk board. The heart of the teaching process is motivation—getting the student to want to learn. The heart of motivation, in turn, is emotional—the bond between teacher and student that makes each party eager to please and communicate with the other. How do I bond with students when I only see their heads—and sometimes not even those? When I cannot tell what they are doing with their hands or their bodies? It’s as if someone made ballet dancers do the Dance of the Cygnets on six-foot high stilts. What follows is a description of some of the best experience I’ve had in online teaching, some unresolved questions, and some analysis of lessons I’ve learned.
M. Saul New York, NY, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 A. Wonders (ed.) Math in the Time of Corona, Mathematics Online First Collections, https://doi.org/10.1007/16618_2020_28
M. Saul
1 A Child’s Insight “I know how to tell how many divisors a number has. You factor it into primes. . . .” Alejandro was with a virtual group of four enthusiastic ten year olds, in the midst of exploring a problem. He gave the usual result, using his own somewhat makeshift words. But not too distant really from what I would have said: “If N factors as paqbrc : : :, then the number of divisors is (aþ1)(bþ1)(cþ1):::”. His description was less economical, but still accurate. His virtual friend Xue said: “That’s great. Let’s look it up on Wikipedia.” I was thinking, at this point: how nice! They can just conjure up Wikipedia and look something up. This would be clumsy in the usual classroom. I’m already tapping into new resources. But my hasty self-congratulation was quickly blown away by Xue’s next comment. “No. Let’s not look it up. Let’s pretend we don’t know it and see if we can prove it.” Dear Reader: I swear to you, on Galois’ grave, that I am not making this up. Nor the rest of the vignette I will be recounting here.
2 The Venue During the COVID Spring (2020), I was part of a team developing an online ‘webinar’ for the Julia Robinson Mathematics Festival (JRMF) program. At the time, I was its Executive Director. In normal times, we ran non-competitive afterschool mathematics events (“Festivals”) in which students are offered interesting games, puzzles and problems, assisted by a facilitator. Since face-to-face work with students became impossible, we sought to continue the wo
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