AWM Education column: 'Please, Do Tell' by UNL's Yvonne Lai

Yvonne Lai, associate professor of mathematics at UNL
Yvonne Lai, associate professor of mathematics at UNL

by Yvonne Lai, University of Nebraska–Lincoln
AWM Newsletter, Sept-Oct 2021 edition, pp. 17-20

“Be a guide on the side, not a sage on the stage.” “Ask, don’t tell.” “Math is not a spectator sport.” “Lecturing is educational malpractice.” These slogans rally some mathematicians to teach classes that feature “active learning,” where lecturing is eschewed for student participation. Yet as much as I believe that students must do math to learn math, I also find blanket statements to be more about bandwagons than considered reflection on teaching. In this column, I urge us to think through the math we offer students and how we set up students to learn.

Although I draw primarily from my experiences teaching proofs in abstract algebra and real analysis, the scenarios extend to other topics in first year undergraduate education and beyond.

Showing and telling the public and private spaces

If you have ever taught real analysis, you have seen students struggle. The nested quantifiers, new proof structures, and abstraction can feel like an avalanche. Those students who succeed find new mathematical doors to measure theory, topology, and more. Many students don’t though, and instead experience real analysis as an exercise in frustration and a message that they cannot do mathematics. The rewards of real analysis may be rich, but most emerge poor.

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