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Nathan Pinsky

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Mathematical Knowledge for Teaching and Visualizing Differential Geometry

Weiqing Gu
Second Reader(s)
Darryl H. Yong


In recent decades, education researchers have recognized the need for teachers to have a nuanced content knowledge in addition to pedagogical knowledge, but very little research was conducted into what this knowledge would entail. Beginning in 2008, math education researchers began to develop a theoretical framework for the mathematical knowledge needed for teaching, but their work focused primarily on elementary schools. I will present an analysis of the mathematical knowledge needed for teaching about the regular curves and surfaces, two important concepts in differential geometry which generalize to the advanced notion of a manifold, both in a college classroom and in an on-line format. I will also comment on the philosophical and political questions that arise in this analysis.


Differential Geometry through Discrete Approximations: A Video Pedagogy

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