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Nathan Pinsky

Picture of Nathan Pinsky.

Thesis

Mathematical Knowledge for Teaching and Visualizing Differential Geometry

Advisor
Weiqing Gu
Second Reader(s)
Darryl H. Yong

Abstract

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.

Proposal

Differential Geometry through Discrete Approximations: A Video Pedagogy

Additional Materials

Poster