PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Pedagogical challenges of communicating mathematics with students: Living in the formal world of mathematical thinking
Page: 964
In this paper we examine an Abstract Algebra professor and one of his students’ thought processes simultaneously as the class was moving toward the proof of the Fundamental Theorem of Galois Theory. We employed Tall’s theory of three worlds of mathematical thinking to trace which route (embodied, symbolic, formal) the mathematician was choosing to take his students to the formal world. We will discuss the pedagogical challenges of proving an elegant theory as the events unfolded.