Paul's Dilemma: Is This a Polyhedron?

摘要

Teachers play the believing game when they honor students’ mathematical thinking, even when it means they must suspend their own mathematical thinking momentarily. The study reported here tells the story of what happened in a university mathematics classroom when one student did not think that a particular figure satisfied the definition of a polyhedron and the instructor chose to play the believing game. The result was a very rich discussion, where both students and the authors grappled with their own mathematical understanding. One author served as the instructor of the course and the other author was an observer, taking field notes and video recordings that provided evidence.