"Analyzing the teaching of advanced mathematics courses
via the enacted example space"
Department of Mathematics and Statistics
University of New Hampshire
Thursday, February 16, 2012
11:00 - 12:00 Candidate Presentation in RI-224
1:15 - 2:00 Teaching RI-224
Abstract: In advanced undergraduate mathematics, students are expected to make sense of abstract definitions of mathematical concepts, create conjectures about those concepts, and write proofs and exhibit counterexamples of them. In all of these actions, students may draw upon a rich store of examples in order to make meaningful progress. We have drawn on the concept of an example space (Watson & Mason, 2008) to explore how they do this. We took the definition and expanded its application to the concepts of example neighborhood, methods of example construction, and the functions of examples to create a methodology for studying the teaching of proof-based courses. We demonstrate our method via a case study from an undergraduate abstract algebra course.