"Analyzing the teaching of advanced mathematics courses

via the enacted example space"

Timothy Fukawa-Connelly

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.