PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Public versus private mathematical activity as evaluated through the lens of examples
Page: 524
Lecture has often been critiqued as obscuring the mathematical habits such as sense-making about abstract statements about mathematical concepts, the creation of conjectures about those concepts, and to the processes of proof-writing and exhibition of counter-examples. In all of these actions, a mathematician or student should be able to draw upon a rich store of examples in order to make meaningful progress and researchers have argued that it is via examples that they are best able to engage in such processes. Inquiry-based classes have, as part of their promise, making more visible the mathematical promises that lecture obscures behind the polished formalism. This preliminary report explores whether and how students in an inquiry- based abstract algebra class engage in public example-based reasoning as a means to explore public versus private mathematizing.