PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
The role of examples in understanding quotient groups
Page: 609
This poster investigates two students’ use of examples in the transition to advanced mathematical thinking in the context of a teaching experiment focusing on quotient groups. Based upon the theoretical perspective of Edwards, Dubinsky, and McDonald (2008), this poster extends the construct of imperfect models to include instances of generic examples. This study found that students leveraged examples to construct conjectures, form justifications, clarify misconceptions, and provide analogies for further reasoning. However, attending to the specific features of particular examples also led to over-generalizations and invalid reasoning.