PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Pedagogical Considerations in the Selection of Examples for Definitions in Real Analysis
Page: 778
This study investigates mathematicians’ pedagogical practices and associated beliefs about the use of examples to instantiate definitions in a real analysis textbook. We used task-based interviews, asking participants to revise the introductory presentation of a concept, including definitions and examples, to be of higher pedagogical quality. All mathematicians believed that examples and counter-examples are important in learning about a concept. In this report, we concentrate on how mathematicians take the collection of examples and student thinking into account when deciding on which examples to use and the types of criteria they use to determine an appropriate collection of examples for a definition.