Student-Generated Examples in the Learning of Mathematics.

Examples, illustrations, occurrences, and instances play a central role in the learning of mathematics. Deliberately getting students to generate examples is a particularly powerful tool in teaching, but, while some of the possibilities they offer are used by many teachers, their full potential is rarely exploited. The authors came to this notion through reflection on their experience of observing teachers in classrooms, of getting students to take initiatives, and of creating examples while working on their own mathematics. They examine the roles played by examples constructed and generated by students, give illustrations and analyses of the use of this tool, and develop a theory for the act of exemplification as an act of cognition. A framework is developed for researchers and practitioners to further this work. [ABSTRACT FROM AUTHOR]