Encouraging Example Generation: A Teaching Experiment in First-Semester Calculus

Abstract

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article presents three student case studies. These case studies are representative of our findings and serve to summarize the activities we found useful. They also serve as examples of various student experiences during the teaching experiment. One student expressed a continued negative view to using example generation. Two increased in skills and experience and expressed positive changes in views.