PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Mathematical actions, mathematical objects, and mathematical induction
Page: 53
Proof by mathematical induction is arguably the most difficult proof technique for students to master. We explain this difficulty within an action-object framework. Specifically, we report on results from clinical interviews with two mathematics majors in which the first author administered tasks designed to elucidate each student’s understanding of logical implications as mental objects. We found that the framework explains much of the difficulty inherent in proof by induction, even the students’ struggles with hidden quantifiers.