PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Making Jumps: An Exploration of Students’ Difficulties Interpreting Indirect Proofs
Page: 2-7
This paper reports findings from an exploratory study that examined undergraduate mathematics students’ proof preferences, as they relate to indirect proof. While many have suggested that undergraduate students dislike and have metatheoretical difficulties with indirect proof, findings from 15 proof-preference surveys provide evidence that students' preferences are in fact more nuanced that previously anticipated and that in certain contexts students' prefer indirect proofs. Building on this work, 5 clinical one-hour interviews were conducted with a sample of survey participants, so as to better explain the discrepancy between these findings and those of other researchers. Data from the clinical interviews with advanced students are used to show: (1) aspects of indirect proofs, which others have argued are the root of students’ dislike, were not salient to the students, and (2) students’ difficulties recognizing secondary statements, rather than their metatheoretical difficulties, may account for their dislike of indirect proof in the form of proof by contradiction, but not of indirect proofs in the form of proof by contraposition.