PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Partial Unpacking and Indirect Proofs: A Study of Students’ Productive Use of the Symbolic Proof Scheme
Page: 2-47
This paper examines mathematics majors' evaluations of indirect proofs and of the compound statements used in this form of proof. Responses to survey items with a cohort of 23 students and six 1-hour clinical interviews, indicate that the students who could successfully evaluate indirect arguments and who could successfully recognize logically equivalent statements, tended to use partially unpacked (Selden & Selden, 1995) versions of the statements and the proofs and, in so doing, demonstrated a productive use of the symbolic proof scheme, whereas both successful and unsuccessful students tended to use a proof framework (Selden & Selden, 1995) for indirect proofs. Moreover, successful students' approaches are suggestive of activities, which are rarely found in introductory proof texts, yet may benefit novice proof writers.