PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
An Investigation Into Students’ Use Of Given Hypotheses When Proving
Page: 868
The mathematical practice of strengthening or weakening a theorem requires careful attention to hypothesis and conclusion. Selden and Selden (1987) reported that students often unintentionally weaken theorems raising concerns of undergraduates’ attention to hypothesis. In this paper, I consider both the prevalence of this error and what the practice of strengthening/weakening a theorem may look like. A survey of prove/disprove prompts was piloted with five graduate students. A subset of these prompts was then given to undergraduates in an introductory group theory course. Preliminary results indicate that the error of weakening the theorem is prevalent amongst both populations. The graduate students participated in follow-up interviews where they were prompted to strengthen/weaken conjectures to further examine their attention to the hypotheses. In this preliminary report, I will present the survey results and one graduate case to illustrate what the practice of strengthening/weakening a theorem may look like.