PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Undergraduate students’ holistic comprehension of a proof
Page: 554
In this paper I explore eleven undergraduate students’ comprehension of a proof taken from an undergraduate abstract algebra course. My interpretation of what it means to understand a proof is based on a proof comprehension model developed by Mejia-Ramos, et al. (2012). This study in particular examines the extent to which undergraduate students are able to summarize a proof using the proof’s higher-level ideas. Additionally, eleven doctoral students in mathematics were asked to provide a summary of the same proof that the undergraduate students received. Undergraduates’ holistic comprehension of the proof was then analyzed in light of summaries that the doctoral students provided. The main finding of the study is that undergraduates’ comprehension of the proof was overall inadequate—notably, they demonstrated limited skills in summarizing a proof via the proof’s key ideas. Moreover, undergraduates failed to recognize the scope of the method used in the proof.