PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
What’s the Big Idea?: Mathematicians’ and Undergraduates’ Proof Summaries
Page: 1-373
In this study, seven mathematicians and seven undergraduates were asked to read and summarize mathematical proofs that they read to investigate which ideas they consider to be important in a proof. Mathematicians’ ideas consisted of a) the overarching goals of the proof, b) the ideas they found novel or unfamiliar, c) theorems or facts used in the proof, d) encapsulations of inferences as applications to general methods, e) diagrams, or f) cues for reconstructing the proof. Students did not mention the goals, important theorems or facts, or the methods as being important, but some focused on whether the proof was indirect or direct. We present a model for accounting for many of the different types of ideas found important by mathematicians.