PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
Do Generic Proofs Improve Proof Comprehension?
Page: 1-480
In an influential article, Rowland (2001) suggested “generic proofs” might improve students understanding and appreciation of the proofs that they study. In this paper, we present a qualitative and quantitative study exploring how well students understand generic proofs. In a qualitative study, we found students generally have positive opinions about generic proofs, believing generic proofs can be a useful tool for improving understanding. In a larger quantitative study, we conducted a randomized experiment where we assessed how well undergraduates understood the same proof when presented traditionally and generically. Those who read the proof generically performed somewhat (although not statistically reliably) better on questions applying the ideas of the proof to specific examples but statistically reliably worse on other types of assessment questions.