Mathematics majors’ beliefs about proof reading

Abstract

We argue that mathematics majors learn little from the proofs they read in their advanced mathematics courses because these students and their teachers have different perceptions about students’ responsibilities when reading a mathematical proof. We used observations from a qualitative study where 28 undergraduates were observed evaluating mathematical arguments to hypothesize that mathematics majors hold four specific unproductive beliefs about proof reading. We then conducted a survey about these beliefs with 175 mathematics majors and 83 mathematicians. We found that mathematics majors were more likely to believe that when reading a good proof, they are not expected to construct justifications and diagrams, they can understand most proofs they read within 15 minutes, and understanding a proof is tantamount to being able to justify each step in the proof.

Keywords:

• beliefs
• proof
• proof reading
• proof comprehension
• undergraduate mathematics education

Acknowledgements

This research in this paper was supported by a grant from the National Science Foundation (NSF #DRL0643734). The views expressed here are not necessarily those of the National Science Foundation. We would like to thank Aron Samkoff for useful advice on how to structure this paper as well as Kristen Lew for helpful comments on earlier drafts of this paper.

Notes

In general, these universities were either named “[state name] University”, “University of [state name]”, or “[state name] State University”. In states where multiple options were available and one of the universities had a reputation of having a prestigious mathematics department, we chose not to invite this university to ensure we were examining the beliefs of a typical, rather than “elite”, mathematics major. If there were still multiple universities to choose from, we would choose “[state name] State University”.