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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 89-103 |
| Number of pages | 15 |
| Journal | International Journal of Mathematical Education in Science and Technology |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2014 |
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Education
- Applied Mathematics
Keywords
- beliefs
- proof
- proof comprehension
- proof reading
- undergraduate mathematics education