Conventions of the language of mathematical proof writing at the undergraduate level

This dissertation consists of three studies investigating the language of mathematical proof writing at the undergraduate level by considering a series of potential breaches of the conventions of this language. The first study describes interviews with eight mathematicians and fifteen undergraduates and their opinions on the potential breaches present in student-produced proofs. In the second study, mathematicians and undergraduates from top mathematics departments in the United States completed a survey investigating how a larger sample of mathematicians and undergraduates perceived some of the potential breaches discussed in Study 1. The third study focused on how some undergraduates described and justified their use of potential breaches of the conventions of proof writing in the proofs they wrote throughout their introduction to proof courses. These three studies present a jumping-off point for future research considering how undergraduates learn to write proofs and how mathematics instructors present the linguistic aspect of proof writing.Ph.D.Includes bibliographical referencesby Kristen Le