What Constitutes a Well-Written Proof?
The purpose of this study was to identify some of the characteristics mathematicians value in good proof writing. Four mathematicians were interviewed. First, they evaluated and scored six proofs of elementary theorems written by students in a discrete mathematics or geometry course, and second, they responded to questions about the characteristics they value in a well-written proof and how they communicate these characteristics to students. Preliminary results indicate that these mathematicians agreed that the most important characteristics of a well-written proof are (a) correct logic and (b) clarity. Although these mathematicians differed in the attention they give to layout, grammar, punctuation, and mathematical notation, they agreed in giving these characteristics relatively little weight in the overall score. The results also showed that, in addition to demonstrating good proof writing in class, writing comments on students’ papers is an important way they teach their students to write good proofs.
Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education
Moore, Robert C., "What Constitutes a Well-Written Proof?" (2014). Faculty Publications. 8.