Effective Proof Reading Strategies for Comprehending Mathematical Proofs

Abstract

In this paper, I identify five effective proof reading strategies that mathemat- ics majors can use to comprehend proofs. This paper reports two studies. The first study is a qualitative study in which four successful mathematics majors were videotaped reading six proofs. These students used five proof reading strategies to foster compre- hension: (i) trying to prove a theorem before reading its proof, (ii) identifying the proof framework being used in the proof, (iii) breaking the proof into parts or sub-proofs, (iv) illustrating difficult assertions in the proof with an example, and (v) comparing the method used in the proof with one’s own approach. The qualitative analysis of these proof reading strategies illustrates how they may foster comprehension. The second study was a quantitative study in which 83 mathematics professors were surveyed about whether they desired that their students use these strategies. Most mathematicians indicated that they desired that students use them.