Investigating and improving undergraduate proof comprehension

Undergraduate mathematics students see a lot of written proofs. But how much do they learn from them? Perhaps not as much as we would like; every professor knows that students struggle to make sense of the proofs presented in lectures and textbooks. Of course, written proofs are only one resource for learning; students also attend lectures and work independently or with support on problems. But because mathematics majors are expected to learn much of their mathematics by studying proofs, it is important that we understand how to support them in reading and understanding mathematical arguments. This observation was the starting point for the research reported in this article. Our work uses psychological research methods to generate and analyze empirical evidence on mathematical thinking, in this case via experimental studies of teaching interventions and quantitative analyses of eye-movement data. What follows is a chronological account of three stages in our attempts to better understand students’ mathematical reading processes and to support students in learning to read effectively.