From course design to presentations of proofs: How mathematics professors attend to student independent proof reading

Abstract

Undergraduate mathematics students are expected to spend a substantial amount of time outside class studying proofs independently. Yet, little is known about how such expectations shape instruction in proof-oriented courses. This paper investigates this issue in a case study of an experimental teaching strategy, designed by a mathematics professor, for scaffolding student independent proof reading. On the basis of interviews and classroom observations we scrutinize the instructor’s course image – his envisioning of the teaching and learning activities, inside and outside class, throughout the course. We examine a representative case of proof presentation through the lens of the instructor’s course image. Our analysis reveals complex relationships between various teaching and learning activities in the course, and demonstrates that unpacking these relationships can provide valuable insights into specific teaching practices. Findings suggest that the concept of course image can be useful in enhancing our understanding of mechanisms underlying collegiate mathematics instruction.