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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.

This paper investigates the variability in the content of lectures by different university mathematics instructors teaching concurrently in the same course. The instructors enacted a shared lesson-plan and coordinated their teaching to ensure students in different sections of the course will receive equivalent academic preparation. However, classroom observations and interviews with the instructors indicate that while explicitly discussing the same definitions and theorems and working out similar examples, the instructors were implicitly trying to convey different informal content. An analysis of the instructors’ mathematical discourse during the lectures and the interviews reveals that the instructors coordinated with each other content corresponding with object-level learning, while implicitly orienting their lectures towards fostering meta-level learning. This found gap highlights miscommunication between the instructors and points to the need of a shared and explicit discourse on meta-level learning at the collegiate level.