Variability in the formal and informal content instructors convey in lectures

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.