The author discusses their experiences teaching an upper-division seminar course in a traditional face-to-face setting, and re-designing a "long eighteenth century" survey course for delivery online. The article thus explores spatial strategies in both face-to-face and online courses, and suggests ways in which they can be particularly…

Real Analysis is a required class for most undergraduate mathematics majors, but it is also one of the most difficult classes they will take. In this article, the author compares two approaches to teaching in the two analysis classes she has taught. The first one was taught in a traditional lecture-homework-exam format, while the second was taught…