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 using active learning tasks, such as before-class reading assignments and in-class discussions of some homework problems. The students in the second class were more actively engaged with the material, and their performance on graded homework and exams was better. This article also discusses the author's transition from conducting a lecture-based class to teaching with a more active format. (Contains 4 tables and 1 figure.)