I discuss my experience with teaching an advanced undergraduate Real Analysis class using both lecturing and the small-group guided discovery method. The article is structured as follows. The first section is about the organizational and administrative components of the class. In the second section I give examples of successes and difficulties…

This paper describes writing assignments from a modern algebra course which were used to foster the development of proof-writing skills. Each assignment consists of proofs and mathematical work supposedly written by fictional characters, where the proofs are designed to illustrate common misconceptions, difficult points, and typical writing flaws.…

Many undergraduate students have difficulty with the transition to proof-based courses in mathematics. This paper discusses students' beliefs about proof and justification in mathematics just prior to entry into such courses. The paper is based on in-depth interviews with students. The data suggests that some students have beliefs that may in part…