(Talk runs from 10:00-11:30 A.M.) \\ In reform-oriented mathematics classrooms, students are expected to learn from hearing the arguments of their classmates. In advanced mathematics classrooms, mathematics major are expected to learn from observing their professors present proofs and reading proofs in their textbooks. Both modes of instruction rest on the specific assumption that students are able to learn from the arguments of others. Unfortunately, research suggests that most students are not convinced and do not comprehend the arguments that they observe. in this talk, I will present two studies that investigate the reasoning processes that mathematics majors use when they read mathematical arguments. The data from these studies will be used for three purposes: (1) to provide data on what competences mathematics majors have and lack when reading arguments, (2) to explain why mathematics majors have difficulty with comprehending and evaluating mathematical arguments, and (3) to delineate strategies that successful students use to learn when reading mathematical text.