How students perceive lectures in advanced mathematics
Keith Weber, Rutgers University
Lecture is the common means by which we teach students in our advanced mathematics courses. However, students sometimes do not learn as much from these lectures as we would like, even when these lectures are of high quality. In this colloquium, I discuss why this is the case by focusing on what students attend to and perceive during a mathematics lecture. First, I present a case study in which illustrates how and why students can miss or misinterpret the main points of a lecture in advanced mathematics, even if these points were presented clearly by the lecturer. Second, I present several large scale studies on students' note-taking and their beliefs about proof, suggesting that what students choose to record (and omit) from their notes and the unproductive beliefs about proof that students hold can limit their comprehension of a lecture. Third, I provide suggestions for how students' understanding of lectures might be improved.