OPPORTUNITY TO LEARN FROM MATHEMATICS LECTURES

Many mathematics students experience proof-based classes primarily through lectures, although there is little research describing what students actually learn from such classroom experiences. Here we outline a framework, drawing on the idea of the implied observer, to describe lecture content; and apply the framework to a portion of a lecture in an abstract algebra class. Student notes and interviews are used to investigate the implications of this description on students' opportunities to learn from proof-based lectures. Our preliminary findings detail the behaviors, codes, and competencies that an algebra lecture requires. We then compare those with how students behave in response to the same lecture with respect to sensemaking and note-taking, and thereby how they approach opportunities to learn.