SOCIOCULTURAL FACTORS IN UNDERGRADUATE MATHEMATICS: THE ROLE OF EXPLANATION AND JUSTIFICATION

This paper extends the study of social interaction patterns as a means to characterize mathematics learning to the learning and teaching of mathematics at the undergraduate level. We present here the analysis of teaching episodes from a discrete mathematics course to document the change in social and sociomathematical norms over the course of one semester. First, the instructor established the social norm that students justify, explain and share with their peers their thinking and solution processes. We show how the instructor of the course established an expectation for explanation and justification, and how students ’ interactions developed in accordance to this normative understanding through the semester. That is, we trace students ’ development from the passive acceptance of the instructor’s authority to the expectation that students become contributors to the class and that they all share common understandings. We then shift our focus to the sociomathematical norms – normative interactions specific to mathematics. We discuss the development of students ´ explanations from the procedural level to ones that are grounded in deeper conceptual understandings. We finally link the shift in the aforementioned social and sociomathematical norms in students ’ interactions to the development of students’ ability to reason deductively