Positioning in an upper-level undergraduate mathematics course

Abstract

This study examined classroom interactions in an upper-level undergraduate mathematics course in order to investigate how they can be seen as positioning students in relation to mathematics. Students’ experiences in undergraduate mathematics courses are often negative, yet few studies have focused their attention on what happens inside undergraduate mathematics classrooms, particularly for advanced-level courses in which proofs are the focus. This study took place over the course of a semester in one section of an Introduction to Analysis course. Thirty-six of the 40 class sessions were observed and audio-recorded, and detailed field notes were taken. Additionally, selected students were interviewed at the beginning, middle, and end of the semester about their experiences, and the professor was interviewed at the end of the semester. These data were analyzed qualitatively to support the creation of a narrative description of patterns of interactions over the course of the semester. One particular moment of mathematical disagreement between the professor and a student was examined closely to reveal the potential positioning of students in relation to mathematics. And patterns of commonly used phrases across the semester were analyzed as well, in order to reveal how the repeated use of language could potentially position students in relation to mathematics.

This analysis of classroom interactions suggested that the use of a traditional lecture format in an advanced mathematics class offers few opportunities for students to develop positive relationships with mathematics. Institutional constraints made it hard for the professor to shift away from a typical lecture format that efficiently covered the necessary content. But within this traditional lecture format, there is possibility for variation. The professor was able to establish a relatively comfortable classroom environment and to engage students in different kinds of mathematically meaningful classroom interactions. Within these interactions, different resources were available that could potentially position students as doers of mathematics, including storylines about mathematics as a logical system and about the classroom as a shared space of mathematical work.