UC San Diego

Across the nation, there is increasing national interest in improving the way mathematics departments prepare their graduate teaching assistants (GTAs) because of their integral role in teaching lower division mathematics courses, particularly within the Calculus sequence (Speer, Deshler, & Ellis, 2017). While there have been several studies that look into the ways departments prepare their GTAs (Belnap & Allred, 2009; Speer, Smith, & Horvath, 2010), little is still known about how GTAs make sense of and understand the active-learning teaching practices introduced to them. In order to better support GTAs, we need to understand how GTAs are interpreting and making sense of these teaching practices.

The GTAs within this study were running break-out sections twice a week for Calculus I and II, with one of the break-out sections involving the facilitation of activities and group work. GTAs engaged in a three-day pre-term seminar, a semester-long PD course on leading student-centered classes, and weekly meetings with the course coordinators. Lead TAs provided support and feedback to their fellow GTAs.

Using a modified framework based on a socio-cultural learning theory, known as the Vygotsky Space (Harré, 1983), I analyzed the ways in which the discourse around the teaching practices, for both "active-learning" and "traditional" classrooms, changed over the course of a semester and the role lead TAs and others had in their publicized interpretations. Two different types of changes were recorded, elaboration and transformation, and each was tracked as they were publicized over the course of the semester. I created criteria to determine whether or not the discourse around a particular teaching practice was conventionalized within a community. Results from this study give insight into what teaching practices were challenging to understand, as well as the interpretations taken up and conventionalized by the GTAs. Approximately 20% of the practices showed evidence of some form of conventionalization; some of the conventionalized practices were transformations of the original version. The lead TAs may have influence over GTAs' instructional practice, but they did not have much influence over the interpretations publicized. These results yield insights useful to faculty involved in the professional development of GTAs.