Identifying and Recontextualizing Problems of Practice Using Representations of Leading Classroom Mathematics Discussions

• In Event: Representations of Practice to Scaffold Teacher Learning to Enact Equitable and Disciplinary Classroom Discussions

Abstract

Purposes and Perspectives. Problems of practice (PoPs) are endemic to facilitating classroom mathematics discussions where teachers not only support students’ engagement with disciplinary ideas but also manage students’ collaborative interactions and the way they negotiate authority, identity, and positioning in the classroom (Lampert, 2001; Langer-Osuna et al., 2020). In this paper, we use the context of a job-embedded professional development (PD) focused on facilitating math discussions to investigate how teachers use representations of practice to construct a joint problem space around a central PoP: how to navigate inviting multiple student voices and contributions with an eye to the mathematical purpose(s). We elaborate the way teachers construct the problem space for this tension over time, elaborating its various aspects and relevant resources.
Theoretical Framework. PoPs can be generative spaces for teacher dialogue (Horn & Little, 2010). Representations of practice can support teachers in (re)contextualizing PoPs in various activity contexts. Recontextualization is a process of continuous sensemaking (van Oers, 1998), where activity, communication, and representation become mutually constitutive aspects of knowing (Teasley & Roschelle, 1995). Teachers can dynamically construct the problem space for a PoP over time using representations of practice by examining their goals, describing the current problem state, and identifying available problem solving actions. The associations they create between these three elements are aspects of their problem solving.
Methods and Data Sources. We used a PD called Learning Labs (LLs) focused on facilitating mathematics discussions. Each LL involved teachers in analyzing and discussing artifacts of practice, collaboratively planning and enacting a lesson, followed by debriefs (Kazemi et al., 2018). We collected video and audio recordings and field notes from eight LLs. We identified PoPs relevant to leading whole class discussions by focusing on instances of classroom interactions experienced as troublesome, challenging, or confusing (Horn, 2010). We then condensed these instances into categories of PoPs and analyzed how teachers unpacked them as they debriefed joint lesson enactments, tracing the way they associated features of the current problem state with their goals and perceptions of available actions.
Results and Significance. Supporting students’ broad participation while attending to a mathematical purpose(s) was a central tension for teachers. It arose in relation to the following pedagogical goals: representing students’ diverse thinking, engaging students with discourse practices, designing tasks that give access to student thinking, and supporting students’ understanding of content. Teachers considered associations between this central tension and their goals through the lens of the affordances and constraints of various contextual factors (e.g students’ characteristics, students’ and teachers’ actions, curriculum). Over time, teachers exhibited shifts in the way they associated the PoP with student characteristics. They shifted to considering how teachers’ pedagogical actions influenced opportunities for students’ voice and inclusion and their access to mathematical content.
Instructional tensions are genuine and legitimate, and always present in teaching. Teachers’ collaborative examination of these tensions–how they understand them and what they do to address them over time can support pedagogical reasoning in the service of students and professional knowledge.

Authors

• Hala N. Ghousseini, University of Wisconsin - Madison

• Sam Prough, University of Delaware

• Eric Cordero-Siy, Boston University