Making the Familiar Strange: Teachers Collaborating to Discern Complexities in Discussions Supporting Mathematical Argumentation

• In Event: Understanding Teachers as Learners Through Their Collaborative Sense-Making

Abstract

Purposes and Objectives: We examine how teachers with established discussion-based instructional practices made sense of how to more robustly engage students in mathematical argumentation.

Theoretical perspectives: We frame teacher learning from a sociocultural perspective as a process of changing participation in a community of practice (Rogoff, 1995). This process entails the development of principled goals, commitments, and ways of thinking valued by a community, as well as the continual refinement of a set of principled practices for supporting mathematical argumentation in the classroom.

Methods: The study context is a school where teachers have engaged in the job-embedded professional development structure, Math Labs, over a period of seven years. Mathematical discourse is a school-wide emphasis, and teachers enact shared instructional materials, including a set of instructional routines that develop students’ mathematical talk, number sense, and problem solving. The context provides a case in which to investigate how teachers who have already developed discussion-based instructional practices make sense of how to further engage students in mathematical argumentation. We worked with five 4th and 5th grade teachers with a range of teaching experience. A school-based coach worked with the authors to design and co-facilitate the Math Labs. Teachers collaboratively experimented with an argumentation learning trajectory that involved students:
● Working with a task and making descriptive observations
● Looking for patterns in repeated reasoning
● Articulating claims or conjectures based on those patterns
● Exploring ways to explain or disprove claims using diagrams, models, words, expressions
● Evaluating and revising their explanations
Transcripts from six labs and pre- and post- interviews with all participants were analyzed for how teachers collectively learned about and investigated facilitation of discussions that not only elicited varied student ideas but also supported students to engage in mathematical argumentation.

Results:
As collective inquiry and organizing instruction around student thinking was valued and prominent throughout the school, teachers did not question the importance of discussion but instead grappled with the nature of talk that was happening in their classroom. First, teachers realized that while they were frequently supporting students to describe their strategy, they needed to facilitate differently in order to support students to engage in explanatory talk. Second, teachers reflected on student participation in their discussions and how they relied on particular students and forms of participation, for instance calling on certain students who could carry the conversation forward. In response to these two challenges, teachers experimented with how to facilitate familiar instructional routines (e.g., True/False Equations, Choral Counting) differently to support broader participation and argumentation. For instance, teachers collectively experimented with how to repurpose these routines to support students to observe patterns in repeated reasoning and develop and revise claims and arguments about properties of number and operations that are true in general.

Significance: Our findings indicate that the structure of Math Labs supported teachers for whom discussion-based instruction felt familiar to re-examine their instructional practice and collectively experiment with how to invite broader student participation and foster student engagement in mathematical argumentation.

Authors

• Elham Kazemi, University of Washington

• Alison Fox Resnick, University of Washington - Seattle

• Elzena McVicar, University of Washington - Seattle