Back-Pocket Strategies for Argumentation

Mathematical argumentation is an essential part of the discipline of mathematics and a key indicator of mathematical proficiency. In the process of constructing arguments and critiquing the reasoning of others, students build their understanding of underlying mathematical ideas and engage in critical sense-making activity (Yackel and Hanna 2003). Despite the importance of this practice, teachers--both novice and experienced--have difficulty incorporating argumentation in the classroom. At the high school level, constructing arguments has often been equated to proof writing in geometry. Limiting argumentation to verifying formulas neglects the explanatory role that proof can play in learning mathematics at all levels (Hanna 2000). Adapting or designing activities for students to investigate why something is true and to communicate their reasoning requires intentional work on the part of teachers. In this article, the authors describe strategies for promoting mathematical argumentation developed by a group of teachers as they participated in four cycles of Mathematics Studio focused on argumentation. Mathematics Studio (Teachers Development Group 2010) is a research-based professional development model that is similar to Japanese lesson study in that teachers collaboratively plan, observe/enact, and analyze a classroom lesson. The focus of Mathematics Studio is not on creating a lesson to be used by others but rather to increase teachers' understanding of mathematical argumentation and ways to develop students' abilities related to this practice (Lesseig 2016).