An exploratory study of teachers’ use of mathematical knowledge for teaching to support mathematical argumentation in middle-grades classrooms

Mathematical argumentation is fundamental to doing mathematics and developing new knowledge. Working from the view that mathematical argumentation is also integral to teaching and learning mathematics, this study investigated teachers’ use of mathematical knowledge for teaching (MKT) to support student participation in mathematical argumentation. Classroom observations were made of three case-study teachers’ implementation of a three-day curriculum unit on mathematical argumentation and supplemented with paper and pencil assessments of teachers’ MKT. Teaching moves, or teachers’ actions directed toward supporting argumentation, were identified as a unit of discourse in which MKT-in-action appeared. Teachers’ MKT showed up in three types of teaching moves including: Revoicing by Reformulation, Responding to Student Difficulties, and Pressing for Generalization in Defining. MKT that was evident in these moves included knowledge of core information in argument, heuristic methods, and vii formulation of mathematical definition through and in argumentation. Findings highlight that supporting mathematical argumentation requires teachers to have a sophisticated understanding of the subject matter as well as how concepts develop through argumentation. Findings have limitations in understanding complex teaching practices by considering MKT as a single factor. The study has implications on teacher learning and MKT assessments.