Supporting students' mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers .We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher Moves for Supporting Student Reasoning (TMSSR) framework, which organizes moves vis-à-vis their function and their potential for fostering student thinking. We describe the TMSSR framework, illustrate its affordances for studying teacher practices, and highlight its utility for teachers, teacher educators, and researchers. [For the complete proceedings, see ED583989.]