Case 10: Moving Beyond Our Own Experiences To Facilitate Meaningful Mathematical Discourse: A Coordinated Use of the “5 Practices”

Mathematical discourse includes “the purposeful exchange of ideas through classroom discussion, as well as through other forms of verbal, visual, and written communication” (National Council of Teachers of Mathematics [NCTM], 2014, p. 29). Facilitating meaningful mathematical discourse to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments is a recognized goal of “effective” mathematics teaching (NCTM, 2014), but how do we support mathematics teacher candidates in this challenging practice? This case presents field dilemmas based on our experiences as teacher educators with a middle school mathematics methods course (Gatza) and companion middle grade learners practicum course (Hancock) collaboration where both courses were taught at a middle school. In particular, we share our experience of helping a class of secondary mathematics teacher candidates (MTCs) move beyond their own mathematical experiences to better see and hear the brilliance of their students and translate theory about facilitating meaningful mathematical discourse into practice. The dilemmas presented in this case reflect compilations of scenarios rather than exact accounts of particular situations in order to illuminate common problems of practice across MTCs and maintain anonymity. Furthermore, we present this case as an ongoing discussion of efforts to support MTCs to facilitate meaningful mathematics discourse, rather than a “case closed” answer. As a result of this semester collaboration, MTCs improved their ability to notice nuances in student thinking and began to orchestrate discussions aligned to learning goals; however, there remained opportunities for growth in translating coursework pedagogies into field implementations.