Identification and Establishment of Social and Sociomathematical Norms Associated with Mathematically Productive Discourse
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For some time, the mathematics education community has sought to involve students more actively in classroom mathematical discourse, but realizing this goal has been problematic. This study has two goals: the first is to better characterize mathematically productive discourse by identifying social and sociomathematical norms that accompany it. Mathematically productive discourse is defined as discourse which holds mathematics as the authority, focuses on sense-making, and strives to create mathematical coherency. The second goal of the study is to identify strategies that teachers can use to establish these norms in their classroom. An in-depth case study was performed of a 5th grade classroom where mathematically productive discourse regularly occurs. Twenty-five observations were performed over the course of the 2014-2015 school year, as well as twelve interviews with the teacher. Observations were video-recorded and interviews were audio-recorded. The data were analyzed using principles of grounded theory including open coding, axial coding, and the constant comparative method. One social norm, active listening, and four sociomathematical norms, coherency, justification, computational strategies, and multiple perspectives, were identified in the classroom. To establish these norms, the teacher employed four “in-the-moment” strategies: direct prompts, normative comments, highlighting positive examples, and modeling. However, the teacher also had a more comprehensive vision for the progression of her class’s mathematical development over the first two months of the school year. This was reflected in the way that she established a conducive classroom environment, systematically taught her students mathematical skills and practices that built upon each other, and in her concept-focused use of mathematical tasks. The results of this study offer insight into how mathematical discourse, tasks, and practices should be conceptualized. They also underscore the importance of the teacher’s content knowledge in enabling these norms to emerge.