UCLA

The purpose of this study was to understand the relationship between teacher discourse around social norms, student mathematical roles, and student mathematical explanations in the classroom. Mathematical explanations are important for learning mathematics and professional organizations encourage their use in the classroom. This study sought to understand aspects of the social environment that support explanations in the classroom. Using a mixed-methods approach, the researcher attempted to make sense of how student roles, explanations, and teacher discourse practices were related in four elementary classrooms. One-hour videos of one to two lessons per classroom were coded for the enactment of student roles, mathematical talk (explanations and non-explanations), student participation structures, and teacher follow-up.

Quantitative analyses using chi-square tests examined student patterns of explanations and roles across different participation structures in the classroom. Results indicated Classroom A had significantly more explanations than Classrooms B, C, and D because students enacted the role of Sharer of Details of Problem-Solving Strategy more often; this role was always associated with students giving explanations. In addition, students in Classrooms B, C, and D enacted the roles of Agreer/Disagreer and Comparer which were not associated with explanations.

Qualitative analyses indicated that the teachers used seven different discourse practices across the classrooms in different ways. All teachers used Directives and General Announcements, but in some classrooms these practices elicited the role of Sharer of Details of Problem-Solving Strategy, while in other classrooms, they elicited the roles of Comparer or Agreer/Disagreer. Teachers used Voting Exercises and Modeling of Comparing Behavior to elicit the Comparer role; teacher practices for the Agreer/Disagreer role included Voting Exercises as well as Validation Statements to students who enacted this role. Finally, the Classroom A teacher used Modeling Behavior to model Sharer of Details of Problem-Solving Strategy.

This study corroborates previous work findings that teacher follow-up is important to elicit explanations in the classroom; without it, certain discourse practices did not result in the explanations that would have occurred otherwise. This study extended previous work by looking at how students enacted mathematical roles across multiple classroom settings, and how these roles were supported.