Mathematical Discourse

Mathematical Discourse

            Mathematical discussion in the classroom is not a new idea or concept in education. Educators utilize this as one of the most powerful tools in the development and assessment of student learning. How is the level of mathematical discourse in your classroom?

Connolly and Smith (2002) studied classroom discussion and “the way it should be.” They found student and teacher viewpoints differed in terms of the teacher’s role within small group discussion, competition versus collaboration, familiarity with the discussion topic and comfort within small group settings. As a result of their studies, Connolly and Smith stated the importance of teachers “talking about talk.”  Students not only benefit from knowing the teachers expectations for discussions but also benefit from the definition of norms pertaining to who gets to speak, in what manner, about what, and in what format. 

            Cohen (1992) addressed the value of focusing on the concepts and the type of interaction desired by the teacher. Teachers should not base the value of a discussion solely on the frequency of the student interactions. Instead, teachers must turn their focus on the fact that if students are not taught differently, they will tend to operate at the most concrete level. Exposure to deliberate skill building or motivation techniques can enrich what is happening in the classroom. This means creating tasks which are resource and goal interdependent, individual and group rewards, role assignments and constructive controversy; tasks which require teacher direction. The teacher’s role should be delegating authority to the students and fostering conceptual and elaborate discussions by teaching specific and relevant behaviors.  

Discussing the various roles individual students can take and assigning students these various roles can have a direct affect on the quality of the mathematical discussions. Defining the components of quality discussions and the roles that individuals play within discussions can clear student misconceptions and provide the necessary tools needed to meet teacher expectations. Providing students with role assignments and on-task tools are simple ways to increase student responsibility, bring ownership to the individuals, increase participation and enhance the quality of the discussion.

          Engaging in a quality mathematical discussion is as a complex task. Despite the exposure during the elementary years, teachers must have an awareness of student dependence on teachers as models for communicating with peers and take an active role in establishing expectations. Focus on how students contribute to mathematical discussions over time and the role of the teacher in this process.  Focus on the student’s ability to construct useful or useable concepts to take part in the society of the classroom. Pay special attention to the elements of student discourse including patterns of discourse, levels of response, teacher and student roles, norms and classroom practices. Bring the level of mathematical discourse in the classroom to a new level.