Engaging students in a variety of classroom talk formats that afford knowing and doing in school mathematics

Classroom talk is regarded as essential in engaging and developing student understandings in the domain of mathematics. The process of classroom talk, however, may occur in quite different ways. In this paper we analyse two forms of classroom talk – replacement and interweaving. These provide a heuristic for considering how teachers might develop a repertoire of practices that they may deploy to afford student learning. In an analysis of student talk in a Year 7 classroom we found that replacement and interweaving can facilitate learning. We conclude that teachers should use classroom talk formats reflectively and intentionally in their classrooms to afford students a range of opportunities to develop their mathematical thinking. Introduction The history of coming to know and do mathematics in the school classroom has focused on teacher activity through the employment of transmission, discovery, and constructivist approaches to teaching and learning. Recent emphasis has centred on the mediating role that language plays in assisting students to participate in the sociocultural practices of mathematics (see Lampert, 1998; Cobb, P., McClain, K., & Whitenack, J., 1997). The sociocultural practices of mathematics encompass the privileged ways of knowing and doing that characterise mature communities of mathematicians, for example, inquiry approaches to knowing and doing. Wertsch and Rupert (1993), sociocultural theorists, promote a view of human action that complements this emphasis. Wertsch and Rupert (1993) advocate a view of teaching and learning that positions individual functioning within systems of collective practices that are culturally and historically situated. This approach, which they label ‘mediated agency’, describes the “irreducible tension” manifested between agent/s on the one hand and the mediational means (language, signs, symbols, etc.) that they employ or have access to on the other (Wertsch & Rupert, 1993, p. 230). From this point of view, issues that effect the sociocultural organisation of mental functioning on the social plane, such as issues related to power and authority, are seen as essential aspects of functioning on the personal plane. A key theoretical claim of ‘mediated agency’ is that human action, including social and personal functioning, is fundamentally shaped and constrained by mediational means such as the ways the teacher and students talk to each other when engaged in teaching and learning. In this paper we consider the mediating role played by different formats of classroom talk on students’ participation in the sociocultural practices mathematics.