Merrilyn Goos, Peter Galbraith and Peter Renshaw
We have been developing a research programme in mathematics education based on key concepts from socio-cultural theory that foreground the interactive and communicative conditions for learning, and the inherently social and cultural nature of cognition itself (Goos, Galbraith and Renshaw, 1994; Goos, Galbraith and Renshaw, 1996; Renshaw, 1996). The socio-cultural perspective is one of a number of contemporary models of learning that is attempting to reform classroom practices by promoting less hierarchical, more interactive, more networked forms of communication within the classroom, and more explicit consideration of the connection between classrooms and the cultural and institutional practices of related communities, specifically in this context, knowledge communities where mathematics is an important cultural tool. The centrality of community in socio-cultural theory reflects the view that knowledge acquisition should be seen as progress to more complete participation in the practices, beliefs, conventions and values of communities of practitioners, and not primarily as the acquisition of mental structures per se.
In this chapter we focus on how a particular type of mathematics classroom can be created, a classroom that enables the practices, values, conventions and beliefs characteristic of the wider communities of mathematicians to be progressively enacted and gradually appropriated by students. One case - a mathematics classroom at the upper secondary school level - is analysed in detail in order to reveal the working assumptions, the tacit classroom culture, that underlie the interaction patterns between the teacher and the students. Leone Burton (1999) presents a view of mathematics learning as a narrative process in which mathematical knowledge is validated by the community of knowers, and outlined the different agendas for teachers and different responsibilities of learners that this position presents. Our own analysis highlights changes to the roles of teachers and students that are required for this local community of practice to take hold and thrive.
The current research programme has taken shape in various partnerships with teachers, where our suggestions about possible classroom practices consistent with socio-cultural theory, have been taken up selectively by the teachers and implemented in ways that they considered were feasible, and compatible with the complex conditions of their particular schools. The research programme, therefore, should not be