Abstract
For a number of years we have been pursuing a research program in mathematics education based on key concepts from sociocultural theory that foreground the interactive and
communicative conditions for learning, and the inherently social and cultural nature of cognition itself (Goos, Galbraith & Renshaw, 1994; Goos, Galbraith & Renshaw, 1996; Renshaw, 1996). The sociocultural perspective is one of a number of contemporary models of learning that is attempting to reform classroom practices by promoting more interactive 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.
In the majority of contemporary secondary school classrooms, learning mathematics is seen as mastering a predetermined body of knowledge and procedures. The teacher's job involves
presenting the subject matter in small, easily manageable pieces and demonstrating the correct procedure or algorithm, after which students work individually on practice exercises
from the textbook. Such reliance on the teacher or text as the source of knowledge reduces students to a passive, accepting role, and leads them to expect that there must be a readily
available method or rule for every kind of problem. As a result of school experiences such as these, students associate mathematics lessons with meaningless practice on routine
exercises, andlearn that mathematics is notmeant to make sense.
In contrast to the goals and practices of traditional instruction are those promoted by recent mathematics curriculum reforms in the USA and Australia, which are concerned with the
development of reasoning and problem solving skills, as well as the ability to work collaboratively and to communicate mathematical ideas (Australian Education Council, 1991; National Council for Teachers of Mathematics, 1989). Our research has investigated the ways in which such a pedagogical space can be established, and the changes to the roles
of teachers and learners that are required for such a community of practice to take hold and thrive. In the next section of the paper we summarise the key concepts from sociocultural
theory which have guided our observations of classrooms and our interpretations of these experiences.