The Emergence of Mathematical Meaning: Interaction in Classroom Cultures

The Emergence of Mathematical Meaning: Interaction in Classroom Cultures

The Emergence of Mathematical Meaning: Interaction in Classroom Cultures

The Emergence of Mathematical Meaning: Interaction in Classroom Cultures

Synopsis

This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. to unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers. The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.

Excerpt

The collaboration that gave rise to this book began in 1985 when the two of us shared a room at the Gordon Research Conference on Cybernetics. It was evident from our initial conversations that we were interested in many of the same issues, including that of accounting for the messiness and complexity of mathematical learning as it occurs in classroom situations. However, it also became apparent that we approached these issues from different theoretical perspectives. Bauersfeld stressed the social and interactional aspects of mathematical activity, whereas Cobb treated mathematical development as an individual process of conceptual construction.

In the following years, these initial conversations broadened into a series of meetings that included our colleagues Götz Krummheuer, Jörg Voigt, Terry Wood, and Eena Yackel. These interactions were punctuated by both the exhilaration that comes from a meeting of minds and the perplexity associated with differences in perspectives and languages. Frequently, observations that either the American or German group treated as central appeared peripheral to the other group. It eventually took us 3 years to establish a reasonable basis for communication, and classroom video recordings served as a primary means by which we came to understand each others' positions.

In the course of these discussions, we arrived at the conclusion that psychological and sociological perspectives each tell half of a good story. What was needed was a combined approach that takes individual students' mathematical interpretations seriously while simultaneously seeing their activity as necessarily socially situated. a 3-year project that had as its goal the coordination of psychological and sociological perspectives was subsequently supported by the Spencer Foundation. This book reports the results of that collaboration.

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