Theories of Mathematical Learning

By Leslie P. Steffe; Pearla Nesher et al. | Go to book overview

1
Emergent and Sociocultural Views of Mathematical Activity

Paul Cobb Vanderbilt University

Barbara Jaworski Oxford University

Norma Presmeg Florida State University

Taken together, the six plenary chapters presented in this section indicate that a wide range of approaches fall under the rubric of sociological and anthropological perspectives. These contributions all reflect the contention that knowing and doing mathematics is an inherently social and cultural activity. This claim does not merely mean that social interaction serves as a catalyst for otherwise autonomous cognitive development. In the view of each of the contributors, social and cultural influences are not limited to the process of learning but also extend to its products, increasingly sophisticated mathematical ways of knowing. Consequently, in describing their own positions, the contributors each challenge the assumption that students' mathematical activity can be adequately accounted for solely in terms of individualistic theories such as constructivism or information- processing psychology. Three of the contributors, Voigt, Stigler et al., and Saxe and Bermudez, develop analyses that complement psychological constructivism. In contrast, the perspectives developed by van Oers, Forman, and Crawford are proposed as alternatives to psychological theories that focus on the individual.

In this commentary, we first consider the key assumptions of these two groups of theorists, giving particular attention to the role they attribute to individualistic theories. We then contrast their differing treatments of a variety of key issues and conclude by discussing possible ways in which their perspectives might be complementary.


EMERGENT PERSPECTIVES

Voigt, Stigler et al., and Saxe and Bermudez use differing theoretical constructs to address a diverse range of issues. In our view, this diversity belies several

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