Chapter 3 Reflection and communication: Cognitive considerations in school mathematics reform

Abstract

The mathematics education reform efforts in the United States are shaped partially by our understanding of how students learn mathematics. Two traditions in psychology influence our current thinking most forcefully — cognitive psychology with its emphasis on individual mental operations and social cognition with its emphasis on context and group interaction. Reflection and communication, as cognitive processes and as representatives of these respective traditions, are used to establish the cognitive-based rationale for the reform and to analyze the nature of recommended changes. Issues addressed include the interdependence of reflection and communication and the way in which these processes can be used to analyze aspects of the school mathematics program, such as the way textbooks ordinarily treat written symbols. Although the theoretical arguments for reflection and communication are being increasingly well-articulated, the empirical data that address the claims are comparatively sparse. Future research efforts should aim to test theoretical claims for reflection and communication and to increase our understanding of the relationships between these cognitive processes and learning mathematics.