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THEORETICAL PERSPECTIVES ON TEACHING AND RESEARCH

AFFORDANCES, CONSTRAINTS AND ATTUNEMENTS IN MATHEMATICALACTIVITY

Pages 23-34 | Published online: 21 Apr 2008
 

Abstract

This paper begins with an examination of one approach to describing learning mathematics as participation in practice. Greeno's articulation of affordances, constraints and attunements as an ‘ecology of learning’ appears to provide a unified view which can be applied to mathematics learning at several levels. While this framework is useful in thinking about mathematical tasks and activity, analysis of some subtle differences in mathematical tasks suggest that there are some characteristics of mathematical activity which require a more detailed approach. It is demonstrated that analysis in terms of mathematical variation gives insight into these differences. Marton's identification of learning as discernment of variation in near-simultaneous experiences, seen as an ecology of mind, describes more closely the learner's experience of mathematical examples.

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