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Understanding Mathematics

CHARTING ARGUMENTATION SPACE IN CONCEPTUAL LOCALES: TOOLS AT THE BOUNDARY BETWEEN RESEARCH AND PRACTICE

Pages 89-111 | Published online: 14 Apr 2008
 

Abstract

We describe a procedure for developing pedagogical knowledge about the argumentation of groups of children in relation to conceptual locales. The method involved the collection of small groups of children who had made different but significant responses to diagnostic test items, the recording and analysis of their subsequent researcher-managed discourses, and the mapping of the main productive elements of argument and charting a flow through it. Two examples of the method are presented which show how children can develop argument, and how these can be charted. These charts and other tools encapsulate research knowledge on children's learning in a form designed to help teachers to plan argumentation in their classroom practice: i.e. as pedagogical content knowledge. In addition to content-focused results, we also find general teaching strategies which appear to be effective generally, i.e. across conceptual locales. We discuss the relationship of this work to the development of teacher's pedagogical content knowledge and practice.

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