Reasoning With Tools and Inscriptions

The unit of analysis that I use when discussing the 2 sample episodes is that of a classroom mathematical practice together with the students' diverse ways of contributing to its continual regeneration. Analyses cast in terms of this unit account for the mathematical learning of the classroom community. As I clarify, a classroom mathematical practice is itself composed of 3 interrelated types of norms: a normative purpose, normative standards of argumentation, and normative ways of reasoning with tools and inscriptions. In keeping with the theme of this special issue, I step back from the sample analysis by focusing on the last of these 3 aspects. In doing so, I introduce the notion of a chain of signification to illustrate a way of accounting for mathematical learning in semiotic terms.

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