Sfard, Anna; (2007) When the Rules of Discourse Change, but Nobody Tells You: Making Sense of Mathematics Learning From a Commognitive Standpoint. Journal of the Learning Sciences , 16 (4) pp. 565-613.

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Abstract

In this article we introduce a research framework grounded in the assumption that thinking is a form of communication and that learning a school subject such as mathematics is modifying and extending one’s discourse. This framework is then applied in the study devoted to the learning of negative numbers. The analysis of data is guided by questions about (a) the discourse on negative numbers as such, and the features that set it apart from the mathematical discourse with which the students have been familiar when the learning began; (b) students’ and teacher’s efforts toward the necessary transition to the new meta-discursive rules, and (c) effects of the learning teaching process, that is, the extent of discursive change resulting from these efforts. Our findings lead to the conclusion that discursive change, rather than being necessitated by an extradiscursive reality, is spurred by communicational conflict, that is, by the situation that arises whenever different interlocutors seem to be acting according to differing discursive rules. Another conclusion is that school learning requires an active lead of an experienced interlocutor and is fuelled by a realistic communicational agreement between her and the learners.

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