When the Rules of Discourse Change, but Nobody Tells You: Making Sense of Mathematics Learning From a Commognitive Standpoint

TLDR

The commognitive framework posits that mathematical learning is a communicative process in which students modify and extend their discourse, and that discursive change is driven by conflict arising when interlocutors operate under differing rules. The authors applied this framework in two studies—one on a class learning negative numbers and another on first graders learning triangles and quadrilaterals—analyzing how new mathematical discourse differs from prior discourse, how students and teachers work toward transformation, and the resulting extent of discursive change. The studies confirm that effective school learning depends on an experienced interlocutor’s active guidance and on a mutual learning‑teaching agreement between the interlocutor and the learners.

Abstract

The interpretive framework for the study of learning introduced in this article and called commognitive is grounded in the assumption that thinking is a form of communication and that learning mathematics is tantamount to modifying and extending one's discourse. These basic tenets lead to the conclusion that substantial discursive change, rather than being necessitated by an extradiscursive reality, is spurred by commognitive conflict, that is, by the situation that arises whenever different interlocutors are acting according to differing discursive rules. The framework is applied in 2 studies, one of them featuring a class learning about negative numbers and the other focusing on 2 first graders learning about triangles and quadrilaterals. In both cases, the analysis of data is guided by questions about (a) features of the new mathematical discourse that set it apart from the mathematical discourse in which the students were conversant when the learning began; (b) students' and teachers' efforts toward the necessary discursive transformation; and (c) effects of the learning–teaching process, that is, the extent of discursive change actually resulting from these efforts. One of the claims corroborated by the findings is that school learning requires an active lead of an experienced interlocutor and needs to be fueled by a learning-teaching agreement between the interlocutor and the learners.