Reinterpreting the numerical discourse: a commognitive study of teachers’ support of students’ transition into the proving discourse

Abstract

Although much research encourages working with proof in school, it is recognised as a complex topic to teach. This paper investigates proof from a commognitive perspective, drawing on the assumption that a change in the uses of words, visual mediators, narratives, and routines implicitly conveys the meta-rules of the proving discourse. Teachers' reinterpretations of the four discursive aspects are thus recognised as promoting interdiscursivity. With data from an intervention in a Norwegian primary school, interdiscursive moves are identified by analysing the practice of two teachers with no experience with teaching proof. Illustrating examples show teachers interacting with students in small groups or whole-class situations, showing how blending two discourses can play out. The episodes confirm the complexity of teaching proof and illustrate the rich potential for scaffolding students' learning. The article sharpens the commognitive lens on proof learning and emphasises the role of the old discourse in interdiscursive situations.