for the learning of mathematics

an international journal of mathematics education

Alf Coles - Vol. 40 Num. 0 (2020)
 Communicating ‘nots’: a journey in mathematics education


This article is about how to establish ways of working mathematically (whatever that is taken to mean) with a group of learners, or ways of working on becoming a teacher of mathematics, with a group of teachers. It is well recognised that metacommunicative frames are crucial to the smooth functioning of human communication; frames, among other things, define what counts as relevant to a group. This article proposes the concept of the organisation of communications in a group, to mean the set of relations between communications that mean they exhibit or shift between particular metacommunicative frames. A further key idea is that an organisation has multiple boundaries, which distinguish between what is and is not relevant to the communications of the group. The argument of the article is that communicating when something is not within a given boundary is particularly effective at establishing that boundary within the organisation of communications and, hence, is significant for developing desired ways of working. The practice of communicating nots is exemplified in three contexts of mathematics education.