Communicating ‘nots’: A journey in mathematics education

This article is about communicating what is “not” said when something is said, or, what is not observed when something is observed by an observer. I have come to believe it is powerful and particularly relevant to mathematics education to engage in “seeing ‘nots’” (Brown, 2015, p.194) and to communicate about them. I have collaborated with Laurinda Brown since 1996, in overlapping phases of work: being a research subject; collaboration within a classroom; supporting my practitioner research (as a Master’s and then PhD student); co-researching on funded projects; co-observing prospective teachers; co-teaching on a teacher education course; co-supervising PhD students. Laurinda describes herself as observing nots, in all these contexts. I have only slowly come to realise what it might mean to attend to what is not being said by a learner and what this might afford. And so, in this article, I firstly set out a theoretical position about some features of communication. I then offer three illustrative stories of communicating nots, chosen from across as wide a span of mathematics education as I have been involved with: a mathematics classroom; working with a prospective mathematics teacher; working with in-service mathematics teachers on using video.