Commognitive analysis of a teacher’s mathematical discourse on the derivative

Research on the teaching of the derivative (and limit) is still not as extensive as the research on students’ learning of calculus. This paper introduces the commognitive theory and reports on a commognitive analysis of a teacher’s discourse on tangents, gradient and differentiation with a Year 12 class in England. Mathematical discourse is characterised by four commognitive constructs: word use, visual mediators, endorsed narratives and routines. These constructs provide discursive foci for analysing mathematical discourse. Data sets include two face-to-face interviews with the teacher and an observation of an introductory lesson on differential calculus.