Coherence and connections in teachers’ mathematical discourses in instruction

In this article, we share our combination of analytical concepts drawn from the literature with a set of grounded framing questions for thinking about differences in the nature of coherence and connections in teachers’ mathematical discourses in instruction (MDI). The literature-based concepts that we use are drawn from writing focused on transformation activity as a fundamental feature of mathematical activity. Within this writing, the need for connections between stated problems and the representations introduced and subsequently produced through transformation steps are highlighted. Drawing from four empirical episodes located across primary and secondary mathematics teaching, we outline a set of framing questions that explore coherence and connections between these concepts, and the ways in which accompanying explanations work to establish these connections. This combination allows us to describe differences between the episodes in terms of the nature and degree of coherence and connection.