In this article we consider data arising from student-teacher-researcher interactions taking place in the context of an experimental teaching program making use of multiple modes of communication and representation to explore three-dimensional (3D) shape. As teachers/researchers attempted to support student use of a logo-like formal language for…

This analysis joins together two lines of work: research on students' mathematical identities and on curricular organization that supports equitable academic outcomes. This article conceptualizes students' sense of mathematical competence as emerging through the interaction between their extant identities and the mathematical worlds they encounter…

The notion of assumptions permeates school mathematics, but instruction tends to highlight this notion only in the advanced grades. In this article, I argue that it is important for even young children to develop a sense of the role of assumptions in proving, and I investigate what it might mean and look like for instruction to promote this goal.…