In this chapter we focus on the concept of proof, which is important for students'
mathematical education but also hard for teachers to teach and difficult for students to learn …

This article presents a way of studying the rationality that mathematics teachers utilize in
managing the teaching of theorems in high-school geometry. More generally, the study …

Building on our earlier work conceptualizing teaching as the management of instructional
exchanges, we lay out a theory of the practical rationality of mathematics teaching—that is, a …

This chapter documents efforts to develop an instrument to measure mathematical
knowledge for teaching high school geometry (MKT-G). We report on the process of …

This study compared conversations among groups of teachers of high school geometry that
had been elicited by a representation of instruction (either a video or an animation) and …

This chapter characterizes the practical rationality of mathematics teaching as a middle
range theory, a theory that is developed through the practice of research. We argue that a …

Launching a problem is critical in a problem-based lesson. We investigated teachers'
perspectives on the use of a problem that was analogous to the one provided during a …

We inspect the hypothesis that geometry students may be oriented toward how they expect
that the teacher will evaluate them as students or otherwise oriented to how they expect that …

Using a multimedia questionnaire we explore the extent to which secondary mathematics
teachers recognize a hypothesized norm of doing proofs in geometry—that the teacher is in …

Learning to teach is difficult for prospective teachers because of the complex nature of the
work of teaching. Practicing (Lampert in J Teach Educ 61 (1–2): 21–34, 2010), interacting …