This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

In this paper we explore the growth of understanding of a group of preservice teachers, and their instructor, as they work collectively together on what we describe as a "mathematics for teaching" task. Through drawing on elements of improvisational theory, in particular the notion of the "better idea," we analyse how the preservice teachers'…

This paper analyses how the mathematical knowledge needed by a teacher has been described by several mathematics educators, all based on Shulman's notions of Subject Matter Knowledge and Pedagogical Content Knowledge. In particular, it looks at the notion of Mathematics Knowledge for Teaching, as elaborated by Ball and her research group. It then…

Discusses the dichotomy right/wrong in students' images of mathematics as they start to work at becoming teachers. Shares stories as teacher educators with a filter of dichotomies that seem to be avoidable. Identifies ways to overcome those dichotomies. (Contains 18 references.) (ASK)

When asked to give a talk at a mathematics teacher conference that focused on research in mathematics education, Ruhama Even viewed the invitation as an opportunity to address the meta-question: what can teachers learn from research in mathematics education? The reason for her view was her way of feeling, as a researcher and teacher educator, that…