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…

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…

Considers what value there could be in talking of institutional trauma and connecting it to elements of the theory of trauma in a psychoanalytic setting. Seeks out the origin of these traumas in the successive crises that the mathematical knowledge of secondary teachers has had to confront over the course of history. (Contains 12 references.) (ASK)

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)

Proposes three thought experiments on various contexts of teaching mathematics. The experiments are intended to raise questions about the mathematics curriculum and to engage discussion about what topics should have high priority in arithmetic teaching. (DDR)