Mathematics for teaching matters

In this paper, I clarify the notion of mathematics for teaching (its matter) and argue that it matters (it is important), particularly for mathematics teacher education. Two examples from studies of mathematics classrooms in South Africa are described, and are used to illustrate what mathematics teachers use, or need to use, and how they use it in their practice: in other words, the substance of their mathematical work. Similarities and differences across these examples, in turn, illuminate the notion of mathematics for teaching, enabling a return to, and critical reflection on, mathematics teacher education.