In this paper we examine two instances of the use of competence models in formalised in-service teacher education courses, finding that they prioritise the use of the visual as a central resource for the modelling of teaching mathematics and of the teaching and learning of mathematics. The way in which the visual is used in competence models produces an emphasis on the sensible that at the same time seems to disrupt the intelligible and so principled reproduction of mathematics teaching and of school mathematics. These instances of teacher education practice raise challenging questions about the selections from mathematics and teaching in mathematics teacher education.