A research-based teacher education rests on research on the practices of teacher education. We undertook a survey of the opportunities to learn mathematics pedagogy and to teach mathematics perceived by students in their last year of teacher education. Questionnaires were distributed to 753 students graduating in June 2020 from 13 Swedish universities, and the response rate was 11.2%. Overall, new graduates perceived good opportunities to learn mathematics pedagogy, but there were substantial variations in opportunities to learn specific competencies of teaching, such as analysing learners' answers or leading a mathematical discussion. A similar unevenness in perceived opportunities to learn from the practicum experience was found. These results point to less-than-optimal opportunities to learn core practices of mathematics teaching. We recommend that institutions take a more systematic approach to programme coverage, and to create opportunities to use theory/research to deconstruct practice and to inform rehearsing 'approximations of practice' in campus-based activities.