The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical competencies such as problem-solving, exploration, modeling, reasoning, representation, generalization, and abstraction. We perform a design study utilizing a systematic, iterative development process for designing teaching sessions, focusing on one mathematical competence at a time. We apply the proposed methodology on a set of teaching sessions that are developed, implemented, and tested in a range of classroom settings. Based on this development process, we conclude that programming can be used to develop mathematical competencies. Furthermore, we identify a set of teacher practices that can be used to facilitate mathematical competence development in programming activities.