In this paper, we explore the potentials for learning mathematics through programming by a combination of theoretically derived potentials and cases of practical pedagogical work. We propose a model with three interdependent learning potentials as programming which can: (1) help reframe the students as producers of knowledge and artifacts, (2) support abstraction and encapsulation, and (3) promote thinking in algorithms. Programming is a topic that has recently gained interest in primary and lower secondary education levels in various countries, and hence a specific analysis of the potentials in relation to mathematics is paramount. Analyzing two cases, we suggest a number of ways in which didactical attention to epistemic mediation can support learning mathematics.