This paper focuses on MOOCs (massive open online courses), a fairly recent paradigm in e-learning educational projects. Despite the high dropout rate, and the impossibility of benefiting from the opportunities that bring with it a face-to-face dialogue, several factors make MOOCs a good option for ongoing teacher professional learning. The MOOCs on which we focus address mathematics teacher education. In particular, we illustrate our experience based on four MOOCs that we organized in Italy in the last 4 years within the "Math MOOC UniTo" project, the aim of which is the professional development of mathematics in-service teachers. In the paper we articulate the conceptual framework that has guided the design, data collection, analysis and interpretation of findings for the project. It is mainly based on the hybridization of the meta-didactical transposition (MDT) model with the instrumentation/instrumentalization processes of the instrumental approach and the network of knowledge of Connectivism. We offer this new framework (called MOOC-MDT) to stimulate discussion with colleagues in the mathematics education research community about ways in which it might be refined and extended, towards building a shared understanding of the process of mathematics teacher education through MOOCs.