The relationship between the mathematics taught in teacher training and the mathematics demanded in teaching practices is an issue that has been problematized for many years in the field of Mathematics Education. Nonetheless, recent studies show it is still a focus of interest in the field. In this study, we have identified different connections that teacher educators are able to establish between the mathematics they teach and that which their students, prospective mathematics teachers, will have to teach eventually. We have conducted an in-depth case study and have identified that teacher educators establish content connections, modeled instruction connections, and disciplinary practice connections. Furthermore, we have reported the main difficulties that arise in establishing these connections. Additionally, we have identified a new type of connection, which we call "professional practice connections."