This three-paper dissertation investigates how mathematics coaches support teachers to develop ambitious instructional practices that will provide richer opportunities for students learning. The goal of the first study was to identify types of activities established in the professional learning literature as being likely to support teachers development of high quality instructional practices. Therefore, I conducted a conceptual analysis to determine the potential value of different types of activities in terms of the learning opportunities they provide for teachers to develop deeper understandings of mathematics, student reasoning, and ambitious instructional practices. The results of this analysis delineated a range of activities that, when facilitated effectively by coaches, have the potential to support teachers learning. In the second study, I used social network and interview data collected across seven middle schools in a large urban district to examine what influenced mathematics coaches to become a central source of expertise. The findings suggest that teachers perceptions of the coachs competence, specific structural aspects of the school setting and principal support may influence whether a majority of teachers within a school go to their coach for advice or information about teaching mathematics. Finally, in the third study I analyzed interview data of one coach across four years to investigate what, in addition to being relatively accomplished teachers, mathematics coaches need to know and be able to do in order to engage teachers in activities that are likely to support their development. This analysis identified potential practices that coaches need to be able to do and aspects of knowledge that coaches need to provide individualized support for teachers. Overall, I sought to understand how mathematics coaches can support mathematics teachers development. Together, these three interrelated studies constitute a significant step towards this goal and contribute to research on content-focused coaching. In addition to research contributions, these studies have pragmatic implications as the findings can assist district leaders in implementing or revising current school-based coaching designs.