Despite the evidence of its effectiveness on student learning, ambitious mathematics instruction has proven to be challenging for teachers to enact. Increasingly, instructional coaching programs have become a way of providing intensive one-on-one support to teachers to improve the quality of mathematics instruction. Researchers have identified various design features of effective mathematics coaching programs (e.g., lesson planning, co-teaching, deep and specific discussions of instruction). However, there is a lack of theoretical explanation for how and why these design features support teacher learning, which is critical for successfully implementing and adapting what "works." Motivated by the need to illuminate what current research has left in the shadows, we first identify the processes of teacher learning based on past research and then illustrate how specific design features of a new coaching model can work together to activate these processes and consequently produce teacher learning. We use the conjecture mapping approach to achieve our goal, informed by a research-based high-level conjecture: Effective coaching programs engage teachers in learning processes similar to the learning processes that students experience in ambitious classrooms. This work will guide the development of an empirically grounded theory for teacher learning through coaching. The reification of teacher learning processes is particularly important for the adaptation of coaching practices in different contexts and content areas. We also argue that focusing on these processes will bring a new perspective to coach navigation of tensions, for example, between responsiveness and directiveness.