Background/Context: Discussion is central to mathematics teaching and learning, as well as to mathematics as an academic discipline. Studies have shown that facilitating discussions is complex work that is not easily done or learned. To make such complex aspects of the work of teaching learnable by beginners, recent research has focused on approaches to teacher education that decompose practice into smaller tasks or routines that can be articulated, unpacked, studied, and rehearsed. Purpose/Objective/Research Question/Focus of Study: Drawing on the elements of Grossman et al.'s (2009) framework for pedagogies of practice in professional education, this article describes an approach to analyzing teaching practice that supports the design of teacher education in which novices to learn how to engage in high-leverage teaching practices and simultaneously develop a sense of why the work is done. Setting: The context for the study is a mathematics methods course for prospective elementary teachers. Research Design: The study involved qualitative analysis of both the design of the course and its implementation. Conclusions/Recommendations: Results from this study suggest that: (1) Decomposing teaching into nested practices of varying grain sizes that maintain the connection between techniques and domains can support beginning teachers in attending simultaneously to the how and the why of practice, as well as provide a map of teaching that teacher educators can use to support the learning of teaching. (2) Nesting early approximations of practice inside subsequent ones is a way to support beginning teachers in building toward recomposed teaching practice. As practices are nested, teacher educators can increase the complexity of the approximations by adjusting the content and authenticity of the context of practice as well as by decreasing the amount scaffolding provided. (3) Assessment is vital to pedagogies of practice. Decompositions, approximations, and representations of practice need to be developed in ways that support assessment for the array of teacher education purposes. (4) Because subject matter is at the heart of teaching, it is crucial to attend to the ways in which the content interacts with pedagogies of practice.