Filling the knowledge gap in the limited research on professional development leaders is an urgent issue if teacher learning is to be improved. This research and development project is studying how leaders learn to cultivate mathematically rich professional development environments. The authors adapted two frameworks from classroom-based research--sociomathematical norms and practices for orchestrating productive discussion--to support leaders' understanding of facilitation of mathematics professional development. In this article, the authors describe the use of these frameworks in their work and argue for a third framework--the mathematical knowledge for teaching. Based on the analysis of their work, they believe that mathematics professional development leaders need to cultivate particular sociomathematical norms for teacher explanation and employ practices for orchestrating discussions to achieve the purposeful development of teachers' specialized knowledge of mathematics for teaching. (Contains 1 table and 8 notes.)