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In this article, we report on Researching Mathematics Leader Learning (RMLL), a project designed to support leaders in learning how to facilitate robust opportunities for teachers' mathematical learning. Our two-phase research design allowed us to construct a set of videocase seminars, enact the seminar design with leaders, analyze these data, refine our seminar design, and implement a second set of seminars with a new group of leaders. We drew on the noticing literature to examine leaders' pedagogical reasoning as they discussed videocases of professional development. In this article, we demonstrate how changes in our framework for leader development and the resulting changes in the prompts and tasks shaped leader noticing in three ways: (a) accounting for the mathematical work of the facilitator and teachers in the videocase; (b) linking the mathematical work to goals for teacher learning; and (c) reasoning around the facilitator's work in advancing those learning goals. Analysis indicates that in Phase II, leader discussions were more focused on the mathematical and pedagogical work needed to advance teacher learning. Based on our research and development work with over 70 leaders, we offer a set of design principles for leader professional development. [ABSTRACT FROM AUTHOR]