Providing opportunities for learning through professional development requires the examination of facilitation of sessions with teachers. This study investigates facilitation of professional development to promote teacher learning when using animations and videos in a study group with five teachers. We ask: What practices (and moves within those practices) do the facilitators enact during high-quality conversations and specific to the professional development activities? We found that moves for sustaining an inquiry stance were more frequently performed than other moves, suggesting that the facilitator’s practices increase teachers’ learning opportunities when studying representations of teaching. In addition, the study suggests that there are no significant differences when facilitating discussions of animations and videos. The teacher learning goals seem to be more important than the type of representations of teaching used for the enactment of facilitation moves. Our findings are relevant for designing and implementing professional development that supports teacher learning through inquiry and collaboration.

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a b s t r a c tGiven the current emphasis on the use of transformations for the teaching and learning of geometry, there is opportunity to consider how students' understanding of geometric transformations can be used to build connections with interrelated concepts. We designed a sequence of three problems, collectively referred to as "the pottery lesson," to elicit evidence of students' understanding of reflections. We asked: What conceptions of reflection did students use while working on the pottery lesson? How did students' work on a sequence of problems requiring reflecting create opportunities for establishing connections between reflections and perpendicular bisector? We identified opportunities for the use of perpendicular bisector to shift between an operation of students' work and a measure of control. The characterization of students' conceptions of reflection, and students' related use of perpendicular bisector, provide a resource for the teaching of these concepts to build upon students' prior knowledge to promote learning.