In the two decades since the introduction of the Professional Standards for Teaching Mathematics (NCTM, 1991) describing effective mathematics instruction, researchers have found U.S. teachers still lack the ability to foster productive mathematical discourse. Three instructional practices are key to teachers' ability to support rich discourse in their classrooms: posing rich tasks, interpreting students' ideas, and responding to students' mathematical thinking. Abundant research and resources exist to help teachers learn the practices of posing and interpreting. Likewise, adequate research exists to demonstrate that a typical teacher's practices of responding is overly-evaluative, as well as what alternative responding practices might look like. Professional resources designed to support teachers in learning better responding practices, however, are scant.The purpose of this qualitative case study is to understand the extent to which a professional learning experience, which was designed to help teachers learn about the practices of responding, influenced the ability of three mathematics teachers to envision and enact alternative responding practices. To understand change in the participants' imagined responding practices, I administered a survey on three occasions across the year-long experience. To measure change in participants' enacted practices of responding, I collected five videos from each participant across the experience. This research describes and explains how the three teachers' imagined and enacted practices changed during and following participation in professional development and action research.A major contribution of this work is its observation frame, constructed to highlight changes to the breadth and focus of teachers' responding practices. I found many similarities in participants' post-professional-development and post-action-research changes including: a shift from focusing on mathematical products, a shift toward focusing on mathematical processes, a shift away from evaluative responding moves, and a shift toward responding moves that encourage student reflection of peers' ideas. I also found a few differences among the three participants, particularly in the action research cycle, where teachers aimed to sustain changes they had made following the professional development intervention. From their initial changes, one teacher mostly furthered her changes, another mostly maintained her changes, and a third teacher reversed many of her changes during the action research. At the end of the action research cycle, however, the three teachers' practices of responding were remarkably similar to one another, and all represented practices that differed dramatically from their baseline data. These results and their implications are discussed in relation to future iterations of this professional development as well as continued lines of research that could easily develop from this work.
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