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Sustained, innovative professional development is now widely acknowledged as essential to the improvement of mathematics instruction in the nation’s schools. In recent years, this recognition has prompted the production of a variety of materials designed to support new teacher development programs. However, with the availability of such materials, serious concerns arise as to the kinds of knowledge required of professional development providers, often teachers who have been assigned Mathematics Specialist roles, and the means by which this knowledge is to be acquired. The authors of this paper address such questions in the context of one professional development seminar, Developing Mathematical Ideas [1]. Our paper builds on the research of Remillard and Geist who identify the potential for learning in those moments of discontinuity—“openings in the curriculum"—in which the beliefs, knowledge, and commitments of seminar participants diverge from those of facilitators or materials developers [2]. By looking closely at several such moments. we establish how successful facilitation entails deep content knowledge, awareness of seminar goals, and appreciation of the beliefs and understandings of seminar participants. We then describe the kinds of supports available to DMI facilitators to help them cultivate the skills and knowledge needed to exploit these openings productively. While the paper focuses particularly on professional development seminars. we suggest that our conclusions apply to Mathematics Specialists‘ tasks more generally.





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