| Summary: | In this paper, we analyze and detail the knowledge incorporated by mathematics teachers in their participation in lesson study. Utilizing an extended theoretical framework of mathematics teacher knowledge, combining the cognitive frameworks of Mathematical Knowledge for Teaching and Levels of Teacher Activity, we detail the knowledge articulated in teachers’ collaborative lesson study conversations. This theoretical framework is presented as a theoretical tool to detail the incorporation of mathematics teachers’ knowledge in planning, conducting, and reflecting on research lessons in lesson study. Using data generated in two case studies, one from the Republic of Ireland (post-primary) and another from Switzerland (primary), we examine the knowledge articulated by mathematics teachers in their planning and reflection of a research lesson. We detail this knowledge using qualitative excerpts and provide quantitative analysis of the knowledge categories incorporated by teachers in each phase of a lesson study cycle. Our analysis provides evidence that, in their participation in lesson study, teachers draw on and incorporate all elements of their mathematical knowledge for teaching at all levels of teacher activity when planning and reflecting on a research lesson
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