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The successful use of lesson plans as the primary vehicle for storing and sharing teachers' instructional knowledge in Japan has given impetus to calls by US researchers for the development of a system for sharing teachers' knowledge through instructional products to improve teachers' capacity to implement high-quality instruction and to build a knowledge base for instruction. These products would be created by, and for, teachers to use in guiding instruction, thus building and sharing teachers' instructional knowledge. In this study, we try to characterize one aspect of teacher knowledge that is central in building a knowledge base for instruction, knowledge of student mathematical thinking. We analyze ten written instructional products from the USA and Japan to better understand what knowledge of student mathematical thinking can be shared in such products. We also look at how knowledge of student mathematical thinking is used to guide and justify instructional decisions. One key finding is that the knowledge of student mathematical thinking shared in the top written instructional products is specific to a task or mathematical topic, varied with descriptions of multiple solutions or ways of reasoning, and sufficiently detailed to make the knowledge usable for teachers.

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