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*Professional Standards for Teaching Mathematics* (NCTM 1991) focuses on analyzing and interconnecting teaching and learning. The standard calls for the analysis of teaching and learning to be ongoing by “[o]bserving, listening to, and gathering other information about students to assess what they are learning.” Teachers examine the “[e]ffects of the tasks, discourse, and learning environment on students' mathematical knowledge, skills, and dispositions.”

*Professional Standards for Teaching Mathematics* (NCTM 1991) include a standard on the use of concrete materials. The use of concrete materials seems to be assumed unquestioningly.

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