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Validating the ecological assumption: The relationship of measure scores to classroom teaching and student learning

Abstract

"In validating any assessment, a critical question is its relationship to the domain of practice: whether success on the assessment, which is constrained to be either a small sample of the knowledge or even simply an indicator of knowledge needed for a practice, actually predicts proficient performance. Following Kane (2001, 2004), we formulated an assumption and several observable inferences regarding the relationship of our measures of teachers' mathematical knowledge for teaching to their actual classroom mathematical work. This assumption is the third detailed in Schilling and Hill (this issue): that the measures capture the content knowledge that teachers need to teach mathematics effectively to students. This paper provides a summary of our attempts to uncover links between our measures, classroom mathematics instruction, and student learning."

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