Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, an analysis of video, interviews with teachers, and an analysis of textbooks, the authors define categories of knowledge and practices of teaching for understanding and assessing teachers' knowledge for teaching algebra. They argue that the combination of categories and practices must be covered in assessments of teacher knowledge, if the assessments are to be used in research that investigates the presumed links among teachers' content preparation, their knowledge, their practice, and student learning.
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