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  1. Researchers conceptualize mathematical knowledge for teaching in different ways, but a coherent approach to the mathematical education of teachers requires teacher educators’ understanding to be robust and shared. At present, we know little about how teacher educators interpret and operationalize this important domain. Our analysis of interview data indicates two sites of divergence in teacher educators’ understanding. Some view this knowledge as a resource for the mathematical work of teaching, treating it as distant from actual practice, whereas others view it as a slice of the dynamic and situational work. Also, some view the mathematical work of teaching, and its knowledge demands, as detached from particulars of students and schooling, while others view this work as inseparable from student identities and the larger environments within which instruction occurs, thus integrating regard for equity. Implications are discussed. 
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