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Stakeholders agree that the mathematical education of teachers needs to focus on mathematical knowledge for teaching, but the practice-based nature of this knowledge poses challenges for mathematics teacher educators — for understanding it, developing tasks that maintain its integrity in practice, and teaching it to teachers in ways that meaningfully support their learning to teach. We know little, however, about how mathematics teacher educators conceptualize the teaching that knowledge is to support. Our analysis reveals that thinking develops from a view of teaching as straightforward, where aspects can be treated in isolation, to a view of it as requiring focused attention while maintaining mutual regard for the whole. This difference has implications for how mathematics teacher educators understand specialized mathematical knowledge and for how to support their understanding and teaching of it. 

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.