Abstract
This critical appreciation of major lines of thinking about mathematical knowledge in teaching shows how they have given rise to productive reconceptualisations. By identifying types of subject-related knowledge distinctive to teaching, Subject knowledge differentiated demonstrates that expert teaching calls for more than ordinary subject expertise. Subject knowledge contextualised highlights the significance of the embedding of such knowledge in professional activity mediated by teaching tools and social organisation. Subject knowledge interactivated illuminates the epistemic and interactional competences that teachers require in leading the (re)construction of mathematical knowledge in the classroom. Subject knowledge mathematised illustrates how teachers must draw on expertise in mathematical modes of enquiry to enact authentic mathematical activity with students. The chapter concludes by suggesting that key problems of mathematical knowledge in teaching reflect broader inadequacies of received practices of mathematical communication in making accessible the thinking processes and learning strategies that underpin the development of mathematical knowledge.
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