Abstract
This chapter discusses interfaces between the development of mathematics and the teaching of mathematics. Contrary to traditional convictions of teaching as being restricted to a receptive and passive role, productive interactions between the two poles are analysed here. Four cases even for an impact of teaching upon mathematical practices will be presented and discussed, featuring the issue of elements and elementarisation, the institutional impact of teacher education on research in pure mathematics, and the dissemination of set theory and of non-Euclidean geometry by German school textbooks in the second half of the nineteenth century.
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