We discuss some fundamental differences between scientific mathematics and school mathematics and then consider the concept of didactical mathematics, which can be seen as a kind of applied mathematics in mathematics teacher education, in order to bridge the gap between those two subjects. Introducing didactical mathematics aims at finding a natural framework to reassert mathematicians’ role in research related to the teaching and learning of mathematics. We also consider some exemplar research topics how didactical mathematics can help us to find a more common ground for mathematics researcher training and mathematics teacher education.

mathematicians, mathematics, teacher education, teaching.