Designing a Geometry Capstone Course for Student Teachers: Bridging the gap between academic mathematics and school mathematics in the case of congruence

At Paderborn University, a new 6th semester geometry-course for upper secondary student teachers has been designed and taught by the first author of this paper. To show links between academic mathematics and school mathematics we established so-called interface weeks. These are weeks during a course in which lecture, exercises and homework focus on topics that are related to the normal canon of content but specially chosen for their relevance in school contexts. In this article, we want to present our design for an interface week on the topic of congruence. In order to do so, we first illustrate how so-called interface aspects are used to systematize the mathematical background of the topic, thus giving future mathematics teachers the chance to act professionally. We then show examples of learning activities and first results of the accompanying research.