The study at hand investigates the development and the refinement of the university course “Introduction into the culture of mathematics” as a Design-Based Research project. The course was designed as a bridging course at the University of Paderborn with the aim of helping first-year preservice teachers to accomplish the transition to higher mathematics, especially concerning mathematical proofs. Using the theories of “diagrammatic reasoning” (Peirce) and “sociomathematical norms” (Yackel and Cobb), four cycles of the course were accompanied by qualitative and quantitative research, evaluating the courses benefits and analyzing students learning. As output of this research, several findings can be specified. First, a contribution to a local instruction theory concerning the learning of mathematical proof for first-year pre-service teachers is formulated. Second, various test instruments were developed to examine central aspects of the learning of mathematical proof. Third, the previous knowledge concerning proof and proof competencies of first-year university students are described. Finally, several theoretical issues and discussions can enriched by the outcomes of this project: the discussion of generic proofs as valid mathematical proofs, the enculturation function of mathematical proofs, the importance of the concept of ‘proof acceptance in the learning of proof and the benefits and limits of ‘proofs that explain.