At the Jacobs University Bremen we offer a lecture on General Computer Science to an international student body. We are challenged with the students' different mathematical backgrounds. The majority of our students believe that these mathematical discrepancies are very problematic, especially in the beginning of a course. Students reported that they had problems to get acquainted with the professor's notation systems; some had the feeling that the pace of the course was inappropriate, while others did not face any problems.

We believe that the theory of Communities of Practice can help to understand and countervail these discrepancies. Students do not share the same understanding as the lecturer. They actually form various sub-communities that differ in their preferred notations, basic mathematical assumptions, and motivating examples. Instead of enforcing students to become acquainted to the lecturer's practice, we want to adapt the lecture taking the social context of students into account.

In this paper we present our vision of a prototype web application, consisting of an online precourse and online course, which allows to overcome discrepancies and to adapt course materials. The precourse prepares new students before arriving on campus. Students can solve and discuss multiple-choice and non-interactive problems, provide feedback, and rate the presented materials. Based on the students' interaction, we want to identify discrepancies, eventually allowing us to spawn communities with shared understandings. In turn, course forum and rating facilities in the online course allow students to provide constant feedback, e.g. to report difficulties with specific sections or the pace of the lecture. Moreover, we aim towards preparing the course for the identified communities from the precourse: For example, slides and homework will be adapted to the notation system of a specific community of students allowing them to focus on the content.