In this paper we introduce a link between the Theory of Didactical Situations and the Documentational Approach to Didactics, in order to study teaching/learning phenomena at the beginning of university mathematics studies. Specifically, we investigate the didactic contract at three levels: institutional, mathematical subject, and specific mathematical content level, and link it to the use of resources by students. Using this link, we analyse data stemming from two complementary case studies: one in the UK, and one in France. We identify didactic contract rules at the three levels for the students, and for the teachers. Moreover, we find discrepancies between students' and teachers' rules, and also between those and the explicit rules of the institution/s. These gaps may cause misunderstandings and prevent students from learning mathematics effectively at university level; we claim that these gaps can be reduced. Teachers could make their expectations more explicit in terms of resource use and support an appropriate use by students. The university institution could also contribute to a better alignment of the resources offered with actual student practices.