The aim of this paper is explain how the notion of "study and research course", a recent construct in the anthropological theory of didactics, provides a general tool to model mathematical knowledge from a didactical perspective. We do this from two points of view. First, the notion itself arose as a tool for didactic design, particularly in mathematics teaching involving modelling type subjects, and we introduce a new diagrammatic representation in order to present and analyse a selection of such designs. Secondly, we demonstrate how the same representational tool can be used to analyse other didactic processes as study and research courses. In both cases, our examination of cases reveals that designers and teachers are often more explicit about their intention to enable students to do "research" (e.g. exploring a challenging problem) than to enable students to engage in autonomous "study"; moreover, the role for students is mostly confined to search for answers to questions raised, essentially, by the teacher. These observations point to directions which deserve more attention in design research related to the notion of study and research course.