Résumé
Mathematical reasoning based on definitions and theorems and the attention towards generalisation are important for the transition from calculus to analysis or topology. We analyse proofs of a task about the equivalence of the continuity of a real-valued function on an interval and the pathconnectedness of its graph. In doing so, we examine elements of "pre-structuralist praxeologies" at the crossroads from calculus to more advanced courses. The proofs take pre-structuralist aspects into account in different ways. This holds for the mobilisation of levels of pre-structuralist praxeologies as a means of generalisation. Thus, we contribute to calculus education by focusing on the transition from a more intuitive to a more formal way of reasoning based on underlying structures about functions and graphs.