Empirical positivism,an epistemological obstacle in the learning of calculus

Using Chevallard’s anthropological approach to the didactics of mathematics considered as an evolution of Brousseau’s theory of didactic situations, we envision the development of calculus as an epistemological transition between two types of praxeologies, pragmatic and deductive, a praxeology being an anthropological and epistemological model of knowledge. This allows us to depart from a form of dichotomy between formal and intuitive aspects of limits where a mathematical activity should finally become rigorous on some formal definition: we give credit to limits being a pragmatic model of magnitudes relying on mental objects. This understanding of limits is used to argue the relevance of empirical positivism, an epistemology held by Belgian students, as well as pupils, as an obstacle to learning calculus, and show how it is reinforced by learning institutions as a consequence of their inability to give credit to a pragmatic level of rationality.