Questioning Mathematical Knowledge in Different Didactic Paradigms: the Case of Group Theory

What is questioned and what is taken for granted when carrying out research into the teaching of a given mathematical topic such as Group Theory? This paper presents two different questioning procedures using the methodological tools provided by the Anthropological Theory of the Didactic (ATD). The first one, leading to an undergraduate instructional proposal called “workshop of practices”, is based on the praxeological analysis of the official content to be taught, assuming the prevailing pedagogical paradigm in tertiary education, which the ATD characterizes as “visiting works”. This also seems to be the procedure many investigations adopted with regard to the teaching of Group Theory, centered on the construction or reinvention of concepts. The transition towards the inquiry-based paradigm of “questioning the world” requires another questioning strategy, to put the raisons d’être and uses of the mathematical works to be taught at the core of the analysis.