<!----> <!----> Most of the teaching of mathematics in higher education concerns students who are not specialising in mathematics. The challenges of defining, designing, motivating and assessing mathematics teaching and learning for such students is therefore an important field both at INDRUM and in similar venues. The authors outline recent research presented at INDRUM. They propose that interaction between different specialisms becomes increasingly important in this area, both to make sense of actually observed teaching and learning, and to devise new and more relevant and efficient didactical approaches, for instance to help students engage in autonomous mathematical modelling. <!----> <!---->

Taking the example of teaching mathematical modelling in university degrees, this paper focuses on how the unit of analysis adopted by different research frameworks in mathematics education transforms a teaching problem into a research one. The transformation starts by including a specific way of conceiving not only the activity of modelling but also its possible evolutions and connections with more general mathematical or scientific activities. This epistemological dimension of the research problem can be enlarged by what we call the ecological dimension, that is, the set of conditions and constraints that allow or hinder the existence of specific mathematical activities, such as modelling, as normalised school practices, in particular, at the university. The institutional perspective adopted by the Anthropological Theory of the Didactic integrates both dimensions. This integration leads to the formulation of new research questions in the domain of modelling and applications and provides new tools to address them systematically.

Implementing inquiry-oriented instructional proposals at the university level collides with many constraints related to the current pedagogical paradigm based on the transmission of previously established works of knowledge. One such constraint comes from defining subjects’ curricula by a set of topics to study, not questions to inquire. Our research team has been working for more than 15 years in designing and implementing an inquiry-oriented instructional format called ‘study and research paths’ (SRPs) within the Anthropological Theory of the Didactic. This paper focuses on the commonalities and specificities of the implemented SRPs to identify critical strategies and didactic devices that facilitate their integration in current university settings. The experimentations also reveal key issues for the sustainability of inquiry-oriented educational proposals related to the question that generates the inquiry and the types of contracts established to approach it.