Problem-based learning trajectories in discrete mathematics education

Our research project is inscribed into the domain of mathematics education (didactic of mathematics): a research domain at the interface of mathematics and social sciences. The project is based on the collaboration of three researchers: Katalin Gosztonyi as Experienced Researcher, assistant professor at the Eötvös Loránd University of Budapest; Viviane Durand-Guerrier as Principal Supervisor, emeritus professor at the University of Montpellier; and Simon Modeste as Co-Supervisor, assistant professor at the University of Montpellier. Our project is focused on the development and analysis of complex problem-networks which will then serve for the conception and implementation of problem-based teaching trajectories. We aim to develop an efficient modelling framework in order to construct, analyse and represent problem-networks and problem-based trajectories for mathematics education – both for research purposes and for supporting teachers’ work in planning their teaching processes. We focus more particularly on problem-networks and teaching trajectories in the domain of discrete mathematics: on their potential place and role in mathematics curricula; their values for conceptual learning as well as for the development of generic mathematical skills (related to problem solving, abstraction, proof etc); and their potential connections with other mathematical domains, including links between mathematics and computer science. A theoretical and epistemological work and a priori didactical analysis of examples of problem-networks will be combined with experimental research on teachers’ and students’ work with problem-networks. The theoretical background of the project combines theories of the didactics of mathematics from the French research tradition with current research on the Hungarian Guided Discovery mathematics educational tradition. Experiments will be realized in both countries.