Problem Solving and Inquiry Based Mathematics Education are in the focus of numerous mathematics education research projects, educational policies and actions in various countries, since several decades. Nevertheless, the efficient integration of problem-solving activities with the learning of mathematical content in ordinary classrooms is not evident.
We proposed to confront these difficulties by developing a modelling tool in terms of problem-networks, combining our respective preliminary research on teaching strategies in the Hungarian Guided Discovery approach to mathematics education on one hand, and the modelling of problem-solving processes based on French theoretical frameworks on the other. The problem-networks modelling tool has two objectives: 1, serving for the analysis of problem-based teaching trajectories and of links between problems; and 2, supporting teachers’ planning work for developing problem-based teaching processes.
Discrete mathematics is a particularly relevant domain for the aforementioned questions. It is often considered as well adapted for developing problem solving skills, since problems of various difficulties can be posed without requiring complex preliminary theoretical knowledge from students. Recent research has also shown the various interests of teaching and learning discrete mathematics, including the potential role of the domain in the learning of mathematical abstraction and proof, and the various connections to other mathematical domains. Furthermore, the need for teaching discrete mathematics emerges recently on the behalf of computer science. Nevertheless, discrete mathematics is often marginal in curricula.
In the ProDiME project, we focused on the construction and analysis of problem-networks in discrete mathematics. Relying on our respective preliminary research on the didactics of discrete mathematics, and the analysis of Hungarian curricula which traditionally accords important place to discrete mathematics, we aimed to investigate the possible place of problem-based discrete mathematical activities in other curricula.
Although the understanding and the support of students’ learning processes remains an ultimate purpose of mathematics education research, the role of teachers in this process gains increasing attention in didactical research. Today it is clear that the implementation, dissemination of innovative teaching approaches is not possible in the form of a simple transmission process from researchers towards teachers: teachers have to be seen as crucial agents in innovation processes. This implies that collaboration between teachers and researchers plays an increasing role in mathematics education research as well as in teachers’ professional development and in the implementation of innovative projects. The ProDiME project implied collaboration with teachers for several purposes: furnishing a tool for teachers to support their work in planning their teaching processes; adapting specific problem-networks for the teachers’ own teaching contexts; analysing the teachers’ choices during the preparation and the implementation of their teaching trajectories and the impact of these choices on students’ work; developing innovative resources helping other teachers’ professional development.
