Abstract
In this work we explore which aspects of the teaching of combinatorics do influence the development of students’ heuristics in problem solving activities. We investigate the teachers’ intended didactical interventions concerning the evaluation of students’ solutions and we make inferences about the relationships between teachers’ interventions and didactical phenomena that have been identified in previous research, and that impede the appropriation and evolution of heuristics on the students’ side. We pay particular attention to teachers’ interventions and evaluation processes after student-centred teaching phases. In particular, we investigate a phenomenon that we call the “funnel-effect”, that is the teachers’ tendency to inhibit counting and enumerating processes in favour of heuristics involving formulas or numerical expressions. Once we identified this trend, we started investigating the motivations behind this teachers’ task orientation, making distinctions between generic teacher-centred approaches and specificities of teachers’ task orientation related to combinatorics. The study is a preliminary step of a qualitative study; we analysed five teachers’ interviews and elaborated several categories of motivations that seem to be due to specificities of combinatorics teaching.