Over four decades of conceptual change studies in education have been based on the assumption that learners come to science classrooms with functionally fixated intuitive ideas. However, it is largely ignored that such pre-instructional conceptions are probabilistic, reflecting some aspects of an idiosyncratic sampling of their experiences and…

To ensure the learning of mathematics, teachers must be able to analyse their students' mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students' difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual…