Resonance: a key word in mathematics teaching research

In this paper a model of cognitive dynamics is proposed, for interpreting classroom as well as teacher training processes, nowadays supported also by some recent neuroscience results. Core relevance in the model is assigned to a basic resonance dynamics, assumed to work at the root of all the modulations, from perception to abstract thinking, and interferences characterizing knowledge construction. On the basis of this theoretical framework, teachers are seen as "resonance mediators", i. e. experts who favor the resonance process in their students; correspondingly, any teacher training process has to accomplish this result. Finally, we will briefly examine a school episode, showing how a teacher, playing this role, acts effectively both on students' understanding and on their motivation.