How students link quantum concept and formalism

Quantum Mechanic is the theory of reference for the modern description of the world and therefore it is important to include its basic concepts in the physics curricula starting from the upper secondary school. Its formalism assumes an interpretive role, which gives rise to the physical meaning of entities and quantities. Literature shows that research based innovative proposals focused on the fundamental concepts activate a quantum vision of phenomena, at the same time documenting areas of learning knots for students. In particular the physical meaning of the formal quantum constructs emerges as a problematic area both for secondary and college students. To give a contribution to the ways in which student's link formalism and quantum concept, a study was performed with 17 students of a 13 grade class of an Italian secondary school. An experimentation was performed involving students in the exploration of an educational path based on the Dirac approach to the basic concepts of the quantum theory in the phenomenology of light polarization, developed and valued in a long time research program. The data about how students approach the formalism was collected by inquiry based worksheets and a posttest. A research finding is the individuation of four modalities activated by students approaching the quantum formal constructs, among which the geometrical one plays a relevant role in bridging phenomenology to the concepts and their formal representation