The mathematical formalism in quantum mechanics gives meaning to the physical concepts and entities, as the birth and the historic evolution of quantum theory tell us, as well as it is evidenced by the entanglement between the different interpretations of the theory and the formal aspects of the theory itself. Concepts characterizing quantum mechanics, as quantum entanglement or non-locality, were recognized and really understood in their implications only after the formulation of quantum theory. Teaching quantum mechanics in upper secondary school cannot leave out the consideration of the interlacing between formalism and concepts.
On this peculiar point there are centered pilot experimentations in Italian last year upper secondary school classes. The experimentations are carried out following a learning/teaching quantum mechanics proposal developed in previous researches. According to this proposal students face quantum knots and concepts in the phenomenological context of light polarization. The aim of the proposal is the construction of the formal thinking creating a challenging educational environment in which student explore hypothesis and, step by step, build a coherent interpretation of the specific phenomenology explored, generalizing the results in other contexts.
From analysis of students learning path many indications emerged on how students use the vectorial representation of state as cognitive organizer of state concept. Moreover the linear operator representation of observables was used as an instrument to yield the quantum description of microscopic systems. The integration of these results with phenomenographic studies on classical vs quantum conceptions developed by students showed diverse grades of coherences of the conceptual students schemas and the formal ones.
