  In order to support students in the development of expertise in quantum
mechanics, we asked which concepts and structures can act as organizing
principles of the non-relativistic theory. The research question has been
addressed in a multi-step process based on the analysis of categorization
studies, on a content analysis of a sample of undergraduate textbooks and on
the results of existing research on learning difficulties. The answer consists
in seven concept maps, intended as models of the organizing principles of
quantum knowledge needed to account for the results of measurement and time
evolution. By means of these instruments, it is possible to visualize and
explore the different facets of the interplay between the vector structure of
the quantum states and the operator structure of the observables, and to
highlight the educational significance of the relations between observables.
The maps can be used by instructors as a support for helping students build a
well-organized knowledge structure and by researchers as a basis for the design
of investigations into student understanding. While this framework may be
adapted to different approaches and interpretive stances, it provides
indications in favor of a spin-first approach over a waves-first one.
