Misc,
Analyzing the structure of basic quantum knowledge for instruction
(2019)cite arxiv:1908.04231Comment: 23 pages, 9 figures, 1 table.
Abstract
In order to support students in the development of expertise in quantum
mechanics (QM), as well as to provide insight on teaching, we asked which
concepts and structures can act as organizing principles in basic QM (RQ1). 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
upper-undergraduate course textbooks and on the results of existing research on
learning difficulties in QM. The answer to RQ1 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 both at a qualitative
and quantitative level. The central element of this network is the interplay of
the vector structure of the quantum states and the operator structure of the
observables, with a particular focus on the relations between observables.
These relations explain how information on measurement and time evolution is
encoded in the modulus and in the phase of the probability amplitudes
associated with the representations of the state, a topic identified as
difficult by educational research. At upper-undergraduate level, the maps can
be used by instructors as a support for helping students build a well-organized
knowledge structure independently of the approach used, be it a spin-first or a
waves-first one. However, this framework provides indications in favor of the
former over the latter. At high school level, a simplified version of this
framework has been used as a basis for the design of a teaching-learning
sequence.
