In a study published in Physical Review-Physics Education Research, a
research team led by Academician Guo Guangcan from the University of Science
and Technology of China (USTC) of the Chinese Academy of Sciences has
successfully constructed a theoretical framework of
Activation-Construction-Execution-Reflection as well as a thinking mechanism
model based on Overgeneralization to help students solve bound and
scattering state problems in quantum mechanics education.
Education research on mechanics is an emerging field in physics. The
research on quantum physics is notably appraised as "just the tip of the
iceberg" by C. Wieman, a Nobel Prize winner for physics. The research team
led by Academician Guo Guangcan appropriately pays close attention to and
enters this emerging frontier field.
There are two schools in the field of research on physics education. One is
represented by G. Parisi, a Nobel Prize winner for physics, who values
statistics from the perspective of complexity science. The other one is
represented by C. Wieman, another Nobelist for physics, who values empirical
investigation from the perspective of pedagogy. The research team from USTC
combined these two methods to do research on the thinking framework of
students learning bound and scattering state in quantum mechanics by
statistical analysis of 406 undergraduates from the School of Physical
Sciences for a six-year duration. The team has successfully constructed a
theoretical framework of Activation-Construction-Execution-Reflection as
well as a thinking mechanism model based on Overgeneralization.
A complex circuit network has numerous nodes. These nodes are either
connected or disconnected. Only if all the nodes are of a series connection
will the percolation threshold be attained and the whole circuit network
will achieve connectivity.
Similarly, the knowledge memory of one student is also composed of different
nodes that represent different knowledge fragments in a specific field of
physics. Students need to connect these nodes in their brains according to
the relation of physical knowledge. When all the knowledge nodes are
connected through a right relation in a proper manner, the students'
thinking process will achieve a percolation threshold, which enables
students to master relevant physical knowledge and solve physical problems.
The researchers used the above knowledge model to concentrate on students'
difficulties with solving bound and scattering state problems in quantum
mechanics and found an interesting framework in their mind including
activation of relevant concepts, construction of differential equations,
execution of analytic calculation, and reflection on problem-solving
processes. Common difficulties focused on three key nodes: (1) recognizing
when the time-dependent Schrodinger equation is the appropriate model; (2)
selecting a range of the energy constants that satisfies the bound or
scattering state; (3) deciding when to use a superposition form of the wave
functions. These research findings not only provide students with a profound
understanding of the underlying reasoning mechanisms for quantum physics,
but also offer abundant resources to quantum physics instruction. That is to
say, if students get help when solving these crucial nodes, they will
acquire knowledge from an overall connected perspective instead of a
partially connected view. That is the proper learning mode.
The findings of the study show a new breakthrough of USTC in this field and
will have significant implications for education research in China.
Reference:
Tao Tu et al, Students' difficulties with solving bound and scattering state
problems in quantum mechanics, Physical Review Physics Education Research
(2021).
DOI: 10.1103/PhysRevPhysEducRes.17.020142
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