There are different types of “knowing”, and they permit different varieties of activities. You can know how to do the math for QM, but you can’t necessarily translate that type of knowledge into an ability to judge other paradigms which strive to explain the same observations. That would also require a conceptual comprehension.
If you knew the concepts of QM as well as the concepts of that competing paradigm – and the various arguments which make the case in both directions – you can develop a qualitative assessment which can guide you towards good questions and experiments which can differentiate between the two.
There is a huge amount of research which supports the use of concept maps within science education. Joseph Novak, the inventor of concept maps, has consulted for some very prestigious institutions, including the NSA. When an intelligence analyst is trying to decode a very complex situation, they graphically map the problem out in various ways. Business modelers do the same thing with systems thinking diagrams.
Bob Gowan invented the vee diagram to help students to understand the structure of science. Research demonstrates that students generally don’t even know how to extract scientific structures like concepts, propositions, assumptions (and so forth) from a scientific paper.
It’s a very simple idea: Why not simply draw these complex models out? Graphs and lattices are used in many other similar endeavors. Learning would be faster if the students could see the conceptual structure of the theories under examination. Comments could simply attach to this structure.
