In his recent paper (https://www.researchgate.net/publication/308568264_Analysing_the_Competency_of_Mathematical_Modelling_in_Physics) Prof. Redish analyses the set of mathematical skills physics students need to have in order to success in a physics course. He also touches methodology behind his analysis.
As a practitioner, I have developed and successfully used for many years a hands-on approach to the problem of math in physics courses (and I have evidence that this approach has been appreciated by my students: www.GoMars.xyz/evvv.html).
As a teacher, I don’t need to guess what math skills do students need to know, I need to know that!
And the full set of such math skills comes from the full set of problems students need to be able to solve (actually or potentially) during (and after) the course.
Since it is I, who writes the syllabus, selects topics, problems, assignments, it is I, who has to make the match between physics problems and mathematical skills. And, of course, I did.
But I did not express the result of that match using a textual description (“students need to know …, and need to be able to perform …”), I expressed it in the form of a set of math problems students need to be able to solve in order to be ready for the math required during the course; which is basically, a mathematical analogy of FCI.
The methodology behind this approach is presented here: http://www.teachology.xyz/2020.html.
The general methodology to teaching physics is presented in the series of publications:
1. What does “thinking as a physicist” mean?
2. A General “Algorithm” for Creating a Solution to a Physics Problem.
3. Learning aides for students taking physics.
4. A Map of Operationally Connected Categories as an instrument for classifying physics problems.
5. On a definition of science, Intelligence, and AI
The developed set of math problems (see the links below) is presented to students at the beginning of each course in the form of a laboratory exercise. Initially, it was handed out to students during the lab time, but eventually it was converted into a webassign.
The instructions note that the “test” will not be graded, but students should apply the best effort, and take notes to all difficulties they may have during the test (and work them out as soon as possible).
There is a natural intention to search for correlations between the grade on the math test, and the final grade for the course. However, that correlation would be misleading. In education, like in quantum mechanics, measurement affects the system. When student know they weaknesses, they can concentrate on fixing them quickly enough, so those weaknesses would not affect their progress in study physics.
The “test” is not an assessing tool,
but a motivational instrument.
The link to the html version of the test: http://www.gomars.xyz/mst/mst.html
the link to the pdf: http://www.gomars.xyz/mst/mst.pdf