**What Math Skills do Physics Students Need to Have?**

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 C*reating* 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