Thank you for your effort! And by that I mean big Thank You!
University math classes were pure pain and suffering for me, because what was presented, taught and required for passing the tests was not understanding of the underlying theory at all - it was memorisation of solving alogrithms and only the hollow, overly formalistic envelope of what math actually is. Actually - it went that far that not even the formal proofs were presented, it was just being said "It is this way, believe it. Now carry on to solving examples.".
A principle that I don't have intuitive understanding of, that I cannot make visual approximation/model of is not an understood one. That I remember algo how to solve it (== pass exams) means nothing. Showing real life examples of use, the patterns and how do they extrapolate to other problems and even wholly different fields is the correct approach how to understand something, and in most cases much easier for the student than others.
Problem is - this hollow, formalistic shell of mathematics creates enclosed, sometimes eltistic, self-supportive culture by itself, and I had met a mathematician that actually wasn't - with high formal degree of education, yet was failing to show signs of intuitive understanding of the presented problems - waaay too many times.
I don't say a word about formalism in proof, there it is >>the<< correct approach to take, however, this approach does absolutely no favour when one is trying to actually understand the principle being presented.
If anyone wants to read this in much better worded version (despite talking about highschool education system in US, the issue is all the same), have look here:
https://www.maa.org/external_archive/devlin/LockhartsLament.pdf. It actually even came out in a book form as expanded version of the previous essay.
May I suggest one thing?
Dig into Unity or other free acess game engine, try to explore how you can make 3D visualisations of the problems that require it.
I will be more than glad to help you later with trasnfering those visualisations into world of virtual reality (that is now knocking on the doors of consumer electroncis world) and how to make them comfortable and easier to use for the interested end user. Making custom shaders for visualisations of vector fields and such is not an issue either - depends just on how much free time I will have at that particular moment.