Most people are aware of M/S as a miking technique: That you can capture mid and side components and encode them to stereo. Lots of people are aware you can decode stereo to mid and side components for processing mixes.
However, in my experience most people rely on plugins to do the matrixing and do not understand what happens under the hood. I have made a Pro Tools template which decodes a stereo file to m/s and then encodes it back again to stereo. I use this as an exercise for my students. Even if they don’t understand how it happens, they recognize the sound of m/s and how to read a phase scope. If for no other reason, you can use it as a listening tool to listen to the sides only of some of your favourite music and get a new perspective on the arrangement and especially the use of reverb. I know I’ve learned a lot doing exactly that.
I have created this session to help students understand how Mid/Side works.
To use the session just import a stereo file to the clips list and drag it onto the audio track. Show the phase scope on the master fader and play with the aux faders.
You could show the hidden tracks and follow the signal flow through the busses. The comments in the mixer should help.
Here is a version of the session in .ptf format for Pro Tools.