I know you already have a few responses for pneumoics, but here was how I learned it for my checkride: memorization and correlation.
My personal feeling is that if a student only has the list memorized they still have a ways to go understanding Vmc, however, soapbox aside I liked the Mulllllti ops one.
I used
TO
TO
TO
TO
TO
CG
CG
WI#
Take Off (flaps, trim, cowl, power, weight)
CG - unfavorable
Gear
Critical Engine
Ground Effect -out of
Windmilling prop
ISA
5* bank - up to, zero sideslip
150# rudder
---
20* heading
To explain it to students (like a pro)
I draw out the chart and explain the relationship between the factors, for example:
Take Off Flaps: can be either up or down depending on your airplane, so Joe student how would Vmc be affected when flaps are up as compared to when flaps are down all other things being the same?
Hopefully Joe student will get to the point where he says that when the flaps are down it is a stabilizing factor, performance is increased and Vmc decreases; however if flaps are raised control is effectively reduced which increases Vmc and decreases performance. Vmc is predicateed on rudder effectiveness, so although flaps increase lift, drag is also created. Drag counteracts thrust, thrust being the most important cause of Vmc loss of directional control....blah blah blah.
You can see what I'm getting at, while the memorization of the factors are important because you can't get to correlation without having gone through rote memorization. getting your student to that point is an objective. Its also really satisfying to see someone be able to actually understand Vmc factors and smile when you throw them a curve ball because they actually know how to answer.
That being said I also teach how critical engine is identified by comparing p-factor, torque, accelerated slipstream and spiraling slipstream on counter rotating engines vs. conventional. That seems to help in the understanding of Vmc as well. Finally asking the student which are the top three or four most critical out of all the factors and why is a good way to understand if they are getting it.
If the student can understand that power is the cause of the loss of directional control I get happy. I have them use #'s going through each factor startig with max power, then zero sideslip, etc. When they come up with how many knots (or mph) change from most unfavorable to favorable they actually SEE why each affects Vmc.
e.g.) max power @ 90 kts vs no power = difference of 90 knots.
zero sideslip (lets say 2*bank) vs. 5* bank = 15 kts.....
then they have a chart also explained in knots of the differences in the factors. Overkill? I don't know, they seem to have a grasp on it by this time. Will I think it will save a life? I hope so, I just didn't want to underestimate that for a checkride they can actually impress the examiner by actually knowing their stff as opposed to regurgitation.
Hope I don't come across as swaggery, this is just my experience and I hope it helps; besides It's 4 am and I just woke up for my flights.