What about experience points?
Personally for a school setting I wouldn't find that enough, because mechanically you need to give out experience points that results in gaining a level every semester/school year or so and it is again a 100% approach - you reach the XP threshold, you got 100% or you don't and you got 0%.
Maybe the simplest subsystem for better simulation of learning and training abilities without changing 5e to much would be something like this:
Use XP. Subdivide the XP to get to.next level by 5 or 10, so you got sublevels.
Lime at 0 XP you are level 1 (10). 300 XP you are level 2.
At 30xp you are level 1 (9), at 60xp you are level 1 (8) until you are at 300xp, which is level 1 (0) = level 2.
So, now, at level 1 you are allowed to use Level 2 abilities, but when ever you use of abilities of the next level, you need to beat a DC of 13 + the Number in the brackets.
So a Level 1 wizard with 0 XP is Level 1 (10). He now can try a level 2 ability- for wizard that could be any level 2 arcane tradition feature or any level 1 spell he hasn't learned yet, but in order to succed he needs to do a DC 13+10 - dc 23 check (Intelligence).
A Level 1 wizard wit 150xp would be level 1 (5), the DC to use a level 2 abilities would be DC 13+5 = DC 18. At 270xp that would be a DC 14 check.
This is just a quick and dirty rule to simulate learning at a school.
Heck, I even would implement something like this in normal D&D to simulate the learning experience, make it an ability that, if it succeds you can do it once per long rest or something.