To make sure I'm answering the right question: you want to find the best approach to representing ranks, in iOS icon format, to a specific audience.
Short answer: use something appropriate to your audience that represents a numerical value.
Metals and their pitfalls
Firstly, if you go with those metals you suggested, you limit yourself to 3, perhaps 4 colors which can be clearly distinguishable ranks. Bronze (or copper, brown), silver (light gray) and gold (yellow). If you want to add platinum, it'd have to be white, which can be hard to distinguish from gray, but not impossible.
More importantly, color-blind people could have issues with this approach.
So I'd suggest maybe combining it with numbers. Stick a number on these colors, and it becomes a lot more clear. However, gold is often associated with number 1, so what does that make platinum?
Rankings in real life
Perhaps take a page from real life. There are plenty options there. Military or police ranks (Stripes, stars, the lot). School ranking systems (A, B, F?)
Stars ... or something similar
Perhaps instead of the above, go for a simple graphical representation of a number. Stars for example.
A single star for first rank. Two for rank two. Etc.
If you run out of space, introduce a border to the edge of the icon, and start with 1 star again. This could be a level 2, 1 star rank. Etc.
Theming the ranks
All that remains, if you go with that last option, is that you find some fun, simple representation of a number that fits your audience. Now, this is not the place to ask for a specific style-guide (try https://graphicdesign.stackexchange.com/) but here are a few ideas that might kick-start your brain;
- Think school-board; white on a dark green background, drawn?
- Possibly pen-drawn on a white blue-lined paper-ish background?
- Perhaps something from the playground, like a number of marbles?
All of these depend on your audience, and I took kind of a childish approach, since that's the first thing I thought of when you mentioned "education". However, these examples can easily be swapped out with examples that fit a more grown-up audience. Best of luck.