This is how I've interpreted them thus far:
Lighter Purple - Mind.
Students: Arantxa, Dounia, Logan, Lorna, Manfred, Praxie, Sasha.
Teachers: Caelus, Hemdall, Navi.
These powers stem from or focus around using the mind to control the world around the user.
-Praxie is something of an odd man out as he could easily belong to other classes like Blue or Green but if the class focuses on the mind affecting the external world, then it can be seen why he's included. Remember, he doesn't control ice, he just makes it.
Dark Purple - Magic, Occult, and Death.
Students: Belgosi, Damian, Danae, Minerva, Tomas,
Teachers: Dr Falkenstein, Greem, Kephren, Mandrak.
This class focuses on dealings with the supernatural - demons, occult, magic, etc. - even extending to the subject of death.
Green - Nature, Hybrids.
Students: Carter, Chiara, Corvus, Eloxia, Otto, Snowflake, Todd, Zeke.
This class contains individuals who either interact with nature in some way (Aigwon, Carter, Chiara, Snowflake) or are hybrids of human and animal DNA (Corvus, Eloxia, Otto, Todd, Zeke).
I once joked to a few fellow fans that the academy staff just threw Michael in since there were only two kids in the time and space class at the moment. "Eh, he's pretty smart, toss him in." But I like the other theories.
@axelusthered: That makes sense about Kephren.
I feel like the orange uniforms originally stood for a combat focused class/major (Cley's bio literally says 'head teacher of the Art of Combat'). Students in this class have abilities that emphasize combat ability.
Plunk's 'ability' is not that he has spikes, but that those spikes create an 'anti-magic poison' in which no 'enchanted doorway, magic barricade or bewitched window can resist'. This anti-magic poison is probably really effective against other Skeelz (and possibly nightmare) in combat, hence why he is in the combat class.
My take on carter is that he can actually use his ability in a variety of ways barring actual combat, unlike Jay.
The freedom to be any material may raise the power to turn into a similar material as sparkle to absorb magic, and even be antimatter.
He can turn to conducive materials to absorb electricity and throw it in the ground and act as a lightning rod, and may turn into an invisible material for stealth. He might ( this seems kinda farfetched) turn into clay and mould his bodies shape to looklike someone else and infiltrate the enemy.