depends on the rest of the room, really...most people tend to put some rugs under the drums...but it all depends on the rest of the room.

You know, there's no place like a nice, big wooden room to record a drumkit. Awesome. But your classroom is certainly no "wooden room" and placing some plywood under the kit may make things worse, not better.
For starters, even with nice wooden floors and walls around the kit, you'll find the drums sittting on....a RUG! Why? To anchor the drum spurs. Ever see a puppy slipping around on a tile floor? That's what the drummer is going to be doing trying to beat the skins on a bare wooden floor!
And then, the carpet plays another important role. It helps keep the sound reflections from the floor from reaching the OH (and other) mics in a matter that aggravates phasing issues (especially if you have low ceilings). Hard reflections from the wooden floor can also wreak havoc on the actual acoustic tone of the drums sitting on it.
I know a drummer who does carry his own "platform" he made himself using 3/4" plywood bonded to another 3/4" piece of particleboard, and then he covered the top (the plywood) with carpeting. Anywhere he goes, he has a sturdy area to set up his kit, and his sound is very consistent from room to room. That might be a solution to your situation.

You could look at it this way. Here's a new experiment, lets see how you can best utilize this room. You only get one hint.
A Carpet Isn't Going To Matter unless it is to keep the drums from walking around.

Not knowing anything about this space, look at what positive things you have to work with here. At one time, no one would have thought of micing the back of a guitar cabinet for effect! Maybe you will engineer this thing and discover a cool new sound. Isn't that the fun of engineering and experimenting? Sometimes things that are always and entirely predictable can be boring.
Good luck,
Cheers,
Tommy

P.S Try a little someting (sample) and throw it online and we can have a bit to hear.
Tommy