Make everyone buy a couple flash drives.
Flash drives are one solution but I can see a lot of problems with them as well. Back around 2000, I was an instructor at a college for an AutoCAD course and all the kids had to bring a disk to store their files on. I can't tell you how many times the disks were forgotten, broken, currupted, lost, erased, my dog ate it, etc., etc.. Keep in mind I'll be working with middle school students, ~12-14 yrs old. If the college kids had so many problems with their portable storage, I worry about the issues the middle school kids might have. Flash drives are going to be more reliable than the old 3.5" disks, but they can still be forgotten, broken, lost (or eaten).
Thanks for the suggestion though. I think I will ask all the kids to maintain a flash drive as a back-up for all their files, and to store all their files once we're done with the course.
Thanks for this lead. This is exactly what I was looking for. The software isn't expensive either, only $35 a seat. With this, it sounds like I can specify a "Thaw" zone where the kids can keep files on the hard drive and yet, when the computer is restarted, all computer settings go back to the original settings. The Thaw zone would be easy to clean out periodically while the software keeps the computers as clean as the day SW was originally installed.
Your question is something that most companies can not do correctly when left to their own vices.
There are a couple solutions that you can do to manage the SolidWorks files;
Use SolidWorks Workgroup, which is a part of SolidWorks Premium and above (There is no additional out of pocket expense)
Use SolidWorks Enterprise PDM, this is a separate and distinct program that you can buy. (There cost may be prohibited)
Most of the issues you will find with managing SolidWorks files will be with the References from model to model and from model to drawing. Remember these are 3d models and the references can be complex.
There are sertvices that can host EPDM, BYOL (Bring your own licenses) and get you up and running farily quickly
Check out http://www.Stratus-x.com
As for the Class Environment,
VM Ware, Virtual machines, etc... This is what will get everything back to the original state.