When used in class or on tests, it can run a built-in program from its ROM. For use in full computer mode, you boot it off an SD card. Anti-cheating can be done via DRM features that are already available on the chip (although open-source purists wouldn't like this part, but it shouldn't get in the way in "full computer" mode).
The way the anti-cheat code could work is simply a calculator function which gives a digital signature hash based on user input. Student enters a serial number from the test, and writes down the function's output (which is derived using a private key burned into the chip, and only accessible by the built-in calculator-mode code).
The reason I think a calculator form factor would work better for the education market, is that every high school already requires a $100 graphing calculator, so might as well make it the calculator be of more use.