This can be done using Configuration Profiles.
You can lock the desktop picture, restricting it from being modified. Have a look at the screenshot attached!
Hope this helps.

You could also restrict the Desktop & Screen Saver System Pref. Screenshot attached :)

This IS helpful, yet I'm just trying to restrict the use of folders and randomization of desktop picture slideshows. Making the process restricted itself will cause more complaints than the change is actually worth.
@TBenolkin Then restricting students from using the pictures folder to change their desktop background is going to have the same affect as my suggestions above.
The solution I have used in the past is to set the desktop background to change back to default on every login. If students want a custom background, they will change it.
This can be done quite easily with an ongoing policy!