You can mount floppies on Linux. However, a floppy disk may not be large enough to hold many documents. If you can't transfer files on a network, a usb key drive would work out better.
Does Edubuntu have a /media/ directory. It may be setup to recognize floppys and mount them automatically when someone inserts a floppy disk. There may even be an icon popup on the desktop. If you have a floppy icon on the desktop, right-click on it and see if there is a mount and unmount option. It is important to unmount the disk before ejecting it. The contents will be cached in memory until you umount it or run "sync".
I'm bringing up the graphical solution first because then the kids will be able to transfer the files themselves.
You can also mount a floppy manually. You might want to use "visudo" to allow ordinary users to mount and umount floppies without a password. There is a commented entry for mounting and unmounting the CDROM. You could add a similar entry for the floppy device.
If edubuntu uses the HAL and UDEV daemons, then there may be a /dev/floppy that is automatically linked to correct floppy device (e.g. /dev/fd0H1440, /dev/fd0, /dev/fd0H0720). You need to explore a bit after inserting a floppy to see which device is best to use.
Here is a YoLinux tutorial on using floppies in Linux. It includes commands to check for bad blocks, format a new floppy, etc.