You may want to try out this new IOS 7 solution using Airdrop which allows you to share items between compatible IOS devices via bluetooth. Wifi needs to be turned on, but not necessarily connected for Airdrop services to work. Currently it's available for all iPhone 5 models, 4th generation iPads, iPad mini, and 5th generation iPod Touches.
It's quite simple to use, as you select what you want to share and if there are available Airdrop recipients within close proximity, they show up as possibilities.
To enable your IOS device to receive Airdrop items, you need to go into the control panel, tap on AirDrop, and choose either from contacts or everyone.
If the teacher has their iPad, or even iPhone 5, set to receive Airdrop shared items, students could go in and share their work to the teacher's device.
Shared items include anything with the Sharing button; photos, notes, videos, and completed items in apps. The shared item will be stored in the same location as where it came from; photos in camera roll and notes in notes.
If all iPads in a center or 1-1 classroom are set to receive Airdrop items, then students will be free to share with each other.
Currently IOS devices can not Airdrop to a Mac, as I'm hoping that feature becomes possible in the near future.