Full Disclosure: I found this thread while looking for ways to screw with some vulnerable airplay devices in the school library, so OP probably wouldn't like me much. In addition the next few paragraphs are definitions and my personal editorial commentary. I must be biased, so take it all with a grain of salt.
It's almost a year later, (so this is really for anyone who comes here in the future), but if memory serves me right Yosemite was out last year by the time this post was written. I know yosemite has had airplay from the start, possible Mavericks as well. Basically it isn't new. It's forgivable to confuse airdrop and airplay, because apple lacks the creativity to come up with new names. They are however not the same.
Airdrop is the ****** second cousin twice removed from Bluetooth File Transfer. For some reason, neither can send files from your Mac to your iPhone, but they work fantastically with android. I rarely transfer files between mac's via wifi. Besides if I decide to transfer a file via the local network, how is it easier than dragging and dropping into the targets local public dropbox/share folder. (which will show up conveniently in the sidebar.) TL;DR: Don't bother with Airdrop, its been around since the dawn of wifi, and standard wifi sharing settings are incredibly easy to set up.
Airplay is basically Apple's version of Chromecast, (Google protocol for sending browser, video, desktop, etc through your wifi to another screen such as a TV.) They both have arbitrary limitations on what can or cannot be streamed. (Truthfully it's not that arbitrary, both facilitate communication between devices in their respective ecosystems via wifi, and very likely get handicapped so that they do not intrude on other markets. I digress.)
Airplay is available on both iOS and OS X but they behave differently, purposefully handicapped like airdrop. If you have an Apple TV then you have way more freedom, because you bought into their ecosystem. oddly you don't need apple tv to stream via your phone, rather you can natively send it to whatever smart OS your TV has. OS X requires Apple TV, if you aren't air playing to a another mac ( Why you would decline to use the second computer to browse the internet, instead of a complicated device daisy chain beats me, but too each their own. I too enjoy making things complicated, simply to see if it would work.)
I am going to assume this student probably sent **** or something similar to the laptop during lecture to get a laugh, which I am sure he/she/ze received.
Here is my response to OP that I believe he should have received a year ago.
1. Unless you specifically go out of your way to enable airdrop to accept ANY AND ALL shared files, then not only would your teacher have had to open up airdrop in finder, but they would also have to accept the files that the student sent.
2. For either of these services to work your teachers' and students' would have to be logged into the same wifi network. This is a completely amateur move. Fire your IT guy if this is the case. This was the school's negligence not the work of a brilliant hacker.
3. If you are really determined to ruin this kids life because your teacher is an idiot (or the IT guy) then you can probably just hit command+i on the files and check out who the owner is. (remember we are not looking for a brilliant hacker deleting meta data, rather the class clown who has seen the latest apple keynote....)
FINALLYif OP is still around I am really curious what you guys ended up doing to deal with this situation. When I was in high school, my buddy was able to get into the schools system and mess with grades and records, basically like a cliche movie. Instead of punishing my friend, the school instead gave him an admin account on the schools (student) network, and sought his advice on how to fix their system.
With regards to our assumed amateur **** distributer, I think you guys owe him/her/ze thanks rather than an expulsion. This guy hooked you up with a FREEEE security audit. Besides all those students turn on private browsing at least once by the end of the day anyways....
I encourage the schools administration to educate (go figure...) their staff in how to keep their computers secure. The biggest computer vulnerability is HUMAN ERROR, and you guys have clearly got an issue with this. (though your IT guy is kinda hopeless as well..) It is the users responsibility to protect their hardware. No teacher in their right minds gives students keys to their house (**** most are unlisted cause teenagers are evil). Which is basically what you have got going on over there.
TL;DR: Your network is less secure than my parents wifi. You guys have been negligent and this kid did you a favor. Reward this kind of behavior. This kid used his brain to figure out a somewhat novel way to make the class laugh. He isn't an evil hacker.