Here is a good work-around solution:
Using Internet TTY relay service on a connected laptop computer, call into the classroom phone using the TTY service. Make sure the classroom phone headset is next to the TV.
So it is like the TV is talking into the phone and you can read what is being said on your laptop. Alternatively, you can also use IP Relay on your Sidekick to call into the class and read the captioning on your Sidekick.
Of course, the whole thing won't work if there is no classroom phone to receive a call.