It depends on a couple of things, and it's rather complicated.
First, copyright law says the video that you make with your equipment belongs to you the videographer, not the performer or the parents. You own the physical object, just like the photographer who takes your picture owns the original negative and photograph, not the person who sat for the photo. There's no question about that. When you need copies, the photographer/videographer sells you copies but not the originals. They own the originals and the rights to it.
Second, the rights to the performance vest with the performer or their agents. So while you may own the video recording/photo original, you do not own the rights to the performance. SAG, AFTRA, BMI and ASCAP have made sure of that. If you intend to sell copies, then you will need permission from the artist or their agents. Performances are usually sold by license from the artist(s).
Third, I myself would never sign a video release for my kid under these conditions. You'd never know what use it could be put to.
Fourth, are verbal agreements binding in your state? They are in California. You should find out before discussing the issue with your students.
If your intent is to use those videos strictly in-house, for you and the parents, you don't need to get them to sign anything. And with this intent, I don't believe you need their express permission to make such a recording. De facto, I think they give this tacitly when they walk through your front door. Just don't post them or try to sell copies without permission or fair compensation changing hands.
Last edited by laguna_greg; 07/13/13 01:57 PM. Reason: more thought of something more