Sit down and tell them just how important these schools are to you. Be sincere and gracious, but definitely stay away from a deserving or "I'm entitled" type of persuasive argument. This is your future they're handling, and make sure they understand that. That said, make it as easy as possible for them, by doing things such as printing the forms out for them and addressed, stamped envelopes. Make it seem like a big deal that, assuming this teacher is apprehensive about going the whole 9 yards, requires little effort.
P.S.-When I did mine, I put chocolate with the forms. If your teacher is that way at all, it's never a bad idea.