Did you know in order to teach stay correctly and quickly you should always return to the dog?
If you don't come back to the dog you're not actually rewarding the dog for staying. A common mistake I see people making is they will ask their dog to stay and then recall it. That won't help your dog learn as fast!
The goal in moving the treat over the dog’s head is that, as he is looking up at the treat, he’ll will then place his back-end on the ground, and sit to look at it. At that precise moment, we would reward the dog (tasty treat, petting, play, etc…) for doing so.
During this stage, he is becoming more and more alert to what he’s been seeing and/or hearing, and proficient in knowing what he needs to do about those things, when he sees or hears them.