Jazz improv lessons at the beginner level involve teaching students what to play, having them emulate it, and gain "fluency" as they apply it. At the advanced levels, lessons are totally different. The idea is to get the player connecting with what is already inside and explore further possibilities. For this reason, it is important to help musicians get over their fear of singing and vocalizing. (I can't tell you how many musicians I work with who refuse to sing what they play.) My experience is that once a musician can sing what he plays or hears, he or she will quickly learn that most of what there is to learn is already there, it's just a matter of connecting the hand with the mind of the mouth. After that comes the "Why don't ya's"... for example, why don't you raise this or that tone, or why don't you combine it with this or that idea? The end result, is a method that involves listening to and studying other players, coming up with ideas, then engaging in "self transcription" in order to connect with one's true inner voice and combine different influences an ideas.
Here is an example of a typical approach:
This is an example of an advanced level lesson!