Creative art is a process of shaping into physical reality what originates in the imagination, tied to emotion. There are, as yet, no effective objective standards by which to test artistic creativeness. Schools are smart enough not to give degrees in it. But, they effectively obfuscate this situation by producing teachers who become accepted as such because they have been given a degree to teach in this or that art. The scientific process is to objectively observe - to analyze.
Analysis belongs to study.
Playing and studying are two different things. To try to put the two together simultaneously is much the same as to both see and be the view simultaneously. Teachers who themselves cannot make jazz cannot teach it. Perhaps what they can do is approximate jazz. There are exceptional musician-teachers.