One of the best vehicles for teaching group improvisation is Soundpainting, a sign language for live composition.
Steve Soundpainting, see video below
Soundpainting was created by Walter Thompson in 1974 while studying with Anthony Braxton at the Creative Music Studio. The language is multi-disciplinary, so each gesture can be interpreted by musicians, dancers, actors, visual artists, and poets.
I had a blast Soundpainting with a high school jazz band last weekend. I give an explanation and demonstration to the audience and composed/conducted a couple pieces. (I simplified some of the gestures and incorporated a couple signs from Butch Morris’s Conduction system).
Be sure to watch a student and 7-year-old volunteer conduct the band at 9:30: