Advanced Players: the assumption at this level is that you are already gigging, playing publically, professionally or on the verge of doing this.
Ensemble Roles and Interaction: As drummer, bass player, comping instrument
( guitar / piano ), horn or voice, your have very specific and traditional roles within the context of a jazz band. And there are other roles that you should be using to make the ensemble more "happening". The drummer is of course the time keeper, 'punctuator', framer of the soloist's phrases, the over all engine that drives the music forward in time. They can also play 'melodically', individual phrases, polyrhythms. The bass, like the drummer reaffirms the time keeping groove, but ties in harmonically with the piano player and the melody soloist. They can also leave the "walking fours" and play counter melodies and rhythms a la Scott LaFarro.The piano /guitar can be a harmonic "drummer", leading and following the soloist, playing counter melodies, reharmonizing the original changes. There are many more possibilities of course. For example a sax player can become the "drummer" or play vamp bass lines behind the bass players solo. Imagination is limitless.
However, the key to all this is "listening ", listening to yourself and the other players equally. Hearing each event you and the others are playing each moment of each bar. Why ? Jazz is a collective and normally demeocratic art form. Any member of the ensemble can take the song in a whole new direction at any moment. For this to work, every one must be listening. And so each band member decides in every moment: "what could I play that would most support the expression of the song as it is being newly created this time round?". And so at this level the focuss is on learning how to be an effective ensemble player.
Rythmic, Melodic and Harmonic Forward Motion: J.S. Bach used this and Bill Evans too. By learning to incorporate this underlying priciple of music, your solos really began to have musical integrity. Now your phrases sound like real jazz, because the rhythmic, harmonic and melodic levels are now working in sync and follow the way the ear naturally hears music.
Jazz composition: A study of composition is very important in order to learn the process of music from the opposite position of already composed pieces of music. This gives you the understanding of how the parts work in a complimentary way to make the whole. Since jazz improvisation is "composing" in the moment on one level, it is the same energy you draw upon when you compose original songs. Here we work on chord progressions / harmonic colour -their cause and effect, melodic shape, motivic development, rhythmic impact, etc., starting with standard AABA structure, Blues structure and progress to other forms. Composing in various generes, modal, bebop, latin, outside, etc., really opens up your artistic potential.
Irregular Tme Signatures: Tchaikovsky was using these by 1860, and certainly Paul Desmond's "Take Five" of the 1950s established the use of less common metres. These days one can easily encounter songs in 5/4, 7/8, 11/16. At this level you learn not only how play the heads naturally but how to phrase and feel your own improvisations in these asymetric groupings. In addition learn how to take 3/4 and 4/4 original standards and adapt them to these time signatures.
Lifting ,Transcribing solos: Jazz like any other language is well learned by imitation. One of the best ways to do this is by lifting solos by ear from recordings of various jazz artists, both for your instrument and other instruments.(there is some good "slow -down"software out there now to help with this) Then being able to play the whole solo with the original is the next step to pick up the nuances, phrases, tone colour, rhythmic feel. It is also really good to transcribe the solo, notating it gives you a much better understanding of why the solo works.