With piano improv, I’ve found it best to work on 2 levels at once:
1. Practicing something very specific which you drill and drill over and over.
2. Relaxing our previous way of trying to play and broadening into a deeper experience of the music. This creates vast improvement very quickly.
An example of #1 would be to focus on RH soloing. Focus on one aspect of soloing at a time, and go into it in great depth. One thing I teach my students, for instance, is how to take a melodic motif through the chord changes of a jazz standard, such as Have You Met Miss Jones. Then to use a different motif, then another, and play with each motif through all the chords in the tune. Once the student can do this thoroughly and on a few different tunes, we begin to explore various methods of motivic development, and then the overall construction of solos. You can do the same thing in any musical genre, including rock, pop, blues, Latin styles, folk, and classical improv.
#2 depends on the individual student, and it’s different for everyone. Some players greatly benefit by playing simple melodies very slowly so they “hear” each note deeply, while others benefit more from doing improvisational exercises in all 12 keys. Some players need to think about the music more analytically, while others improve instantly by “letting go” and feeling the flow of the music more naturally.
In general, it’s best to follow through with what you’re working on, and not bounce around too much. Or, you can have fun bouncing around after you’ve assimilated while practicing #1 above.
And at the same time, go deep. Very deep.
Working on 2 levels at once is essential for our musical improvement.
As always, be sure to enjoy the journey and “let the music flow!”