"Good improvisation communicates harmonic progression melodically. Effective melodies manipulate harmonic content through the use of guide tones and preparatory gravity notes, masterfully woven in systematic tension, release, and transparent harmonic definition."
Sooner or later most serious musicians take a look at jazz. The first thing that they notice is that the chord changes are more complex that rock, blues, bluegrass, fiddle tunes, or just about any type of music they have played before. These chords, combined with the fact that you may be in a new key (not just chord) every measure or so, make this music the perfect vehicle for the improviser.
Mandolin players coming from a fiddle tune background may be comfortable improvising based on the melody of a tune by using scale patterns, triplets, drones, etc. This is all good but not enough to dive into the world of jazz. In jazz, the chord changes are in many ways just as important as the melody. Another important thing to note is that the chords are not just the stuff that the rhythm section does when you are playing your glorious solo. ALL members of a jazz ensemble need to be aware of the chord changes.
As soloist we need to be aware of the chords one note at a time. In classical music we call these arpeggios. In jazz we just call them chord tones. I can't overemphasize the importance of learning (memorizing) chord tones. I believe that leaning chord tones in jazz is the equivalent of memorizing you multiplication tables. Remember those? Remember how we all sat there behind our desks wondering how we could ever do this and why were we being forced to memorize this rubbish that would never help us later in life.
OK. In Jazz we have melody and harmony (chord changes). In order to interpret, embellish, or replace the original melody, we look to the harmony or the chord changes. This first thing we need to have memorized is the chord progression to a song. Next would be to know ALL of the notes in each and every chord in the song.
Once you have reached that point with a jazz tune, I have an exercise that will work wonders on your ability to solo over the chords. It is quite simple. Play through the changes of the tune using only chord tones and only quarter notes. When moving from one chord to the next, try to use the shortest distance possible. We call this good melodic voice leading.
Take it slow at first. Don't Give Up! This is tough but it is really worth the effort.