I just started listening to a history of Jazz online course I discovered on iTunes. The author makes a distinction between Jazz and Improvisational Jazz. Jazz being the more formulated genre and improv being more of the departure from the formula. I was wondering if any jazz players would like to discuss some techniques on how they begin with a formula and then depart from it and into improv.

What I want to learn is if I take a simple chord progression like: I, VIm, IIm, V, which chord(s) in that phrase would I modify to make it swing more? The instructor in the class took a simple song in, "Mary Had A Little Lamb." He played it once straight to form. Then, over the next several times he and his accompanist went off on a trail that was beautiful. But, between the guitar accompanist walking a bass line while chiming in with a chord here and there and the melodist (a trumpeter) jumping off the chordal phrase to add and resolve tension that it lost me.

I know that there are more genres of Jazz than there are people in the world. What I am most interested in is understanding the swing and big band styles where the horn/vocal led the melody.

Any ideas?
Thanks,
RickeG