You know a good place to start might be to find easier arrangements of jazz melodies (with a bit of a classical influence.)
I know George Shearing for example has written many nice arrangements with a classical influence. There are also many others and if you like a can PM you my favorites. I have a few books that use all the standard jazz voicings and embellishments that are also really easy to play and I think good for sight reading practice for example.
Strictly speaking a big part of jazz instruction is learning to play without notes and adapting you're playing style to the environment. That is, as a jazz pianist you might expect to play with or without a bass player, with or without a soloist and or other rhythmic instruments. I know some jazz pianists don't start out playing jazz by reading music but some of course do. I suspect most classically trained pianists would feel comfortable starting with a score in hand.
Also playing without a score is not something we learn over night I think (not that I am the expert here.) Its really a different way of looking at practicing and playing the piano (which requires a lot of discipline.)
Also, I meant to ask on that last post, but forgot.
I have a student interested in Jazz. I was wondering if you could give me the early composers that had the most influence on jazz. And, I know this is a classical forum, but maybe someone could give me tips on teaching jazz. I'm classically trained, so I will have to learn a lot of it as I go.
The reason for this post is that I still think he needs to play the classical stuff, but I thought I could gear it towards jazz to make it interesting for him.