The primary skills of jazz are improvisation and ear training. All jazz music is rooted in the blues, so in order to learn jazz, one must first learn to play blues. Rhythm challenges abound in the music, so students must become rhythmically strong in the early stages of learning. I also recommend some classical training for all of my jazz students, as jazz and blues evolved from European as well as African music.
Partly because jazz is much newer than classical music, the pedagogy is much less developed. Although many effective teaching resources have emerged in the last two decades, they generally require students to have intermediate ability. Because of this, I created a ten level curriculum similar in concept to the MTNA classical curriculum (see my “Classical Piano” section for more on the MTNA), in part to enable beginners to play blues from their first lesson. I also have used my recording technology and music software to create playalong tracks, which simulate playing piano with a bass player and drummer.
Many people feel a strong affinity for music but struggle with traditional piano lessons. I believe Multiple Intelligence theory gives insight into the discrepancy. Multiple Intelligence theory breaks down overall intelligence into different aptitudes, such as kinesthetic, auditory, visual, interpersonal, etc. Thus some people can easily identify notes on the piano by ear (auditory), but struggle to read music (visual). In addition, highly creative people are often more drawn to the freedom of jazz improvisation.
To see more about how I teach jazz beginners, please watch the video below. The clip is from a presentation I gave about teaching blues and jazz improvising. The audience is a group of piano teachers who belong to the Oregon Music Teachers Association.
I don't hang my hat on my drumming, but drums are a useful way of teaching a lot of concepts, and I can create live interaction with my students as in the video below.