What a classic, catchy folk song! I use this with 4th graders to teach syncopation and dotted quarter note. The instrumentation shows how I group different students to play the patterns that I want them to experience. A xylophone bordun could be added on D and A if desired. However, when I play the piano, I change chords.
Speaking of jazz, see the youtube videos below of John Coltrane's Giant Steps. I also highly recommend the book that goes with it.