As teacher and player, Byard was renowned for his knowledge of the history of jazz piano. This meant that some aspiring young musicians sought him out as a teacher. One of these was pianist Jason Moran, who described their first meeting, at a performance by the Apollo Stompers: Jaki had all these toys and whistles and bells and things that he was playing from the piano, and also screaming and yelling from the piano in joy. I remember thinking, 'This guy's out of his mind.' After the set, I went up to him, introduced myself, and said that I would be studying with him. He said something to the effect of, 'get ready'. Moran studied with Byard for four years, and credits the older man with developing his skills, building his awareness of jazz history, and creating his willingness to experiment with different styles. Another student, Fred Hersch, reported that Byard was both organized and chaotic as a teacher: giving his students worksheets and having them study early stride piano, but also behaving eccentrically and missing lessons. Classical composer Bruce Wolosoff was taught by Byard at the New England Conservatory and counts him as an important influence.