The following passage is from Wolfe and Lornell's book The Life and Legend of Leadbelly, it doesn't really answer your question, but it gives a little more information:School itself even offered different types of music to a young boy fascinated with sounds and rhymes. During recess most of the boys played ball while the girls would organize "play-parties" or "ring" games. Sometimes the boys would join these activities that combined actions and songs into an infectious game, which could be expanded to fit a specific length of time. Such games fascinated young Huddie and gave him one of his first opportunities to actually sing about some part of his life. The "play" that he best remembered was one that later became one of his favorite musical pieces, "Ha, Ha Thisaway."
Leadbelly would have been at school at around 1900.
It would be interesting to know more details about the book that you found the song in.
Brian