It was originally written to be choreographed as a morris dance for the film by Marc Breaux and Dee Dee Wood (Mary Poppins, The Happiest Millionaire, The Sound of Music) and adapted for the stage by choreographer Gillian Lynne who also created the choreography for Cats and The Phantom of the Opera.
The song and dance are performed by Dick Van Dyke and about fifteen other men.
[1] In the film, Caractacus Potts does the dance to escape an angry victim of his malfunctioning hair-cutting machine.
Songwriter/lyricist Robert B. Sherman was inspired to write the song by his own use of a bamboo walking stick, which he used after a World War II knee injury.
[1] It is very similar to the song "Step in Time" from Mary Poppins, also written by the Sherman brothers, with a dance choreographed by Breaux and Wood, and performed by Van Dyke.