This is covered off a bit more in wikipedia http://en.wikipedia.org/wiki/This_Old_Man

Origins and history

The origins of this song are obscure. The earliest extant record is a version noted in Anne Gilchrist's Journal of the English Folk Dance and Song Society (1937), learnt from her Welsh nurse in the 1870s under the title "Jack Jintle" with the lyrics:

    My name is Jack Jintle, the eldest but one,
    And I can play nick-nack upon my own thumb.
    With my nick-nack and pad-lock and sing a fine song,
    And all the fine ladies come dancing along.

    My name is Jack Jintle, the eldest but two,
    And I can play nick-nack upon my own shoe.
    With my nick-nack, etc.[1]

The more familiar version, with references to the "old man" and "knick-knack paddy-whack" was included in Cecil Sharp and Sabine Baring-Gould's English Folk-Songs for Schools, published in 1906.[2] It was collected several times in England in the early twentieth century with a variety of lyrics. In 1948 it was included by Pete Seeger and Ruth Crawford in their American Folk Songs for Children and recorded by Seeger in 1953. It received a boost in popularity when it was adapted for the 1958 film The Inn of the Sixth Happiness by composer Malcolm Arnold as "The Children's Marching Song", which led to hit singles for Cyril Stapleton and Mitch Miller.[3]
[edit] Sanitized lyrics

The term "Paddywack" was used from at least the early nineteenth century to describe an angry person, specifically a "Brawny Irishman".[4] From at least the 1970s sensitivity over possible racism has meant that the song is often sung as "Knick-knack patty-whack", particularly in the United States.[5]