The one I remember is slightly different. I think we learned it in grade 2 or 3. This is what I remember:

There was an old man
and he came from China;
His name was Chicka Racka Ching Chong Chang
Chicka Racka Ching Chong Char Chicka Roney Alaballa Fatman Oh Kokoney
Icka bye icka bye oh koh koh.

His legs were big and his feet were small,
This little man couldn't walk at all
Chicka Racka Ching Chong Char Chicka Roney Alaballa Fatman Oh Kokoney
Icka bye icka bye oh koh koh.

Here he comes
And there he goes,
Funny little man with a screwed up nose;
Chicka Racka Ching Chong Char Chicka Roney Alaballa Fatman Oh Kokoney
Icka bye icka bye oh koh koh.

**I think there may have been one or two other verses but don't remember them****
Boy were the songs politically incorrect in those days. And attitudes were a lot more racist. My family had migrated to Australia from Holland, and we were also looked down on. People called us "new australians", or "wogs".