Stepping into the Hacienda Commons on a Tuesday a little after 7 p.m., I was greeted by the sight of two separate groups of dancers bouncing gracefully up and down in time to a drum, as if on springs.

TLC’s newest show, “The Big Jig” follows five American girls, all under the age of twelve, as they practice and compete for the 2012 World Irish Dancing Championships held earlier this year in Belfast ...