The Collaborative International Dictionary of English v.0.48:

Dancing \Dan"cing\, p. a. & vb. n.
   from Dance.
   [1913 Webster]

   Dancing girl, one of the women in the East Indies whose
      profession is to dance in the temples, or for the
      amusement of spectators. There are various classes of
      dancing girls.

   Dancing master, a teacher of dancing.

   Dancing school, a school or place where dancing is taught.
      [1913 Webster]

WordNet (r) 3.0 (2006):

dancing school
    n 1: a school in which students learn to dance