In this paper we demonstrate how Stroemgren uvby photometry can be efficiently used to: 1. identify red giant branch stars that are members in a dwarf spheroidal galaxy; 2. derive age-independent metallicities for the same stars and quantify the associated errors. Stroemgren uvby photometry in a 11'x22' field centered on the Draco dwarf spheroidal galaxy was obtained using the Isaac Newton Telescope on La Palma. Members of the Draco dSph galaxy were identified using the surface gravity sensitive c1 index which discriminates between red giant and dwarf stars. Thus enabling us to distinguish the (red giant branch) members of the dwarf spheroidal galaxy from the foreground dwarf stars in our galaxy. The method is evaluated through a comparison of our membership list with membership classifications in the literature based on radial velocities and proper motions. The metallicity sensitive m1 index was used to derive individual and age-independent metallicities for the members of the Draco dSph galaxy. The derived metallicities are compared to studies based on high resolution spectroscopy and the agreement is found to be very good.