Lewis & Short

măgistrātĭo, ōnis, f. [magistro],

  1. I. instruction, schooling (post-class.): quae magistratione discuntur, App. Dogm. Plat. 2, p. 15, 15 (al. magistrā ratione).
  2. II. Transf., concr., a school: in publicis magistrationibus, Cod. Th. 14, 9, 3.