Source : Webster's Revised Unabridged Dictionary (1913)

Approving \Ap*prov"ing\, a.
   Expressing approbation; commending; as, an approving smile.
   -- {Ap*prov"ing*ly}, adv.

Source : WordNet®

approvingly
     adv : in an approving manner; "she nodded approvingly" [syn: {with
           approval}] [ant: {disapprovingly}]