Source : Webster's Revised Unabridged Dictionary (1913)

Wrongheaded \Wrong"head`ed\, a.
   Wrong in opinion or principle; having a perverse
   understanding; perverse. -- {Wrong"head`ed*ly}, adv. --
   {Wrong"head`ed*ness}, n. --Macaulay.

Source : WordNet®

wrongheadedly
     adv : in a wrongheaded manner