The Collaborative International Dictionary of English v.0.48:
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. [1913 Webster]WordNet (r) 3.0 (2006):
wrongheadedly adv 1: in a wrongheaded manner