Green’s Dictionary of Slang

1. (US, also dunce-cap) a fool, a simpleton.

1868		G.W. Harris ‘Chapter from his Autobigraphy’ Chattanooga Daily Amer. Union 31 Mar. in Inge (1967) 195: Don’t talk to me, but get a broom an’ sweep me, sweep me quick, dunce head.
1912		Dly Public Ledger (Maysville, KS) 17 Feb. 12/1: A cabbage head is now worth nearly as much as a dunce-head.
1949		Monteleone Criminal Sl. (rev. edn) 77: dunce cap A backward person; a dull-witted person.
2005		aussiethule.blogspot.com 3 Mar. [blog] Bush was just a lucky dope in the right place at the right time – ala Duncehead Reagan.

2. (US black) one who shows off, ‘acts the fool’.

1980

E. Folb Runnin’ Down Some Lines 40: The implication of the social fool is aptly embodied in such name terms as [...] duncehead.