Generally, I highly recommend the use of Wikipedia for preliminary research and common-sense doublechecking.  Once in a while, though, I find something that reminds me that if Homer nods, so surely must the Wikipedants^{[citation needed]}:

Duns Scotus was the originator of the instrument.
[…]
However, with the advent of the Renaissance and the New Learning, and then the Protestant Reformation, many of Duns’s theories and methods (e.g. hair-splitting) were challenged or rejected by Humanist and Protestant scholars, who used the term “Dunsman” or “Dunce” in a pejorative sense to denote those who foolishly clung on to outmoded doctrine. (The form “Dunce” reflects the medieval pronunciation of “Duns”.) Gradually “dunsman” or “dunce” was used more widely for anyone stupid or dull-witted.
[…]
the Oxford English Dictionary (2nd edition) records that the term “dunce cap” itself did not enter the English language until after the term “dunce” had become a synonym for “fool” or “dimwit”. In fact, “dunce cap” is not recorded before the 1840 novel The Old Curiosity Shop by Charles Dickens.

(source: Dunce cap – Wikipedia, the free encyclopedia)

Note the flat contradiction, here.  D’oh!