A dunce is a dummy — someone who isn't smart. You might be tempted to call your little brother a dunce when he walks out the door with his shoes on the wrong feet.
It's not nice to call someone a dunce, though you might call yourself one when you study the wrong chapter before a big history test or get pulled over for yet another speeding ticket. The word dunce comes from a thirteenth century Scottish philosopher, John Duns Scotus, whose resistance to new ideas and mystical beliefs inspired opponents to equate his followers, the "Duns disciples," to "dullards." Later, some teachers made children wear pointed paper "dunce caps" when they misbehaved.