A dunce cap is a mystical and traditional piece of headgear.
It is named for the Scottish theologian-philosopher John Duns Scotus. As it is today, just being a Scot alone was good enough for derision, but fundie Protestants mocked him for being a thinker and Catholic at the same time, an obvious oxymoron.
Soon, pointy hats made of rolled-up paper were created and named for him. Not very creative, but only Buddhists knew how to do origami at the time. Those dunce caps or dunce hats were used to then mock and punish misbehaving schoolchildren, small animals and mass murderers. However, those groups got the last laugh since they now had ready-made costumes for Halloween. Meanwhile, as a badge of martyrdom, Catholics adopted the pointy hat for members of the Spanish Inquisition as well as their offshoot, the Ku Klux Klan.
Today, the dunce cap is known as a fashion statement used by wizards as well as a place for them to hide snack food and rolled-up comic books. This is an example of ironic behavior as most wizards were class clowns as children.