1) Conical headwear 2) Old school headgear 3) Quaint humiliator 4) Symbol of bad behavior 5) Topper for lazy pupil 
A dunce cap, also variously known as a dunce hat, dunce`s cap or dunce`s hat, is a device formerly used to bring about a change of mind via focusing energy into the brain, usually taking the form of a pointed hat. In popular culture, it is typically made of paper and often marked with a D or the word `dunce`, and given to unruly schoolchildren...
[n] - a cone-shaped paper hat formerly placed on the head of slow or lazy pupils
dunce`s cap noun a cone-shaped paper hat formerly placed on the head of slow or lazy pupils
a tall, cone-shaped hat formerly worn by slow or lazy students as a punishment in school.
a cone-shaped paper hat formerly placed on the head of slow or lazy pupils