The Dunce Hat was an archaic form of punishment in schooling that has since been decried as a form of public humiliation and is thus no longer used - prior to the Dunce Hat students were whipped by leather straps or canes, such cruel methods of discipline are no longer utilized though there is considerable controversy over whether or not to bring back the cane as a disciplinary tool.
However, the Dunce Hat will likely remain in the past as it was designed to humiliate a student, who was forced to sit in a corner - usually facing away from the class - while wearing a tall cone-like hat with a "D" on it: the punishment was most often used to try and enforce "good behavior" and was used when a child was rude, noisy, disruptive, obstreperous, or generally what we now call a "class clown".
However, some teachers also used the Dunce Hat to punish students who failed to achieve satisfactory results - though this was rare.
Examples of behavior that warranted a dunce hat included throwing spit wads, passing notes, and even laughing at a student wearing a dunce hat. Class clowns were frequently admonished with the dunce hat.