dunce cap

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A cone-shaped paper cap, formerly placed on the head of a slow or lazy pupil.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A conical hat one pupil is forced to wear to indicate he is a dunce.
• noun The topological space obtained by identifying the sides comprising the boundary of a triangle, two sides with consistent orientation and the third with the reverse orientation.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a cone-shaped paper hat formerly placed on the head of slow or lazy pupils