From Wikipedia:

A dunce cap, also variously known as a dunce hat, dunce's cap or dunce's hat, is a pointed hat, formerly used as an article of discipline in schools in Europe and the United States—especially in the 19th and early 20th centuries—for children who were disruptive or were considered slow in learning.

I might be bad at searching but I didn't see one for Illustrious so I thought, why not?