When most people think of a dunce cap, what comes to mind is the pointy hat that was formerly used as a means of punishment for students in the US and Europe. The cap would often be marked with the letter D or the word "dunce," and placed upon the head of a young student who had misbehaved. The child would often have to sit or stand in the corner and face the wall while wearing the cap. Behaviors such as exchanging notes underneath the table, tossing spitballs, and being the class clown warranted a dunce cap session. Nowadays, dunce caps are not used in classrooms.
Dunce caps weren't always used for punishment, though, as the original intent behind the cap was actually a metaphysical one. An esoteric 13th century thinker named Duns Scotus (also called John Duns) believed that wearing conical hats would stimulate the brain and work as so-called "thinking caps."
From Atlas Obscura:
Scotus' life's work was all about the study of this world and the next. For some reason, Scotus was also a proponent of the use of pointy hats. It has been said that he was inspired by the use of such hats by wizards, and also conversely that it was Scotus' love of the headgear that inspired the popular image of wizards wearing conical caps. Whichever version is true, they were both meant to denote wise men. In fact, Scotus believed the pointed shape of the hat would, in some metaphysical way, act as a reverse funnel for knowledge, with wisdom flowing into the pointed tip, and spreading into the brain below.
Call me a nut, but I love the idea of a hat acting as a metaphysical funnel and I am now on a mission to make my own mystical dunce cap. I was born after dunce caps had become out of vogue in schools, so I've never gotten the chance to try one out. If the cap allows me to transcend this earthly realm, I'll let you all know.