This was a 1960's style hat consisting of a beanie-style cap with small brim in front and often with school initials or logo, once optimistically 'required' of freshman males at certain universities. To be seen in one permanently labeled one as a dork.
Rat caps seem to be making a comeback, as ironic retro wear.
Freshmen were supposed to wear rat caps while on campus at Georgia Tech. You risked the penalty of having your scalp shaved if you didn't.