[Throwawayaerlei]

While I'd already done real research in high school in a NSF Summer Science Training Program, the UROP work I did was as you describe. We didn't actually solve the problem, it was hard enough it took academia and industry another half a decade, but the process under the direct face to face supervision and participation of a professor was fantastic. The background to the specific problems I learned in both research experiences help me to this day.