Mysteries of the (Harry Potter) Universe

We know that Professor Binns the History of Magic teacher at Hogwarts is a ghost. We know from Nearly Headless Nick's Deathday Party (Chapter 8, Chamber of Secrets) that ghosts can't affect physical objects. We know that Professor Binns assigns essays to be written on rolled parchment (Chapter 1, Prisoner of Azkaban). How does Binns grade the essays?