Symbolism, Imagery, Allegory
Ichabod is a smarty-pants. At least the people in Sleepy Hollow think so. We are seriously starting to doubt that he has read anything besides that old copy of Cotton Mather's History of Witchcraft that he carries around with him, because that is all he talks about. On the other hand, he owns a book! Several of them, actually! Back then, that was like having a bunch of iGadgets the day they come out. It meant that you were fancy people.
But being a teacher in Sleepy Hollow isn't all it's cracked up to be. Parents find it hard to see why they should pay such a hefty fee for schooling, and they think that teachers are just "drones" (1.12). And in the end, Hans Van Ripper burns Ichabod's books and takes his kids out of school because he thinks it just causes trouble (1.70).
The reaction that Sleepy Hollow residents have to Ichabod and his books is the same reaction that they have to any science or any other "facts" that come into the town. Sure it's interesting at first, but in the end it's no good. In that way, Ichabod and his books might be symbols for truth and reason.
What the townspeople are saying is, "We don't want your reason, thanks. Our system works just fine without it." So they reject the man who says Ichabod is alive, ignore Brom's laughter, and assume that the Headless Horseman took their schoolteacher away. These are people who believe in the supernatural and are stubborn about it, to boot.