What kind of school is Yancy Academy?

Yancy Academy is a private, boarding school for troubled children in upstate New York.  Percy tells us that the school encourages the students to learn by taking them on a number of field trips, trips like the one he takes with Mr. Brunner and Mrs. Dodds (a Kindly One in disguise) to a local art museum.  He says that most field trips that he's gone on since continuing his studies at Yancy have been "torture," but this could have more to do with Percy's sense that he is not a good student rather than anything to do with the school itself.  He does admit that field trips never seem to go well for him no matter what school he's attending.  So, other than the fact that a demigod and satyr attend the school under the protection of a centaur, Yancy Academy seems like a pretty typical school trying to work with students who have struggled academically and personally in the past.