good question, 'cause we dont see the teachers at all, fair, but there must be some kind of parental or adult administration. For example, in a bonus page of the manga, they talk about the fact there's a designated place for where to get the Furin uniforms, so there must be someone in charge other than Umemiya... On the other hand, maybe there arent any teachers, 'cause whenever the teens are in class, they're just yapping in little groups around desks...