If you're incurious, you don't care very much or aren't interested. There's nothing more frustrating to a teacher than a classroom full of incurious students.
The adjective incurious is useful for describing someone who really couldn't care less — who doesn't ask questions or wonder why or how something happens. Incurious people don't make good scientists, journalists, or researchers, because they lack curiosity, or the impulse to know more about something or someone. The roots of incurious are in-, "not," and the Latin curiosus, "inquiring eagerly."