One of the main goals of introductory courses of a university is to make freshmen well prepared for subsequent intermediate courses. But nowadays it becomes difficult because academic skills of freshmen differ very much. To resolve this problem, this paper proposes an ontology-based backward learning support system called EduGraph. If a student cannot understand some learning item, EduGraph, based on its ontology, suggests him or her prerequisites for understanding the item, and he or she can learn them using EduGraph. For the student, to understand the incomprehensible item can be a short-term goal because prerequisites for it are suggested, and he or she is expected to keep intrinsically motivated to understand the item. EduGraph can also support a student to organize what he or she learns into his or her integrated knowledge, because its ontology is based on a well-designed upper ontology for learning and can organize learning items properly. Actual applications to several introductory courses from 2015 suggest that EduGraph is effective.