I certainly agree that class notes are owned by the author/student. Does this reasoning extend to work completed by students on exams? State and national standardized exams routinely collect student work and keep it, for reasons of test security. Do students have a right to retain this kind of IP as well? Or is this work in some way different from the note-taking?
Full disclosure: I work in the Science department at a K-12 school where teachers occasionally re-use problems from one year to the next, often AP problems for which we have statistics that we can use in helping to evaluate a student's work. We routinely retain tests, again in the interest of test security.