Okay, here goes. You indicate your age by remembering that the masculine prevails. If it’s any consolation, when I went through school, it did too; but long ago women argued rightfully that this was sexist. So, if you know the student is a male, it’s fair to say, “The student left his books at home.” And, if you know the student is a female, it’s equally fair to say, “The student left her books at home.” If you don’t know the gender, using his or her every time becomes awkward; so the best thing is to remove the pronoun in front of books. You could say, “The student left the English books at home.” As for your students who want to substitute “their,” they can do that only if they know that more than one student left books at home. In case they don’t understand why, it’s because “their” is a plural possessive pronoun and refers to students rather than student.