A catalogue with copies, issues and returns, and fines that follow the student rather than living in a separate notebook that only the librarian can read.
Titles and copies are different things
A title carries its ISBN, authors, publisher, edition, language, category and tags. Copies are counted against it with a shelf location, so six copies of one book is one catalogue entry and six things that can be issued.
Issue, return, overdue
Books are issued to members and returned against the same record, so what is out and what is overdue is a list rather than a memory. Members are the students and staff already on the roll.
Fines that can be waived
An overdue fine can be charged and, when the school decides, waived — with the waiver recorded. Librarians forgive fines all the time; the software should let them do it openly.