Many schools have an assignment book. The students write down their short- and long-term assignments in them.
We don't have "grade books" for students - the teachers have grade books to record the grades/marks they assign.
Report cards are issued once every marking period (we get four a year here) and students don't write anything on them. In the younger grades, parents would sign the report cards; that doesn't happen in the upper grades.
We don't monitor their day-to-day behavior with the same degree of attention, apparently. For minor behavior issues, the teacher simply handles it. The student might have to miss recess, for example, or instead of enjoying lunch with their friends, might have sit in the classroom with their teacher.
The teacher can send a note home with the student that the parent has to sign.
The teacher or the principal can call the parents.
If the situation is serious, the parents might be called in for an in-person meeting.