Model of teacher, student relationship

An important characteristic of education is the relationship between the student and the teacher. Not an intimate one, obviously, ew! But what I mean is there is a relationship between variables like the amount of time the students spend with their teacher and assessment of the student's progress in the semester compared the teacher's goal for the dynamic of the semester. So the student could go towards the approximated line the teacher sets as where they want their students to reach or away if the student struggles and never meets the line. There must be some model of the relationship between the teacher and the student. I'm not sure what it is, but it might be fun to think about it further. What do you think about the relationship between the teacher and the student?