Teacher's pressing assault charges

Another post got me thinking. Should teachers be able to press assault charges against a student or is it considered being injured on the job? The particular post was about a Middle School girl upset over a teacher who was punched breaking up a fight between her and another girl. The teacher was going to press charges for assault. Should teachers be allowed to press charges against their students in cases of assault? Would it be different if the student directly assaulted the teacher? Would the age of the student matter, say Middle School vs High Schooler? Or should all punishment of the student land on the school (suspension, expelled?).