Maybe in final chase teacher doesn‘t give a damn f*** anymore, if you look at him or not and we come back to the good old running away as fast as you possibly can part. As for the doors, maybe later it‘s possible to open them, even if you‘re not directly looking at them. Or maybe on a map with a teacher like that, there will be no doors at all.
Edit: And when you solved a notebook, you have about 5 to 10 seconds time, before teacher attacks you. For that time, he/she could be disabled, so he/she doesn’t attack you even if you‘re not looking at them.