Okay, I have some ideas for the notebooks. We aren't even getting into my curriculum and other subject ideas here (which would be very good), just the currently-existing notebooks.
First, pausing the game will reload any unsolved notebook problems (or restart the notebook in History).
Secondly, if you make a mistake, you can go back to the task and try to solve it correctly to reduce the teacher's anger by 1. However, if you make more mistakes, the teacher will become angrier accordingly.
Because of that, in math and history notebooks, you can click on examples to select them (except for ones you haven't reached yet).
You might also be able to put notebooks in your inventory. If taking up slots is too much of a problem, you could have them in seperate slots, or have a deposit for the notebooks you collect. That way, you can also use them again to look through problems you've solved. You should also be able to "return" any notebook.
I also think the notebook UI should be like those of the rest of the items, and dim the background instead of replacing it with black. That way, you can look up at the door while solving a notebook and make the final chase more cinematic if you want.