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Apropos of nothing - a random HP thought.
Where does half the fandom get the impression that Harry is cheating by using a book with notes in it?
They are allowed to use their book while brewing and are supposed to have read up on the potion they are preparing in class.
And in written tests, I doubt they are allowed to use their books anyway, so the notes won't be any help to him there.
The only difference I see between Harry and a Ravenclaw (in this instance) is that the Ravenclaw would have made the notes himself - and probably not in the book, but on a spare bit of paper.

no subject
Imo, he did both. One of Hermione's pet peeves in HBP was that Harry seemed to carry the book everywhere, whether or not they were actually in class. In the library before Madam Pince arrived, he was taking notes from the book -- this qualifies as learning, same as taking notes from a chemistry text would. Furthermore, we know for a fact that he learned the spells of the HBP from the book. We know for a fact that, even if he used the "bezoar" trick in class, the lesson actually stuck, so this, too, qualifies as "learning".