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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.

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If making potions is supposed to be a test, then using the HBP book is cheating--but it makes no sense that the students are allowed to use textbooks at all. If it's supposed to be classwork/homework, it's not, any more than I was cheating by asking a friend to take notes to me or explain those notes, or than someone reading a Cliff's Notes volume is cheating at English class, or so forth.
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I mean Snape gave his class a wonderful mixture of theory and fact-based study, grading them on written homeworks he asks to hand in as well as class performance, from what we've seen. I guess with such bad teachers as Slughorn, the question of whether one of his students is cheating becomes sort of moot.
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Both require the brewing of potions, both give homework, both don't actually explain very much. (I might not remember it correctly, but I think Slughorn actually has more scenes where he explains things than Snape.)
And where did you get the impression that Snape actually requires an understanding of theory in class? Since no one but Hermione has any idea what to do in the antidote lesson, I'd say the concept of understanding the inner workings of potions was a new one to the whole class - after five years of Snape's teaching.
Potions is an open-book class that is graded on the results in the first five books as well, the only thing that's changed in this book is Harry's attitude.
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As someone else said, the closest subject to Potions is probably cooking. As I've never taken Home Ec, I'm not sure of the grading system there--if you were baking cookies, your mother had always put in lemon instead of vanilla, you did it that way, and they turned out better than everyone else's, is that cheating? Would it be cheating if you'd brought in a recipe from _Good Housekeeping_? And what's the difference?
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