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Half-Blood Prince clearly shows that Snape's instructions regarding 6th year potions are superior to those given in the books, so much so that just blindly following them without even understanding the reason behind them lets Harry make better potions than Hermione. It's also heavily hinted that Snape invented or discovered these techniques himself, most likely while he was using the books as a student himself. Some of these techniques are so unorthodox that Hermione doesn't want to follow them, nor does she want to believe that they work.

Did Snape ever teach any of his discovered techniques to any student? Perhaps to students of Slytherin house, or in special classes to Malfoy?

Any canon level answer is welcome.

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    It's actually criminal that Snape did not.
    – TheAsh
    Mar 10 at 0:02
  • Perhaps it goes to show that Snape does not really care about being a teacher. He's a talented potion-maker, obviously, but does not seem to bother teaching past the "approved curriculum".
    – Turbo
    Mar 10 at 14:32
  • @Turbo in his defense he only gets paid for teaching the "approved curriculum"
    – user13267
    Mar 10 at 15:31
  • @user13267 Yeah but I meant to allude that he doesn't really have a "teaching spirit". . . He's only teaching to A: Watch over Harry, B: Conspire with Dumbledore, and C: Make Voldemort believe he's an undercover Death Eater. I don't know of anywhere in canon it says "Snape wanted to be a teacher."
    – Turbo
    Mar 10 at 15:40

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Not that We Know of

There doesn't seem to be anything indicating Snape taught the techniques from his copy of Advanced Potion Making. However I would disagree that we have proof Snape invented/discovered these techniques.

Potions is generally billed as being the equivalent of a chemistry class, where students follow specific directions to observe specific results. However by NEWT level that does not appear to be what's happening.
For example in Harry Potter and the Half-Blood Prince Slughorn states that "by an almost alchemical process" a student can divine the extra ingredient needed to create an antidote for a multi-poison potion. He also claims in his first class that he "does not expect" students to create a perfect potion even though they have step-by-step instructions and all the ingredients to do so. Later (forgive me I don't recall the exact quote) Slughorn expresses the thought that a "real" potion maker needs independent thought.
Therefore I submit that, at the NEWT level, the potion instructions are INTENTIONALLY DESIGNED to create not-quite-perfect examples. Students are expected to either use the theory to determine what extra needs to be done, or presumably the not-perfect potions are discussed in lecture.
Hermione not being able to progress beyond the given instructions even though she memorized the theory (and remember even in their antidote-making class she doesn't seem to get it quite right) is in keeping with her coming in second in Defense Against the Dark Arts, where her problem of turning "book smarts" into actionable results also comes into play.
Therefore I submit that Snape's notes in his textbook are more in keeping with a cheat-sheet of answers rather than "new techniques" and teaching them on the "front end" would miss the point of the practical potion-making exercises.

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    Overall this is sound logic, but as for the last part about it being a "Cheat Sheet", if I recall correctly some of his notes directly contradict the explicit instructions in "Advanced Potion Making"
    – Turbo
    Mar 10 at 14:29
  • This is precisely why the test-results based teaching paradigm we use in the US is so useless. It teaches wrote regurgitation, not the ability to think. </OT rant>
    – FreeMan
    Mar 10 at 16:56
  • @FreeMan: Eh, except, of course, that we get examples in the book of how badly things can go when the instructions aren't followed, c.f. Neville's various accidents. Similarly, high school chemistry classes often discourage changing of parameters, although my high school teacher welcomed people questioning, and would supervise approved modifications under proper safety precautions (and would warn us if the materials were likely to create a hazardous situation).
    – FuzzyBoots
    Mar 10 at 17:20
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    Turbo they contradict the instructions but, as the book shows, he still gets the best answer. Potions doesn't seem to be a "show your work" type class, you just do the thing and the end result is what matters.
    – Dario Quint
    Mar 10 at 17:42
  • @Freeman things CAN go badly wrong. Which is why I don't think the pre-NEWT potions classes worked this way. The OWL requirement weeds out those students that can't handle the added complexity/danger of "the instructions aren't necessarily correct". I would also point out Hogwarts/wizarding world in general are much more unconcerned with injury than the real world. Even the normal potions class has FAR more accidents and serious injuries than would ever be acceptable in a chemistry class.
    – Dario Quint
    Mar 10 at 17:46

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