tl;dr version: Dumbledore and most of the magical world believe in the Platonic idea of knowledge - it's discovered within, rather than taught.
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In a fic I'm writing, I've somehow written myself into answering the "Why didn't Dumbledore train me?" cliche. I wanted to throw out my answer to DLP and get your thoughts.

To set up the scene, Dumbledore is dead, as well as almost all of the teachers and students in a massacre when Voldemort returned. Harry is attending Durmstrang, where he's learned quite a bit of theory about Dark Arts. During a discussion with Sirius at Christmas, he asks why Dumbledore didn't teach him this stuff, and how to fight if the prophecy was hanging over his head this whole time.

My answer is:

1. Because either a person has magic or doesn't have it, magic cannot be taught.
   
2. Most people, and the overall teaching theory at Hogwarts (and the wizarding world) is Platonic, rather than Aristotelian. Each wizard or witch has the knowledge within to use magic. The role of the educator, is to illuminate the pathway so the student can find that knowledge within themselves.
   
3. Harry had to learn far more than just magic due to the prophecy. He had to learn how to use his courage, make quick decisions, face death, etc.
   
4. In order to do accomplish that, Dumbledore allowed Harry to save the Philosopher's Stone his first year, and had plenty wards in place that protected them from getting hurt more than they would have in any normal Auror's training. (though Dumbledore was surprised and saddened by the death of Quirrell).
   
5. Since Dumbledore is dead and Sirius never asked about Harry's second year, (He did ask about the first year in the background of my fic), Sirius surmises that Dumbledore was as caught by surprise as the rest of the school concerning the Basilisk. But that he kept tabs on Harry and watched how he was discovering his knowledge from afar. But Dumbledore was afraid of getting personally involved and throwing off Harry's discovery of his knowledge. He also didn't know what was happening to Ginny, or he would have gotten involved immediately (staying the hell away from manipulative Dumbledore/Greater good Dumbledore tripe).

Obviously, for something like history, this methodology doesn't work (which is why Binns lectures). But since, in all the classes where elements of magic are taught, there seems to be a little discussion/lecture up front, followed by a whole lot of experimentation - or the students finding their own knowledge in using magic.

Wand waving and speaking the charms/spells/etc. is part of illuminating the pathway to their knowledge.

 

You come across a little contradictory here. I think you need to really consider the differences between knowledge and understanding. You say magic can't be taught, but clearly spells are taught in the manner of basic factual information. Wave a wand, say a word, and a feather floats. It may be only part of reaching the greater knowledge of magic as a whole, but it is knowledge nonetheless.

Better to approach it as an understanding of magic must be discovered by each individual. There are basic immutable facts, such as the methodology of casting a levitation spell. This can be taught. But that's just a tiny facet of magic, a single example of cause and effect. A series of taught things like this, the spells, give experience and exposure to magic, and form a fundamental bedrock from which the aspiring wizard can find what you described as the knowledge discovered within.

Think of it as music. Someone who has never played an instrument could learn the movements to make and play a single piece of complex music perfectly,yet not know what they're doing. Someone who has studied it beyond this level has gone beyond mimicking tunes and sees the way sounds fit together, what effects they can have when used just so, and can theoretically strive towards playing anything or composing something different to gain a new or specific effect.

Rather than claiming magic cannot be taught, say it can only be taught up to a point, and after that, the student has to develop their own insight and understanding.

I know I'm arguing semantics here, but if you want to focus on this kind of diretion, they are very important. If you want to have magic literally unteachable, and everything I've said so far is irrelevant, you'll have to change the system of charms and spells completely, which your last line seems to imply you're not doing. If you were, you'd do well to look at the Dresden style of magic, where mages essentially create their own spells to suit their needs, reflective of how they approach the issue.

 

This conflates two very separate issues: having magic, and using magic. Having magic is binary - you have it or you don't. Skill at using magic isn't binary, but forms a continuum. It can be taught.

Not sure why you're bringing either Plato or Aristotle into this. I don't see what either adds to the discussion.

We see very few lessons at Hogwarts, and not once do we know the structure of the full lesson. Either we see the beginning and not much else, or we enter into the lesson in a "practice" part, where Harry, Ron and Hermione are chatting while practicing something as a backdrop. So I think you're reasoning from a flimsy base here.

Anyway, a "PPP" lesson - Present, Practice, Produce - is a pretty typical lesson format in the Muggle world for learning languages, and Hogwarts seems to adhere to it pretty strongly. Which isn't surprising, as JKR was a foreign languages teacher. Snape, on the other hand, teaches using a more modern (and supposedly more effective) method - the TTT method. Test, Teach, Test.

I've always thought that learning magic in HP is very similar to learning a language. You have theory (grammar) and spells (vocabulary). A student learns how to produce spells correctly via structured practice, where they are following the grammar. After a time and much practice, the spell seems to come by instinct (fluency). If one wishes to go deeper, there's more esoteric theory to learn while underlies the spells (linguistics).

Again, given that JKR was a language teacher, not surprising.

The answer to the question "why didn't Dumbledore train me?" has two very simple answers.

Firstly, Harry isn't that good, and magical knowledge is just like Muggle knowledge. You can't learn quantum field theory without first learning calculus (and a load of other stuff besides). You can't learn advanced magic without knowing the more fundamental stuff. Given that Harry was struggling in HBP to perform (not even master, just perform at all) the magic he was learning in class, it would be pointless to try to teach him more advanced stuff.

Secondly, Harry isn't that good, and even if tutoring him intensively did improve his ability, he still wouldn't be anywhere near good enough to beat Voldemort by conventional magical means.

 

The whole "let's leave Harry at the Dursleys so he doesn't know magic exists" thing is quite contradictory to the idea of Dumbledore passive-actively guiding Harry to "find magic in himself". And to be honest the "Dumbledore set the obstacles around PS as a test for Harry" -cliché is ludicrous and beaten to death. Why he didn't do something similar in the later years, if it really was a good idea?

You can rationalize away Dumbledore not personally tutoring Harry (maybe he didn't believe Voldemort would return before Harry turned, say, thirty, or maybe he just didn't believe in the prophecy in the first place), but I don't think you can say he actually was teaching him, only in an extremely convoluted roundabout sort of way.

The idea in itself is interesting I think, but it requires more than just trying to rationalize canon with it, just like CareOtters said.

 

This seems like it could be an interesting idea, with some work. Like, a teacher just shows them one method of casting a spell, and not necessarily the easiest. There could be a dozen different ways to cast a Levitation Charm for example, and there's nothing to say that there aren't more than one. Also, the important part of the lesson wouldn't be the spell itself, but rather the methodology being it, the feelings when being used, subtle techniques that you will only learn from practice and aren't something that can be taught. Magic responds slightly different to everybody, and it's up to the individual to figure out all the quirks, and how to be the most efficient with what they got.

It could be interesting, and the old saying 'You can lead a horse to water, but you can't make them drink' would seem to fit perfectly.

 

I forgot to mention - My universe is AU after GoF, so anything after that doesn't matter for my story.

Also, (though it's probably fanon more than canon), I'm accepting the idea that magic really can't be controlled until they're a bit older, which is why Harry isn't really as far behind everyone else as he seems to think, and by the end of the third book, at least with the Patronus Charm, he's got a good handle on at least part of his magic, and it's very strong as well.

Let me clarify a bit what I mean by "not taught." I'm taking the example from Xenophon's Economics (which is why I started thinking about this, and yes, I'm paraphrasing tremendously here). Socrates doesn't know about threshing, and Ichomachus is illuminating the path for Socrates to find out that he does know about it.

This is opposed to approaching Socrates as if he knows absolutely nothing about threshing, and must be educated on every element of it.

So, reapplied to magic, especially in the way Dumbledore was using the method, instead of a Socratic question and answer, he was putting things in Harry's path that made him ask the right questions for himself, or discover the answers for himself.

Applied to classwork, I can see where you're coming from, CareOtters, and maybe there's a combination there, where certain elements are taught, because that is the best way for the student to then discover their own knowledge of their magic.

Understanding/Knowledge, you're right, I do need to think that out a bit more, because I want to default to understanding when it comes to magic.

 

Pedantic mode: active.

That saying is about effort. The idea is that you can provide a person with every opportunity to succeed, but if they don't want the opportunities then they still won't succeed.

Here it's not about effort. The idea being presented is that magic fundamentally cannot be taught. In such a case you could try to create opportunities for someone, and that person could try as hard as possible to grasp those opportunities, but they still fail because the idea is intrinsically deterministic: if potential skill with magic is inborn and the process of education is just drawing that knowledge out, then the level you are going to reach is pre-decided. It's Calvanism all over again.

So the appropriate idiom would be "You can lead a horse to water, and the horse can try to drink, but God has tied some horses' mouths closed."

 

Imagine my surprise to see a reference to Calvinism here. I've grown to understand the level of knowledge on this board is rather high, but that was a shock.

I'm not sure that it's Calvinism however. There is much individual effort needed in order to seek out the knowledge/understanding (still haven't worked that out) of one's magic. Also, other things may hinder the discovery. Neville is a good example, as his issues with his parents hinder him quite a bit (again, fanon, but it makes sense).

So here, "learning" is really showing the students the pathway to their magic, and then it's their own magic which ultimately teaches - once the path to the magic is fully and completely exposed. It's why it seems that there's a lot more magic being used then what's taught at Hogwarts, even amongst those who probably would have never researched on their own. I think it also explains the differences in abilities - such as Harry and defense, the twins and charms, Hermione, etc.

 

Really? You find reference to Calvinism shocking? Maybe you should stay away from other threads, because they may blow your mind.

The canon is rather clear that Neville's problem was his father's wand that didn't work properly for him.

While I like some parts of your idea, I disagree that it fits with what we know about magic from the canon. But hey, it's fanfiction, so do whatever you want.

 

Really? His wand didn't break until the end of OotP, but the real turn around happens as a consequence of Dumbledore's Army. He starts to learn spells nearly as fast as Hermione because he finally has confidence, not because he has a new wand. It's never even mentioned again after he says something about it at the beginning of HBP.

EDIT: Well, maybe it's motive. Bellatrix's escape did upset him quite a bit.

 

But there is something in the books about his father's wand making it harder for him to use spells, right? Or did I just mistake fanon for canon which would be somehow embarrassing.

 

I think it may be fanon. I certainly don't recall him complaining about his wand once he had started to do well in DA. I'm sure it was a factor to some degree, but Neville's problem, IMO, was always primarily mental. Not so much that he was stupid, but that he found it impossible to believe in himself.

And say what you will about the academics of magic, but believing you can do it and having the determination to keep going until you do are essential, and Neville never had that until fifth year. Having his own wand probably helped him pwn in DH, but confidence was the major hindrance.

EDIT: IIRC, he does mention having his dad's wand, but he never cites it as an excuse for poor magic. I think that was left to the reader.

 

I think you've overestimating Neville's late blooming. He still didn't get a good enough grade to get into NEWT Transfiguration, remember, and only an E in Charms.

It seems to be a rather DADA-specific blooming of talent. And even then, perhaps only when it's taught by Harry.

 

I'm not saying he's that good, just that the problems he had were more about confidence than having a lame wand. Or at least, his dad's wand didn't stop him from improving significantly in OotP.

Unless it's a question of whether his agitation at Bellatrix's escape overcame the lameness of his wand. At that point, I wouldn't know.

 

I just find it shocking because I don't come across it that often in general discussion, and definitely not in the fanfiction world. I'll be fine, as long as we don't get into a friggen discussion over TULIP. :awesome

I think that can be surmised from canon with the whole, "The wand chooses the wizard" thing, but it's not the whole issue. And I think I can make a case as well for a wands to be part of the "illuminating the pathway to knowledge" each person has to take.

 

You're writing the fic, you can do whatever you want. But trying to claim a canon basis for what you're writing when there isn't one is just silly. Don't focus on defending what you're writing by trying to connect it to canon. Defend it by saying "I'm writing an AU fic, this is how magic works."

As an idea for magic, it could make an interesting fic. Personally I think its potentially a bit limiting, making Hogwarts about self-discovery rather than being taught how to use magic. It kind of majorly changes how Hogwarts would work. Classes wouldn't be based around the teaching of spells, but of understanding the concepts behind using magic, and facilitating students in working out how their magic works.

God alone knows how standardised testing would work...

So yeah, the idea has merit if you make it wholly AU. Which is fine, its fanfiction. Make it as AU as you want, so long as the writing is good people'll still read it.

 

Calvinism comes up unusually frequently in the context of HP (i.e. more than not at all) due to that it's pretty easy to argue that the entire series is a misunderstanding of the Calvinist idea of predestination.

 

Interesting, though I don't see a lot of similarity, since Calvin's institutes are much more about the sovereignty of God than about predestination of man. Hence, if there is no deity determining general course of history, the entire Calvinist system (whether the institutes, or later 5 points of Calvinism) falls apart. Since I don't see the question of a sovereign deity in the HP books, I'm not sure how that connection can even be made, except by the most overgeneralized terms.

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Thanks everyone for the input. I think I'm going to scale it back to it being Dumbledore's methodology and the way he taught specifically, and that the newer teachers use a much more integrated method. That'll sidestep a lot of these questions I believe. Since this is really only going to be used in the discussion between Harry and Sirius, I've decided that I don't need to be as detailed as I was here. It'll just be a general discussion, and then I move on with the fic.

 

When talking about teaching methods at Hogwarts, I always like the idea of it being like upper class schools in Britain of over a hundred years ago when Dumbledore was in Muggle school, where it was based around Grammar-Logic-Rhetoric, with everyone having to give a talk at the end of the year to the whole year or school about one spell/potion/plant/constellation. Timed of course so some people don't talk for hours.

Along the idea of everyone also having lessons in wand movements, Latin and choir practice (to get better at pronounciation) while also having all the canon lessons. They also get open ended essay questions like "How much magic is there in a cubic metre of air?" to make them have to think. The talk at the end is to show research, rehearsal, logic and rhetoric.

I'd also add that corporal punishment was banned sometime after the Marauder's time because of all the Muggleborns getting pissy about some newfangled laws. Filch has all the whips and chains because they really have just been put away.