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I always wondered if children who graduate from Hogwarts have an education that is actually worth while in the real world.

Do the children learn math and English?

I can see History of Magic as practical. I know of Arithmancy, but that's the study of the magical properties of numbers, not math.

Since Hogsmead is one of the very last all-magical towns, it's a fair assumption that a majority of the students at Hogwarts will be living in non-magical towns or cities. If practical classes (like math or English) aren't taught, then how do these students function in the non-magical cities?

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There's an essay that mentions this here: The kids have 5 years of education before Hogwarts, so maybe that's enough for their world. ISTM if there were mathematics classes at Hogwarts there would have been at least one mention of it. – Tony Meyer Dec 2 '11 at 9:42
Also, it would make for a boring book if there were sentences like, "Harry asked Hermione for help with his algebra." – Wikis Dec 2 '11 at 12:33
Based on this question most families have a muggle ancestry in their background, so at the very least those muggle born wizards/witches would have received traditional non-magical educations through the 4th or 5th grade, which should include addition, subtraction, multiplication and division. It could then be imagined that these wizards/witches would pass those skills to their children, if they didn't send them to normal muggle schools to begin with anyway as mentioned by @Slytherincess – Xantec Dec 2 '11 at 14:15
@SeanMcMillan I use calculus on a daily basis, lol... I don't see how I could survive on basic arithmetic. – OghmaOsiris Dec 2 '11 at 19:09
@Sean: Pretty much every self-sufficient adult uses algebra on a regular basis (most of which involve money, and the majority of it is probably done instinctively). You might've had more of a point had you said calculus, though even then it's a pretty myopic view. Likewise, you may not discuss Grapes of Wrath at work, but literacy is a skill that is largely developed through reading, and reading good literature is essential in providing a well-rounded education and definitely has practical benefits when you look at the bigger picture. – Lèse majesté Dec 2 '11 at 19:19
up vote 21 down vote accepted

History of Magic and Muggle Studies are both indeed non-magical classes. History of Magic is probably more immersed in the study of magical topics than is Muggle Studies.

Astronomy is another discipline taught at Hogwart which straddles the magical/Muggle worlds. Study of the stars.

I can see Divination as being mostly non-magical, at least how its described in canon. There is the reading of tea leaves (non-magical equipment), presumably the reading of tarot cards and the like, and reading crystal balls (the one item that I think could possibly have more magical properties). Hermione describes Divination as "a very woolly discipline" in Prisoner of Azkaban, which I interpret to mean she doesn't find it particularly useful or possibly non-magical or less magical. She sees Divination as subjective. Frankly, in the end, Divination came in use when Professor Trelawney provided crystal balls as weapons during the Battle of Hogwarts. Note: I see the ability to receive Harry's prophecy on Trelawney's part as separate from the actual course material taught in Divination the class. Certainly there are many "psychics" who hang out their shingle all over the Muggle world, not to mention religious practices that use symbols, interpretation of texts, objects, and incantations as part of their worship.

Herbology might include some knowledge that could cross over into the Muggle world, such as growing potions ingredients that both magical and Muggle folk use for making potions and herbal tinctures/supplements respectively. If you look at the list of known potions ingredients at the Harry Potter Lexicon, you will find ingredients that are just naturally occurring in the world, and are not strictly magical plants or herbs.

ETA: The study of Ancient Runes might help prepare for a career in archeology, if a magical child were to take that route. Runes are found in the Muggle world and are not exclusive to the Wizarding world.

I think that Squibs would need a strictly Muggle education in order to get by in the world. Ron Weasley confides that a family member (a cousin, I believe) is an accountant but the family "doesn't talk about him much." Otherwise, magical folk seem to stay fairly insular, working in magical jobs and careers.

REPHRASED: Some professions, whether wizarding or Muggle, require advanced math and/or science. Canon does not explain how a magical child would receive advanced instruction in math or science at Hogwarts, or should their chosen career path call for it. Perhaps advanced skills are taught through apprenticeships (canon mentions wandmakers study under other wandmakers to learn wandlore) or specialized on-the-job training (such as an Auror might receive). Many people -- magical or not -- are able to go day-to-day using only addition, subtraction, multiplication, division, and fractions, even though they've been taught advanced math, such as algebra, calculus, and trigonometry. How relevant advanced math will be will vary profession to profession. Most children -- again, magical or not -- are familiar with basic math by the time they leave elementary school, so this kind of learning would precede a Hogwarts education, as Hogwarts students are either in Muggle primary schools or homeschooled prior to going to Hogwarts (no mention is made of all magical elementary schools in the Wizarding world). The skill of writing is reinforced at Hogwarts through essay writing; it's just that the subject matter is magical, not Muggle.


Pottermore states that some students are allowed to study Alchemy at Hogwarts and receive special instruction in that discipline. Alchemy could be related to chemistry, which could be bridged between the magical and Muggle world.

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I don't see how you could consider divination non-magical. "the reading of tea leaves (non-magical equipment)" -- without them being magical in some fashion, how on earth could they reveal useful information? Or perhaps the teas are non magical bit it is magic that allows them to be interpreted usefully. Either way, definitely some kind of magic in there.. – zipquincy Dec 4 '13 at 17:01
Although alchemy would require some chemisty (and really is in many ways how chemistry got its start) and herbology might require the use of chemistry in making tinctures and the like, I would consider both a far cry from providing a good scientfic background. My sense was that those with a magical education generally don't do well in "real world" careers - most of them don't take them after all. However, they must do something because they have positions such as the one Kingsly Shacklebolt fills where a wizard would have to get on well in the muggle world - including convers etc. – balanced mama Dec 6 '13 at 0:28
@zipquincy likely, like it works on our world, it's just the art of bullshitting the listener, using some known patterns and tricks. – o0'. May 28 '14 at 21:46
I spotted this meme;…. If you can work out which scene it comes from, it would make a nice addition to your answer... – Valorum Apr 30 at 7:44

Asking "how do these students function in the non-magical cities?" is a bit like the way the Weasleys are astounded by things in the muggle world. In the books we have Arthur exclaiming how "ingenious" magic free muggle contraptions are and how Molly exclaims aloud that she doesn't know "how the muggles get by without magic." It isn't exactly because they haven't been taught properly, it's because the traditional sciences are essentially as unfathomable and ultimately unnecessary to a wizard as magic is to a muggle.

Consider a couple things.

Wizards do not understand muggle currency. This is important because currency in the "real world" works on basic, logical, mathematical concepts dealing with systems like a decimal numeral system; tens turn into hundreds, hundreds into thousands, and so on.

The Weasley's have a muggle (squib?) cousin who is an accountant but they "never talk about him." Some consider this a mark that even the Weasleys hold a small amount of prejudice towards muggles but I prefer to think that the main reason would be that the concept of accountancy simply confuses them. As they explain in the books, squibs are encouraged to integrate into muggle society not as a way to alienate them from the magic world but out of kindness. They can't participate effectively in a magical world and would always be seen as a pitiable being, it's better to live in a world that they can learn to adapt to, one they're non-magical affinity may be more suited to.

Arithmancy is not arithmetic. Arithmancy deals with the magical properties of numbers. It is more numerology than mathematics. It does not really rely on addition or subtraction or algebra, etc. Most likely Wizard currency, with its odd (to us) denomination separation, is based on arithmancy concepts and it is because magical numbers have natural meaning to magical beings that it largely second nature, that wizards find the denominations so easy to understand.

And numerology is important. In theory, Voldemort may have been correct that a 7 part soul housed in horcruxes might have been the most powerful because of the magical properties of the number. But he never really achieves a seven part horcrux. At a couple points his soul was split into seven pieces but, according to JKR, Harry was not technically a real horcrux, so maybe he didn't count. So, because the diary was destroyed before Nagini was made into a horcrux, there were never 7 of them. The point being that this is not a world based on arithmetic, the only real use for numbers is based on the magical properties of them.

As Hermione says, most wizards don't have a bit of logic. It's like the answer to the question "Why did flightless birds lose the ability to fly?" the answer is "because is it difficult to fly and their environment made it unnecessary to continue." Wizards don't understand the traditional sciences because they are difficult to understand and it is basically unnecessary for them to understand them.

Why check your side view mirrors when you can use a super sensory spell?

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Just a note: it may not be that even the Weasleys hold a bit of predujice: the muggle cousin is an abandoned plot thread -- that cousin would have a witch daughter, who would live with the Weasleys and be an intellegent Slytherin, being a foil for Hermione; I believe the character was abandoned in favour for Rita Skeeter. – Mac Cooper Jun 19 '14 at 13:48
@MacCooper - JKR FAQ anout Mafalda the cousin – DVK-in-exile Dec 1 '14 at 2:26

There are 2 non-magical classes that I am familiar with. The first is the History of Magic class that you mentioned. The second is Muggle Studies. However, both of these classes are heavily involved in the magical world.

There is some evidence that skills are required and worked on, such as essay writing, some math, etc. These are certainly required.

It seems like while most people don't live in magical cities, there is magic in their homes. Magic seems to be enough to get by from day to day, with the simple skills that are required otherwise.

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It appears that Numerology or Arithmancy may be somewhat close to "general math." Defined as the study of numbers and their magical properties, the class would most likely have something to do with mathematics.

"Oh, it's wonderful! It's my favorite subject!"

Hermione Granger, when challenged on Arithmancy homework -- Chapter 12, Harry Potter and the Prisoner of Azkaban

Conversely, one of the Third-Year books for students taking Arithmancy is "Numerology and Grammatica." It is pretty safe to assume that a class covering the magical properties of words (ha, spells) has something to do with grammar. Or, Hogwarts offers some class that has a relation to grammar.

"Has either of you seen my copy of Numerology and Grammatica?"

Hermione Granger, Chapter 16 - Harry Potter and the Prisoner of Azkaban

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