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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: hp-lexicon.org/essays/essay-hogwarts-education.html. 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
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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
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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
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@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
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@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
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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.

Also, (POTTERMORE SPOILER)

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
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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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