Why don't Hogwarts students take muggle subjects?

I don't mean Muggle Studies; I mean the classical basics of a well-rounded education. The muggle and wizard worlds aren't that completely different, after all.

Students are only 11 when they enroll, and for most wizard children, that's the beginning of their formal education. You can't tell me they've already learned all there is to know about reading, 'riting, and 'rithmetic by the time they start school.

There's got to be wizarding lore and literature worth learning in the equivalent of an English class. And why aren't they learning foreign languages, in the name of international wizard cooperation? Not to mention mermish or troll? Come to that, why the heck isn't LATIN a required subject, seeing as how most of the incantations are based on Latin?

And then there's math -- algebra and geometry, at least, would certainly have many magical applications, and at least in an American education, a child wouldn't be proficient in those things by age 11. How can they do potions and astronomy without a fundamental understanding of mathematics? They don't even have calculators, after all!

And Hermione vividly demonstrates in the very first book that magical prowess can't substitute for a command of basic logic. Why isn't that taught?

Most of the Hogwarts subjects have obvious analogs to standard subjects: Potions = Chemistry, Herbology = Botany, etc. I suppose Hermione's Ancient Runes class would be the equivalent of Latin in certain respects. It's interestingly a very science-heavy curriculum in a world that doesn't use muggle technology. Perhaps Hogwarts employs a "writing (and arithmetic) across the curriculum" model, in which fundamental skills are integrated into their practical subjects. Although that would be difficult without a certain baseline.

Of course, the ultimate reason that there are no English or Math classes at Hogwarts is that it wouldn't make a very good story -- hard to capture the imaginations of kids with a vision of an alternative school if they thought they would still have to take the same old subjects. Still, the curriculum as viewed through the storyline seems woefully inadequate for wizards as well as muggles.