Hogwarts School of Witchcraft, Wizardry, and Advantageous Public Education

I've been thinking.  It seems that wizarding schools only start taking pupils once they reach the ripe age of eleven.  It made me wonder about a few things, such as, do wizards or witches from magical families go to muggle school until they're eleven? If not, is it up to their parents to teach them math, writing, reading, etc- all of the skills necessary to take magic classes- or is there some sort of non magical school for children who are magical but not yet eleven years old?

If magical children do not attend school of any sort before their eleventh year, what do their parents do about child care? Not everyone is wealthy enough to hire a full time babysitter, much less attract house elves or the like to watch their kids.  I think in the case of the Weasley's, Molly was a stay at home mom while Arthur worked at the Ministry of Magic.  What about single parents? I'm thinking about this too much, aren't I?

Still.  I want to know. Who teaches the magical children the basic schooling required before they head off to Hogwarts or Durmstrang?  I don't remember there being an "arithmetic" class, but at least basic math skills are required for classes such as potions.  Harry, Hermione and Ron are always writing a few scrolls' worth of essay for History, but they all had to learn basic essay writing before Professor Binns could assign them such a task.

In Harry's case, he didn't know he was a wizard until Hagrid found him on that sad little island with the Dursley's, so he went to whichever muggle school the Dursley's sent him to until he came of age- same with Hermione.  What about Ron? Or Draco for that matter, his family had money and could have hired a tutor or something.

In the end, I'm pretty sure wizarding schools took advantage of not accepting students until they had already learned the basic schooling required to start their courses. I'd imagine it is also easier to start teaching self control and discipline to eleven year olds versus six year olds like our muggle system.