I know that at one point, a few years back, it was quietly assumed that there was some kind of school system or other in Doma. My character Feisal was put into it by Fresca and Kyle, right after they adopted him. We never really talked about what he would learn there, though.
Shada was the child of nobles and was tutored privately, and I had her learn so very basic chemistry as a result of that; She knows a very small portion of the real periodic table, she doesn't know any atomic weights on those, I'm pretty sure. I have another character who knows high school level physics, but he's also a mage and almost forty years old, studying all manner of things privately.
My guess is that children would learn how to write Doman characters with pieces of charcoal and/or ink quills, math as far as division and multiplication... history? I wouldn't expect to see social studies, or science of any great significance... I'm not sure they'd learn magical theory either, actually. As I understand it, even in Doma there are enough people who aren't gifted with magic and who don't use it regularly that it's not really integral. At any rate, not as a child. Maybe it would be taught at a secondary school?
Anyway, done rambling for the moment.