The best chance for “schooling” in the book sense was having your kids enter the priesthood. Note that in the Middle Ages priests still weren’t required to be celibate, that alone is a big change in requirements with later times.
Other forms of schooling available were the trades: while there were times and places where Guild regulations made it very difficult to 'prentice your kid to someone in a Guild not your own, other places and times were much more flexible. Being apprenticed might mean in a trade as we think of them now, or sent to someone else’s farm/household so they learned that someone else’s ways as well as your own. And depending on the location, there were trades that were specifically defined as being doable by one gender only; for example and always assuming the info from the tourist office was correct, at one point in Córdoba only men could be jewelers while only women could embroider in precious metals.