Oh Grow Up!
Education
Children did attend school. Not in the countryside; there, children were educated only in the labors of home and field. If a child showed promise, or if the family simply made the decision, he might be sent to a monastery to learn to be a priest, but that act alone took him out of the village. Overwhelmingly, schools were in the towns.
Lower schools were mixed in gender. For example, in 1380 the basses écoles (lower schools) in Paris had 41 male and 22 female teachers. The historian Jean Froissart attended a mixed school. Beyond the beginning grades, however, only males proceeded.
Grammar school was prep for university and was indeed a school where grammar was taught. It was also boys only. Wealthy girls could continue with a tutor, but not in a school system. There was nothing like a middle school or high school: you went straight from grammar school to university.