In general, only boys go to school. A girl's education is accomplished at home, although it usually includes reading and arithmetic. Of course, noble children get their education at home, from private tutors.
Public education refers to going out to school, as opposed to being tutored at home.
It does not mean they are paid for out of public funds. It is understood that students must have their education beaten into them, like their manners and deportment. The most elementary level of schooling is called petty school . You learn to read and write in English and do sums, but the main idea is to get you into grammar school. The primary study of a grammar school is Latin grammar, using Lily's Grammar as the basic text, with Plautus, Terence, and Seneca as classical sources.