Oh Grow Up!
Apprenticeship
Somewhere around the age of puberty, children could enter into an apprenticeship. While some apprenticeships could begin at a much younger age, the more usual age was anywhere from ten to fifteen (it was thirteen in many Italian towns, sixteen in England). The length varied considerably, and money could buy a shorter term. I have a separate essay on the guild system, so I won't go into any further details here.
The chief thing to note is that there is a noticeable shift in the role played by children around this age. In the countryside, boys began working out in the fields and girls began learning the skills they would use in adulthood. In the towns, the apprenticeship system did much the same (girls could apprentice, though only in certain occupations). In short, children began to become proto-adults. If there's any point where the idea that childhood is a modern invention, it's here, in the pre-teen years, the middle school years. In modern times, these are still children, with a legal status no different from a child of eight. The only distinction I can find is in the entertainment ratings, with the special category of PG-13, which recognizes that this age group is different from both younger and older. For the most part, though, we have extended childhood right up to the later teens.
In the Middle Ages, though, these years were focused on training for the workplace.
One writer says
If you have a son who does nothing good, so you believe, in his present place, deliver him at once into the hands of a merchant who will send him to another country. Or send him yourself to one of your close friends.... Nothing else can be done. While he remains with you, he will not mend his ways.
Education for Girls
Girls stayed in the family circle. A common girl went to the court of Ferrara at age eleven. Her mother went with her. This was unusual.
Learning at home—girls learned cleaning and laundering, spinning, cooking, gardening, how to tend small livestock, and shopping. These are not trivial skills but each requires a whole set of skills and a thousand pieces of knowledge.
Bourgeois girls also learned riding, dancing, singing, parlor games, and religious training.
All girls learned family lore and relationships. It was vital to know everyone's reputation and to know how to know. Male writers dismiss this as gossip, but it was key. How was a girl to learn all the above if she was wasting her time learning multiplication tables or reading Seneca?