Dwarven children. By far the most useless dwarf imaginable. It's like sand, they're coarse and rough, they irritate and they get everywhere. So much so that their mothers are force to roll their asses to their position if they get too far. So while the little lads are growing up and reach the age of 12, what could dwarves do with them? Here's a few suggestions regarding children in fortresses.
Orphanages
Orphanages would be a bit peculiar. As you may have noticed, dwarven couples love to a do a lot of short sturdy dwarven shrex. Which causes them to give birth to tons of baby dwarves. Which forces you to create new bedrooms and beds. Much ressources for a dwarf that will only be useful in twelve years. Also, while these children grow and thrive in the fortress, it might be highly likely that their parents die, either because they belonged to the military, or because of some !!FUN!! accidents. Enters the orphanage!
A zone can be assigned as an orphanage, as long as there's beds and an assigned manager. Once created, children without bedrooms, children without parents or newborns will proceed to sleep in there. With tables and chairs, they will take their meals there to eat. The orphanage manager will make sure that dwarven children are entertained and educated, and thus they will partake in many activities. Mostly the same as playing, however such activities implies the teachings of a certain discipline, such as wood/stone/bonecrafting or engraving.
[EDIT : Due to recent comments, orphanages could be assigned as simple nurseries or day-care rooms for parents to leave their childrens at.]
Pass time with parents and [VOCATION]
Children have parents. Shocking, I know! While working, some dwarven children will interested into what their parents are doing, or what any other adult is doing. I was thinking of a [VOCATION] sphere. This sphere will determine what the dwarf is interested in, or wants to do later on. As a child, he will attracted to certain jobs, or appreciate specific activities. For example, if a child is seen around carpenter workshops and such, the [VOCATION] sphere will turn into [VOCATION:WOODWORKING]. This vocation will not fully determine what will the child become afterwards. However, it will have an impact on what he would like to do. This vocation will encourage the dwarf to learn prematurely the intricacies of the professions he aspires to have. The child will read books about it, observe other dwarves partake in such jobs, or even practice in the corner. So you might not end up with a peasant in twelve years!
Schools
Just like orphanages, zones can be assigned as schools. Scholars are likely to make good teachers. They shall teach chidren how to read, count, maybe even enhance their spatial sense and critical thinking (and much more). Eventually, children will grow to have less flaws than their predecessors, for example being less clumsy, less lacking spatial sense, and be able to engage in conversations more swiftly. The teacher, however, must have the same qualities as a trader; good conversationalist, good judge of intent, good persuader, etc. This will help greatly and engage the children more and more into what they're learning. The more a teacher is charismatic, the more likely they're going to listen. A class must have chairs and desks, for each student and the teacher.
I have some more ideas, but I'll see where this thread goes first.