In the West in the 1800s, practically any woman with an education could teach school. These were either spinsters or young women who didn't have children themselves yet. There was no need to have credentialing; if you could read, write, teach basic math you were hired. We made it, didn't we? Those who had the mind and will to learn more sought it out for themselves. Children aged 5 to 16 are the focus. If they haven't grasped the basics by then, they never will.