Doing research on how educational practices in Ancient Yisrael (both the Northern and Southern Kingdom), I could only find reference to how schooling (formalized) was done post-Babylonian Exile. I did find some insight explaining that the brunt of education was done by the tribes, communities, and households (makes sense due to everybody not being qualified to do everything):
"prior to the exile of 586/587 B.C.E, the primary teachers were the shevet (tribe) and the family, particularly parents, and education was focused on the children. The Jews being originally nomadic tribes, the training involved participation in the various agrarian occupations, such as farming, tent-making, making of tools, and fishing. Knowledge was passed from generation to generation through stories and allegories"
Did formal, centralized schooling come to existence only after the Israelites returned from Babylon? If there was formalized schooling prior, how were the classrooms ran? What was the pedagogy? How were teachers trained? How long was the average student in school for? Did wealth play a role? Were women educated? As always book references, articles, research, and personal insight are welcomed. Todah Rabbah/thank you.