"the social group has always had an interest in educating its young members in the ways of the group"
If you are referring to the actual family then that is fine. If you are referring to a govt. then that is called indoctrination and was a prime method of changing society in the USSR.
Public education is not a new idea (it's older than the Greeks of Plato's time). And I don't equate public education with indoctrination (believe me, I know the difference between the elementary school classes that I attended during the school day and the catechism classes that I attended in the evenings).