What is the process by which schools pass a society's core values from one generation to the next? ?

The process is called Cultural Transmission of Values.  It is the way a group of people in the society, like school, teach or transmit a society's culture.  The dependence of human at their early age allows them for cultural learning before they enter adulthood. As what a Functionalist perceives, education is essential to keep our social body functioning.  It's role is to create and maintain social unity and solidarity because it passes on the culture of a society, especially its core values.