First and foremost:

Primarily.

As in the primary place that a public education system is codified is in the constitutions of the states of the United States of America.

The state assuring the greater good for individuals........hmmmmmm......

I know perfectly well what Pres. Adams was referring to, you seem to miss the concept completely. There is nothing Marxist about what I stated, and there cannot, by definition, be anything Marxist about what Pres. Adams was stating.