A commenter on a recent thread writes that, "When the founding fathers wrote the Bill of Rights, they never envisioned that state actors would be running schools."
I'm no expert at all on the subject, but I'm a bit skeptical about this assertion. The Public Land Ordinance of 1785 provided that "There shall be reserved the lot N 16, of every township, for the maintenance of public schools, within the said township." The Northwest Ordinance (1787) said that "Religion, morality, and knowledge, being necessary to good government and the happiness of mankind, schools and the means of education shall forever be encouraged." Jefferson in 1779 proposed a public education system for Virginia, though such a system was ultimately not adopted until considerably later. (The University of Virginia was founded in 1819.) In 1780, the Virginia legislature donated land seized from British loyalists for the purposes of establishing a "publick school."
The Massachusetts Constitution of 1780 said that "it shall be the duty of legislatures and magistrates, in all future periods of this commonwealth, to cherish the interests of literature and the sciences, and all seminaries of them; especially the university at Cambridge, public schools and grammar schools in the towns." The 1792 Charter of Yale College provided that the Governor and several other government officials would sit ex officio as part of Yale's board of trustees. The North Carolina Constitution of 1776 provided that "a school or schools shall be established by the Legislature, for the convenient instruction of youth, with such salaries to the masters, paid by the public, as may enable them to instruct at low prices; and all useful learning shall be duly encouraged, and promoted, in one or more universities." The University of North Carolina was chartered pursuant to this in 1789, and apparently started operating in 1795.
Now I don't know the precise role of state governments in education during the early Republic -- how extensively they actually acted on the education-should-be-supported sentiments, and on the extent to which the action involved control over the institutions, rather than just the provision of money or land to entirely privately run charitable schooling organizations. I also don't know about the extent to which the Framing generation would have seen school officials, even officials of government-run schools, as "state actors" in the modern sense of the word. (Note this 1783 Virginia law that treated trustees of a state-created school that used state-provided property as a sort of public officer, obligated to take an oath of office, though also note that during that era corporations, whether business or nonprofit, were always chartered by special legislative act.) I suspect some readers of the blog do know this, though, and I'd love to see their comments on it.
Nonetheless, the evidence I point to -- and other similar materials -- suggests that the concept of government-supported, and perhaps even government-run, schools wasn't alien to the Framers of the Constitution and the Bill of Rights.