I disagree:
Every child in America should be acquainted with his own country. He should read books that furnish him with ideas that will be useful to him in life and practice. As soon as he opens his lips, he should rehearse the history of his own country.--Noah Webster--
I know no safe depository of the ultimate powers of the society but the people themselves, (A)nd if we think them not enlightened enough to exercise their control with a wholesome discretion, the remedy is not to take it from them, but to inform their discretion by education. This is the true corrective of abuses of constitutional power.--Thomas Jefferson--
There are many more indications that the Founders prescribed an education regarding their own governance.
Nothing in those quotes included advocacy for federal funding. Indeed, childrens' education at the time of the founding wasn't federally funded. Further,
Even in Boston, the capital city of the colony in which the government had the greatest hand, children were taught to read at home. Samuel Eliot Morison, in his excellent study on education in colonial New England, says:[10]
Boston offers a curious problem. The grammar (Boston Latin) school was the only public school down to 1684, when a writing school was established; and it is probable that only children who already read were admitted to that . . . . they must have learned to read somehow, since there is no evidence of unusual illiteracy in the town. And a Boston bookseller’s stock in 1700 includes no less than eleven dozen spellers and sixty-one dozen primers.
There is no way the Founders intended for the Feds to pay for educating children in the ways of free speech or firearms handling. I'll grant the the militia clauses in the Constitution provide for federal funding for many militia activities, but again that's at the adult level.
Prescinding from the funding issue, the Founders also hadn't any intent for the government to get into education. For example, the "collective model" of gun rights is a contemporary fabrication because there is no evidence that such a mindset existed in the 1700s. Same deal with education:
Home education was so common in America that most children knew how to read before they entered school. As Ralph Walker has pointed out, “Children were often taught to read at home before they were subjected to the rigours of school. In middle-class families, where the mother would be expected to be literate, this was considered part of her duties.[9] Without ever spending a dime of tax money, or without ever consulting a host of bureaucrats, psychologists, and specialists, children in early America learned the basic academic skills of reading, writing, and ciphering necessary for getting along in society.
I get the conservative desire for the federal government to pay for the GOOD stuff, and to starve the beast on the stuff those dregs over there like.
Leviathan, however, cuts both ways.