The Constitution of the US grants absolutely zero power to the fedgov as regards public education. None, nada zilch.I'm not by any means an expert on the US constitution (as the Swede I am), but I know that the Court did rule, in part, on basis of the Lemon test (no matter its legitimacy). Interesting enough, the test itself was written by a conservative judge, said to be a "strict constructionist", in the Supreme Court.
But forget the court decision, cite me the section ganting the fedgov power over local school issues.