What are some examples of the federal supremacy of federal versus state law in education law?

Almost one hundred years later, the United States again upheld the supremacy of federal over conflicting state law in Cooper v. Aaron (1958) 358 U.S. 1, 78 S.Ct. 1401, 3 L.Ed.2d 5, the famous Little Rock, Arkansas school desegregation case, in language not wholly dissimilar to Chief Justice Taney's in Ableman: "It is, of course, quite true that the responsibility for public education is primarily the concern of the States, but it is equally true that such responsibilities, like all other state activity, must be exercised consistently with federal constitutional requirements as they apply to state action." (358 U.S. at p. 19, 78 S.Ct. at p. 1410.)