Is the U.S. Federal Government's "Interventions" in Educational Affairs Unconstitutional?

It is a more controversial issue that whether it is unconstitutional for the Federal Government to "intervene in" educational affairs. Although the 10th amendment established the fundamental principle of education power belongs to "the states or the people", exploring through history, the Federal Government continually "intervene in" educational affairs in a variety way. On the surface, the action of the Federal Government "intervene in" educational affairs based on the reason of "tradition", "national security" and "social welfare", "democracy and justice", but in fact, it is influenced by "pragmatic philosophy", "trend of social development and the whole transition of the Federal Government's power". Analyzed from the perspective of the concept "Power", according to the theory of "force", the Federal Government hasn't violated the federal constitution, however, according to the theory of "influence", the Federal Government has violated the federal constitution; but if we ignore the divergence caused by the vaguely character of concept "Power", analyzed form the dimension of the core spirit of "check and balance", "education power belongs to the people" of the Constitution, the Federal Government "intervene in" educational affairs hasn't violated the spirit of the Constitution.