The Federal Government was never meant to participate in the affairs (such as education) that are clearly domain of the states.

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according to their own website, their involvement is somewhat limited...
"the Department does not
establish schools and colleges; develop curricula; set requirements for enrollment and graduation; determine state education standards; or develop or implement testing to measure whether states are meeting their education standards."
It engages in four major types of activities:Establishes policies related to federal education funding, administers distribution of funds and monitors their use. Collects data and oversees research on America's schools. Identifies major issues in education and focuses national attention on them. Enforces federal laws prohibiting discrimination in programs that receive federal funds.