The U.S. Constitution's 10th Amendment is pretty clear on the limits of federal power. It is also quite clear that the U.S. Department of Education is illegal.
The powers not delegated to the United States by the Constitution, nor prohibited by it to the
states, are reserved to the states respectively, or to the people.
And since the powers listed for the federal government doesn't grant the federal government any authority over education, The Dept. of Education is clearly unconstitutional. Such powers then fall to each individual state, if their own constitutions permit it.