You do know that President Jimmy Carter "bought" the endorsement of the teachers' unions by promising the creation of the Department of Education in the event of his election? Public schools existed well before the D of E's creation, and did a better job at actually teaching.
Why does there need to be a Department of Education for handing out money? The Feds could give money to each states directly, without strings, so each state could determine how best it could be put to use. Get rid of the middle man that pays itself first.