The federal government is able to involve itself in education because it is not simply dictating to the states what they must do. Instead, it is telling them what they must do if they want federal aid. This is the important legal distinction.
The federal government gives states large amounts of money to help fund their educational systems. The states have no constitutional right to this money. Instead, the federal government has the right to set whatever conditions it wishes on the money. This is why laws like No Child Left Behind are constitutional. The states have a choice. They can comply with the law and get money from the federal government or they can decline to comply and forego the money. They are not simply being told what to do.
Because the federal government is just putting conditions on money it give the states (rather than simply ordering the states to do certain things), it is allowed to involve itself in education.