10th Amendment
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.
I understand that amendment. I believe it has no bearing on the topic. If you think it does, please make your point with references and a logical progression of stated thought. Convince me that you aren’t just a parrot.
The states each establish their own school system. The Federal Government does not establish the schools. The DOE assists the states in their education efforts. You see, under the 10th Amendment, the states DO have Constitutional authority to establish the schools and their operational standards; and that is precisely where the originate.