Read
this. It will answer a lot of the questions you have.
It didn't come from a twitter link, though, so maybe you don't want to.
Some crib notes...
Secondary education isn't controlled by the Federal government. It's controlled by individual states. The federal government does have the power of funding, though...
Before the public school system of today it was mostly a free-for-all mix of church-funded, township-funded, and charitably-funded schools. Rural and urban. Everything was different and there weren't any standards or compulsory attendance.
States manage education, not the federal government. That's why secondary education is so different in each area of the country.