What was the first public school in America? When was it established? In 1787, what percentage of schools were public vs. private?
The following link provides a decent timeline of public education in the U.S. (It should be noted that the Applied Research Center of the Race And Public Policy group has a definite agenda and provides its information with a particular slant.
While it does not provide a linear history, the PBS program, SCHOOL: The Story of American Public Education also provides a lot of info.
Run a search with the words “Horace Mann.” He was a (Massachusetts?) state legislator back in The Day who was instrumental in pioneering the idea of public education.
NOTE: There’s an insurance company bearing his name in Springfield, IL, so your first few Google hits will likely be for insurance.
The first public school in the U.S. was Boston Latin established April 23, 1635.