What was the first American public high school founded in the new nation after the Civil War?

Boston, MA
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The first free public school was established by Benjamin Syms in the city of Hampton, VA on February 12, 1634. One of the most notable events during our colonial period was the creation of the concept of a free public education. This theory became reality in 1634 with an endowment from the will of Benjamin Syms. The bequest consisted of 200 acres of land and eight cows that were to be used for "a free school to educate and teach the children of the adjoining parishes of Elizabeth City and Poquoson from Marie's Mount downward to the Poquoson River." Twenty-five years later, Dr. Thomas Eaton bestowed five hundred acres of land and other sundry items for a school. He stipulated that this school was to be used to educate the poor children of the county. A trust fund established from the sale of land has never been disturbed and is used for the upkeep of the school which is now a part of the Hampton Public School System