I can't make this stuff up!
The public school was actually a Greek idea - so was forced sodomy on all young boys to toughen them up (not for the pleasure of a bunch of perverts /sarc> ). The Germans believe the publicly funded and state controlled schools are necessary to maintain social homogeneity ie control the citizens - hence their vehement outlawing of home schooling.
A little known fact - Thomas Jefferson was superintendent of the DC public schools and required that every class be taught from the Bible and Watts hymnal.
The most direct foreign influence for the creation of the common schools/public schools was the Prussian school system that was created after the humiliating defeat of Prussia at the Battle of Jena. From the second decade of the 19th Century onward many American intellectuals and students visited and studied in the German states. The Prussian/German schools and other Teutonic intellectual trends impressed the Americans and, unfortuantely, deformed public policy and intellectual trends here. The situation wasn't helped with the failure of the revolutions of 1848, which led to the emmigration to America of a great many leftist ethnically German intellectuals (Germany wasn't created are a unified country until 1870).