I didn't say all modern schooling was based on the Prussian model. I said the (U.S.) public school system is. You can just google it, but here is an excerpt from the wikipedia page about Prussian Education:
Emulation of the Prussian education system in the United States
American educators were fascinated by German educational trends. In 1818, John Griscom gave a favorable report of Prussian education. English translations were made of French philosopher Victor Cousin's work, "Report on the State of Public Education in Prussia." Calvin E. Stowe, Henry Barnard, Horace Mann,George Bancroft and Joseph Cogswell all had a vigorous interest in German education. In 1843, Mann traveled to Germany to investigate how the educational process worked. Upon his return to the United States, he lobbied heavily to have the "Prussian model" adopted.
Mann convinced his fellow modernizers, especially those in the Whig Party to legislate tax-supported elementary public education in their states. Indeed, most northern states adopted one version or another of the system he established in Massachusetts, especially the program for "normal schools" to train professional teachers. In 1852, Mann was instrumental in the decision to adopt the Prussian education system in Massachusetts. Soon New York state set up the same method in 12 different schools on a trial basis.
And an excerpt from John Taylor Gatto's writing:
Thirty-three years after Prussia made state schooling work, we borrowed the structure, style, and intention of those Germans for our own first compulsion schools.
Traditional American school purpose—piety, good manners, basic intellectual tools, self-reliance, etc.—was scrapped to make way for something different. Our historical destination of personal independence gave way slowly to Prussian-purpose schooling, not because the American way lost in any competition of ideas, but because for the new commercial and manufacturing hierarchs, such a course made better economic sense.