Horace Mann looked to Prussia for his ideas on public education and its superior trained armed forces at the time. He wanted to instill political stability and social harmony with public schools. He argued that universal public education was the best method to create disciplined, orderly, republican citizens.
His sister-in-law Elizabeth Peabody (who was also sister-in-law to Nathaniel Hawthorne) had different ideas on education. She believed that the premise of children's play had intrinsic merit and educational value. She helped to establish the kindergarten system in the US based on German educator Friedrich Froebel's original ideas and principles. Froebel had rejected fear-based discipline in favor of fostering a child's curiosity and senses, which Peabody supported.
If anyone has read Walter Isaacson's brilliant biography on Steve Jobs (highly gifted, Reed College dropout), you'll notice that Jobs operated with intuition, curiosity, and like Peabody advocated, though he definitely wanted a disciplined workforce. Then again, Jobs seemed to be one of those rare creatures who was at the crossroads of the arts/humanities and technology/science -- which too often public schools entirely forget about it.
Problem is, imo, except for a handful of schools like Montesorri and others, we're stuck with linear, rigid objective thinking with public schools. Even if you un/homeschool, college applicants are still often required to produce 'evidence' of following or adhering to a degree what the public schools do and this includes standardized testing.