I went to SJC Santa Fe in '65-'68.
About fiften years ago I was reading child development books. I discovered this wonderful thinker Jean Piaget.
I think Piaget's first book translated into English caused a great deal of excitement, especially at the University of Chicago. Piaget's book "The Language and thought of the Child" I conjecture was the inspiration for organizing a school around a great books list and also for teaching mathematics by the demonstration and discussion method.
At St. John's the freshman math tutorial meant each student stood up, drew a triangle, lettered the corners, and recited the proof and discussed and explored the ideas and assumptions.
For myself at St. John's the great books seminar became a very slow process of analyzing and trying to restate writings. By the end of the Junior year, my final academic review called a Don Rag I can say It Did Not Go Well ("what happened Lee?").
Regarding the math side of things, a few years later I got a technician job at Cal Tech and I was allowed to enroll in Cal Tech a calculus class. By November I was dreaming of flying, I swooped on updrafts of assumptions and bold substitutions and clever identities.
I couldn't solve the winter mid term exam problem but to this day I am grateful that I saw and did the two extremes of math.
These days, I don't do much Calculus, but I do and think about knot theory and coiling. I keep stumbling across pi/2 as I coil or fold air hoses or ropes. Why must three utility pipes connecting to three houses cross? Why are the computer wires always a tangle"?
Regarding the Great Books, I recommend the Meno and then the Socratic big 5. These books are still a source of puzzlement to me.
A final question: What happens in the brain when a student stands up and does a proof at the black board? Why do opera singers stand up to sing? Why is standing up to walk a neurological milestone in the development of the child?