One may ask: is there nothing this dude cannot link to schooling?
No, there is not.
Reading the totally excellent and highly recommended Fall of Rome by R. A. Lafferty – maybe 25% through. Gripping as any novel and elegantly and wittily written, it’s how history should be written if historians want regular people to care about history. Just reached the part where Alaric, at age 17, is called from his schooling under the Emperor Theodosius in order to raise and provision 10,000 men and rendezvous with other troops in defence of the Empire – to a location over 1,000 miles away. He is given 6 weeks.
He pulls it off. (He had help, but still – 17 year old kid? Impressive.)
But today let’s take a brief look at the school he was attending. Theodosius wanted to ensure the future of the Empire, and knew such a thing would take strong skilled leadership. So, he recruited boys from among the leaders of the barbarian tribes, and brought them together to learn, among other things, half a dozen languages, civil engineering, military strategy, and all the requisite martial arts – use of the various weapons and horses – as well as instilling in them the idea that the Empire was a good and holy thing worthy of a man’s life and efforts. These boys were told that any one of them might be called upon to lead the Empire, and so must be prepared for war, peace, diplomacy and intrigue.
Alaric was 12. He spent 5 years traveling from place to place to see first hand how all this worked in practice. He and the other boys were instructed by a number of experts, including the Emperor himself, and well as Stilicho, the great Master General of the Empire. They were introduced to and made a part of the Imperial court and family.
It worked, at least to the extend of creating a cohort of extremely competent leaders. Alaric was himself the most outstanding of the group, but the others were no slouches.
I’ll do a review of the book when I get done with it. What I want to do now is point out that what Theodosius did in setting up his school is both amazing and obvious. His foresight and thoroughness is amazing. Once he had a goal in mind, he chose the obvious way to educate those boys, indeed, the only way to truly educate people for a particular role: immerse them among the experts in that role. This is how we today teach such things as musical instruments and car repair: learn to play or to repair by actually playing and repairing in the presence of experts.
Alaric was by all accounts a very intelligent and driven boy. By 17, he had achieved a level of mastery of languages, engineering, diplomacy, warfare, and so on very probably out of reach of most of us – but we’ll rarely find out, since teaching such mastery is almost never tried.
A modern exception did spring to mind: the Russian School of Mathematics
Rifkin trains her teachers to expect challenging questions from students at every level, even from pupils as young as 5, so lessons toggle back and forth between the obvious and the mind-bendingly abstract. “The youngest ones, very naturally, their minds see math differently,” she told me. “It is common that they can ask simple questions and then, in the next minute, a very complicated one. But if the teacher doesn’t know enough mathematics, she will answer the simple question and shut down the other, more difficult one. We want children to ask difficult questions, to engage so it is not boring, to be able to do algebra at an early age, sure, but also to see it for what it is: a tool for critical thinking. If their teachers can’t help them do this, well—” Rifkin searched for the word that expressed her level of dismay. “It is a betrayal.”
Rifkin doesn’t have an Empire to preserve, so I’d imagine there’s less pressure in her schools. Yet notice the key feature: students are having direct personal contact and even relationships with stone experts in what they are supposed to be learning.
Imagine that.
These kids, and others educated in similar ways, then go on to dominate the world Math Olympiads for their age groups. Recap: math is awful, horrible, and hard, and we’re WAY behind the rest of the world – except for those taught it in a manner that is related to how people actually learn, who seem to both enjoy it and do it exceedingly well.
While math talent varies greatly among individuals, our school’s failure to produce many graduates competent in even basic math is not, I think, due to the nature of math itself. Rather, to see how it is taught in the standard schools, one would imagine the goal is to turn off as many students as possible to math. That’s how it works, at any rate.
Plato taught that true education can only take place between friends. We today lack not only the most basic understanding about how children and all people truly learn, the sort of intense, even passionate, friendship that has characterized great men and women through the ages is rare, denigrated when it does appear, and mocked as somehow unclean. Thus, it seems, even the more restrained friendships that should be characteristic of the relationships between teachers and students is rendered almost unimaginable.
Aside: another great thing about St. John’s Great Books program: a whole bunch of kids with widely varying degrees of math training and talent are all thrown together to study Euclid. In small classes (12-15 people) lead by a ‘tutor’ (professor) everybody has to grapple with math from an angle almost certainly completely foreign to how they’ve ever been taught math before. (Among people who have the hardest time are often those good in analytic geometry – the beauty of the non-numeric, non-algebraic proofs is hard for them to see.)
Even the least mathematically gifted student will have that ‘a ha!’ moment, when it all clicks. They discover that it’s not math they hate, but the way they’ve been taught.
Yard Sale of the Mind 
To go back to what you said about learning musical instruments, the relationship between band members and the instructor tends to be much closer than the relationship between the average teacher and student.
There’s something about an objective output that encourages proper relationships, where student and teacher are united by the desire to do well – and well is something you can see or hear. I certainly was much closer to my various piano teachers than to any school teacher.