David Foster Wallace mentioned the Trivium and the Quadrivium in Infinite Jest as the foundation of the curriculum at Enfield Tennis Academy. The Trivium/Quadrivium was (and still is) the classical liberal arts curriculum. This was how the young were taught to reason and communicate in the classical era and through the Middle Ages.
My son gave me a book on the Trivium, titled The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric, by
Sister Miriam Joseph. The Trivium explains the three liberal arts that compose the Trivium, grammar, logic, and rhetoric. This isn't your standard "i before e, except after c" kind of grammar. This is grammar in its most abstract, most general, all-encompassing form, applicable to any language, really. This is more like foundational linguistics than grammar. The book links grammar to logic, and logic into rhetoric. Thus, the student learns how to express thinking, how to reason, and how to present thinking and reasoning to others.
This is such foundational stuff that I wonder why it isn't taught in this form any more. (If it is taught, it is exceedingly rare, e.g, E.T.A.) The ability to express ones' thoughts, to reason, and to present would seem to me to be the most important abilities any young student could cultivate. The ability to reason and to discourse seems to me to be fundamental to any civilization as complex as ours has become. It was certainly fundamental in the classic years.
I've been taking reading notes, but the book is very tightly written. There is not a word that goes to waste in this book. It is demanding very close and very careful reading to grasp what it is presenting. It's difficult to note it without leaving out large and important pieces. I'm halfway through, and my copy looks like it was salvaged from the Titanic.
This is really valuable stuff to know, and worth the struggle to know it. But I wish I had learned this stuff back in grade school.