I twisted the Latin a little. Trivium and quadrivium are old terms for components of curriculums past. The history of what is to be taught is not a thrilling subject. We have no science or proof of what our kids or we ourselves 'need to know'.
The ancient Greeks had no public schools. Writing was slow and laborious and most people couldn't read anyway. You may have heard that wise and critical thinker Socrates expressed distaste for this new stuff "writing", predicting that the practice would weaken peoples' use of their memories.
The city-state was not enormous by the standards of our population sizes but still a crowd could gather to listen to a speech or a plea for a collective action or to elect this person. Not so easy to project your voice over a crowd and for many, not easy to decide off-the-cuff what to say. So, public speaking, persuasive speech and good thinking emerged as important skills. Later, maybe a thousand years, the quadrivium of important subjects emerged, the set of arithmetic, geometry, music and astronomy.
So, some thinkers thought the liberal arts were those subjects "worthy of a free person". There were often said to be seven such arts: grammar, rhetoric, logic and the four parts of the quadrivium.
Of course, all those subjects were quite different from today's version. For instance, the arithmetic skills of multiplication and division were developed in the Middle Ages and for a time, were only available at the most advanced Italian universities.
When the Pilgrims started schools on this continent, they were very intent on teaching children to read the Bible. The famous reading, 'riting and 'rithmetic foundation of an education emerged. The trio of elementary, secondary and post-secondary levels took a long time to emerge and are still questioned for various reasons in various parts of the world. Part of the impetus came from the leading religious institution in the West, the Catholic church. Training priests and scholars couldn't really begin until the students were mature or nearly so. Around the year 1000 AD, colleges and universities began to emerge.
It is worth noting in today's terms that most of the curriculum was aimed at learning what the wise (men, mostly!) had written. I didn't hear today's key word "research" until we got to the American settlers moving into the Midwest. They called for universities, smart minds and RESEARCH to explain why their animals got sick and how to make more crops grow.
The subject of what to teach, how to teach it and how to test for learning is still up in the air. Watch for changes amidst a world that sees more and more clearly that learning, updating, revising and researching is never going to be over.
