Much ink has been spilled (or, one might say, much CRT, LED, LCD and touch screen space has been displayed) in classical education circles about the trivium and quadrivium model of classical education, which was noted by Dorothy Sayers in the Lost Tools of Learning and harks back, ultimately, to the middle ages. The trivium (grammar, logic, and rhetoric) conforms to what we think of as elementary school learning, where students read, write, and learn to form basic explanations and descriptions, and, hopefully, argue in favor of simple prepositions. (“Why do you think Huck Finn is a ‘bad boy,’ Johnny?” “Because he wears rags instead of clothes and lives in a barrel by the river instead of a house.” “But does that make him ‘bad?’ “Well … )
I digress. The point is, a modern classical school can hew quite close to the traditional grammar school “trivium” curriculum. It is when we get to the quadrivium (arithmetic, geometry, music and astronomy) that we run into trouble. I have not heard of any modern classical schools that claim that they are focusing the middle-ages quadrivium by itself.
We still study math — though these days arithmetic is generally considered to mean the four basic functions (addition, subtraction, division and multiplying) and thus falls into elementary school, and geometry is considered an extension of arithmetic, often taught in 9th grade or thereabouts. Then there’s music. We study music, usually mostly in middle school and high school, but it’s now considered voluntary, an elective. And finally, astronomy, a topic that is now only studied in college, and by few. What can we say, then, about the “quadrivium” in the modern school?
Well, the quadrivium, which represented the applied sciences and the university studies of the middle ages, is now too abbreviated to cover what students should study to be considered fully conversant with the current day’s knowledge. You now tend to see in classical high schools, in addition to an augmented math program and music, the subjects of science, ancient and possibly modern language, and history. At a minimum.
The utility of the quadrivium in the current day, then, is to allow us to see the two-stage progression in the classical education structure: mastery of the tools of thinking, and applying the tools. The fact that the quadrivium’s original topics are somewhat antiquated does not change the fact that the basic premise of trivium and quadrivum still hold, the difference being that the quadrivium’s place is now held by a wider and more developed group of applied sciences, studied in high school and college, concordant with our greater modern knowledge base.