As I am wont to do, I assigned my students an essay. As I am also wont to do, I wrote the essay myself. 

The essay topic was free choice within parameters. This was for my College Readiness class: a tangled web, that one is, since it is, first of all, not much about readying the students for college; more about readying them for the college application process, primarily the ACT – which just happens to be the standardized test used to determine the school’s success rate and overall quality rating. Which is, understandably, more important to the school than it is to the students. Also, the class has two sections, and three teachers; so I have one group only on Tuesdays and Wednesdays, and the other group Thursdays and Fridays; they also have math two days a week, and “college and career counseling” on the fifth day, with the school counselor. In addition, the class is required, but it doesn’t fit into the usual categories, so the students get elective credit: making it a required elective, an amusing little oxymoron. Also, it is not required for everyone, because in theory all Juniors have to take the class – but if there happens to be a conflict with a “more important” class, such as math or science, then the student is excused from College Readiness: but if the class is a mere elective, such as life drawing, which happened to be scheduled for the same period as College Readiness this year, then the students who want to take the art class are instead forced into College Readiness.

But all that is beside the point. (Actually, it’s not, which is why I said all of it. But hold on.) The point is, I assigned my class an essay, and then gave them free choice in the topic of the essay. I love doing that, because they SUCK at picking topics. Completely terrible at it. There are some with interests of their own, and enough capacity for words to have something to say about their interests; they have a very easy time of choosing a subject and then writing about it, and good for them. But for the most part? Yikes. Free choice is the worst kind of essay.

So to help them out a little, I gave them a resource. My part of the CR course has two elements: first, yes, I do try to prepare them for the ACT, and the SAT if they want to take that one; college application tests are valuable and difficult, even though we make far too much of their ability to predict success, which is limited at best. But in my part of the class, we do practice the test, work on process of elimination and strategies for finding information in a reading passage, and so on. The second element is application essays: if they are planning on going to college, then next year, when they are Seniors, they will need to write an application essay; so we work on that now, in Junior year, in this class. I use the Common App, a website that creates a single set of application materials which the students can use to apply to any number of colleges around the world; it’s a useful efficiency, and also a good generic application format, for practice. For those who aren’t going to college or who aren’t sure, I see these essays as simply good writing practice: also, I want them to get better at speaking well of themselves, and advocating for themselves, which are both useful skills in all walks of life, and both things most teenagers suck at, because they think talking about themselves is cringey, and bragging about themselves is appallingly arrogant. So we practice essays.

For the first three, I insist they choose a topic from the Common App, which has seven generic topics – things like “What is a problem you overcame and how did you learn from it?” “What is a part of your background or identity that isn’t on your application, but which you think we should know?” – but then for this last one, I show them the University of Chicago supplemental questions.

You see, U. Chicago has, for the last several years, offered a specific question as part of their application. The first question they ask is of the usual type: How does the University of Chicago, as you know it now, satisfy your desire for a particular kind of learning, community, and future? Please address with some specificity your own wishes and how they relate to UChicago.

But then for the second essay, they do this:

Each year we email newly admitted and current College students and ask them for essay topics. We receive several hundred responses, many of which are eloquent, intriguing, or downright wacky.

Those essay topics, which can be found here, are everything they say they are. They include topics like this:

What advice would a wisdom tooth have?

–Inspired by Melody Dias, Class of 2025

And

You are on an expedition to found a colony on Mars, when from a nearby crater, a group of Martians suddenly emerges. They seem eager to communicate, but they’re the impatient kind and demand you represent the human race in one song, image, memory, proof, or other idea. What do you share with them to show that humanity is worth their time?

—Inspired by Alexander Hastings, Class of 2023, and Olivia Okun-Dubitsky, Class of 2026

And

UChicago has been affiliated with over 90 Nobel laureates. But, why should economics, physics, and peace get all the glory? You are tasked with creating a new category for the Nobel Prize. Explain what it would be, why you chose your specific category, and the criteria necessary to achieve this accomplishment.

—Inspired by Isabel Alvarez, Class of 2026

And

Genghis Khan with an F1 racecar. George Washington with a SuperSoaker. Emperor Nero with a toaster. Leonardo da Vinci with a Furby. If you could give any historical figure any piece of technology, who and what would it be, and why do you think they’d work so well together?

-Inspired by Braden Hajer, Class of 2025

And so on. 

Last year, my students challenged me to write an essay to this prompt:

Find x.

—Inspired by Benjamin Nuzzo, an admitted student from Eton College, UK

Because they were hoping to force me to talk about math, which I frequently and loudly say I dislike. (I don’t, but the whole school community where I work promotes STEM and talks smack about the arts – why do you think the math and science students get out of College Readiness, but not the art students? – and I want to push back a little bit. Also, I do have some issues with math, but that’s not important right now.) So I wrote about a pirate finding treasure where X marks the spot. 

Checkmate, Math Nerds. 

This year they didn’t want to choose a topic for me: so I chose one for myself. Here it is:

 The seven liberal arts in antiquity consisted of the Quadrivium — astronomy, mathematics, geometry, and music — and the Trivium — rhetoric, grammar, and logic. Describe your own take on the Quadrivium or the Trivium. What do you think is essential for everyone to know?

And here is the essay I wrote about it.

Understanding the Trivium and Quadrivium

Dr. Jeffrey Lehman Explains the “Arts of the Word” and the “Arts of Number”

Written by Finn Cleary

The trivium consists of grammar, logic, and rhetoric, while the quadrivium consists of arithmetic, astronomy, music, and geometry. Together, Dr. Lehman says they lead students to see a “unified idea of reality.”

“The trivium was always pursued first,” Dr. Lehman says. “It’s commonly called the ‘Arts of the Word’ and focuses on different ways you can attend to words. Grammar is used in logic, which is used in rhetoric, for example. All of them move toward a proper presentation of the truth, which speaks to the mind and to the passions.”

Next, students of the liberal arts traditionally move to the quadrivium, or the ‘Arts of Number or Quantity.’

“Humans communicate with each other using words. Humans communicate with the natural order in numbers and in quantities. By discerning those natural relationships, we come to better understand the cosmos. It speaks to us, and we can talk to the greater universe. “

Source

I have often thought that I was born in the wrong century. I would like to exist a hundred years earlier than I do; because my professions and my passions would be, I think, more valuable then; I would still be able to teach, perhaps at a college instead of a high school (but also, I think I would make a decent one-room-schoolhouse teacher) and my writing would be more marketable, and would perhaps furnish me a non-teaching career, which would be lovely. 

But there is an attraction with going back even further in time: perhaps to a time when universities taught the quadrivium and the trivium, the two sections of what are bafflingly called the liberal arts, even though they were at the time pretty much all sciences. I appreciate that there is a professor at a small liberal arts college in southern Michigan who teaches about the quadrivium and the trivium, which I quoted above, but I’m not sure I agree with his explanation of them and how they work and why they are important. 

Math is how we interact with the natural order? Is it really? I guess we quantify and measure and compare natural things, all of which are math-adjacent if not actually math; but is that all we do? What about living in the natural order in the natural world, of which we are a part? But okay, we’re not talking about life, we’re talking about academia and education. Still: what about art inspired by the natural world; is that not how humans communicate with the world around us? It seems to me like it is. Of course, the classic quadrivium did include music, which I appreciate; but I’m leery of music being the one art when someone starts speaking about mathematics (and when two of the other subjects are math, and the last of the four is a math-heavy science), because there is a strong correlation between music and math. I don’t think that’s all of music, by any means; but I suspect that studying the quadrivium in a program that thinks math is the key to the universe would not teach me so much about improvisational jazz.

(Somewhere right now there’s a math/music geek just revving up a lecture on how there is many maths in jazz. The silences and the spaces between the notes on the scale, the rhythms and repetitions and so on. I get it, sir. Keep your beret on.)

I also take some issue with the trivium, as Dr. Lehman describes it and as ancient universities taught it: grammar to logic to rhetoric as the “arts of the word” is a good way to study language, I agree. But the idea that you could even consider the arts of the word and not talk about poetry? About the great works of literature, past and present and future? That doesn’t even make any sense to me. And “logic” as part of the art of language is a little too close to the math of language, as well: logic is important, both to life and to the proper use of language; but it’s also just about the only place where language can be turned into formulae and equations and functions. 

The other place is grammar. Or word problems, but I think we can all agree that those are abominations.

However: I do think the study of language as a foundation for further learning makes perfect sense. I don’t know that I would split it out in that manner, though. I don’t know that studying grammar would be as effective now as it was in the long-ago past; partly because people are far more grammar-savvy now (assuming that they actually read) when they get to university than they would have been in the illiterate ages where nobody had access to books or very much printed media at all; and partly because I don’t think that studying grammar really helps appreciate and understand language all that much. It helps you to understand grammar. And that enables you to write correctly, but writing correctly does not mean writing well, and I think writing well is far more important. 

So I have some suggestions for an update of the trivium and quadrivium. 

If we consider the trivium to be the stage when we learn how to understand things, instruction in the processes rather than the actual content, I consider that both a reasonable lens to look at the curriculum through, and also a reflection of how we do most school: elementary and middle school are largely about learning how to learn, learning the basic processes and systems of thought, including learning how to read and write, learning how to do math, learning how to think scientifically. Basically for the first seven or eight years of school, we are learning how to think. Then high school, and even more so college, is where we learn things to think about: this is where the serious content appears, and gives us something to understand, which then allows us to build what should be the final goal of all education: our own understanding of the world and our place in it. Every individual should find and create that understanding for themselves, and since that understanding shapes all of one’s life afterwards, it seems like the right goal to see as the pinnacle of education: as the final project before graduation.

So the trivium in university should be the fundamental ways that we think: Language. Mathematics. Art. (“What?!” I hear you cry. “You’re including math?!?!” Sure, I don’t like it, but I respect what it is and what it can do for people.) I think there is room in these to allow for some individual course selection, meaning that the “art” umbrella can comprise visual arts, music, dance, and even poetry, though that might focus too much attention on language when combined with the other strand of study. Definitely we need to learn more about language and how language works and how to manipulate it: too many people focus on too few aspects of language, and that leaves most of us open to manipulation in various ways, and whenever we are manipulated, we don’t learn something we should learn – and that makes it easier to manipulate us next time, and the next thing you know, Donald Trump is president. The same is true for mathematics, and I’d like the university trivium study of mathematics to be more in applied mathematics: probability, statistics, and probably economics, though I’m certainly open to a stronger statement from a more mathy perspective on the specifics there. The language study in the trivium should include some study of grammar in the sense of learning how language is constructed and how we construct meaning with it; I tend to think of that as rhetoric. It should also, without a doubt, include the learning of a foreign language, and I’d like to see that be a different language than the one people “learned” in high school, and I’d like to see the study of that language include study abroad. 

But I’m getting a bit far afield here. The point is that the trivium should be about the ways that we can interact with the world, the ways we can construct thought, the ways we can create meaning: it’s the modes of thought that we can control, that we can manipulate. It’s how we think and how we learn, not necessarily the content, yet.

That’s where the quadrivium comes in. That’s when we learn the material that we are now ready to understand better, to chew and digest, to manipulate and shape, to make something out of. The raw material for building, after the trivium shows us how to build. Where the trivium focused inward, on the ways we think and the ways we communicate – communication with others would be outward, of course, but we also communicate with ourselves, through language and math and art, all three – the quadrivium should focus outward. It should show us about the world we live in, and the people we live with, and how we all, world and people, fit into the larger universe. My first quadrivium subject, then, would be history, as that would give us some understanding of who we are as a people, as a human race. (I would also start with that because I think of “liberal arts” as being the humanities, so science can wait its turn.) I think we need to learn history, but I think we struggle with it in school because we don’t follow the thought process of the trivium and quadrivium, first learn how to learn and then learn things worth learning; learning history when one is still mastering how to read is too difficult, because there is so very much information to take in. Learning the impact of history without having a grasp on the mathematical concepts of probability and statistics means we miss the scale, we fail to understand the interactions between events. Recognizing here how important it is to understand causation, I suppose I should include some focus on logic in the trivium: though I think that would happen best as an interaction between language and mathematics; I also think art wouldn’t be lessened by some connection to logic.

So history (And again, opportunity for individual courses here such as sociology or anthropology, along with the study of civilizations and recorded events), and then, I suppose, it’s time for science. Just like with history, I think we need an understanding of both language and applied mathematics before we can really appreciate science: my science study in high school was just a set of difficult courses to master, where my science study in college was eye-opening. Not that my science teachers in high school were sub-par compared to my college teachers; quite the opposite, in fact. But I wasn’t ready for science, I didn’t understand the full implications of chemistry and physics and biology. I think that’s the best argument for college and university education coming at the end of thirteen years of compulsory education: we’re not ready to really learn until we reach college age and college-level mastery of the fundamentals. (I do also think there’s a great argument for having a break in schooling somewhere between 6th grade and 9th grade, but that’s a whole other topic.)

The quadrivium should include a study of biology and ecology. We need to understand where we fit in with the rest of life on this planet and in this universe, if for no other reason than just so we don’t kill it all. Almost all of the problems we face in our future are related to biology and ecology, so if there is material in our world of knowledge which we need to be chewing and digesting once we learn how to chew and digest, it’s biology and ecology. I also think we should study astronomy: because just as humanity is one race of beings in an almost infinitely complex web of life, so the Earth is one tiny planet orbiting one tiny star – but also intricately connected to the rest of the universe, affecting and affected by it all. And if we do ever manage to solve the problems we face as a race (And I should also point out that the problems which are not covered by biology and ecology will be covered by history: though not solved by it), then astronomy will show us where we need to look in the future, to find our next set of challenges to face and adapt to: the stars.

So that’s three of the four (and please note, two sciences, one a lab and one a theoretical science; I’m a little disappointed in myself that my education plan is so similar to high school curriculum; but also, I think that shows the curriculum we have now is not bad) – and that’s where I got stuck. I think there is probably value in studying the world of computers and the internet, but I’m not convinced that’s a good subject for university study. I don’t know that a whole lot of overarching theoretical work has been done, that a body of knowledge about the internet and computers has been created; that is, several different bodies of knowledge have been created – and then made obsolete. Are there theories and concepts that can teach students about both the personal computer revolution and Tik-Tok? I don’t know. If there are, if there is a reasonable course of study that would be general enough to include most of the important themes, but also specific enough to be useful, then computer science would be a good choice for the fourth part of the quadrivium. Certainly the digital age is well begun, and understanding and navigating it will be critical. 

If that’s not a reasonable course – or, if like many other things in life, the study of related subjects makes us sufficiently well-prepared to deal with the computer world (which is the same reason we don’t really need to study how to do our taxes in high school, and all those smarmy memes about the Pythagorean theorem can shut it), and personal experience fills in the gaps – then the fourth subject had me stymied for a bit. I think philosophy would be useful: but I don’t know that it needs to be its own study separate from the logic and language of the trivium and the history of the quadrivium. Physics might be a good science to work with, as it enables so many other applied sciences like engineering; but I don’t know that it is applicable enough outside of that, if physics is actually how we solve the problems in our world (And my physicist father is cringing right now, as I write this. Sorry, Dad. I think physics is cool.).

But I did have a thought. As I said, there is a gap in the original trivium of grammar, logic, and rhetoric: the study of actual literature. I do recognize that in the Medieval period, when the trivium and the quadrivium were being codified and then taught, there wasn’t quite the wealth of material that we have today; there was Chaucer, and Sir Gawain and the Green Knight, and a whole ton of stuff about Christianity – and I guess a couple of Greek plays – but it was more limited. Still: I don’t think you can say you understand language unless you understand the art of the language. The same goes for music and visual arts and all of it; you have to know the history of it, have to study the past masters, to know what is possible and how to build for the future. 

So it seems like a good idea for the fourth quadrivium subject would be the history of the subjects in the trivium. Literature, as the history of language that has already been created; the history of mathematics, both the people who built it and how it got built; and the history of art and music and whatever other elements were included in the trivium – and more, if possible, because I don’t really think you can learn too much art. All of that seems to me like good material to chew and digest, and then use to make something new. 

And isn’t that what education is all about?

(Also, this is in no way connected to this topic, but I couldn’t stop thinking about the band Trivium every time I wrote it for this, and this is my favorite song of theirs. So enjoy.)