The Quadrivium ???
A little over a year ago, I posted an essay I had written for The Atrium class I was taking through the Circe Institute on the seven liberal arts. Our fall semester was spent taking a close look at the history of education and the first three arts, known as the Trivium. That essay is here.
I've been meaning to follow that up with some thoughts on the Quadrivium. It's been more of a challenge than I anticipated. After reading Beauty for Truth's Sake (twice), The Liberal Arts Tradition (three times) and listening to Andrew Kern wax eloquent on the quadrivium for about 16 weeks, I feel like I know just enough to know that I know nothing.
Over the past 40 years, the renewal of classical education has done a lot of really great work and made some wonderful discoveries about true education. There's been a lot of great discovery and reconstruction of ideas in a modern context specifically related to the Trivium arts. A quick search of "classical curriculum" companies yields multiple options of Latin, logic workbooks, fallacies, formal and material logic, composition, rhetoric, and more. We've got the language things covered. Or, at least we're well on our way.
The quadrivium is another story. The quadrivium, most simply defined, are the four upper mathematical arts; the arts of mathematical reasoning. The four arts composing the quadrivium are:
-arithmetic
-geometry
-astronomy
-music
I don't know enough to write a proper essay on this. So I'm just gathering my thoughts enough to barely offer a blog post. Because I've been trying for a year, and this is as good as it's going to get.
Here's my basic definitions of these four mathematical arts. When talking about these things as liberal arts, we are not talking about them as subjects. My previous essay on the Trivium covers the differences between types of arts, and what a liberal art is. It is not a subject or area of study.
The liberal art of arithmetic is the understanding of number as a quantity. It is the physical number of things, and the truth of the essence of number as well. For example, there can be seven paperclips on the table. That's a quantity. But "seven" is a reality whether there are seven somethings to count or not. Seven was a reality before any human ever counted seven of anything.
The liberal art of geometry is the understanding of relationships between quantities in space.
The liberal art of astronomy is the understanding of relationships between quantities in space across time (this is also called cosmology, but is different from origins theories/science). Astronomy/Cosmology seems to me to be more about observing the heavens and understanding how the bodies of the heavens shift in relationship to each other, in ways that form beautiful patterns, across time.
The liberal art of music is the understanding of relationships between quantities across time. Music is all about ratios and proportionalities of mathematical notes on a page or relationships, moving across time together in harmonious ways. Music is the crowning art of the quadrivium.
The purpose of the quadrivium is to raise us above our senses; from the material to the immaterial. Studying the quadrivium arts gives us a window into the mind of God and how the universe is ordered and held in motion in harmony. Material to the immaterial.
Honestly, this is really all I've got at this point. It's clear there's a lot left for me to learn, and a whole lot left to be developed as far as recovering the quadrivium for the purposes of being applied to true education. I have a long list of books I'd like to read, with Augustine's de Musica being at the top of that list, to start peeling back the layers here. One thing I have had to accept though, is that this is still too raw to really be able to give my kids much if anything of the quadrivium. It's also become clear to me that in ancient education, this level of study was *not* happening before the age of twenty. Or maybe even thirty. It was not a teenager's game. Up until mid twenties, students were largely focused on the trivium from what I've gathered, with some exposure to arithmetic and geometry.
So as to not leave us totally hopeless, I want to find things we can do to give our kids just a taste of some of these things. Here's a few ideas I've tried for quadrivium arts, or will try at the proper time.
Arithmetic:
-We focus on solid numeracy and number theory in elementary school. I really like Math-U-See because of it's mastery-based focus on learning to use the four operations really well.
-In middle school, we started slowly working our way through A Beginner's Guide to Constructing the Universe. We watch the DVD, I read aloud from the text, and both of my kids have a workbook and work on the constructions on our Friday Schole days as often as we can. This set of materials focuses on number more as idea and pattern than quantity. It's fascinatingly beautiful!
-Continue to use math curricula through high school that focuses on mastery and mathematical reasoning.
Geometry:
-Constructing the Universe begins to bridge into geometry a little bit by teaching the students to construct shapes with the number patterns they're learning.
-We will study two years worth of geometry: one with a more traditional plane/solid geometry program. Our second year will be reading Euclid with Classical Math One by Daniel Maycock as a guide. (I realize this link leads to a discontinued item. Daniel is revising the guide book and re-releasing it this summer. So check back! It will be there!)
Astronomy:
-The best thing I've been able to find for this is Signs & Seasons. I guess I should qualify that with the best thing I've been able to find that is also do-able/affordable for us. Remember astronomy is not a science subject, but a liberal art in this context. So I'm not looking for a traditional astronomy course. Signs & Seasons teaches at least observation of the night sky and charting over the course of an entire year and navigational skills by the sky. The math required to actually do astronomy is prohibitive. So this is the best we can do. I'm going to pair this with some history/biography of astronomers as well. At least we'll be turning our eyes to the heavens, above and out of ourselves, and learning to see and observe what's going on.
Music:
This is the big unknown for me. There are some practical things we can do to start off with.
-Learn to play an instrument: piano, guitar, violin, anything really. This has always been a priority here and we've got piano lessons starting at an early age, and in 5th grade, adding another instrument. Our older two kids have added choir around 7th grade as well. Playing and singing daily is pretty crucial to laying a foundation of music in a liberal arts education.
-Listen to good music. What they listen to shapes what they crave. Expose them to the best music from history. Professor Carol's music programs do a great job of this. So do classical radio stations. There are lots of great YouTube channels on classical music, like Rousseau. We could watch these visualizations for hours. Get to know different composer's music as a whole body of work. Teach them how to listen to music. Memoria Press has a great program called Music Appreciation that teaches them basic elements of music that help them listen intelligently to great works.
Here's the thing though. There is much more to music as a liberal art than listening to and playing music. There are three different aspects of music as a liberal art, according to Augustine:
-musica instrumentalis : instrumental music, as described above
-musica humana : the proportionalities that exist in human society
-musica mundana : the proportionalities that exist in the world
That last one, I'm pretty sure I don't understand that. It seems to have some cross-over with cosmology/astronomy. Maybe it has to do with the sounds of the stars? Pretty sure we'll watch this video every year just in case that's what it means. :)
But that middle one. I think this is where music as a liberal art is really pointed: proportionalities that exist in human relationships. Augustine wrote,
"Musica est scientia bene modulande" - Music is the knowledge of modulating well.
This is about learning to order and harmonize ourselves with other people. Harmonize our own lives and live proportionally, within our limits. Learning to bring ourselves back into the harmony of God when we've stepped out in sin and are creating dissonance. To learn to see the master harmonizing skills in Jesus as he redeems and makes all things new. The harmony of the Trinity and Jesus as Logos of all things.
Music is not extracurricular. It is foundational, and ultimate, at the same time. By laying the foundation of music through playing and listening, we have an experience of harmony to draw on. We have heard harmony. We have felt discord and dissonance in our soul. We have experienced that relief when a dissonant chord resolves into harmony.
The point of music is to learn to modulate well. In life, keeping relationships healthy across time is all about modulation. Parenting is about modulation: not treating our children at twelve years old in the same way we did when they were two. Marriage is all about modulating to each other, on a daily basis.
"The well being of the human soul is a matter of internal and external modulation." (Andrew Kern. He must be credited with far more than this quote. Most of what I've written here is simply a narration of listening to him for a couple of years on the quadrivium and processing. It's a regurgitation of Kern's thoughts).
How do we teach this? I have no idea. But one thing I can do is to keep learning about it and modeling it in my own life and home.
There's so far we have to go yet. So much left to do. I'm so so thankful to those blazing the trail like Andrew Kern, Carol Reynolds, Christopher Perrin, Daniel Maycock, Martin Cothran. Support their work if you can! It is so important! And join me in giving our kids what we can and resting in that as being enough!
Over the past 40 years, the renewal of classical education has done a lot of really great work and made some wonderful discoveries about true education. There's been a lot of great discovery and reconstruction of ideas in a modern context specifically related to the Trivium arts. A quick search of "classical curriculum" companies yields multiple options of Latin, logic workbooks, fallacies, formal and material logic, composition, rhetoric, and more. We've got the language things covered. Or, at least we're well on our way.
The quadrivium is another story. The quadrivium, most simply defined, are the four upper mathematical arts; the arts of mathematical reasoning. The four arts composing the quadrivium are:
-geometry
-astronomy
-music
I don't know enough to write a proper essay on this. So I'm just gathering my thoughts enough to barely offer a blog post. Because I've been trying for a year, and this is as good as it's going to get.
Here's my basic definitions of these four mathematical arts. When talking about these things as liberal arts, we are not talking about them as subjects. My previous essay on the Trivium covers the differences between types of arts, and what a liberal art is. It is not a subject or area of study.
The liberal art of arithmetic is the understanding of number as a quantity. It is the physical number of things, and the truth of the essence of number as well. For example, there can be seven paperclips on the table. That's a quantity. But "seven" is a reality whether there are seven somethings to count or not. Seven was a reality before any human ever counted seven of anything.
The liberal art of geometry is the understanding of relationships between quantities in space.
The liberal art of astronomy is the understanding of relationships between quantities in space across time (this is also called cosmology, but is different from origins theories/science). Astronomy/Cosmology seems to me to be more about observing the heavens and understanding how the bodies of the heavens shift in relationship to each other, in ways that form beautiful patterns, across time.
The liberal art of music is the understanding of relationships between quantities across time. Music is all about ratios and proportionalities of mathematical notes on a page or relationships, moving across time together in harmonious ways. Music is the crowning art of the quadrivium.
The purpose of the quadrivium is to raise us above our senses; from the material to the immaterial. Studying the quadrivium arts gives us a window into the mind of God and how the universe is ordered and held in motion in harmony. Material to the immaterial.
Honestly, this is really all I've got at this point. It's clear there's a lot left for me to learn, and a whole lot left to be developed as far as recovering the quadrivium for the purposes of being applied to true education. I have a long list of books I'd like to read, with Augustine's de Musica being at the top of that list, to start peeling back the layers here. One thing I have had to accept though, is that this is still too raw to really be able to give my kids much if anything of the quadrivium. It's also become clear to me that in ancient education, this level of study was *not* happening before the age of twenty. Or maybe even thirty. It was not a teenager's game. Up until mid twenties, students were largely focused on the trivium from what I've gathered, with some exposure to arithmetic and geometry.
So as to not leave us totally hopeless, I want to find things we can do to give our kids just a taste of some of these things. Here's a few ideas I've tried for quadrivium arts, or will try at the proper time.
Arithmetic:
-We focus on solid numeracy and number theory in elementary school. I really like Math-U-See because of it's mastery-based focus on learning to use the four operations really well.
-In middle school, we started slowly working our way through A Beginner's Guide to Constructing the Universe. We watch the DVD, I read aloud from the text, and both of my kids have a workbook and work on the constructions on our Friday Schole days as often as we can. This set of materials focuses on number more as idea and pattern than quantity. It's fascinatingly beautiful!
-Continue to use math curricula through high school that focuses on mastery and mathematical reasoning.
Geometry:
-Constructing the Universe begins to bridge into geometry a little bit by teaching the students to construct shapes with the number patterns they're learning.
-We will study two years worth of geometry: one with a more traditional plane/solid geometry program. Our second year will be reading Euclid with Classical Math One by Daniel Maycock as a guide. (I realize this link leads to a discontinued item. Daniel is revising the guide book and re-releasing it this summer. So check back! It will be there!)
Astronomy:
-The best thing I've been able to find for this is Signs & Seasons. I guess I should qualify that with the best thing I've been able to find that is also do-able/affordable for us. Remember astronomy is not a science subject, but a liberal art in this context. So I'm not looking for a traditional astronomy course. Signs & Seasons teaches at least observation of the night sky and charting over the course of an entire year and navigational skills by the sky. The math required to actually do astronomy is prohibitive. So this is the best we can do. I'm going to pair this with some history/biography of astronomers as well. At least we'll be turning our eyes to the heavens, above and out of ourselves, and learning to see and observe what's going on.
Music:
This is the big unknown for me. There are some practical things we can do to start off with.
-Learn to play an instrument: piano, guitar, violin, anything really. This has always been a priority here and we've got piano lessons starting at an early age, and in 5th grade, adding another instrument. Our older two kids have added choir around 7th grade as well. Playing and singing daily is pretty crucial to laying a foundation of music in a liberal arts education.
-Listen to good music. What they listen to shapes what they crave. Expose them to the best music from history. Professor Carol's music programs do a great job of this. So do classical radio stations. There are lots of great YouTube channels on classical music, like Rousseau. We could watch these visualizations for hours. Get to know different composer's music as a whole body of work. Teach them how to listen to music. Memoria Press has a great program called Music Appreciation that teaches them basic elements of music that help them listen intelligently to great works.
Here's the thing though. There is much more to music as a liberal art than listening to and playing music. There are three different aspects of music as a liberal art, according to Augustine:
-musica instrumentalis : instrumental music, as described above
-musica humana : the proportionalities that exist in human society
-musica mundana : the proportionalities that exist in the world
That last one, I'm pretty sure I don't understand that. It seems to have some cross-over with cosmology/astronomy. Maybe it has to do with the sounds of the stars? Pretty sure we'll watch this video every year just in case that's what it means. :)
But that middle one. I think this is where music as a liberal art is really pointed: proportionalities that exist in human relationships. Augustine wrote,
"Musica est scientia bene modulande" - Music is the knowledge of modulating well.
This is about learning to order and harmonize ourselves with other people. Harmonize our own lives and live proportionally, within our limits. Learning to bring ourselves back into the harmony of God when we've stepped out in sin and are creating dissonance. To learn to see the master harmonizing skills in Jesus as he redeems and makes all things new. The harmony of the Trinity and Jesus as Logos of all things.
Music is not extracurricular. It is foundational, and ultimate, at the same time. By laying the foundation of music through playing and listening, we have an experience of harmony to draw on. We have heard harmony. We have felt discord and dissonance in our soul. We have experienced that relief when a dissonant chord resolves into harmony.
The point of music is to learn to modulate well. In life, keeping relationships healthy across time is all about modulation. Parenting is about modulation: not treating our children at twelve years old in the same way we did when they were two. Marriage is all about modulating to each other, on a daily basis.
"The well being of the human soul is a matter of internal and external modulation." (Andrew Kern. He must be credited with far more than this quote. Most of what I've written here is simply a narration of listening to him for a couple of years on the quadrivium and processing. It's a regurgitation of Kern's thoughts).
How do we teach this? I have no idea. But one thing I can do is to keep learning about it and modeling it in my own life and home.
There's so far we have to go yet. So much left to do. I'm so so thankful to those blazing the trail like Andrew Kern, Carol Reynolds, Christopher Perrin, Daniel Maycock, Martin Cothran. Support their work if you can! It is so important! And join me in giving our kids what we can and resting in that as being enough!
Comments
Post a Comment