The Dance of Number

Once upon a time, my heart brimmed with a love of fairy tales. As a small girl, I wanted nothing more than to live in the universe of the Brothers Grimm, to wander the world of Hans Christian Andersen, and to discover caves filled with treasures just like Ali Baba in “The One Thousand and One Nights.”

When I was five, one of my older brothers read Tolkien’s “Hobbit” to me. That began a love affair with Middle Earth that continues to this day. I read it myself soon afterward. For years to follow, I regularly read it and its companion tale, “The Lord of the Rings.” Even today, when I see a river meandering through some woods, I wonder if I will hear Tom Bombadil singing. When I pass a grassy mound, I suspect that within there might just lurk a barrow-wight…

I have a vivid memory of my father talking to me, when I was a bit older, about a man named C. S. Lewis who had written a fanciful book called “The Lion, The Witch and The Wardrobe.” That Christmas, the book was a present for me under the tree, a treasure nestled in a big box with other delightful books my father thought I’d enjoy. (Of all the gifts I’ve ever received in my life, that box of books is second only to the puppy I received the following year.) Like so many other people, I can’t see a wardrobe without catching a scent of pine. And don’t get me started with lamp posts…

For decades, one of my liturgies was to reread both Tolkien and Lewis yearly, like a pilgrimage to a sacred place. Then I met George MacDonald – who still dazzles me with his mysteries, so much so that whenever I hear the wind howl, my mind is filled with the image of a boy who rode the back of the North Wind.

While my mind swelled with fables, I also was mesmerized by numbers. They seemed exotic creatures, filled with possibilities. But then, along came long division…and math began to plummet on a downward trajectory. The wonder was leeched out of numbers steadily and surely. The mystery faded from enticement into disappointment, and from disappointment into frustration.

In contrast to the world of fairy tales in which the wonder exponentially grew, the world of math to which I was being introduced year by year shrank into pitiless drills, with no accompanying and enticing ambiguities, no stories to unfold—just right or wrong methods (most of which seemed arbitrary and bizarrely legalistic) and right or wrong answers. And wrong (with which I soon became all too familiar as the complexity of the math increased) always felt Just Plain Wrong.

It all went even more awry as the disappointment in the promise of math I’d once thought I glimpsed deepened into a sense of resentful, and eventually cynical, mechanistic futility. I was entranced by stories, enamored by their lessons. I got–or absorbed would be a better way to put it–the point. But I increasingly failed to see any allure or point to the math, and my disillusionment hardened into something uncomfortably close to dislike. The prizes the world seemed to offer–good grades and what seemed a hollow promise that I’d be rewarded some day in some distant future for being compliant–couldn’t convince me that what felt like blind and repetitive submission to The Math Textbook was worth overcoming my distaste.

So, I was not, and am not, a mathematician. But today, despite the eventually cold, hard ground in which it came to live in my heart, math fills me with wonder. How did a heart that had become a wretched grave for calculations, equations, and formulas soften?

It happened because I’m classically educated in the seven liberal arts–not only in the trivium, but also in the quadrivium. I’ve studied a share of arithmetic, geometry, astronomy, and music at St. John’s College. For example, with my fellow students I’ve walked through some Euclid, Apollonius, Ptolemy, Copernicus, Kepler, Descartes, Newton, and Einstein: reading their original texts, demonstrating proofs, and working through the problems these great thinkers themselves struggled with, pondered, solved, wrote about, and published–and with which, each in their turn, they rocked the world.

It was precisely because of this experience that my heart softened, and was wooed and captured by the wonder of the quadrivium. The daughter of musicians, I had grown up with and been surrounded by music all my life. Now I realized how intertwined arithmetic, geometry, astronomy, and music were. I glimpsed the fascinating depths and dizzying heights to which these arts—far from mechanistic, far from mere drills—aspired. And I fell into wonder…a wonder very much like what the stories and tales of my childhood had inspired.

I realized that there were puzzles and paradoxes in math that equaled the most mystifying flights of fancy. I also realized I didn’t have to be “good” at math. I recognized I didn’t have to be a computational wizard, nor did I have to have any brilliant mathematical thoughts of my own.  What I did have to do was learn the language of math–its unique alphabet (i.e. symbols), vocabulary, and grammatical structure (i.e. operations)–in order to wrestle, alongside those giants in the field, with significant and profound ideas that stemmed from some of the deepest questions human beings can ask about the world and our existence in it. Questions like: What is the world made of? What holds it all together? How does it all work together? What are the principles that govern it? How can it be best understood? Best governed?

Then, one day, I had children I wanted to teach. I desperately wanted to teach them math better than I’d been taught. I wanted to protect them from a hardened heart. I tried to do that, but the needed resources for a busy homeschooling mom were difficult, even impossible, to find. What I was looking for didn’t really exist. For my eldest, in fact, I didn’t even use a math curriculum until the fifth grade, so apprehensive was I about simply offering her a cold, unimaginative, textbook that isolated math from all the other amazing things she was learning and putting together in her experience. (Of course we “did” math, just not from a textbook!) I wanted to offer so much more, but time and resources weren’t on my side.

As our household grew, I succumbed to the recognition that I’d need to follow that pattern: in turn, each of my children received a math textbook in about the fifth grade. I tried to postpone the grind, the grim drills, the black and white harshness of “It’s just right or wrong, “ or, “Yes, that’s the answer despite the fact that it probably relates to little you consider important or interesting,” or, “Just do it that way, I promise you it will work even if you don’t understand it.” But ultimately, as algebra loomed the rubber needed to hit the road and the textbooks were ordered.

I tried to balance the use of these textbooks with stories about math and mathematicians. I always sprinkled in some Euclid…a little fairy dust to encourage flights of the mind. I talked about non-Euclidean geometry, paradoxes, the beauty inherent in an elegant proof, and the profound power of startling numerical entities (such as phi). I attempted to bring mathematics to life. I tried to present the beautiful enigmas and the wide-open spaces of mathematical possibilities.

But I was teaching elementary through high school students, and by the time they could’ve focused on some of the things I’d studied as a young adult they were in the throes of their own young adulthood, with so much to juggle and so many boxes that needed checking off that the world was imposing on them. There never seemed to be enough time to draw out the glory of math, to present it’s story and it’s interconnections. Until now.

With the publication of James D. Nickel’s curriculum, “The Dance of Number,” my hopes of a math curriculum that could open up the wonder of math in my student’s heart have been realized: a curriculum rich in history, language and etymology, science, and grounded in the wonder of the Creator and creation; a curriculum that would nurture not just mathematical literacy, but a “classical way” seeking to reveal the breathtaking beauty of mathematics and not bury it beneath the rigid grid of the merely useful.

If you’d like a glimpse into this new math curriculum, you’re invited to come alongside me here as I work through it with my student. Join us in the process, along this classical way, with “The Dance of Number.”

Major conceptual advances in science now require that we recover a view of the universe in which every single thing or event is in fact related to everything else.

Giuseppe Del Re, “The Cosmic Dance”

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