This essay by Shridhar Singhania '18 is the first in our new Voices of SAS web series. Voices of SAS will feature writings and talks by students and faculty that focus on a particular aspect of their St. Andrew's experience.
It's a regular Thursday morning in Middletown, Delaware. I'm running late to my first period math class (Advanced Topics Tutorial: Euclid's Elements) with my tie in my hand, too sleepy to be much excited for anything we might be doing in class that day. We'd been spending our class periods proving what Euclid had already done and documented in the world of geometry way back in 300 B.C, and just why we were doing this, I did not know.
I make it to math, and Mr. Finch divides us into work groups and tasks us with proving Euclid's Pythagorean theorem—the basis for almost all of the rest of geometry. I make my way to the whiteboard with my group. We draw a right-angled triangle and squares around each of its sides, and then flounder, not knowing where to go next in our proof for full on ten minutes, until Mr. Finch checks in and gives us some direction—a tiny hint of exactly one line, drawn by Mr. Finch to form a vertex to a side. Fast forward another ten minutes, and we all have smiles on our faces. Although I didn't quite realize the significance of it in the moment, Tiger Luo '17, Peter Choi '17, and I had put together a proof for the Pythagorean theorem that was very different than Euclid's.
This proof marked the end of our progress through Book I of Euclid's Elements—or rather, our version of Euclid's Elements. We had, as a class, recreated all of Euclid's proofs in Book I without actually ever looking at any of them! You may question our spending our time on such an exercise, since we could just as easily read the Elements and learn these proofs from Euclid himself. Reading through and studying his proofs would have given us the same knowledge—and perhaps more, quantitatively speaking, as we would have gotten through Book I a lot more quickly. The difference? Absorbing information isn't nearly as powerful a way to learn as is producing the information yourself.
Having grown up in India, prior to my arrival at St. Andrew's, I had been educated in a very different manner. Math in particular was taught in a different way, with a focus on speeding through concepts and memorization for maximum performance on tests and exams. As a child, math was by far my favorite subject, but this approach caused me to begin losing interest. Some of my friends really struggled to understand the math we were meant to learn, and resorted to memorizing formulas they didn't understand to ensure good grades.
Luckily for me, before I completely lost interest in math, I was admitted to St. Andrew's. I found that math here was taught in a more holistic way. It was paced so that students could gain a genuine and strong understanding of concepts. We spent our time in class applying concepts to word problems, so that we could gain an applicational understanding of math—it really does apply almost everywhere. My interest in mathematics was rekindled, and I became excited about going to math class (even when sleepy).
This Advanced Topics Tutorial on Euclid has been an even more enlightening experience. It's caused me to think deeply about the purpose of math, and even, in certain moments, my entire education. During the first week of class, Mr. Finch made us do something that felt like a complete waste of time. He asked each one of us for our take on every one of Euclid's definitions, postulates, and common notions. These are very basic and almost "common sense" components of geometry—they include axioms such as "things which equal the same thing also equal each other." Generally speaking, most of us accept and know these concepts even if we've never taken a geometry class. Yet here was Mr. Finch, spending the first three days of class going through each of these axioms. At the end of our discussion of each, he would ask, "Are you willing to stake your life on this?" This simple question showed me how essential it is to not only know but understand common notions, and how deep our understanding must be in order to progress forward mathematically.
A couple months later, here we are having proven the Pythagorean theorem using a proof completely different from Euclid's. Had we simply read and studied Euclid's text, we never would have had the opportunity to explore the proof on our own, on the whiteboard, and we would have been incapable of writing up a proof different from the one presented in the book; we would have been neither mentally motivated nor intuitively equipped to do so.
In having the freedom and ability to collaborate with one another, think on our feet, and actually do the work of a mathematician instead of simply learning from the works of one, we strengthen our overall ability to think. Was this class harder than the previous math classes I had taken? Of course it was; that is exactly why it so challenged my mind to become more sophisticated. I finally understand the true purpose of learning mathematics: it's not to be able to calculate things, or know formulas, or solve equations; we have calculators and computers that are becoming more capable, day by day, of calculating, using formulas, and solving equations. The purpose of actually learning math is to develop new levels of logical thinking and intuition. It is to make us more able to solve the real-life problems we face in our daily lives, not to sit at a desk, surrounded by white walls, and endlessly plug in numbers to formulas.
My St. Andrew's math experience is allowing me to grow as a thinker. It's enhanced my intuition and fostered my creativity. It makes me feel more confident that I'll be able to solve bigger problems and issues off the whiteboard and outside of the classroom. Perhaps the entire point of a good education is learning to think and solve problems, in whatever field one may choose to pursue. I see now that the distinction between learning what to think and learning how to think is massive; this is what separates a good education from a great one.