Every Wednesday in math, the Algebra 2 class takes a break from their normal routine. They set aside their math books and pull out their notebooks to study a section from the most famous geometry textbook ever compiled: the Elements.
This book is estimated to have been written around 300 B.C. by a Greek mathematician named Euclid. At least, he is the one to whom the work is attributed; scholars believe the entire work to be a unification of the works of various Greek mathematicians who lived before Euclid. After Elements was written, it became widely used and revered as a standard of geometrical thought. It was translated into Latin by the Romans, then into Arabic during the time of the Byzantine Empire. Since then, it has continued to be spread, translated, and used in the West to this day.
The book itself doesn’t resemble what many would consider a normal math textbook. It doesn’t have lessons or problems, at least, not in the way we think about lessons and problems. Rather, each “lesson” in Elements shows you a geometrical fact, called a “proposition.” The book does not explain each proposition. Instead, it leads you on a little journey starting at what you know, then it guides you on a clear, logical path in such a way that when you reach the end, you fully understand why that new fact is true. In fact, all thirteen “books” in Elements are one big journey, each book building on the last, all beginning with a set of only a few assumptions. Elements is extremely long, which means there is an astounding number of geometrical facts which (somewhat miraculously) come out of just those few starting assumptions.
If you like math, that might be a fascinating bit of knowledge; if you really like math, you might even work through a part or all of the book on your own. But what are the benefits of teaching Euclid’s Elements to high schoolers? For one, the old Greek approach to learning math is something that has to a large extent fallen out of use in math education. Showing curious mathematical or geometrical facts to students is still part of math, to be sure. But it seems that in many cases, showing facts gets largely taken over by showing methods—“how to do” certain kinds of problems.
Methods are useful, but they can get to be completely overwhelming for students if they aren’t accompanied by an understanding of the actual math facts in reality. I could teach a student how to divide a whole number by a decimal number, and he could learn to do it perfectly. But until he understands what division actually is, or what decimal numbers actually are, I haven’t taught him much at all. Elements seems to be solely concerned with teaching the “what” and not the “how.” It shows the logic behind things like triangles and circles, lets you get to know them well, and helps you understand the logic in them.
There’s something very valuable in that approach in a Christian education. Mathematical methods and tricks are great, necessary even, when we are concerned with serving our neighbors with math in our stations in life. The “how to do” of math is incredibly important. But in Christian education we are also concerned with teaching true facts about reality and the beauty in the world. God is the source of that beautiful order in the world, and we humans are the ones who have the privilege of discovering and enjoying it. Euclid’s Elements is not the only way that discovery can be shared with students, but it is certainly one very wonderful (and fun!) way to do so.
In Christ,
Mr. Hahn
