What's The Point?

In the original The Karate Kid, there's a well-known sequence of scenes in which Mr. Miyagi has Daniel perform seemingly karate-unrelated tasks (waxing cars, sanding floors, painting fences, etc.) as part of his training. Daniel dutifully completes the tasks to the point of exhaustion, but eventually reaches a breaking point at which he protests that these things have nothing to do with the goal of learning the art of self defense.

When I observe students in a typical algebra class, I see them memorizing a lot of formulae, graphing techniques, and mathematical jargon. They do so with varying degrees of effort and enthusiasm (more the former than the latter), mainly owing to their desire to get good grades, or at least pass the class. But much like Daniel waxing those antique cars, they have no idea what any of it has to do with reality.

I recognize that it's often necessary for young people to be trained to do right things before fully understanding the reasons as to why. But at some point, they need to experience an enlightenment as to the purpose of their toils. In the case of mathematics, I submit that such enlightenment comes all too rarely. I further submit that, if the study of geometry (specifically Euclidian) preceded the study of algebra, a great light would illuminate the caves of many young minds.

[I wrote this short piece after observing a series of high school algebra classes, and also reflecting upon my own experiences with the study of mathematics.  It wasn't until I participated as an adult in a course on Euclid's Elements that I came to appreciate the significance of algebra and other math disciplines.  I plan to write a more detailed article that explores the importance of Elements, and why it should be an intregral part of any serious classical education.]