New Math!

Side note: It's not the movement I'm describing (or all that related to it), but I really wanted to share Tom Lehrer's song about the New Math curriculum, which I hear was designed by a Uni alum: https://www.youtube.com/watch?v=UIKGV2cTgqA

With regards to the essay, please enjoy and let me know what you think of the argument!

These days, there is a growing movement to change the K-12 mathematics curriculum. Too many people are growing up hating math and believing it has no place in their lives beyond school. To change this, standardized tests and curricula are increasing emphasis on solving “real world” problems, focusing more and more on gathering information from charts, understanding statistics, and grasping the fundamental ideas of geometry and algebra. However, in doing so they entirely miss the point of math. It’s not a science, it’s an art. Math is intrinsically beautiful and its study is a highly creative endeavour. Focusing only on the most common, specific applications of math in everyday life is like teaching music theory solely based on today’s pop music. Sure, that’s a lot of what people will see later in life, but it’s not nearly as interesting as seeing the full range of the subject. If middle school students aren’t excited by calculating averages, how can we expect them to enjoy calculating a mortgage instead, especially when a plethora of calculators exist to do it faster and better online? No, to be more successful math education needs to go in precisely the opposite direction.

Mathematics is woven from ideas and logic. At the highest level, it’s not really about calculation and numbers at all. It’s about abstraction, deduction, and innovation. New problems constantly arise in the world, ranging from unresolved paradoxes in quantum mechanics to the unpredictability of weather to aimless daydreams about the volumes of coffee mugs. These problems may seem completely unrelated, but more often than not math is able to connect and clarify their solutions. Throughout history, mathematicians have been able to resolve seemingly insurmountable problems just by viewing things differently. For example, Einstein’s theory of special relativity stems from changing a single assumption, flipping one sign in the equations governing reality, and yet it has proved to be one of the most brilliant and revolutionary ideas in physics. In school, we should be teaching people how to be creative, not beating them down with mind-numbing formulas given to us by the geniuses of old.

Even if you agree with me, you may be wondering how students will learn if left to their own devices. After all, it took thousands of years for modern mathematics to be developed, so it’s unreasonable to assume any student could reinvent it in twelve short years. Also, by having students derive formulas for themselves we run the risks of having them fall into traps, making mistakes and learning things the “wrong” way. Those concerns are legitimate, and I don’t think anyone has a full answer to them yet. However, I believe that the key is to mix strategies. Introduce problems and let the students think about them before revealing the answer. Don’t shut down unorthodox methods, reward creative thinking. Have them work individually, in groups, and as a class on different days. Have a teacher work closely with the students to help them get through potential roadblocks. Prompt them with some of the questions that have inspired new branches of mathematics or forced reevaluation of old ones. Change doesn’t happen overnight, but every time a teacher replaces a bit of rote memorization with an interesting derivation, the chance increases that the students will fall in love with mathematics. Or at the very least, learn to tolerate it.