A Plea for Mathematics

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Georg Cantor, the inventor of set theory, which often is regarded as the basis of all modern mathematics, once said, “The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.”

I’m expecting that most of you disagree with Cantor, and I would be surprised if you don’t. As of now, mathematics isn’t exactly viewed in a positive light by the majority of society. Math is portrayed by social media and movies as a boring and overly complicated pursuit for geniuses who have too much time. We are taught that math has some nifty applications that can help you out a lot if you are smart enough to know how to use it, but that otherwise math has no worth. In writing this I hope to at least convince you that mathematics has some intrinsic value, and that you don’t have to be a genius to understand or appreciate it.

Currently, when one enters a math class, one’s reaction is usually a mixture of boredom and dread. Constantly, the value and/or use of a certain topic in math is being called into question. But it’s not your fault for not understanding, it’s the fault of the system.

To be specific, I do not mean that our math teachers are to blame, but rather the entire American mathematical education system is to blame. There are a lot of great math teachers at Tam.

“I think teachers have their hearts in the right place, and I honestly think each teacher is doing what they believe is best for the kids … at least most of the kids … I think there isn’t a silver bullet that inspires everyone to love math,” math teacher Chris Erlin said.

And I must agree — math isn’t for everyone. Those who do not want to learn math will not learn math. Those who are not willing to think in a different way will not learn math. But regardless of intelligence, those who are open to looking at the world from a new perspective have the ability to become great mathematicians. To find this ability, one must recognize the one quality all mathematics has in common: logic. Mathematics is a web of facts that are all connected to each other logically.

You may be thinking, “Hey! That’s not the math I know … Where do all the numbers come in?” And by thinking that, you’ve just hit upon a really good point: math is not about numbers — numbers are just a tool.

“Math is about relationships between/among things. Comparing, quantifying, recognizing patterns and extrapolating. Numbers allow us to more easily see the relationships,” Erlin explained.

But, unfortunately, that’s not the story told by our homework. Doing the same problem over and over with different numbers is not math — it’s busywork. And as much as teachers may want to teach the math that they love, they are trapped by a lack of funds and awareness.

Math teacher Rebecca Henn offered some ideas about the perfect math education. “Ideally, it would be by individual curriculum catered to each student … Some students see the world more abstractly through mathematical proofs or through art, some students understand the world better through solving real concrete problems such as those found in designing and building things. Obviously, catering to each student’s inherent interest would be the best education because it would speak to each student in a more engaging way,” she said.

But as for trying to implement this system, Henn said, “Nope. Unfortunately, at this time, we do not have the resources to make this type of teaching possible.”

Which totally sucks, because everyone deserves to be taught math in a way that they understand.

From what I’ve seen so far, the curriculum has a major flaw: its failure to focus on rigorous mathematical logic. It seems as if the concept of mathematical proof is first introduced in geometry, implying that it is more advanced than the math taught in middle school, which is totally wrong.

From a very young age, we are taught a lot of different rules: no hitting, no biting, if you do something bad then you get punished, etc. But why can’t we also be taught about if-then conditional statements and the other aspects of a logical mathematical argument at the same age?

If we were taught at a young age how to think the way mathematicians do, then we would not have to waste time each school year re-learning the material of the previous year. The more one understands the logical proof of a certain fact, the better one understands, knows, and remembers the fact itself.

According to a 2018 study published on the Wiley Online Library, students who studied a subject and then attempted to teach it to other students did better on tests than students who studied the same subject without attempting to teach it. The study also showed that the students who attempted to teach were able to retain the information much longer than the other students.

This phenomenon, known as “learning by teaching,” can be explained by the fact that in order to teach something, one must understand not only the little details of said thing, one must also understand the big picture. That is, one must understand the reasons that the little details are true, and how the little details relate to each other.

It is clear that we are generally not being provided the tools we need to truly learn and understand the math we are being taught. And for this reason, most people fail to see the intrinsic value of mathematics. So at the end of the day you don’t have to love mathematics, or do it in your free time, or name your kids after your favorite theorems, or anything like that, but you should, going forward, look at mathematics as something of poetic abstraction: capable of uncovering hidden truth, intuition, simplicity, and elegance through nothing but a logical process.

Graphic by John Overton.