Last night I asked my karate instructor, an attorney for 35 years, if he had ever used the quadratic formula in his professional career. His answer surprised me a bit. He said, “No, but I also took many years of French, and I never had to use that either.”
I know that the quadratic formula applies to more than simple quadratics, because quadratics are found in the most surprising of places (logarithms, differential equations, linear algebra, etc…). But why are we learning it if students are never going to use it? You can have a great career that pays great money, but never have to use the quadratic formula, or really any math beyond algebra 1. So why learn it, or any type of higher level math if you’re never going to use it?
I think there are three answers to this question. The first answer is that math is part of the school curriculum. That may not seem like a good answer, but I think it’s an excellent answer. Why is it part of the curriculum? A lot of people have this notion that school should be trade school; strictly for obtaining employment. However, school in the United States (up through college) is not trade school. It is set up to give a liberal education to everyone. That liberal education includes mathematics, science, English/language arts, social studies, and more. Students are learning this for 2 reasons. First of all, nobody knows for certain that they will never use math, so we might as well give them all they can get. Secondly, in a more broad sense, we want the next generation of Americans to be thoughtful and intelligent. We want them to know how to write a letter, how congress works, what The Battle of the Bulge was, how cell division works, and the quadratic formula. Knowledge doesn’t have to be the means towards the end, it can be an end all by itself. There is value in having knowledge, and value in being educated. Education enhances our personal lives by attaining values higher than our basic needs, and it advances our civic lives by being positive contributors to our communities.
We want Americans to be educated because when election time rolls around everyone should know how they’re being affected, or when something is happening in the political scene that you don’t like you can write a letter to your congressman. This answer can apply to most of the school curriculum, but not so much math, or writing haiku, or learning French.
We learn how to write Haiku because we can appreciate its beauty. You can also learn math out of appreciation. Math can be appreciated because of its massive collection of applications, or because of its purity. I’m mostly a pure math person, but I appreciate that all math has application somehow, even if we don’t know yet. What I like about applied math is that I better understand the world around me. I get satisfaction out of knowing that a Google search is a massive exercise in linear algebra, and that throwing a ball has within it the quadratic formula and calculus. Even though I frequently forget how to apply my mathematical knowledge to these applied subjects, I feel good knowing that I have some understanding of how they work. When it comes to pure math I get satisfaction by working hard on a subject and being able to solve the problem. I may not know what I’m try to solve for, but I’ve solved the problem! This leads into the third and final answer, we learn math because it makes us better thinkers.
At my last school I was the only high-school math teacher. I was told by many of my students, colleagues, and superiors that I was so smart and analytic. I sincerely do not believe that I am “smarter” than any of those people who said so. I believe, and I tell my students this, that I am not smarter than any of them, I’ve just been trained in a certain subject matter. Just as the black-belt in karate is good because he practiced his karate, I’m good at math because I’ve practiced math. Learning this math teaches you to think in a certain way even outside of math class. The black-belt walks out of his dojo not realizing that all of his movements are different, not just his karate moves. Similarly when we walk out of math class we are unknowingly thinking differently about the world. This helps us think “smarter” about things. It hasn’t made us smarter, but we’re thinking in a more efficient way.
There is a fourth reason too, but it is an extension to the first answer. More on that in my next blog post.