The Case for Mathematics
Our math education narrative needs revision.
In this season of commencement speeches, students are painfully familiar with the impending anxieties of “the real world.” As student and teacher, I can fairly say this is no less true every day inside the classroom. It seems we students, secondary and post-secondary alike, are always asking: will the material of this class be important in the real world? How will learning these things help me get a job out in the real world? How is my education preparing me for college or the workforce? Will I use this in my daily life in the real world? If not, I live in a fast-paced world — so why should I care?
Advanced mathematics is one of the first to fall against contingencies. Not that arithmetic fails to stand up in the real world — computational skills are a must. Math education apologists rightly underscore the broad uses of mathematical tools in daily life. Ubiquitous word problems, complete with groceries, trains, and skate ramps galore, indicate that our educators buy into this philosophy: math is important because it is relevant. Such a philosophy of education is utilitarian at its core—we assume students should foray into a subject only insofar as it is useful to them.
Further mathematics, such as calculus or linear algebra, is now equally key to navigating the developed world. Science, technology, engineering, and mathematics (together known as STEM) have fast become a focus of Western society and its education. American politicians push for United States competitiveness in a broad range of scientific disciplines, and deplore our students’ performance compared to those of students in other countries. But the focus on STEM is hardly restricted to the public sphere. Individual fervor over STEM jobs is quite intense — doctors and software engineers topping every list of the highest-paid or most-respected professions. And mathematical literacy is a prerequisite for virtually all of this. Its value has thus become largely exigent — inexorably depending on the realities of the social world around us.
Unfortunately, a curricular emphasis on “the real world” creates a learning environment with a gratuitous attention to memorization and a horrifying deficiency of individual exploration. Such misdirection, usually accompanying an unproductive system of archetypes that attribute mathematical excellence to genius and prodigy instead of hard work and practice, muddles our society in rampant, careless innumeracy — what we might call the “I just can’t do math” culture. When mathematics no longer appears useful to a student, or even within their grasp, the relevance-based case for mathematics disintegrates. Math educators find it difficult to motivate students in this frame of mind.
The “I’m bad at math” paradigm is an apology common to students and adults alike. It is self-defeating — a real failure of our culture — and what’s more, a stark contrast to our perspective on illiteracy. We never hear offhand boasts to the tune of “I’m bad at language” or “I won’t use language in the real world” — illiteracy is understandably troubling, even to the point of absurdity. Language is so obviously useful, an imperative skill to command. But note well: we don’t become literate simply to communicate — we learn a language for a whole host of intangible reasons, including to organize and understand our thoughts.
Mathematics too is a more subtle teacher than is widely perceived — mathematical cultivation shows itself in the way we deal with abstract concepts and problems of logic, prioritize, weigh quantities in making decisions, engineer structures to make our lives a little easier, and approach various other obstacles. A strong mathematical education is a training in logic, objectivity, curiosity, intuition, and deduction, not a manual for blind application. We don’t learn mathematics because we will encounter word problems in the real world — we learn mathematics because it teaches us to reason.
That nuance is one that continues to evade society at large. Popular innumeracy has real consequences when we try to solve problems, especially in the poor and disenfranchised communities it disproportionately affects. It also fails us when we make decisions as a society — inaction on anthropological climate change and fear of vaccination being current examples. We face a whole population that doesn’t know why math is useful—and consequently, since we are all absorbed by utilitarianism, one that doesn’t believe it is worth learning at all. We have a case for mathematics that just doesn’t work. How are we to proceed?
“[college education ought to have] one goal, — not to earn meat, but to know the end and aim of that life which meat nourishes”
W. E. B. Du Bois, The Souls of Black Folk
The problem, as I have suggested, is in our foundation. Framing the case for mathematics in the language of relevance, as we have implicitly done, imposes a double standard, and one that makes our case for mathematics significantly weaker than arguments for other subjects.
The liberal case for the arts and humanities is very different. We don’t study the fine arts merely because they are useful to us — but because they help us understand ourselves and each other, preserve our memory, or inspire us to be kinder to one another and keep going. We don’t study literature or composition in order to emulate the great writers, poets, and playwrights of the past — but to know the value in learning shared experiences. We don’t explore the ocean floor, protect endangered species, or look out into the vast depths of space because those pursuits have some tangible benefit to our lives — or some financial gain — but because wonder and imagination are the daily bread of life. Such pursuits push us higher — and in some immeasurable way, they make us better and our lives more meaningful.
We study all these subjects because they endow our lives with purpose. Mathematics is no different — we study mathematics because it is meaningful and beautiful. Beauty is utterly incommensurate with the vaunted ruler of relevance. But the most important things in “the real world” can be found not in our bank accounts or in our daily calculations but in the life of the mind and of the heart.
Communicators for all these other fields have effectively identified the important intangibles in their disciplines — beauty, curiosity, endeavor, truth, and virtue, to name a few. A successful case for mathematics must count math as part of the “end and aim of that life which meat nourishes.” We math educators need to demonstrate with every fiber of our being that mathematics is full not just of incredible opportunity, but of genuine joy. Utility is justification for some, but for many more it is simply not enough. I suspect a glimpse of meaning is what students are hungering for. If we hope to beat the culture of indifferent innumeracy, we will need to proclaim at every opportunity that mathematics is relevant, yes, but also meaningful. Perhaps if we do that, mathematics will finally take its rightful place among the disciplines that matter.
