Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.
By the end of elementary school, as our approach to the discipline currently stands, 95% of people will already have learned all of the mathematics they will need in the real world. Yet schools persist in insisting that students study the subject in an isolated context until high school graduation, while most universities place an inordinate value on success in the subject for college admission, even to programs in the humanities. The continued teaching of mathematics as a discrete subject in the 21st century falls roundly into the realm of those things we continue to do because we have always done it this way in schools. It’s time to question this assumption. It’s time to change mathematics in schools. Why? Because, ironically, it is far too important a subject, with the potential of a beauty that rivals any art form, to be treated the way we dismally continue to treat it.
We should only teach things in school that are, what David Perkins calls, “life-worthy”. The central thesis of Perkins’ work is that, in order to make learning meaningful in our schools today, the concepts and big questions that comprise our curriculum should be life-worthy. He defines this, quite simply, as things, “likely to matter in the lives learners are likely to live.” The majority of mathematics that we teach in our secondary schools will never be used again by most adults in their lives. Andrew Hacker, writing in The New York Times in 2012, references, “a definitive analysis by the Georgetown Center on Education and the Workforce forecasts that in the decade ahead a mere 5 percent of entry-level workers will need to be proficient in algebra or above.” So why do we do insist upon forcing it on everyone?
The truth about the teaching of mathematics as a vital life tool was well summed up by R.P. Boas, writing in The American Mathematical Monthly in 1957: “When I was teaching mathematics to future naval officers during the war, I was told that the Navy had found that the men who had studied calculus made better line officers than men who had not studied calculus. Nothing is clearer (it was clear even to the Navy) than that a line officer never has the slightest use for calculus.”
I am not being dismissive of the importance of mathematics. All learners need to understand arithmetic, but very few of us are ever going to be asked to find x in our real lives nor have we ever genuinely been concerned with his or her enigmatic whereabouts. Returning to the The American Mathematical Monthly, this time, in 1987, Underwood Dudley states: “The vast majority of the human race, and the vast majority of the college-educated human race never need any mathematics beyond arithmetic to survive successfully.” This is my core point, and it’s not just about mathematics. We should consider all subjects in this same context.
We know that mathematics is a critically important part of our world. Hacker also quotes Peter Braunfeld of the University of Illinois who tells his students, “Our civilization would collapse without mathematics.” So much of the essence of future knowledge, extending our very existence, depends upon this discipline. Extending our very existence, in a truly personal sense, also depends on being healthy, but schools don’t require all students to take physical education, for instance. The Holy Grail of mathematics for future learning and the notion of algebra as the gatekeeper to higher education is, frankly, an anachronism. Smartphone applications can take care of most of our mathematical needs and computing has the power to negate the most painful of math classroom struggles. Mathematics as a discrete discipline is essential to the future of schools, but potentially only as an elective for those who choose the higher math route. For the other 90%, the potential to explore mathematics in a more diverse, meaningful context is endless and necessary. There is food for thought in what Hacker suggests:
“Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. … I hope that mathematics departments can also create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet. If we rethink how the discipline is conceived, word will get around and math enrolments are bound to rise.”
I am fortunate to work with an outstanding team of mathematics educators in our middle school. All are true mathematicians, all make exceptional connections with students. They are future thinking, open-minded users of technology who have spent the last two years dismantling the “levels” that have led to the traditional streams in mathematics, the ones that require teachers to pass judgment on future mathematical ability at a young age. The work is compelling and admirable and the goal is to increasingly bring mathematics to life in engaging ways that are authentic and meaningful, through STEAM activities, brain games, and practical applications such as personal finance and business investment. The constraints of forcing all students through a rigid system of learning this otherwise aesthetically powerful subject with little opportunity for students to make decisions about their personal interests will always hamper the future of mathematics in schools. Math education all over the world struggles to get over the myth of nightly homework that is frequently about repetition of things already mastered or the frustration of being confronted by repeated examples of concepts not yet grasped. It is a subject that, traditionally, has reveled in the cult of its own complexity. Many math teachers are subconsciously aware of how they will be judged by their students’ next math teacher, so the cycle goes on, relentlessly. Math scores are higher in Singapore and Finland, so what? What are we measuring and what values do we seem to believe we are falling behind in?
So, much of what we learn in mathematics in school is not life-worthy? How about the facts we memorise in history class or the chemical equations in science that we forget after the exam cram? How about all those things that used to be regarded as consecrated knowledge that are now freely available on Google? The truth is, we face an interesting dilemma as educators and parents: we don’t just want our students and children to be educated; we want them to be cultured, too. In a world of knowledge abundance and digital access, it will become increasingly clear that the most effective learning will be that in which the learning purpose is genuinely clear and valid. No longer can we tell students that fractions, periodic tables, or grammar rules are “going to be important’. We need to engage them in the real work of applying their learning across disciplines to solve or consider real-world problems. Mathematics as a discrete, required subject might not be a requirement by grade 8, if not sooner. The result would be good for students who would be free to explore it in liberal contexts and for the discipline of mathematics with students of higher mathematics soaring even higher.
We teach coding, design, engineering, and an extensive range of subjects in the arts that explore mathematics in a broader context that transcend the textbook and the endless litany of mathematical “skills” that we require students to learn about that are essentially of no value. We need to throw off the shackles of traditional mathematical conformity and liberate both teachers and students to work in meaningful ways on the application and enjoyment of mathematics through interdisciplinary, project-based learning and an exploration of personal passions that will place mathematics as an increasingly valued and treasured learning experience in our schools. Part of the essence of the discipline of mathematics, its growing complexity, that very thing that creates cognitive dissonance and develops resilience, is surely something we want our young people to choose to willingly engage with? How about ensuring that our students can truly understand the purpose of mathematics and its beauty? How about engaging them in a love of the subject in ways that will see them choose to pursue this interest in life?
It’s time to change mathematics in schools. It’s too important to leave it the way it is.