Algebra can be breathtaking. Yet most people don’t encounter it this way.
Algebra’s power and significance remain hidden inside a system of symbols and rules. For far too many, these symbols and rules lead to frustration and disillusionment instead of understanding.
Critics of requiring students to study algebra maintain that the subject is simply too difficult for many students, creating an unnecessary barrier between them and the attainment of their goals. Critics also argue that most people won’t ever use the algebra they learn anyway, so why make them take it at all?
While many recent critiques may seem unprecedented and especially penetrating, they aren’t really new criticisms at all. Powerful and detailed crusades against requiring algebra have been publicly waged for decades.
“The pupils have got to be made to feel that they are studying something, and are not merely executing intellectual minuets.”Alfred North Whitehead, mathematician, 1929
In 1930, a former commissioner of education in Massachusetts stated: “the algebra now taught in American high schools is a nonfunctional and therefore nearly valueless subject for 90 per cent of all boys and 99 per cent of all girls.”
A litany of such harsh reviews can be found in journals and newspapers throughout the first third of the 20th century, a dramatic demonstration of what contemporary mathematician Manil Suri describes as “our nation’s ambivalent relationship with mathematics.” It is high time to more creatively address this ambivalent relationship and redirect these attacks into more productive ways of presenting algebra.
Mathematician Alfred North Whitehead responded to such criticisms by arguing that educators need to do a better job of explaining the importance and meaning of their subject: “The pupils have got to be made to feel that they are studying something, and are not merely executing intellectual minuets.”
In other words, the purposes, relevance and, yes, beauty of school mathematics needed to be made far more transparent to students.
This remains true today, nearly a century later.
Mathematics is an ever-present reality, and we use it a lot more than we think we do. Even a simple thing like setting an alarm clock to link us from one awakened state at night to another in the morning, with precision, is an application of mathematics.
Algebra’s applicability to the general student lies especially in its ability to provide enhanced insight. It is not enough for most students to learn only the computational aspects of the subject; they must also see that algebra is bold and about big ideas. Teachers should document these characteristics through explicit examples that show the subject in action as a powerful and unifying instrument of human thinking.
One way to do this is by making students realize that in setting up one equation for a particular scenario they are simultaneously modeling dozens of other situations that may look different on the surface but whose algebraic DNA is identical.
For instance, have students first experience the laws of exponential growth by working with money, then guide them to the realization that if one thinks of those dollars as people or microorganisms, the same formula could describe the population growth of a town or bacterial colony. Or foster an appreciation that, when performing a routine simplification of a single innocent-looking variable expression, they are effectively, in one fell swoop, doing simplifications for all the infinitely many numerical paths that expression can ever take.
Algebra — more than arithmetic alone — has the capability to show how mathematics singularly weaponizes the human capacity for analogical thinking in symbolic and maneuverable ways that have dramatically impacted our civilization.
Still, many who question algebra’s place in the curriculum have justifiable grounds for doing so. The deepest and most dramatic features of algebra still fail to be conveyed clearly enough to most students.
The usual rhetoric in defense of algebra no longer works in persuading many of those with influence, and the chorus of powerful voices against the subject continues to grow.
If this growing tide is to be stemmed, something different involving more authentic engagement and demonstration must occur between math professionals, learners and educational policymakers to help algebra earn the same unquestioned acceptance in the curriculum that arithmetic has enjoyed since the 1800s.
Perhaps individuals with the influence and resources to creatively bring these groups together can organize, moderate and broadcast various “meetings of the minds” in the form of town hall discussions, forums and the like.
It is time for algebra to consistently be seen and experienced as more than a meandering stream of abstract variables, equations and procedures. By demonstrating and bringing its most dramatic features to the fore, we can forge a powerful tool in the fight against the bewilderment and resignation many learners feel in studying the subject.
In my own attempts at accomplishing this, I have found that my adult students are pleasantly surprised to see some of the similarities between the goals of algebra and those of other great areas of human expression and ambition — such as language, science, art and music — often citing those connections as being one of the more illuminating parts of the course.
Algebra must be appreciated within the context of its vast historical reach, its aesthetically pleasing ability as an organizing force in solving problems and its profoundly important contributions to the world. Although algebra’s meaning and power are often hidden, it is well worth the effort for all of us to work together to make its significance more transparent to students and the general public — they deserve more profound and enlightened experiences while exploring this beautiful subject.
G. Arnell Williams is a professor of mathematics at San Juan College. He’s the author of “Algebra the Beautiful: An Ode to Math’s Least-Loved Subject” (2022) and “How Math Works: A Guide to Grade School Arithmetic for Parents and Teachers” (2013).
This story about teaching algebra was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for Hechinger’s newsletter.