While teaching geography at a college several years ago, I met up with a student in the faculty room during a free period to discuss her ideas for the course project. In the course of conversation, I asked what her major was. “Geology,” she said. “I like diggin’ in the dirt.” Every bit of her appearance said “outdoors person,” from the mountaineering windbreaker to the cargo pants to the hiking boots. I asked where she was in her degree program, just starting, almost finished? She said she should have been graduating this semester… except for calculus. She had failed it. And at this college, as at many other colleges, calculus—a four-credit class—is a requirement for anyone majoring in geology, biology, chemistry, and other physical sciences.
This student had lost four credits’ worth of tuition money, in return for nothing but a lower GPA. But that was the tip of the iceberg. The student said this was the third time she had failed calculus. Twelve credits’ worth of tuition down the drain. She said she would take it a fourth time next semester, and if she didn’t pass it this time, she would have to consider changing majors. Or maybe just not finishing her degree.
The common requirement to pass calculus in order to major in a science is a killer of students’ dreams. And it unnecessarily limits the pool of future scientists.
Charles Darwin is a classic example of a genius naturalist who was not a natural at math. As a young man, he sailed around the world aboard the HMS Beagle and explored the giant tortoises and iguanas of the Galapagos, the rainforests of Brazil, and the coral reefs of the South Pacific. From these sorts of direct engagements with nature, he developed his theory of evolution, which revolutionized science. But Darwin wrote in his autobiography that after studying math as a young man, he found that “it was repugnant to me.” When statistics stumped Darwin during his experiments investigating the advantages of crossbreeding plants, he called his cousin, the statistician Francis Galton, to try to make sense of the numbers.
Similarly, Thomas Edison said that as a boy he had a “distaste for mathematics.” But this did not stop him from becoming one of the most famous scientific inventors of all time. “I can always hire a mathematician,” said Edison, “but they can’t hire me.” Edison was so interested in chemistry that at the age of 13, when he got a job as a newsboy and concessionaire on the Grand Trunk Railroad, he brought a chemistry set aboard so he could do experiments during layovers. Math and science are distinctly different fields, and a talent for one does not imply a talent for the other.
According to professor emeritus Andrew Hacker of Queens College of the City University of New York, less than five percent of Americans will ever use any higher math at all in their jobs, including not only calculus but algebra, geometry, and trigonometry. And less than one percent will ever use calculus on the job. Born in 1929 and holding a PhD from Princeton, Hacker taught college political science for decades and has also been a math professor. His book The Math Myth: And Other STEM Delusions argues that not only college students but high school students should not be required to take algebra, geometry, trigonometry, or calculus at all. Hacker points out that not passing ninth grade algebra is the foremost academic indicator that a student will drop out of high school.
Before the objections tumble forth, I should emphasize that both Hacker and I like math and neither of us wants to remove all math requirements; we want to improve them. And I believe high school students should be required to study algebra and geometry. But Hacker’s larger argument is that both high schools and colleges should switch to teaching more useful types of math that can help students navigate the real world. He says American schools teach basic arithmetic well up to around middle school, but they stop there when they should continue teaching what he calls “adult arithmetic” or “sophisticated arithmetic” rather than veer off into more abstract types of math.
What if, for example, instead of spending months learning about derivatives, quadratic equations, and the interior angles of rhombuses, students learned how to interpret financial and medical reports and climate, demographic, and electoral statistics? They would graduate far better equipped to understand math in the real world and to use math to make important life decisions later on.
So, how did calculus become the gatekeeper for majoring in science? In his essay, “Why Defending America’s National Security Requires Calculus and Critical Thinking,” the American Enterprise Institute’s Michael Rubin explains that it was the Cold War Space Race against the Soviet Union that ushered in the rise of calculus in American education:
The Soviet launch of Sputnik, the world’s first artificial satellite, on October 4, 1957, shattered the drive toward statistical literacy. Until that day, most Americans believed the free world had the technological edge. The Soviet success created a crisis in education as American leaders, politicians, and educators across the partisan divide understood that American education lagged behind the Soviet bloc in math and science. To regain the edge in the space race meant teaching American students calculus and the math necessary for them to become rocket scientists. This was the genesis for the National Defense Act of 1958, the first major federal foray into education since the 1917 Smith-Hughes National Vocational Education Act. For the first time, the 1958 law made funding available explicitly for new programs in mathematics education and elevated the instruction of calculus. A House of Representatives report from the time declared, “It is no exaggeration to say that America’s progress in many fields of endeavor in the years ahead—in fact, the very survival of our free country—may depend in large part upon the education we provide for our young people now.” [...]
[T]he 1963 National Science Foundation conference argued that by the end of twelfth grade, students should have “the equivalent of two years of calculus, and one semester each of modern algebra and probability theory.” Calculus instruction took off. In 1955, 285 calculus students took the Advanced Placement test. Less than twenty years later, that number surpassed fourteen thousand. Today, perhaps eight hundred thousand American high school students take calculus, a twenty-fold increase over forty years.
In short, America’s calculus push was launched over 60 years ago in the belief that calculus was necessary for national survival in the coming Space Age. But times have changed. We are now in the Information Age, and preparing students to build rockets is not as essential for the majority of science majors as learning to interpret and prioritize a sea of information. And far more scientific information circulates in the form of statistics than in any form related to calculus.
Rubin goes on to illustrate how, in the 1980s, American educators began to suggest that statistics might be more important for the future than calculus, which led to the first AP Statistics exams in 1997. He says a college educator told him that this introduction of AP Statistics “occurred despite the best efforts of ‘the calculus mafia.’” The calculus mafia is, unfortunately, still alive and well today: In 2021, roughly 375,000 students took the AP Calculus AB or BC exams, while only about 183,000 took the AP Statistics exam.
Neither Hacker nor I believe that calculus is unimportant or uninteresting, nor that it should not be required for certain majors, like engineering, for example. The real question is: Why should passing calculus be required to major in biology any more than passing biology should be required to major in math?
Hacker says one of the most common arguments colleges make for maintaining calculus requirements is that they put “rigor” into the curriculum. But he argues that there is no evidence that calculus involves any unique rigor. To which I would add that the perceived difficulty of calculus is due largely to the way it is taught, which is highly fragmented, abstract, and divorced from its real-world applications. Students often learn very little about what calculus is actually used for. They are taught to memorize long series of steps in which they manipulate symbols and numbers to produce an answer that has very little meaning to them. Even students who pass calculus with flying colors often leave with little understanding of what the purpose of calculus is—which, ironically, is the most important thing they need to know about calculus.
Yet somehow, the vague perception persists that calculus requirements make science majors “rigorous” and filter out students who don’t belong. But the evidence on the history books is that many of the best scientists have struggled with math, from Darwin to Edison to Alexander Graham Bell, Michael Faraday, and E.O. Wilson. Said Wilson, the “father of sociobiology,” in a 2017 Web of Stories video that should be required listening for science majors:
To be a successful scientist, you need to do what you like to do. If you don’t like mathematics, don’t give up. That doesn’t forestall your being a scientist at all. I have, at best, average mathematical ability. It comes hard to me. If you really have a taste for laboratory work, white coat, experiments, measuring, and so on—and a lot of very promising scientists do not have a taste to be an experimental scientist—don’t worry about it. If you do have a taste for mathematics, or physics, or chemistry, or getting in a lab right away and titrating and watching cultures grow, go that way. Wonderful, great career ahead. But if, on the other hand, you prefer the outdoors, if natural history is what you really would like to do, the world awaits you. And more so now than ever. Never mind that science has as its primary language mathematics. It has other languages as well. And it has a requirement overall for gifts often lacking in those who are enamored of mathematical analysis and laboratory work, namely intuition, the ability to recognize patterns, and, above all, a lifetime devotion to fine detail of the wonders of the natural world. …
A rotting pine stump in the woods is a universe. You can spend a lifetime in a Magellanic voyage around that one pine stump and just spew out one important scientific discovery after another. Let the others—and I’m speaking to future naturalists … students who are thinking of going into natural history—let the others worry about partial differential equations and titration. You go [your own] route because that provides unique knowledge, unique experience. And furthermore, a large part of science in the 21st century is going to be synthesis. We are entering an age of synthesis, of the analysis of complex systems. And that’s going to require an enormous amount of attention to detail … and the way things fit together.
As Wilson explains, there are plenty of students who are drawn to science but not to math, labs, and Petri dishes. Their natural talents will propel them to seek ways to pursue science in some form for the rest of their lives, regardless of their college major. Why impede them from channeling their talent productively in their major, for the sake of maintaining irrelevant, unnecessary calculus requirements? Why stop potential Darwins and Edisons from majoring in science, simply because they couldn’t pass calculus?