The Case Against Mandating Math for Students

Do all students truly need to learn algebra? Andrew Hacker asked that question in a widely read op-ed essay in The New York Times a few years ago and landed on a resounding “no.”

His argument struck a nerve. Algebra has, somewhat controversially, become a vital gatekeeping course, with more and more students taking it at increasingly young ages.

But the courses, he argued, are generally poorly taught. They’re also the chief academic reason that students drop out of high school and college. Mr. Hacker charts the far-reaching impact of math requirements and suggests alternative ways to teach the subject in a new book, The Math Myth and Other STEM Delusions (The New Press), due out next week.

Mr. Hacker, a professor emeritus of political science at Queens College of the City University of New York, draws a careful distinction between mathematics and arithmetic. Math means algebra, trigonometry, and calculus, all part of what he calls the “enigmatic orbit of abstractions.” While he finds those subjects fascinating, even beautiful, he says they serve little purpose later in life and, when required, do students more harm than good.

Typical math requirements, like mastering polynomial functions or parametric equations, unnecessarily trip up students who plan to major in dance or fashion design, says Mr. Hacker, and are seldom used even in many scientific disciplines. “This is disgraceful,” he says. “We’re losing a tremendous amount of talent.”

Arithmetic, on the other hand, is the quantitative literacy that people actually need. But it’s often poorly focused and poorly taught.

This political scientist and occasional math instructor is not afraid to stir the pot. After several books on race and class, he wrote Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids — and What We Can Do About It. In that one, he and Claudia Dreifus lambasted colleges for their escalating costs and luxurious amenities, and faculty members for their fealty to tenure and penchant for churning out research of dubious value.

In his new book, Mr. Hacker diagnoses flaws in the teaching of math at all levels, from elementary and secondary school to college. “There’s enough blame,” he says, “to go around.”

He spoke with The Chronicle about his project. The interview has been edited for length and clarity.

Q. You started researching this book nearly 20 years ago. What originally sparked your interest?

A. This became a bee in my bonnet. I saw the mandating of a full sequence of mathematics as something quite harsh, senseless, and just being accepted without any real rationale. Right now, four million American teenagers are in a class studying algebra. They all have to do it. I’m simply asking a question: Why?

Q. You argue that math has assumed an outsize role both on a policy level and in individual lives. How did math claim such status?

A. Part of it is that math is so mysterious. Most of us can no longer do trinomials or quadratic equations. It’s become a kind of elixir: If we make all of our young people master advanced mathematics, this will rev up the economy and make us much more competitive with other countries. We’re searching for a magic potion, and mathematics became that.

Q. Is there any way in which it actually is a magic potion?

A. None at all. Even if we take STEM (science, technology, engineering, and, of course, mathematics), there’s a lot less math in STEM than we’d like to think. Let’s take, for example, computers and coding. Coding is not based on mathematics. Coding is a series of instructions based on its own internal logic. Most people who do coding, programming, software design, don’t do any mathematics at all.

Q. What do you think of the argument that studying math imparts a certain intellectual rigor and logical temperament?

A. I call that Myth No. 1: that studying mathematics makes us more thoughtful. It is the only field I know of that claims that if you study it, you do better in other fields. There is no evidence for that whatsoever. Would you go to a mathematician to tell us what to do in Syria? It just defies comprehension.

Q. How would you respond to the criticism that reducing an emphasis on algebra is lowering expectations or watering down standards?

A. I propose an alternative to mathematics, what I call numeracy, numerical literacy, or for lack of a better phrase, adult arithmetic. It’s the kind of thing you need to make sense of everything from corporate reports to the federal budget, or to decide whether it’s better to buy or lease a car. Despite the fact that nearly every young American is made to take algebra and geometry, we rank very low in international rankings of numerical literacy. Young people just can’t handle the numbers.

Q. Is it a problem of curricular emphasis, where we pivot too soon from arithmetic to the theoretical realms of algebra, calculus, and trigonometry?

A. Absolutely. What happens is, we pretty much get arithmetic under our belts by fifth or sixth grade. Then in middle school we turn to mathematics, which is an entirely different field. What I’m proposing is that we upgrade arithmetic.

Q. What would teaching that kind of arithmetic look like at the postsecondary level?

A. I’m not setting myself up as giving advice to mathematics departments. I would like to see mathematics treated as a liberal art, in which it is not off in its own world, but you show how it applies to the real world. I’ve tried to do something like that with a course I’ve taught called Numeracy 101. You use numbers in a demanding, sophisticated way so that they enhance your understanding of reality. For example, I compare two countries, the United States and Norway, using statistical indices: What proportion of their populations is in prison? How many hours a week do they work? How much do they spend on military weapons? It shows how using numbers can really be a companion to using words.

Q. So the questions are things like “Are these the right numbers?” and “What do these numbers say?”

A. Absolutely. One thing we should do is be skeptical about numbers.

Q. You quote an expert as saying that algebra is being used today in much the same way that Latin was a century ago, to screen out the unwanted from college. Doesn’t that suggest that math is a symptom of a deeper, longstanding pattern of stratification?

A. I don’t think that’s the case. One of the reasons we impose mathematics on everybody is the mantra of rigor. It’s a bit like going to the gym. A lot of people who don’t remember math at all want to impose it on younger generations. They see young people as soft and mollycoddled. If rigor is good — and I think everyone thinks rigor is good — we should ask what kind of rigor is fruitful, useful, thoughtful, and productive, and not just rigor for its own sake.

Q. You write about the importance of things like aesthetic knowledge and reading Emily Dickinson. Are those examples of fruitful rigor?

A. I would say reading Dickinson or T.S. Eliot is just as rigorous as trigonometry. That’d be interesting — a rigor requirement.

Dan Berrett writes about teaching, learning, the curriculum, and educational quality. Follow him on Twitter @danberrett, or write to him at dan.berrett@chronicle.com.