This weekend, after American students failed to impress on the international PISA exams, the New York Times editorial board ran a piece asking “Who Says Math Has to Be Boring?” By “boring,” the Times apparently means any math that is substantive in a traditional sense: “arithmetic, pre-algebra, algebra, geometry, trigonometry.” So let me answer the question: Anyone with an understanding of what math actually is believes it must sometimes be boring.
The crisis in mathematics education is, as the Times says, severe. It extends all the way to the editorial board of the newspaper, whose members do not appear to understand what mathematics is, how it is used in the sciences, or why it is important. The Times’ solution, “a more flexible curriculum,” is euphemism for erosion of already-lax standards that would only make our present problems worse. What should replace boring old quadratic equations and logarithms (which aren’t really all that scary)? The Times is vague, emphasizing only that standards shouldn’t stand in the way of “nontraditional but effective ways to learn.” The Times doesn’t specify what these novel ways of learning might be, either, but it does lament that too few high school students take engineering classes. Here’s the thing, though: That’s because to do most engineering at a level other than play-acting, you need to already have basic high school math and science mastered. This is like reacting to a study that shows 2-year-olds don’t crawl fast enough by insisting they start running wind-sprints. Later, the piece holds up as exemplars schools that teach computer programming. But programming—worthy in its own right—is not mathematics, and cannot substitute for it.
The Times’ misunderstanding comes from a failure to appreciate that mathematics—even at the basic level taught to elementary, middle, and high school students—is an intellectual discipline with content intrinsic to itself. This content is important and can be made exciting and accessible without reference to the “real world.”
Let’s take a simple example: 3+5=8. It is useful to know this sum without reference to 3 apples and 5 apples, or 3 cars and 5 cars, or 3 computers and 5 computers. It is an abstract fact, just as knowing that 8x9=72 is an abstract fact. Understanding these abstractions then lets us turn to a multitude of real-world applications. It is the knowledge that 3 of anything and 5 of anything adds up to 8. Thinking about apples may help a young child learn to add in the first place, but it isn’t a substitute for subsequently developing the abstract skill of addition, which requires practice. The Times’ dichotomy between “real-world problem solving” and “traditional drills” does not exist. As in learning foreign languages, repetitive drills enable students to master techniques—of which addition is the simplest example—which can then be used to solve problems in the real world, and to develop more mathematical sophistication, which can then be bolstered by using new mathematical concepts in the real world. This is true in arithmetic, and also in algebra, geometry, calculus.
The Times editorial rests heavily on the authority of Anthony Carnevale, an anti-intellectual economist. In his Times interview, he refers derisively to curricula that “teach a lot of stuff that digs up old white guys from Greece.” He entirely misses the power of mathematics, which is that it is universal. Pythagoras’s theorem was true 2,500 years ago. It is true today. It is true for white guys, for guys who are not white, and for women. It is true in distant galaxies and will remain true forever. As such, it’s worth teaching. Proving that it is true is exactly the stuff of critical thinking, which the Times repeatedly says is important.
They never specify what “critical thinking” is. Surely any sane definition includes an understanding of mathematical proof. Many important proofs—such as the fact that there are an infinite number of primes or that the square root of 2 is irrational—are eminently accessible to high school students (and to precocious younger students).
As many have pointed out, the Times loves to chase trends. But what is needed in mathematics education is not a new faux trend (“a fundamentally different approach”) but rather renewed attention to teaching teachers the basics well, so that they can then pass them on to students, as Hung-Hsi Wu, an emeritus professor at the University of California-Berkeley has long advocated.
The Times’ most misguided belief may be the insistence that the reason we need better math education is to train a new STEM workforce. The real reason we need better math education is to equip citizens to understand the world they live in. We need better math education—for all students—to ensure that democracy can continue to function in a world made ever-more complicated by new technologies that rely on sophisticated mathematics. This is achievable only once we realize that math can be made exciting and vital on its own, and not by reference to computer programming or robotics. And that sometimes, it just takes hard work and discipline to reach mastery.