How ‘Big Math’ Is Keeping You Down
Andrew Hacker, author of The Math Myth, thinks algebra is overrated.
In 2012 Andrew Hacker, a professor of political science at Queens College published an opinion piece in the New York Times Sunday Review under the provocative title “Is Algebra Necessary?” In it, he sketched out a cursory argument lambasting the way American educators teach mathematics as needlessly obtuse, abstracted from reality, and ultimately useless for the vast majority of students. As a result, he claimed, algebra and other forms of higher math have become a weight on American potential, pushing countless souls to drop or flunk out of high school or college, denying them access to good jobs that have nothing to do with geometry or trig. Rather than continuing to teach something which Hacker believes has no crossover value, he asserted that we ought to teach rigorous numeracy—agility with basic arithmetic, mobilized for real-world uses—to truly improve America’s mathematical potential and eliminate our harmful educational norms.
After Hacker’s essay was published, all hell broke loose as math lovers and educators rushed to the defense of their craft. The article became the slow-burn locus of an ever-evolving debate about the challenges and future of math in the US. But ultimately, after a surprising stint in the limelight, the Hacker-algebra debate faded.
Almost as soon as it did, though, Hacker struck back with vengeance. Last month he published The Math Myth And Other STEM Delusions, a book-length treatment of his theories on education. Much of the book is devoted to shoring up his previous arguments, while painting a more explicit image of what a new focus on numeracy education would look like. (This positive vision of a post-mandatory algebra world has developed over the past three years, during which Hacker has designed and taught his own numeracy class for freshmen.)
But just as the arguments within The Math Myth are more sophisticated and sharp than those floated cursorily in “Is Algebra Necessary?”, so the critiques of Hacker’s ideas have grown more comprehensive and astute. Some have gone so far as to annotate what they see as errors in Hacker’s analyses, argumentation, and reasoning page-by-page. Eager to hear about how Hacker is dealing with this latest round of disputation, GOOD caught up with the controversial professor to talk numeracy, the mathematical establishment, and the value of diverse educational styles.
Andrew Hacker. Screenshot via YouTube channel BookTV
Did any of the arguments against your article in 2012 change the argument you made in the The Math Myth?
Over half of [the letters I received] were very hostile. In the United States, about 7 percent of adults are really good at math. They’re not teachers or professors, but they’re math mavens. It’s something very important to their life. And they were the ones who really rounded on me. Talking about how math trains the mind, how math is rigorous, how we can’t dumb down what we’re doing. It was interesting to watch them. It’s as if, to [paraphrase] Karl Marx, they owned capital and I had diminished their capital or the value of it. They regarded me as a real threat.
But did that just prompt you to expand your ideas into a book, or did your ideas evolve?
Yes, [there was] evolution. I said, ‘you’ve got to show what you’re in favor of, not just what you’re opposed to.’ So I started to develop this course in numeracy, which I started teaching at Queens College after I wrote the article. I had to put it together absolutely from scratch because there was no such course. I had to show what kind of serious college-level work can be done without the algebra, without the trigonometry, but still involving multiplication, numbers.
Have you made any converts out of math diehards to your way of thinking?
I must have, in the sense that I really got a lot of emails… asking for the syllabus of my class. There are a few professors out there who are trying to teach a numeracy course [in second-tier universities]. But in the uber-universities or colleges, no.
You wanted to teach essential, basic math. How did you assemble that curriculum?
I really have to get across the difference between arithmetic and mathematics. Arithmetic… is pretty well taught up until fifth, sixth grade: long division, percentages, and so on. Then we essentially drop it and in middle school we suddenly thrust kids into algebra.
There’s a lot of serious work that needs to be done with arithmetic—making it more adult, more sophisticated, sharpening arithmetic skills. That is not being done… because the mathematicians are in charge, and they only want to teach their mathematics. They regard… even the most serious arithmetic as dumbing down. If you want to study a corporate report, or a federal budget, or a report about climate change, all you need is arithmetic. But it has to go beyond what you learn in fifth grade. So when I started my course, I just said we’re going to use everything up through percentages, ratios, and those things, then look at real, live situations.
You’ve been teaching your course for a few years now. Has your conception of what constitutes numeracy and how to communicate or teach it changed?
When you do anything experimental, you discover what works and what doesn’t. I had a number of assignments in year one that just didn’t work. But hey, I’m an experienced teacher, and in all my classrooms I find what works best.
Some call you an especially gifted educator. Yet there are so many people teaching mathematics these days who come out of a system you see as flawed and who may not have an equivalent level of educational charisma or even a great deal of what you’d call numeracy themselves. So when you’re dealing with a system like that, how do you achieve the widespread change you’re talking about?
This is very sad. It’s harder to make algebra come alive to a group of students, most of whom don’t want to be there, as opposed to history or literature. And the uber-professors, at least in the United States, don’t teach the introductory courses. They give it all to graduate students, adjuncts, often people coming in who lived in China six months earlier. So the quality of teaching in mathematics is really bad, and as a result the number of students who choose to major in mathematics in university is down to one percent. It used to be a high three percent.
But I do believe a class in numeracy can be done more interestingly because it’s not about abstract numbers. It’s about numbers representing real things like boats or dollars.
One argument I’ve seen for requiring math is that if we get rid of it and focus on the skills people need for their lives, it is synonymous to changing what a diploma means from saying ‘this person is a versatile learner’ to saying a graduate is prepared for a particular set of tasks.
Is what I’m proposing some variant of vocational education? Of course not. I believe in the liberal arts, including mathematics. The class on numeracy is [very] demanding. The notion that only mathematics as the mathematicians teach it will provide this mental expansion is self-serving. Any liberal arts class can challenge your mind. The mathematicians continue [their methods] because they know that most people outside their circle don’t really know math. So we regard them as kind of magicians, holders of the keys to great mysteries, and what they do must be somehow more valuable or demanding than what anyone else can possibly teach.
Some mathematicians agree with you that the way we teach math is broken, but they say that by talking about math without their own level of understanding, you’re alienating them. Have you pushed away strong potential allies in math education reform?
I’m one of these people who took a regular mathematics sequence. If I don’t understand it, is that my fault? Of course I don’t understand it at [their] level. I wouldn’t expect them to understand [the details of] political science, in my field.
They all say: ‘we don’t like how algebra’s taught. Here’s another way to do it.’ One of the proposals we hear all the time is that we’ve got the sequence wrong. We should start with calculus. Okay, let those guys work that out in their own playground. I’m not going to get into that playground. I’m not one to propose how better to teach math. What I do want to do is teach it in a more interesting and exciting way. If they want to do it by counting on your fingers or bringing back the abacus, that’s fine with me, too. In the book, I said I don’t want to abolish algebra. I want to make it more of an alternative with students having other options.
You use specific examples to make arithmetic interesting. But some argue we should instead start more abstract earlier to build the fundamentals of mathematics, as that will be more transferrable math knowledge than, say, reading the Consumer Price Index.
I have nothing against abstraction. But here’s where I part company with a lot of others: I have found no evidence whatsoever that learning the logic, the reasoning, the abstractions in mathematics, algebra, or so on makes you more adept, more agile, more sophisticated at thinking in abstract or concretely about other aspects of reality than mathematics.
I did my own minor experiment. I took incoming freshmen and looked at their math scores. A bunch of them… took an introductory history course as freshmen and I got their grades. So I lined up their math scores, 0 to 100, with their history grades, A+ down to F, and guess what? No correlation whatsoever. History requires reasoning, use of evidence. If [these critics] were right, these ace mathematicians would have also aced history. Didn’t happen.
But leaving aside sample size, you’re talking about people who are leaning math in a system these critics also see as inadequate, but in a different way than you do. I think they’d argue if we started with theory from the start, you’d see different outcomes.
I’m willing to give them a try. If they want to teach mathematical theory to toddlers… see what happens. But I’d say let whoever get a couple of school districts, not nationwide, not statewide, to do this in an experimental way. Don’t enforce it on everybody. One of my problems with math is that we enforce it on everyone in the U.S. My god, that’s akin to totalitarianism.