Since its reincarnation a year or so ago, the NYT Sunday Review section has usually reserved its front page for articles intent on sparking debate or stirring controversy. The pieces often present counter-intuitive arguments graced with hackle-raising headlines. And so witness this week’s above-the-fold inquiry: “Is Algebra Necessary?”, accompanied by an illustration of a trio of poor souls drowning in waves of notation sure to give even MIT’s finest fits.
Andrew Hacker, a political scientist whose most recent book examines “how colleges are wasting our money and failing our kids,” argues in the article that if math is the greatest stumbling block to educational achievement then perhaps we should just remove it. “There are many defenses of algebra and the virtue of learning it,” he writes. “Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong—unsupported by research or evidence, or based on wishful logic.” The issue as he sees it is that this forced emphasis on the mathematical sequence causes large numbers of students to fail, thus depriving them personally and society generally of the further development of their non-mathematical talents.
In place of our current model of mathematics education, Hacker envisions an alternative wherein the focus shifts to “citizen statistics” so as to “familiarize students with the kinds of numbers that describe and delineate our personal and public lives.” He imagines such an approach would be exciting, and he urges us to do away with a system in which math is but “a huge boulder we make everyone pull, without assessing what all this pain achieves.”
Now, very few people with any exposure to the teaching of math in our schools would disagree with Hacker’s contention that it’s broken. But many who feel passionately about mathematics would surely also note the absence of appreciation from Hacker for anything but math’s most obscure and utilitarian applications. For all his focus on the pain and fear of mathematics, Hacker has little to say about its beauty. He does suggest that we should treat mathematics as a liberal art, “making it as accessible and welcoming as sculpture or ballet,” but in the service of rationalizing its marginalization rather than encouraging its embrace.
Interestingly, much of Hacker’s analysis echoes that of Paul Lockhart, who gained a certain degree of fame for his “Mathematician’s Lament,” a stinging critique of the state of mathematics education. The difference between Hacker and Lockhart is that while Hacker is interested in public policy and the efficient use of resources, Lockhart is full of passion for the creative art of mathematics. He’s not so worried about how broken mathematics education deprives students of the development of their other talents; he’s worried about how it deprives them of math. For Hacker reform will come through cuts, sweeping math aside to join art, music, and athletics on the margins of American public education. For Lockhart the solution is to adopt an approach to mathematical education that frees students from memorization and exposes them to the wonders of what he calls “mathematical reality.”
We’re soon to publish Lockhart’s Measurement, a wonderful book that puts into practice the method of teaching for which Lockhart argued in his lament. We recently spoke with him about the book, and he showed himself to be a living, breathing, laughing embodiment of the deep beauties of math that any call for reform would do well to recognize.
But don’t take our word for it: