Andrew Hacker’s provocative weekend op-ed in the New York Times (“Is Algebra Necessary?”) wondered why schools insist on subjecting students to the “ordeal” of algebra. “There are many defenses of algebra and the virtue of learning it,” Hacker wrote. “But the more I examine them, the clearer it seems that they are largely or wholly wrong.” Making algebra mandatory, along with other more advanced math subjects leads to failure and dropping out, which “prevents us from discovering and developing young talent,” he argues.
“The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason. Shirley Bagwell, a longtime Tennessee teacher, warns that ‘to expect all students to master algebra will cause more students to drop out.’”
Well, sure. But expecting competence in any reasonably advanced subject–biology, physics, or English composition–will likely have the same effect. What Hacker is arguing might well be termed Barbie Syndrome: years ago, a talking Barbie doll uttered the infamous phrase, “Math class is tough!” Mattel pulled the doll off shelves, but Barbie might have received a sympathetic pat on the back from Hacker, who proposes a different math curriculum that mirrors the quantitative reasoning most of us will need on the job:
“Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call ‘citizen statistics.’ This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives. It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.”
“There’s a strong argument to be made that math is taught poorly in many schools, with little attention paid to how most people are likely to use numbers in the real world,” Dana Goldstein points out. But Goldstein correctly perceives that any argument about who should learn what is ultimately about tracking. “A great teacher can often spark interest in a subject a student thought she would never enjoy. One reason to have more rigorous academic standards is to leave open the possibility of that magic happening more often for more young people, and to make sure unfair streotypes about who is ‘academic’ don’t prevent kids from discovering unexpected passions,” she writes.
Dan Willingham points out that Hacker is simply wrong in several assumptions. “The inability to cope with math is not the main reason that students drop out of high school, he writes. “Yes, a low grade in math predicts dropping out, but no more so than a low grade in English. Furthermore, behavioral factors like motivation, self-regulation, social control as well as a feeling of connectedness and engagement at school are as important as GPA to dropout [rates]” he notes. Willingham also dismisses Hacker’s argument that too much of what students learn in math class doesn’t apply in the real world.
“The difficulty students have in applying math to everyday problems they encounter is not particular to math. Transfer is hard. New learning tends to cling to the examples used to explain the concept. That’s as true of literary forms, scientific method, and techniques of historical analysis as it is of mathematical formulas. The problem is that if you try to meet this challenge by teaching the specific skills that people need, you had better be confident that you’re going to cover all those skills. Because if you teach students the significance of the Consumer Price Index they are not going to know how to teach themselves the significance of projected inflation rates on their investment in CDs. Their practical knowledge will be specific to what you teach them, and won’t transfer.”
Willingham says Hacker’s op-ed also “overlooks the need for practice, even for the everyday math he wants students to know.”
“There are not many people who are satisfied with the mathematical competence of the average US student. We need to do better. Promising ideas include devoting more time to mathematics in early grades, more exposure to premathematical concepts in preschool, and perhaps specialized math instructors beginning in earlier grades.”
Hacker’s suggestions “sound like surrender,” Willingham concludes, and I agree. It’s hard not to detect a whiff of defeatism–a shrug, a wave, and the weary suggestion that, “Hey, not everyone can be good in math. It’s OK” in Hacker’s putatively sensible piece. But let’s try a more vigorous focus on math–with computational mastery and conceptual understanding given co-equal status–before we throw up our hands and suggest that Barbie drop algebra and switch to “citizen statistics” in 8th grade.
Update: “I think it is dumbing down math — so far down that it will close the door on many careers,” writes Joanne Jacobs. “But it’s better to teach some math than stick unprepared, unmotivated students in dumbed-down classes labeled ‘algebra’ and ‘geometry.’”
Update x+2: Sherman Dorn weighs in.