The Second Great Math Rebellion
Few truisms exist in the politics of education, but you can usually count on two things. When reformers seize control of the policy agenda, whether at the local, state, or national level, they almost always go too far in jettisoning what they don't like and too far in embracing the new, unproven practices they favor. Not only is the baby thrown out with the bathwater, but the baby and the bathwater are frequently replaced by something bizarre.
In 1989, a group of experts in the field of math education, under the auspices of the National Council of Teachers of Mathematics, launched a campaign to change the content and teaching of mathematics. In the intervening eight years, the reforms have been slowly seeping into the schools, ostensibly in an effort to raise standards. Now the earmarks of a grassroots rebellion are appearing. From coast to coast, articles in newspapers and magazines report parents organizing against their districts' math programs. Op-ed pieces are regularly popping up with horror stories about a warm, fuzzy mathematics that values student happiness over student competency. Web sites are buzzing with protest. California is scrambling to write new state standards so it can undo the damage of dancing on "the cutting edge" of math reform. Many of the critics are political conservatives, but not all. This past summer, Sen. Robert Byrd, D-W.Va., took to the floor of the U.S. Senate to warn the nation about the spread of "whacko algebra," declaring that "it is not just nonsense, it is unfocused nonsense."
We've been through this before. In the 1960s, the curriculum known as the New Math was routed from classrooms by angry parents and teachers. Parents didn't recognize the mathematics that children were bringing home from school, and teachers found it almost impossible to instruct students on the strange new topics recommended by reformers. Despite the support of the most prominent reformers of its day, including the NCTM, the New Math fizzled when it hit real classrooms with real kids and teachers.
The second great math rebellion centers on three grievances:
First, teaching. The NCTM math embraces the longstanding doctrine of progressive education. Student-initiated learning is favored over teacher-led instruction. Students spend a lot of time playing math games in small groups. The process of problem-solving is valued over right answers because right answers don't have an objective existence; they are "constructed" by learners. But what happened to reformers' insistence on real-world math? From engineers to airline pilots, people use mathematics to model the world in which they actually work, not to construct their own, more accommodating versions of reality.
The state and district policies that have followed the NCTM standards tend to present reform as religion. And conventional practices appear as sins: teachers delivering direct instruction; students individually working on pencil-and-paper problems at their desks; corrected work (wrong answers clearly marked wrong) cycling back and forth between teacher and student.
|Parents shouldn't be mystified about what their kids are learning in school.|
No wonder teachers and parents have trouble with these reforms. To promote student-centered learning, teachers are to keep an elaborate diary on each child's "mathematical disposition." The teaching that parents most likely hear about is conducted by their children's peers.
The second complaint centers on the downgrading of basic skills. Until recently, the math curriculum from kindergarten through 8th grade focused on basic skills: in particular, learning how to use four forms of number (integers, fractions, decimals, and percents) in performing four operations (addition, subtraction, multiplication, and division). Students who mastered the 16 manipulations embedded in this knowledge, including when and how to employ them in solving problems, were in good shape to move on to higher math.
Not anymore. Basic skills are now de-emphasized. They represent the facts-based learning that math reformers abhor. How will students get the basics? Memorization isn't an option because it's boring. The hope is that basic facts will seep into students--by playing games, working with manipulatives (blocks, beans, and counting sticks), and by using calculators. It's even inferred that computational skills are becoming unnecessary with calculators in wide use. Besides, math reformers argue, the insistence that students learn these skills before progressing in the curriculum condemns countless youngsters to a low-level, repetitious math program.
The problem with this argument is that it's based on conjecture. We don't know if learning by osmosis really works, nor the long-term consequences of students' failing to master basic skills. We don't know whether students who can't grasp, say, the equivalence of ¬ and 0.25 and 25 percent actually go on to successfully learn calculus. Research has yet to document large numbers of students who fly through algebra but are clueless when it comes to fractions. Moreover, parents worry when their 5th graders can't multiply single-digit numbers without pocketfuls of beans and sticks. Teachers are concerned that the mastery of basic skills signifies something more than computational proficiency, that students who learn these facts to an automatic level also gain a deeper knowledge of mathematics, a sense of number unfathomable to those who don't know them.
The third complaint has to do with the dramatic transformation of math textbooks. Progressive educators have never really liked textbooks, feeling that teachers rely on them too much and that texts narrow learning to a series of dull, repetitive tasks. But the textbook has its virtues. Texts publicly declare the curriculum. They link home and school, and by providing a calendar for learning, allow parent, teacher, and child to see what has been covered and what lies ahead. The textbook is the closest thing we have to an enforceable learning contract in the American school, and for the last century, no serious academic subject has been taught without one.
|The hope is that basic facts will seep into students—by playing games, woring with manipulatives (blocks, beans, and counting sticks) and by using calculators.|
Some of the new math programs either use kits rather than texts or provide texts that are flashy in appearance but short on substance. Sen. Byrd couldn't find an algebra expression until Page 107 in the book that appalled him. What fills the book's pages? Discussions of endangered species, air pollution, the Dogon people of West Africa, the role of zoos in society--anything but math. Marianne Jennings, the Arizona State University professor who brought the book to Mr. Byrd's attention, refers to it as "Rain Forest Algebra."
As suggested by this example, the math that is presented in texts may be inexplicably dressed in PC garb. It's no surprise that this irritates conservatives, but readers of all political persuasions should be annoyed because public policy is partly to blame. The California math framework, for example, urges teachers to "illuminate the mathematical side of social issues," offering on Page 26 the following problem as a model: "The 20 percent of California families with the lowest annual earnings pay an average of 14.1 percent in state and local taxes, and the middle 20 percent pay only 8.8 percent. What does that difference mean? Do you think it is fair? What additional questions do you have?" The framework then boasts, "Such problems take percents, one of the most prosaic workhorses in mathematics, and open them up, breathing new life into them by introducing questions about reporting, statistics, and social justice."
Is this problem (which is computation-free, of course) a clear case of injecting ideology into the curriculum, or are 6th graders really perched on the edge of their seats, just waiting to be mesmerized by the distributional effects of the tax code?
The objections I have discussed constitute a rejection of the philosophy, content, and materials of contemporary mathematics programs. They are not trivial. But across the country, disillusioned parents and teachers report a response to their objections that reveals a breathtaking arrogance on the part of administrators implementing these reforms, a belief that teachers with traditional teaching styles need to have their preferences "professionally trained" out of them and that wary parents simply don't have the professional standing to understand why a different mathematics is needed. And things might get worse. If reformers get their way, the new instruction, new curriculum, and new materials in vogue will be evaluated by new assessments. The old tests, you see, can't adequately measure the learning now taking place. This raises a terrible prospect, a Dorian Gray education where everything looks great on the outside--happy children playing games, receiving A's, testing wonderfully--while below the surface there is nothing but ignorance: irreparable and undetected.
Two simple rules should govern all standards-setting projects. First, their purpose is to define the skills and knowledge that students must learn, not to declare some forms of teaching good and others bad. If a particular teacher's students learn what they should learn, who cares about that teacher's pedagogical philosophy or methods? Second, the skills and knowledge stipulated in the standards should be recognized as valuable to the average person on the street. Put simply, parents shouldn't be mystified about what their kids are learning in school.
Today's math reforms violate both of these rules, and in doing so, debase the expertise of teachers and jeopardize the trust of parents--pillars on which the public school stands.
Tom Loveless is an associate professor of public policy at Harvard University's John F. Kennedy School of Government in Cambridge, Mass.