The ‘Fuzzy Math’ Bath March 12, 2003 By Matthew Clavel
“Come on, I need someone to take a chance. Who can start the puzzle?” It wasn’t working. We’d gone. through six straight wrong answers, and now the children were tired of feeling lost. It was only October, and already my fourth-grade public school class in the South Bronx was demoralized. Day after day of going over strange, seemingly disconnected math lessons had squelched my students’ interest in the subject.
Then, quietly, 10-year-old David spoke up. “Mr. Clavel, no one understands this stuff.” He looked up at me with a defeated expression; other children nodded pleadingly.
“Look,” I began, sighing deeply. “Math isn’t half as hard as you all probably think right now.” A few children seemed relieved—at least I wasn’t just denying their problem. “There are different ways to teach it,” I continued. “I don’t want to do this either . . . so we’re not going to—at least most of the time.” I was thinking out loud now, and many of the children looked startled. “We can use these math books when we need them, but I’m going to figure out different ways to teach you the most important things.”
If school officials knew how far my lessons would deviate from the school-district-mandated math program in the months ahead, they probably would have fired me on the spot. But boy, did my children need a fresh approach. Since kindergarten, most of them had been taught math using this same dreadful curriculum, called Everyday Mathematics—a slightly older version of a program that the New York City schools chancellor, Joel Klein, has now unwisely chosen for most of Gotham’s public elementary schools; the district had phased in Everyday Mathematics—grade by grade, and it had just reached fourth grade during my first year of teaching.
The curriculum’s failure was undeniable: Not one of my students knew his or her times tables, and few had mastered even the most basic operations; knowledge of multiplication and division was abysmal.
The curriculum derives from a pedagogical philosophy that goes by several names—“Constructivist Math,” “New-New Math,” and, to its detractors, “Fuzzy Math.” I’ll stick with Fuzzy Math, since the critics are right. Nothing about Fuzzy Math makes much sense from a teaching standpoint.
One weakness is its emphasis on “cooperative learning.” Fuzzy Math belongs to a family of recent pedagogical innovations which imagine that children possess innate wisdom and can teach each other while a self-effacing “facilitator” (the adult formerly known as a teacher) flutters over them. If the architects of Everyday Mathematics had their way, I would have placed my children in various groups, for the most part unsupervised, so that they could work on one elaborate activity after another, learning on their own. I’d derive bitter pleasure in watching a Fuzzy Math “professional-development” expert try using this approach in an inner-city classroom, filled with children whose often unstructured home lives make self-restraint a big problem. –I avoided this loss of control, because right from the outset, even before I chucked the whole program, I felt that pursing cooperative learning with my students was asking for trouble, and so I mostly didn’t do it. I was going to teach; my students were going to learn.
Everyday Mathematics is bad enough from the standpoint of maintaining a disciplined class. Making it even worse is its Fuzzy Math–inspired emphasis on “critical thinking skills” over old-fashioned drilling and the mastery of facts. What matters is showing that you understand a concept, not whether you can perform a calculation and come up with a right answer.
Defenders of critical thinking say we need to rescue our schools from a repressive “drill-and-kill” pedagogy that makes children automatons, spitting back the facts and rules that teachers have drummed into their heads and never learning to think on their own. The truth, of course, is that no one claims that knowing how to think independently isn’t important. But thinking can’t take flight unless you do know some basic facts—and nowhere is this more the case than in math. If you really want your students to engage in “higher-order thinking” in math, get them to master basic operations like their times tables first.
Unfortunately, a student in a Fuzzy Math program—including Everyday Mathematics—is unlikely to master much of anything. The hours of logically linked lessons that old-style math classes spent on practicing operations so that they became second nature to students just are not there.
Equally mystifying, Everyday Mathematics, like Fuzzy Math programs generally, abruptly introduces concepts like basic algebra that students aren’t officially taught until years later. Imagine you’re a fourth grader and see in your workbook, right next to a relatively easy addition word problem, a forbidding algebra exercise you couldn’t begin to answer because, well, you haven’t learned algebra yet. Bewilderment is inevitable.
Teachers frustrated by this incoherent approach got little sympathy from school administrators. District officials told us that we should just keep going—even if not a single child in our rooms understood what we were talking about. Yet the district officials themselves seemed perplexed by Everyday Mathematics. One assessment, created by the district to judge the progress the fourth-graders were making in the program, came with an answer sheet with two incorrect answers. As for students, many just tuned out. The lesson plans jumped around so much that an especially confusing and oddly presented topic was only going to be on the agenda for a few days. Why bother trying to understand it?
The repudiation of skills in Fuzzy Math also encourages a detrimental over-reliance on calculators. The use of these gadgets to replace mental computation raises concerns about learning skills for all school children. According to a 2000 Brookings Institute study, fourth-graders who used calculators every day were likely to do worse in math than other students. But it’s minority children like those in my class who are turning to calculators the most. The Brookings study reports that half of all black school children used calculators every day, compared with 27% of white school children.
There’s mounting evidence that Fuzzy Math doesn’t work. During the 1990s, Fuzzy Math represented the new wave, and President Chnton’s, Department of Education was pushing it, so district after district across the country tried it out. But its popularity among educational elites could not hide the dismal test scores.
California, ever on the cutting edge of educational reforms, enthusiastically embraced Fuzzy Math, in the early 1990s, only to watch state math scores plummet. In 1996, California registered one of the worst scores of all 50 states on the National Assessment of Educational Progress. By the end of 1997, the State Board of Education realized its mistake and produced sensible standards that encouraged more traditional math instruction.
Regrettably, in the heavily bureaucratized public schools, bad results do not necessarily lead to re-evaluation. Fuzzy Math, cooperative learning, and a myriad of other educational fads are the pet projects of very influential, tenured university “experts” who fiercely protect their theoretical turf, in teachers colleges and among school administrators. If test scores seem to rise thanks to Fuzzy Math, great: Campus enthusiasts will tout the results. If they stagnate or fall, the theoreticians will find ways to poke holes in any critical study that blames the theory.
The frustration of parents and community leaders has gathered momentum. Parents overwhelmingly want to set aside ideological preoccupations in math and get back to fundamentals. A big push is on to allow parents to opt their children out of Everyday Mathematics and other Fuzzy Math programs.
“Cooperative” learning that leads to classroom chaos, schizoid lessons that fail to impart mastery, lousy results, parental outrage—shouldn’t every teacher have done as I did and thrown Elementary Mathematics into the garbage?
But it isn’t easy for teachers to disobey mandated curricula—not if they want to keep their jobs. Most teachers are trying to make a career in education, so they teach a newly mandated curriculum even if they know it to be absurd. Nor will school bureaucrats usually be quick to get rid of a deeply flawed curriculum. After all, if the “experts” say Fuzzy Math is the way to go, then the problem must be in how teachers are implementing the theory, not in the theory itself.
By deciding against local control early on and moving to centralize the school system, Mr. Klein and Mayor Bloomberg took a tremendous risk. The advantage of charter schools and decentralized public schools is that they have the chance to innovate and distinguish themselves. Any leader of a school system who decides to put blanket “reforms” in place could achieve great success; he also risks unknowingly stamping out improvements made at the local level. Unfortunately, it appears that Messrs. Klein and Bloomberg, by embracing an all-but-universal Fuzzy Math curriculum, are setting themselves up to lose their big gamble.
The inner-city students subjected to this curriculum will be the real losers. What will happen to children who never adequately learn basic operations like long division—or even their times tables? How will they succeed in the knowledge-based 21st-century economy? Most of them won’t have parents who can afford math tutors to help them catch up. My guess is that most of these children will never get the education they need, and we’ll just brush another catastrophe under the rug.
Mr. Clavel is now writing a book on his teaching experiences. This piece is adapted from City Journal’s Web site, www.city-journal.org. ©2003 New York Sun |