At the Gann household in Sackville, N.B., mom’s math hour is a relentless incursion into summer vacation. The daily lessons are not because 11-year-old Deborah is failing. Far from it. She graduated Grade 5 with an “outstanding” in math, the highest honor her school could bestow. But Deborah’s mother has been a public-school teacher for 25 years and realizes that her daughter is “succeeding” in math without acquiring what most people would call the basic skills.
“I noticed it with my older daughter when she hit Grade 6 as well,” Marjorie Gann explains. “Deborah just finished Grade 5 and she could not multiply using two-digit multipliers. For example, 382 x 28. At school, they had taught her two or three different ways of doing it and she was hopelessly confused.” The school did not care: Deborah understood the concepts and how to solve problems, and calculators were available to do the math. But her mother cared, and in the process has become a modest foot soldier in what, south of the border at least, are called “the math wars.”
Nine years ago, alarmed at the performance of U.S. students on international math and science tests, the National Council of Teachers of Mathematics unleashed a wave of curriculum reforms that is now flowing like hot lava through Canadian schools. The new new math: its proponents call it “exploratory math” or “rich-learning math.” Its critics: “fuzzy math” or “whole math” (a derisive allusion to the whole-language reading debate) because of its emphasis on estimating, calculators and creative, rather than rote learning. California schools, which initially embraced the NCTM standards, are now recoiling. And in some circles, and on the Internet, the debate has become so fierce that U.S. secretary of education Richard Riley has repeatedly called for a “ceasefire” between the NCTM and its critics.
One of the largest educational lobby groups of its kind—with a considerable contingent of Canadian educators and affiliated provincial associations—the NCTM is firmly on the progressive side of the educational firmament. Its stated aim is to integrate the teaching of math—algebra, trigonometry and geometry, for example—in the same lessons, to challenge students with problem solving and to “de-emphasize” (the NCTM’s term) technical skills such as long division. Because of technology, “the NCTM and people like me are saying we don’t need to teach as much of the traditional math as we did 20 years ago,” says University of British Columbia mathematician David Robitaille, a textbook writer who is also the Canadian coordinator for the international math and science tests. “But we do need people who are better at problem solving.”
Another aim of the reforms is to make math readable. “Math should be about exploration, discovery and teaching students to think—not about getting the one ‘right’ answer,” says Peter Taylor, a math specialist at Queen’s University in Kingston, Ont. A member of the team that is writing Ontario’s new math curriculum for high schools, Taylor says math should be taught the way literature is—with sophistication and “real-world” problems, and with books that can be taken home to be read and puzzled over. The back-to-basics proponents have some valid criticism with the new agenda, Taylor allows. But in the long run, he says, “I don’t care so much if Canada doesn’t do as well as Korea on these international tests. That is not what mathematics is about.” Indeed, a five-year pilot project in Connecticut of a new “readable” NCTM-based math curriculum, written in part by University of Western Ontario educator Eric Wood, has shown some promising results. According to Wood, the study found that high-school students following that program performed better on tests than their counterparts using more traditional methods; and that adolescent girls, who tend to turn off math in high school, performed as well as the boys and did not drop out. Both Wood and UBC’s Robitaille caution against comparing the Canadian and American math experiences too closely. Canadian schools already teach more integrated, problem-solving techniques, especially in Alberta and British Columbia where, Robitaille says, the NCTM reforms have become mainstream and students have done particularly well on international tests. Even the politics of math instruction in Canada is much more muted.
Still, the warnings of an experienced grade-school teacher like Marjorie Gann are hard to ignore. Students can learn on their own in small groups, she says, referring to the co-operative learning technique favored by the math reformers. But that does not mean they will all have absorbed the many steps in a solution. Similarly, an overemphasis on problem solving can burden students, and parents trying to help them, with too many techniques at once. “I am fully in favor of the intuitive learning they want to bring about. But that is not going to happen unless a child is completely comfortable with numbers. You don’t expect a child to play in a musical performance without learning the scales. It’s the same thing with math.”
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