But Schaafsma’s animation is not the main reason that Dutch children actually like math and score high, along with Japan, on standardized tests that rank the performance of students in industrialized countries. Down the hall, Rita Folestra’s math class of 12-year-olds sit in ordered rows of desks and solve workbook problems quietly among themselves after she briefly introduces the lesson.
Schaafsma and Folestra may prefer diametric teaching styles, but both use the same revolutionary new system for math instruction called Realistic Mathematics. Developed over the past 15 years by researchers at Utrecht University’s Freudenthal Institute, Realistic Math starts with the premise that children have a natural way of doing arithmetic. The youngest begin by using sticks and dots. Later, work-books allow students to learn at their own pace and structure a solution in their own way, reinventing mathematical concepts for themselves. Students visualize a problem and estimate the answer rather than memorize formulas. Instead of the strict hierarchy of mastering arithmetic before studying fractions, algebra, geometry and statistics that is rigidly adhered to in American schools, Realistic Math integrates all of these skills at every level. Most importantly, the new curriculum introduces each subject with a discussion of a real-world problem to show how integral a part of ordinary life mathematics really is. “You can use this mathematics when you’re watching the news,” says 15-year-old Ronald Kneigt. “You can see something and you understand it.”
Understand it, that is, even when the grown-ups don’t. This fall a British artist planted a wheat field with 250,000 seeds that grew to form an image of van Gogh’s painting “Sunflowers.” One Dutch newspaper reported the area of the image to be 14 square kilometers. Another said the area was about 10,000 square meters. In asking a student to explain which newspaper is correct, a Realistic Math workbook might also give the original measurements of the field, more than 12,000 square yards, state that a yard is equal to .9 meters, and present news photos that show trees, tractor tracks and the van Gogh. (The answer, by the way, is 9,720 square meters, rounded off to 10,000 square meters.)
All Dutch children start with Realistic Math. Future engineers and physicists switch to more structured and abstract math during high school and college. But the Freudenthal researchers argue that most children don’t have the ability or inclination to grapple with abstract math. Nor does it serve any useful purpose in later life. “We must give the students something they can do in society,” says Schaafsma. “There is such a gap between algebra and managing to cook the potatoes in time to eat them with the meat or managing problems at the workplace.”
About 90 percent of high-school students now take advanced-math courses, but there has been no increase in the number of college students majoring in math. Researchers also can’t explain why more high-school girls aren’t attracted to math classes. Still, Utrecht University math professor Jan de Lange was recently invited to Montana to discuss how well the Dutch methods might travel. Montana scored at the top of the 1990 National Assessment of Educational Progress math test for eighth graders. The best in the land, Montana now wants a world-clan program.
