Lessons from abroad: plan better and delve deeper
For educators, the results of the Third International Mathematics and Science Study were the equivalent of the shot heard 'round the world. While for some countries - particularly top-scoring Singapore, Korea, and Japan - the test results released in 1997 were an affirmation. To the US, the scores were an alarming reminder that much was wrong.
And yet TIMSS didn't tell those monitoring math instruction in the US anything they didn't already know. The previous two rounds of international testing (done in the 1960s and the 1980s) also showed US math achievement to be in a precarious position.
"All three studies have consistently shown that children in this country are not achieving on a par with children in other countries," says Glenda Lappan, president of the National Council of Teachers of Mathematics.
But the jolt that accompanied the TIMSS results of this decade has clearly had some salutary effects. One has been to turn the US to the outside world to ask, "What can we learn from what others do?"
There are no easy answers. In fact, if anything, the TIMSS research has served to debunk a number of facile assumptions about where the US may be stumbling in comparison with others.
For instance, TIMSS-sponsored studies show that US math teachers on the average have considerably higher levels of education and work longer hours in the classroom than those in many countries that outperform us.
Math teachers in Japan and Germany generally assign less homework than US math teachers. And Japanese eighth-graders - whose scores soar above those of US eighth-graders - watch on the average about the same amount of TV as do their American peers.
So if toughening teacher requirements, assigning more homework, and turning off the TV are not the main lessons the US needs to learn from abroad, what are they? The US can learn from others in many areas, say math educators, but most point to some key aspects:
*Curriculum and lesson development. Compared with those of most other TIMSS nations, US math curricula are often described as "a mile wide and an inch deep." Seventy-five percent of the countries involved in the study cram fewer topics into math curricula than the US does.
A typical US eighth-grade math class serves up 35 topics. Pressure to get through them all within the school year forces some teachers to rush, critics charge, which can leave many students baffled.
Japanese students, by contrast, will study only five to 10 concepts in eighth grade, but will learn them in much greater depth. Then they move on, building on those ideas. American schools tend to repeat concepts in many grade levels.
"Our teachers always think more is better," says Jerry Becker, a math-education professor at Southern Illinois University in Carbondale. "But Asians think the opposite. They believe less is more."
Another weak point of US curricula appears to be too much focus on arithmetic over too long a period of time. Most US students don't tackle algebraic concepts until ninth grade, at which point they are a year to a year and a half behind many of their peers in other countries.
In another comparative math-education study, dozens of randomly selected eighth-grade math classrooms in the US, Japan, and Germany were videotaped, and professors James Stigler and James Hiebert wrote "The Teaching Gap" (Free Press) based on their observations.
Not only did the tapes allow them to examine how extensively Japanese and German eighth-graders grappled with more challenging material, but they also provided a glimpse of the more carefully crafted lessons particularly evident in Japanese classrooms, where lessons are polished over years.
*Textbooks. Across the US, interest is surging in math textbooks from Singapore. That shouldn't surprise anyone, says Yoram Sagher, a math professor at the University of Illinois in Chicago. Professor Sagher has worked as a consultant to Baltimore public schools, introducing texts from Singapore there.
"American texts are way too big, and filled with extraneous junk that diverts ... students away from the basic simplicity of the mathematics being taught," he says.
By contrast, the Singapore texts, he says, are inexpensive and lightweight, with simple illustrations. Their size encourages kids to keep them in their backpacks and tote them home. That's a virtue not confined to the Singapore texts: While the typical US math textbook is about 700 pages, in most of the other TIMSS nations, math texts were no more than 200 pages.
The excellence of word problems in Singapore texts is often praised by US teachers as well. "They have multistep word problems, with an expectation that the reader will do the work," says Sagher.
*Insufficient teacher planning time. American teachers spend far more time in the classroom than their counterparts in countries like Japan, China, and Russia, all of which provide more planning periods and time for teachers to improve their knowledge of subject matter. American teachers also have little if any opportunity to collaborate to develop lessons - a common practice in Asian countries.
*Expectations. Parents and teachers in the US often don't expect all children to perform well in math. Many believe that children won't like the subject - perhaps because that mirrors their own experience. But in Asia and France, that's not the case. Adult expectations are often borne out in student experience, says Richard Askey, professor of math at the University of Wisconsin in Madison.
*Calculators. Students in US math classes make much more use of calculators than students in most better-performing nations. Eighth graders in Belgium, Korea, and Japan almost never use them. Students in Singapore begin using them only in seventh grade.
But in the US, eighth-graders in a typical math class use calculators as often as every day. Even in fourth grade, more than a third of US students use them at least once a week. But in six of the top seven scoring countries in the study, 85 percent of students didn't use calculators in class.
Of course, in some cases cultural or systemic differences make it hard to compare the US with international practices. Some point out that in a country like Japan, a small group of experts confer to determine a national curriculum.
In the US, where local control is highly valued, it's hard to imagine the kind of carefully crafted, comprehensive, national curriculum that exists in Japan ever taking root. But others say America - even if it never accepts the idea of a national curriculum - ought to take note of the way these countries achieve a greater unity of purpose.
Indeed, there's been tremendous value in scrutinizing the styles of other nations, says Catherine Lewis, a member of the education department at Mills College in Oakland, Calif. The Japanese approaches of not grouping students by ability until high school, the strength they show in helping kids connect to school socially, and their focus on cooperation rather than competition are other examples of methods we could fruitfully borrow, she says.
Through studying other countries, a fresh perspective is also gained, says Mr. Hiebert, professor of education at the University of Delaware and co-author of the "Teaching Gap."
"It's like holding up a mirror and noticing things about yourself that you didn't notice before. And then you realize, they're just practices, they're not written in stone. You can change them."
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