Corrected: The story gave an incorrect location for the National Council of Teachers of Mathematics, a professional organization. It is located in Reston, Va.
The task seemed straightforward enough: Students taking part in a recent international test were asked to review drawings of five triangles with varying angles and midpoints. Then those teenagers were to read over a paragraph describing the characteristics of a particular triangle and, finally, choose the triangle that fit the description.
Of the students from industrialized nations who took that exam, the Program for International Student Assessment, or PISA, 62 percent received full credit for answering the question correctly.
Yet the assignment befuddled a greater percentage of test-takers from the United States, of whom only 46 percent received full credit. That poor showing repeated itself throughout the problem-solving and mathematics-literacy sections of PISA, whose results were released here and in other locations around the world last month. The exam showed U.S. 15-year-olds lagging behind their peers from other industrialized nations in those areas.
By some measures, American students fared better on a second, equally scrutinized international test released a week later: the Trends in International Mathematics and Science Study, or TIMSS. That exam showed U.S. 4th and 8th graders scoring above international averages in math and science, and minority groups improving.
See the accompanying item,
To some education experts, though, the U.S. performance on the two international exams reinforced their belief that American students suffer from an inability to perform complex reasoning and mathematical assignments—the kind they are likely to encounter in college and the workplace.
“We’re not doing as much problem-solving of that type as we need to be,” said Cathy L. Seeley, the president of the National Council of Teachers of Mathematics, based in Arlington, Va.
In other countries—including several Asian ones that outperformed the United States on both PISA and TIMSS—academic work is far more likely to be presented through exercises that students encounter every day, Ms. Seeley and others say. In those nations, a lesson is presented through a real-world situation in a textbook, and students are asked to use a specific skill they are being taught—such as multiplication—to solve the problem. Students later move on to more complicated tests of that mathematic skill, all the while maintaining an understanding of its application in everyday problems, Ms. Seeley said.
In the United States, by contrast, the approach is “Here’s the rule, here’s how you do it, and here are some word problems,” said Ms. Seeley, a former director of mathematics for the state of Texas, who is a research associate at the Charles A. Dana Center at the University of Texas, Austin.
‘Destructive’ Debate
The shortcomings of that approach were evident in U.S. students’ performance on PISA, she suggested. American students scored 477 on the problem-solving section of the test, and 483 in mathematics literacy—the two main subjects the 2003 PISA measured in depth—below the international average of industrialized nations of 500 in both areas, ranking the United States 24th out of 29 nations in each category. The results were released Dec. 7.
“Learning for Tomorrow’s World: First Results From PISA 2003" is available online from the Organization for Economic Cooperation and Development, along with a summary of the report.
“Highlights From the Trends in International Mathematics and Science Study 2003" is also available online from the National Center for Education Statistics. ()
Finland ranked at the top of the list of nations in both those categories, with Japan and South Korea also notching spots among the top performers.
The Asian countries’ strong showing did not surprise Phil Daro, a senior fellow at the National Center on Education and the Economy who has studied differences between textbooks used in that region and in the United States. The Washington-based center studies the impact of education—particularly higher standards—on the American economy and its workforce.
Mathematics textbooks in countries such as Japan are in many cases only one-third as long as those used in the United States, where textbooks tend to be bloated with repetitive drills covering a relatively modest amount of material, Mr. Daro said. Japanese textbooks “are not about activities,” but about concepts, he said. “Each problem builds on the previous one,” he said.
When U.S. students were asked on PISA to demonstrate skills beyond the relatively narrow set of questions on which they had been drilled, Mr. Daro said, they were lost. Japanese students, by contrast, learn to solve “unrehearsed problems.”
In recent years, Mr. Daro and others say, U.S. mathematics instruction has been scorched in the pedagogical blaze known as the “math wars”—a divide between those who see a need for a greater emphasis on basic skills in math and others who say students lack a broader, conceptual understanding of the subject.
That debate has proven “distracting and destructive,” Mr. Daro said, pointing out that Asian nations outscoring the United States on international tests had shown an ability to nurture both aspects of mathematics skills among students.
The TIMSS exam, in contrast to PISA, evaluates 4th and 8th grade students on the material they’ve covered in school, testing them on curricula that are shared by the participating nations. U.S. students beat the international averages in both science and mathematics on TIMSS.
Minority students showed improvement in several categories at the 4th and 8th grade levels. But while U.S. officials found those results encouraging, they also noted that this country’s relative performance among 4th grade students declined, compared with that of other nations, between 1995 and 2003. The relative standing of 8th graders improved during that period.
“While their scores are better, the fact is they’re not keeping up with their peers in other nations,” U.S. Deputy Secretary of Education Eugene W. Hickok said of the 4th grade scores. He spoke at a Dec. 14 press event in Washington on the TIMSS results.
‘A Basic-Skills Problem’
Tom Loveless, a senior fellow at the Brookings Institution, a Washington-based think tank, said TIMSS exposed U.S. students’ weaknesses in basic arithmetic skills. Mr. Loveless probed that issue in depth in a study released earlier in 2004, in which he concluded that the National Assessment of Educational Progress, the premier domestic test of students’ academic skills, was too easy. (“Study Finds NAEP Math Questions ‘Extraordinarily Easy’,” Nov. 24, 2004.)
TIMSS, by comparison, evaluates those skills more thoroughly, he said, particularly through more decimal and fractions problems, and found American students wanting. Overall, Mr. Loveless argued, the international tests show “we have a basic-skills problem.”
Some federal education officials, such as Grover J. Whitehurst, the director of the Institute of Education Sciences within the U.S. Department of Education, interpreted the TIMSS results as showing a need for better alignment in states and school districts between standards for what students should be learning and the curricula guiding what they are actually taught.
But Mr. Whitehurst and others noted that foreign countries with more centralized, nationally driven education systems were able to make across-the-board changes to schools based on PISA and TIMSS results in ways that the United State could not. For instance, a European nation displeased with its results, he said, could “align a national curriculum toward meeting that need.”
David W. Gordon, a superintendent in California and a member of the National Assessment Governing Board, which sets policy for the NAEP test, added that few of the top-performing nations on PISA and TIMSS face as many challenges in educating a diverse population as the United States.
Mr. Gordon pointed out that his former district, California’s 58,000-student Elk Grove Unified School District, served students who spoke 85 different languages. “We’re trying to do something extraordinary, in raising every student to a certain level,” Mr. Gordon said of U.S. schools. “That’s not the goal in some other countries.”
Unwarranted Confidence?
But Mr. Gordon, now the superintendent of the Sacramento County Office of Education, also observed that students from immigrant families displayed a strong work ethic, a diligence he believes was lacking in too many American-born students.
The superintendent also saw an irony in one of the PISA findings: In a survey of 15-year-olds’ attitudes toward studying mathematics, American students showed some of the greatest confidence in their abilities of any group from any country. Students from the United States, for example, were far more likely to say they were good at mathematics and received strong grades in that subject than their peers in Japan and South Korea, whose teenagers easily outperformed them in problem-solving and mathematics literacy on PISA.
“We’re number one,” Mr. Gordon said, “in self-esteem.”
