The average performance of American students in mathematics has apparently neither improved nor declined relative to that of students in 24 other nations since the first international comparison of math achievement was made 20 years ago.
That is the preliminary conclusion of the U.S. researchers who participated in the Second International Mathematics Study, whose early findings were released late last month at the annual meeting of the National Council of Teachers of Mathematics in San Francisco.
“There is not much evidence of any change whatsoever,” said Kenneth J. Travers, professor of mathematics education at the University of Illinois and chairman of the International Mathematics Committee. “There is enormous variation across the United States in how much math is taught and how much is learned, so the high achievers balance out the low achievers and we come out looking pretty average.”
But he also noted of American achievement that “when it is good, it is very, very good, and when it is bad--you know the rest.”
600 Math Classrooms
The mathematics study was begun in 1976 by the International Association for the Evaluation of Educational Achievement (iea), a group of leading education-research institutions headquartered in Stockholm, Sweden. The U.S. portion of the research, which surveyed 8th- and 12th-grade students and teachers in some 600 mathematics classrooms, was conducted by the University of Illinois at Urbana-Champaign.
The intent of the study was “to provide detailed information from each country about the content of the math curriculum, how math is taught, and how much math is learned,” Mr. Travers said.
“The information is designed to help individual nations analyze their school programs, identify areas of strength and weakness, and provide data to national officials as they plan for future directions in school math in their own countries.”
The full results of the U.S. study are scheduled to be made public in September at a national conference at the University of Illinois. The international data will be released next May.
12th-Grade Problems Revealed
According to the study, American 8th graders are achieving at about the same level as average students in other countries.
Although the top 2 or 3 percent of U.S. students are among the world’s best, according to the study, the figures for 12th-grade students reveal that the majority are performing “considerably below the national average in terms of achievement,” Mr. Travers said.
Earlier iea research on achieve-ment--a math study conducted in 1964 and a science study conducted in 1971--found a similar pattern: While top American students perform as well as or better than their counterparts in other countries, those advantages are overshadowed by the fact that the majority of students perform at levels lower than those of their counterparts in other countries. (See Education Week, July 27, 1983.)
This finding, Mr. Travers said, “raises serious questions about the readiness of kids in the ‘regular’ mathematics stream for college-level study of calculus.”
Mr. Travers said he could not reveal the study’s specific findings on student-achievement levels in Japan, where mathematics students have characteristically outscored Americans, but he noted that “there aren’t going to be many surprises along those lines.”
National Agenda
Mr. Travers pointed to America’s lack of commitment to an education-al “agenda” as one reason for the low scores among American students.
“One of the characteristics of U.S. education, in contrast to almost every other country, is that we do not have a national system of education,” he said.
Although he does not support the adoption of a national curriculum per se, Mr. Travers said, he does support a national commitment to an agenda in mathematics education.
“I think there is widespread agreement among mathematics educators as to what characteristics a person who is well educated in mathematics [should have],” he said. “And I support a broad agenda in the teaching of mathematics throughout the grades, from kindergarten through 12th grade.”
Mr. Travers called on curriculum supervisors and state and national education leaders to develop a homogeneous concept of what constitutes a sound mathematics education.
He also recommended broadening the pre-8th-grade curriculum to make it more comprehensive and to challenge high-school students more. “They can do better,” he said of upper-level students. “We have to find ways of getting the best out of them. We have to demand more of them, set clearer expectations for them.”
Role of Computers
In addition, Mr. Travers said he hopes the use of microcomputers in schools will help educators teach more mathematics in increasingly effective ways.
“For the first time in the history of education, we have the opportunity at the high-school level to create, on a large-scale basis, an honest-to-goodness laboratory setting for the teaching and learning of mathematics,” Mr. Travers said. “And the computer will be at the heart of the operation.”
Mr. Travers suggested that American educators use the study’s findings to identify high-quality programs “to figure out what they are doing, ... to spread that wealth of knowledge around to the rest.”
“I think we would be doing a disservice to U.S. education to characterize it as a disaster scene,” he said. “There are many bright spots. One of the things this study shows is that when things are done well, they are done very well.”
Other Findings
Among other preliminary findings of the American portion of the study:
Textbooks are used in classrooms as the predominant instructional material at both the 8th- and 12th-grade levels.
Most 8th-grade students spend the majority of their class time working at their desks or at the blackboard, while 12th-grade students spend most of their class time listening to lectures, working at their desks, and taking tests.
Approximately 145 hours a year are provided for 8th-grade mathematics instruction, compared with about 150 hours a year for 12th-grade mathematics instruction. The study found that this represents about the same amount of time allotted to math in most other countries at the 8th-grade level, but is somewhat less than average for students at the 12th-grade level.
Math Homework
The average 8th-grade math student spends 30 minutes a day or less on math homework; the typical 12th grader spends five hours a week on math homework.
Geometry and probability topics are taught in most countries at the 8th-grade level, according to the study; in the United States, however, these topics are infrequently taught in 8th-grade classes.
Student performance in arithmetic and measurement, which the study calls “mainstays of the typical 8th-grade curriculum,” is “disappointingly low” in the United States, which may, in part, be explained by the use of metric units in international tests, according to the study.
The achievement levels of American calculus classes, which are usually made up of the best senior-high-school math students, was found to be somewhat higher than the average achievement level in those classes in other countries. However, the study noted, the majority of 12th-grade students, who typically take such courses as trigonometry or analytical geometry, demonstrated a much lower level of achievement.
