Each year, students from Bangalore to Betioky wear down millions of pencils working out fractions, ratios, and other mathematical mysteries. Their teachers create mountains of chalk dust explaining these concepts.
But in both groups, some individuals are more successful than others. The question is why? Why do some excel while others do not?
This and other “fundamental questions” of mathematics education lie behind an ambitious international study that researchers hope will leave them with a “portrait” of mathematics teaching, curriculum, and student achievement in 24 countries.
This fall, the Second International Mathematics Study, moving beyond its 1964 predecessor, is going into eighth- and 12th-grade classrooms (or their counterparts) to see not only what is taught, but how the teachers go about presenting various topics.
“We have the curricula, and we have data on student achievement,” said Kenneth J. Travers, professor of mathematics education at the University of Illinois and chairman of the International Mathematics Committee. “We’re looking for the missing link. National studies show that we don’t really have a lot of information about what mathematics teachers do in the classroom.”
Understanding the Differences
Using data gathered on questionnaires for teachers and specially developed tests for students, the researchers will compare the material, techniques, and outcome of mathematics education. They hope that this information will allow them both to understand and to take advantage of the differences.
In the United States, the study is funded by the National Institute of Education (nie) and the National Science Foundation (nsf). But budget cuts by the Reagan Administration have left the study’s organizers with some “uncertainty” about federal funding.
But they point out that their research will address six of the eight goals of Secretary of Education Terrel H. Bell’s recently established National Commission on Excellence in Education. Those goals emphasize not only reviewing educational curricula, but also comparing U.S. education to that of other industrialized nations, defining problems, and making recommendations for improvement.
The study will focus on two broad areas of mathematics education: the curriculum and the classroom. This fall, in the U.S., researchers will visit approximately 150 schools at the eighth- and 12th-grade levels.
Eighth-grade students will take tests in the fall and in the spring; 12th-graders will be tested only once. Each test will include some “anchor items” from the 1964 international study so that the researchers can compare the two sets of data.
For eighth-graders, the topics include ratio, proportion and percent; measurement; common fractions and decimals; integers; formulas and equations; and geometry. Twelfth-grade topics are algebra, trigonometry, and calculus. Items on the tests represent an “international consensus of importance.”
“We’ve had a very good response from the schools,” Mr. Travers said, adding that officials from several schools had heard about the study and called to ask if they could participate. Since it is a statistically determined sample, volunteers could not be accommodated.
In addition to looking at the “classroom process,” the study will examine new aspects of mathematics education.
Hand calculators, for example, are used in many schools to a degree unimagined at the time of the 1964 study. The second study will give educators base-line data on hand calculators: How much are they used? Why do teachers elect to use or shun them? How do students feel about them?
School officials will also be questioned about policies on calculators, the extent to which their use is encouraged, and the number and type of calculators in use, according to study organizers.
All of the information gathered will be used for cross-national comparisons, as well as by the participating countries. In the curriculum study, for which the data have already been collected, researchers will look at three main components--the range and emphasis of topics in each country’s school math program at each level of schooling; the changes in curriculum over the past 20 years; and national responses to important current curriculum issues.
“There appear to be some striking contrasts between the U.S. curriculum and those of several other countries,” says a description of the study.
The 24 participating countries are at different stages of the research; some have finished collecting classroom data, and others, like the U.S., will spend this year gathering data from the schools.
Each country is responsible for translating the materials, which were written in (American) English. A high degree of international cooperation was required in developing the study, since countries that teach the same subject--geometry, for example--may go about it in very different ways, making it harder to compare and test.
Some of the differences are linguistic--one word-problem may use the example of a “snack-shop,” for instance. In New Zealand, a “snack-shop” is a “tuck-shop,” Mr. Travers said.
Not all of the countries on which the educators might want data are participating. Hungary, home of the Rubik cube, the multi-colored block that millions regard as the ultimate brain-teaser, is the only Eastern bloc nation to be involved. The ussr, Mr. Travers said, gives the impression of having “not a great deal of enthusiasm” for sharing classroom procedures. Of the Latin American countries, only Brazil, and possibly the Dominican Republic, are participating.
Final analyses of the data will not be complete for several years, but when they are, there will be something for everyone, the sponsors believe. In addition to several volumes designed for educators and researchers, there will be a “popular” description of the study and some highly technical statistical material. It will be, Mr. Travers said, ''a thorough analysis.”
