• No single factor can be considered to influence student performance in isolation from other factors. There are no single answers to complex questions.
  

• The content of U.S. eighth-grade mathematics classes is not as challenging as that of other countries, and topic coverage is not as focused.
  

• Most U.S. mathematics teachers report familiarity with reform recommendations, although only a few apply the key points in their classrooms.
  

• Evidence suggests that U.S. teachers do not receive as much practical training and daily support as their German and Japanese colleagues.
  

This report has presented highlights from initial analyses of U.S. eighth-graders in international perspective. These findings lightly sketch only a corner of the entire picture of U.S. performance in mathematics and science which will be painted over the next years as further analysis of the eighth-grade data is carried out and findings from grades four and twelve are added.

This section looks across the findings presented in the previous pages for insights into the key questions with which the study started: How do our eighth-graders compare to their international counterparts? What have we learned about mathematics achievement and the factors that may be associated with it? What have we learned about science? What have we learned about how our education system as a whole compares to that of other countries?

Looking for insights into factors associated with student performance is complicated because achievement after eight years of schooling and thirteen years of life is the product of many different influences. Furthermore, education in our country is a vast system with many interrelated parts. No single factor can be properly considered in isolation from others. Realizing that there are no single answers to complex questions, let us review the data.


WHERE DO WE STAND?

The U.S. is far from being among the top nations of the world in mathematics and science. We are far from this goal. Singapore, Korea, Japan, the Czech Republic, and Hungary outperform us in both subjects. Particularly in mathematics, our students lag far behind top-ranking countries. Compared to our goal of excellence among nations, we are not where we aim to be.

However, we are on a par with many of our international trading partners. Our students stand not far from the international average: somewhat below in mathematics, and somewhat above in science. Our math scores are not significantly different than those of Germany and England. Our science scores are not significantly different than those of Germany, England, Canada, and Russia. We rank near the middle of the 41 TIMSS countries, among other nations to whom we frequently compare ourselves.


WHAT HAVE WE LEARNED ABOUT MATHEMATICS?

Our eighth graders score below the international average in mathematics. Although international comparisons over time are difficult, there does not appear to have been much improvement during the past three decades in U.S. students' international standing in this subject. The following factors may be associated with this performance:

• The content of U.S. eighth-grade mathematics classes is not as challenging as that of other countries.

  U.S. eighth-grade curriculum and instruction both appear to be less challenging than those in other countries. Concerning curriculum, topics covered in U.S. mathematics classrooms are at a seventh-grade level in comparison to other countries. Virtually all German and Japanese students study algebra and geometry in the eighth grade, while in the U.S., only students in higher-level classes receive significant exposure to algebra, and few students study geometry.

  Concerning instruction, the content of U.S. classes requires less high-level thought than classes in Germany and Japan. The sequence of mathematical ideas used in lessons was judged to be of low quality in a majority of U.S. classrooms, while this was less frequently the case in the other two countries.

• Topic coverage is not as focused in U.S. eighth-grade mathematics classes as in the classrooms of other countries.

  In the U.S., curriculum is determined at the state and local level, which is atypical among TIMSS countries, most of whom determine curriculum nationally. In all grades 1-8, the U.S. mathematics curriculum recommends coverage of more topics than the international average. U.S. mathematics lessons also include a greater number of topics and activities than those in Germany and Japan.

• Most U.S. eighth-grade math teachers report familiarity with reform recommendations, although only a few apply the key points in their classrooms.

  Ninety-five percent of U.S. eighth-grade mathematics teachers say that they are aware of current ideas about teaching and learning mathematics. Most believe that the lessons they teach exemplify elements of the recommendations. However, the way in which U.S. teachers understand and implement these recommendations suggests that they are focusing on isolated techniques rather than the central message that teaching and learning should involve high-level mathematical thought. Our mathematics teachers' typical goal is to teach students how to do something, rather than how to think about and understand mathematical concepts. In a variety of respects, Japanese mathematics teaching more closely resembles the recommendations of the U.S. reform movement.

U.S. eighth graders score above the international average in science. In the three previous international science assessments, the U.S. scored below the international average. Because comparisons of different international assessments over time are difficult, caution should be exercised in assuming that there has been significant improvement in our international standing in science, but it is a possibility.

This initial report contains less information about science than about mathematics because the questionnaire data have not yet been fully analyzed, and the videotape study of classroom instruction was conducted only in mathematics. Furthermore, because we are unable to use multiple research methods to verify the science findings from different perspectives, our findings are more tentative than for mathematics.

Fuller description of eighth-grade science teachers' instructional practices must await further questionnaire analysis.

WHAT HAVE WE LEARNED ABOUT U.S. EDUCATION AS A WHOLE?

TIMSS provides several insights about U.S. eighth-grade teachers and students, which are true of both mathematics and science education.

• Evidence suggests that U.S. teachers do not receive as much practical training and daily support as their German and Japanese colleagues.

  In contrast to new German and Japanese teachers, new U.S. teachers do not receive a long-term structured apprenticeship in their profession. Once on the job, they have fewer formal and informal opportunities to discuss and share teaching-related issues and questions. Schools are managed in such a way that lessons are frequently interrupted by loudspeaker announcements or visitors at the door.

• Our eighth-graders spend at least as much time studying mathematics and science as students in Germany and Japan.

  During school, our eighth graders spend more hours in mathematics and science classes per year than students in Germany and Japan. U.S. teachers assign more homework, and spend more class time discussing it than teachers in those countries. Outside of school, our students report doing about as much math and science-related homework and other study as German and Japanese students, although most Japanese eighth graders also attend after-school classes in mathematics for an hour or two per week in preparation for the entrance exams to high school.

The initial findings described in this report raise many important questions for further study. Some of these may be answered through continued analysis of the eighth-grade data. Others must await the design of future international studies. For this reason, TIMSS is an important national resource for secondary analysis and further research. Some examples are:

• Why is our international standing lower in mathematics than in science?

  Deeper analysis of the TIMSS data will help us to compare the curriculum and instructional practices used in mathematics with those in science, to better understand the similarities and differences.

• How is student achievement related to curriculum coverage?

  Comparison of the curriculum analysis with achievement scores in the various content areas can illuminate the degree to which our students' performance in algebra, earth science, and other content areas is related to curricular emphasis in these areas.

• Does mathematics teaching in high performing countries resemble the reform movement's recommendations?

  The videotape study found that in many ways, Japanese mathematics teaching resembles the recommendations of the U.S. reform movement more closely than does U.S. and German teaching. Is this an important factor in understanding why Japan also scores among the top nations of the world in mathematics? Undertaking similar videotape observational studies of other high-performing nations and further analysis of the TIMSS teacher questionnaire data could provide insight into this question.

TIMSS is not an answer book, but a mirror through which we can see our own education system in international perspective. It helps us view with new eyes those aspects of our system which we may take for granted. Its findings make us think more deeply about the cultural assumptions and unconscious choices which form the underpinnings of our society's approach to schooling. We come to understand our own system better by comparing it to others. Careful study of our country's reflection in the mirror of international comparisons can provide information to assist educators, business leaders, teachers, and parents as they guide our nation in the pursuit of excellence.