Executive Summary

In recent years, U.S. mathematics and science education has become a focus of considerable public concern. Much of that concern has been generated by the results of the Third International Mathematics and Science Study (TIMSS), which in the mid-1990s assessed the performance of students in different countries at levels corresponding to grades 4 and 8 and the final year of secondary school (grade 12) in the United States. U.S. students performed well in certain areas, but their overall performance was at best average. Furthermore, the TIMSS data reveal comparative declines in performance from fourth grade to eighth grade and from eighth grade to the final year of secondary school, and in particular areas the performance of U.S. students was weak at all three levels. As states, districts, and individual schools strive to implement high standards for learning in mathematics and science, the results from TIMSS demonstrate that many U.S. students are not now achieving at a high level on an international basis.



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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education Executive Summary In recent years, U.S. mathematics and science education has become a focus of considerable public concern. Much of that concern has been generated by the results of the Third International Mathematics and Science Study (TIMSS), which in the mid-1990s assessed the performance of students in different countries at levels corresponding to grades 4 and 8 and the final year of secondary school (grade 12) in the United States. U.S. students performed well in certain areas, but their overall performance was at best average. Furthermore, the TIMSS data reveal comparative declines in performance from fourth grade to eighth grade and from eighth grade to the final year of secondary school, and in particular areas the performance of U.S. students was weak at all three levels. As states, districts, and individual schools strive to implement high standards for learning in mathematics and science, the results from TIMSS demonstrate that many U.S. students are not now achieving at a high level on an international basis.

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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education A BRIEF DESCRIPTION OF TIMSS (CHAPTER 1) TIMSS was the largest and most comprehensive study of mathematics and science education ever conducted. It included assessment of the mathematics and science knowledge and skills of more than half a million students from 15,000 schools around the world, including approximately 33,000 U.S. students from more than 500 schools. Students were tested at three levels: the two grades containing the most 9 year olds (population 1, corresponding to grades three and four in the United States); the two grades containing the most 13 year olds (population 2, corresponding to grades seven and eight in the United States), and the final year of secondary school (population 3, corresponding to U.S. high school seniors). Special efforts were taken to ensure that the samples of students tested in each nation were representative. The result is a detailed portrait of student strengths and weaknesses in specific areas of mathematics and science. Many people describe TIMSS as though it were a ''horserace" where all that matters is where the United States ranked compared with other nations. In fact, TIMSS provided much more than just international assessments of student achievement. It analyzed the curricula used in different countries; surveyed educators and students; performed in-depth case studies of schools and educational systems in the United States, Germany, and Japan; and videotaped mathematics classes in eighth grade in those same three countries. These varied international analyses of mathematics and science education provide much to consider beyond the ability of U.S. students to answer particular scientific and mathematical questions. Taken together, the data provided by TIMSS call attention to factors associated with student achievement, thus identifying promising areas for future study. They also provide deep insights into different ways of teaching and learning, which opens the door to considering new possibilities for U.S. education. STUDENT ACHIEVEMENT RESULTS (CHAPTER 2) To examine the school-related factors that need to be considered to improve teaching and learning in mathematics and science, it is useful to know not only the overall achievement results for U.S. students but also more detailed results, such as the particular areas where students did well or poorly. In mathematics, U.S. students in the upper grade of population 1 (the fourth grade) had average scores somewhat above the international mean when compared with the upper-grade population 1 students in other countries. In science, the only nation's students in the upper grade of population 1 to score significantly better than U.S. students were those of Korea. Among U.S. students in the upper grade of population 2, science scores remained above the international mean, but students in a number of other countries performed markedly better on average than did U.S. students. In mathematics, U.S. eighth graders' performance dropped below the international mean, with about half the countries in the international sample achieving average scores that were significantly higher than the overall U.S. score. U.S. students' worst showing was in population 3. In the assessments of general mathematics and science knowledge, U.S. high

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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education school seniors scored near the bottom of participating nations. In the assessments of advanced mathematics and physics given to a subset of students who had studied those topics, no nations had significantly lower mean scores than the United States. The TIMSS results indicate that a considerably smaller percentage of U.S. students meet high performance standards than do students in other countries. Furthermore, many U.S. students are not achieving even at the level indicated by the average U.S. scores. While the variability of U.S. scores was not markedly greater than in other countries, the existing variability in the U.S. scores was strongly linked to the specific classes a student took (for example, regular mathematics versus algebra in middle school or junior high) and to differences among schools. These findings suggest that many students are not being given the educational opportunities needed to achieve at high levels. At the fourth-and eighth-grade levels, the results were broken down into subareas in both mathematics and science. In science, fourth-and eighth-grade U.S. students exhibited notable weaknesses in the physical sciences. In mathematics, U.S. students' performance tended to be strongest in areas involving whole number operations, fractions, data representation, and probability. Performance was relatively weaker in measurement, proportionality, and (in the eighth grade) geometry and algebra. At both the fourth-and the eighth-grade levels, U.S. students performed relatively well on mathematics items calling for straightforward computation. However, U.S. students had much weaker abilities overall, compared to students in other nations, to conceptualize measurement relationships, perform geometric transformations, and engage in other complex mathematical tasks. These kinds of abilities are among the learning goals called for by the U.S. national standards and benchmarks for mathematics education and by many sets of state standards, indicating that many U.S. students are not now achieving the objectives of those standards. CURRICULAR ISSUES (CHAPTER 3) TIMSS clearly demonstrated that the curriculum affects student achievement. For example, nations tended to perform better in particular areas of mathematics and science emphasized in their countries. One broad measure of curricular emphasis in mathematics and science is the amount of time given to these subjects in schools. The results from TIMSS demonstrate, somewhat surprisingly, that the time spent on these subjects is higher in U.S. fourth-and eighth-grade classrooms than it is in many other TIMSS countries. Only at the secondary level do students in other countries appear to experience more mathematics and science instruction on average than do students in the United States. Even when more time is spent on mathematics and science, however, expectations for student learning in the United States may be lower than elsewhere. In the videotaped eighth-grade mathematics classes in the United States, Germany, and Japan, the content of each lesson was compared to the average grade level across all TIMSS countries in which particular topics

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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education received the most attention. By this measure, the mathematics content of U.S. lessons was, on average, at a mid-seventh-grade level, whereas German and Japanese lessons were at the high eighth-grade and beginning ninth-grade levels, respectively. Attention also has focused on the structure of the curriculum, particularly on measures of curricular focus and coherence. Focus refers to the depth with which topics are treated within and across classes. Several lines of evidence point toward a lack of focus in U.S. mathematics and science instruction. According to the TIMSS curriculum analysis, the number of topics in a broad sample of U.S. textbooks was substantially larger than for textbooks in most other countries, and U.S. textbooks include more review exercises and repeat more topics covered in previous grades. Teachers do not necessarily cover everything included in a textbook, but U.S. teachers reported in questionnaires that they teach many more topics over the course of a year than do teachers in Japan or Germany. This rapid movement from one topic to another suggests that U.S. instruction may be more superficial than in other countries, with students often failing to acquire deeper understanding of any particular topic. Coherence, in contrast, refers to the connectedness of the mathematics and science ideas and skills presented to students over an extended period of time. In a coherent curriculum, new or more complex ideas and skills build on previous learning and applications are used to reinforce prior learning. Again, several factors suggest a lack of coherence in U.S. curricula, although the evidence is not conclusive. According to the TIMSS curriculum analysis, U.S. textbooks tend to switch from topic to topic much more frequently than do textbooks used in other countries. The videotapes of eighth-grade mathematics classes showed that teachers in the United States switch topics more times than do teachers in Japan and Germany and make fewer references to other parts of a lesson. Also, interruptions of lessons (for example, by public address announcements or outsiders coming into the classroom) are much more common in the United States than in Germany or Japan. When summaries of videotaped lessons from the United States, Germany, and Japan were analyzed by mathematics teaching experts who did not know the country where each lesson was taped, the group found that about 45 percent of U.S. lessons, 76 percent of German lessons, and 92 percent of Japanese lessons achieve a predefined standard of coherence. Using several measures of quality in addition to coherence, these mathematics teaching experts also judged the content of U.S. lessons to be of lower quality than the content of lessons from Japan and Germany. U.S. national standards and benchmarks in both science and mathematics cite focus and coherence as critical qualities of curricula in those subjects. Unless a clear set of goals is recognized that can establish connections among topics—goals such as those provided by national, state, and local standards in mathematics and science—it can be difficult to construct coherent mathematical and scientific stories in classes that cover large numbers of topics.

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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education INSTRUCTIONAL PRACTICES (CHAPTER 4) Science and mathematics teachers around the world face many similar challenges. But teachers—and the educational systems of which they are a part—tend to solve similar problems in different ways. These solutions often reflect deeply held beliefs and assumptions that teachers hold about teaching and learning. The questionnaires completed by teachers at the population 1 and 2 levels show that the structure of lessons has some common features among countries, as well as some interesting differences. For example, the two most common activities in U.S. mathematics teachers' classrooms at the fourth-and eighth-grade levels are teachers working with the whole class and students working individually with assistance from the teacher. In fourth-grade science, another common practice is for the class to work together as a whole with students responding to each other. According to the questionnaires, more than half of U.S. eighth-grade mathematics students received fewer than 20 minutes of instruction on new material in a typical 50-minute class period. U.S. mathematics and science teachers use tests and quizzes extensively in the eighth grade, and tests and quizzes played a larger role in teachers' reports to parents in the United States than in most other countries. U.S. fourth-and eighth-grade teachers seem to assign amounts of homework comparable to teachers in other countries (though parents and students in other countries may not think of all studying done outside school hours as homework). The United States is one of just a handful of countries where students were frequently given class time for starting homework assignments. Beneath the observable activities that occur in mathematics and science classes are the external forces and internal motivations that cause teachers to instruct in particular ways. Among the most powerful of these forces are teachers' beliefs and goals, some of which can be inferred from the videotape studies of eighth-grade mathematics in Japan, Germany, and the United States. The videotapes demonstrate that in German mathematics classes there is a concern for technique, where technique includes both the rationale that underlies the procedures and the precision with which the procedure is executed. A good general description of German mathematics teaching at this level would be "developing advanced procedures." In Japan the teacher carefully designs and orchestrates the mathematics lesson so that students use procedures recently developed in class to solve problems. An appropriate description of Japanese teaching in mathematics would be "structured problem solving." In the United States the content is less advanced and requires less mathematical reasoning than in the other two countries. The teacher tends to present definitions of terms and demonstrates procedures for solving specific problems, and students are asked to memorize the definitions and practice the procedures. U.S. mathematics teaching in the eighth grade could be described as "learning terms and practicing procedures." In the United States, skills tend to be learned by mastering the material incrementally, with high levels of success at each step. Confusion and frustration are signs that the earlier material was not mastered. In the style of

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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education teaching dominant in the United States, the teacher's role is to shape the task into pieces that are manageable, providing all the information needed to complete the task and plenty of practice. In Japan, teachers tend to have students struggle with a problem and then participate in a discussion about how to solve it. Confusion and frustration are seen as a natural part of the process and are useful to prepare the students for the information received during the discussion. The teacher's role is to engage the student, reveal the mathematics of interest, and help the students understand the problem so they can attempt to solve it. A useful way to view these instructional differences among countries is to see them as unified "scripts" for teaching. These scripts are deeply embedded in the culture of each country and can be resistant to change. However, by appreciating one's individual script and the scripts common in other countries, teachers can use TIMSS to begin to examine the assumptions they hold toward teaching and the ingrained ways in which they approach their responsibilities. The U.S. national standards in mathematics and science call for an approach to teaching in which students actively explore mathematical and scientific ideas, ask questions, construct explanations, test those explanations, and communicate their findings to others. Achieving this kind of instruction in U.S. mathematics and science classes will require reexamining deep-seated beliefs about teaching and learning. SCHOOL SUPPORT SYSTEMS (CHAPTER 5) Just as curriculum and instruction affect student performance, the broader culture of a school matters as well. Particularly important aspects of this broader culture include the preparation and support of teachers; attitudes toward the profession of teaching; the attitudes of teachers, students, and parents toward learning; and the lives of teachers and students, both in and out of school. Not all of these factors are under the control of teachers, school leaders, and policymakers. Nevertheless, the case studies and questionnaires completed by teachers, administrators, and students in TIMSS point to differences in school cultures that can be changed. The results suggest that school cultures are created by the decisions that policymakers, administrators, and teachers make about how to organize teaching and learning. The structure of the school day and year is quite different in the three countries in which case studies were conducted—the United States, Germany, and Japan. The German school day is much shorter than in either Japan or the United States, and the Japanese school year is longer than in the other two countries. Despite these differences, teachers in all three countries routinely spend time outside of the formal school day to prepare and grade tests, read and grade student work, plan lessons, meet with students and parents, engage in professional development or reading, keep records, and complete administrative tasks.

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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education One of the most significant distinctions between Japanese and U.S. teachers' days is how much time they have to collaborate with colleagues. Compared with Japanese teachers, U.S. teachers spend more of their assigned time in direct instruction and less in settings that allow for professional development and collaboration. In Japan, teachers' time is structured in ways that foster collaboration. For example, they usually share office space with colleagues, and the blocks of time available for Japanese teachers to prepare for classes are typically longer than in most U.S. schools. Preservice teacher education and later professional development are also important factors influencing the learning environment of students. In the United States, teacher preparation tends to be relatively extended compared with the international average. It is even longer in Germany, where the typical pattern is four to five years of university preparation followed by two years of paid student teaching. In Japan, in contrast, field experiences for preservice teachers typically last a mere two to four weeks, but the Japanese approach views preservice preparation as only a small beginning in a career marked by mentoring relationships. In-service development also differs markedly from country to country. Japan in the past decade has mandated an intensive mentoring and training program for all teachers in their first year on the job, reflecting the culture's widespread assumption that elders should guide novices. Japanese teachers also rotate among schools every six years, creating career cycles unlike those common in other countries. Professional development opportunities are varied, ranging from formal training at local resource centers to peer observation and informal study groups. In the United States, professional development is less formal and coherent. Schools and districts offer a range of staff development programs, but these tend to be short term, vary widely in focus, and often appear to teachers as a menu of unrelated opportunities. Although some districts engage in more systematic efforts at sustained professional development, including sustained mentoring programs, short-term workshops remain the dominant format. Educational systems vary in the degree to which they treat teachers either as professionals or as skilled workers. These differences in treatment surface in such forms as hiring practices, the organization of teacher time, the degree to which teachers control aspects of their work and time, opportunities for continued learning, and the fostering of collegial relationships among educators. The material and symbolic benefits accorded teachers reflect the extent to which they are treated as either professionals or skilled workers. For example, teachers in Japan are paid more in comparison to other workers with similar backgrounds than are teachers in the United States. Employment benefits also tend to be better in Japan and Germany. On the other hand, Japanese teachers report that their profession is respected but not as much as it was in the past. Finally, student attitudes toward mathematics and science, another powerful influence on the culture of mathematics and science education, tend to be positive across countries. Most U.S. fourth and eighth graders report that they like both mathematics and science, although

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Global Perspectives for Local Action: Using TIMSS to Improve U.S. Mathematics and Science Education fourth graders are more positive than eighth graders. However, students in some of the highest-performing countries recorded markedly lower perceptions of their own performance compared with students elsewhere, suggesting that students in high-performing countries may work especially hard to meet perceived shortcomings. The national mathematics and science standards call attention to the critical importance of the broader culture in shaping teaching and learning in the United States. Teachers need the support of administrators, policymakers, parents, and the broader society to make lasting improvements in mathematics and science instruction. A READER'S GUIDE TO THIS REPORT The value of TIMSS lies not only in the questions it answers but also in those it raises. Reflection on how education is conducted in different countries is a rich source of insight into the potential of alternative educational approaches. The findings of TIMSS do not suggest that the United States should seek to replicate aspects of other countries' educational systems. However, the findings offer many ways to increase understanding of the U.S. educational system and to identify possible changes that could improve teaching and learning. To foster careful analysis and creative thinking about educational practices in the United States, Chapters 3, 4, and 5 of this report include sets of questions keyed to the topics discussed in those chapters. These questions are directed toward a wide range of readers with interests in the education system, including parents, teachers, administrators, policymakers, textbook writers, publishers, those who work in science centers and museums, scientists and engineers, business people, university faculty, and the general public. By examining these questions, readers of the report are invited to consider both the steps that can be taken to improve U.S. education and the additional information needed to help establish future directions. Different readers might be particularly interested in certain chapters of the report. For example, curriculum developers, parents, and teachers might want to concentrate on Chapter 3, ''What Does TIMSS Say About the Mathematics and Science Curriculum?" Teachers investigating alternate classroom strategies might want to focus on Chapter 4, "What Does TIMSS Say About Instructional Practices?" Administrators and teacher educators can read about the culture of U.S. education in Chapter 5, ''What Does TIMSS Say About School Support Systems?" The final chapter, "Frequently Asked Questions About TIMSS," summarizes important information from earlier in the report in a question-and-answer format.