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ACKNOWLEDGMENTS

COMMISSIONER'S STATEMENT

NSF DIRECTOR'S STATEMENT

LIST OF FIGURES

EXECUTIVE SUMMARY

CHAPTER I: INTRODUCTION

What Is TIMSS?

Comparing the United States to Other Countries

The TIMSS Research Team

What Questions Does This Report Answer?

CHAPTER 2: ACHIEVEMENT OF ALL STUDENTS

Key Points

Mathematics and Science General Knowledge

Mathematics General Knowledge Assessment

How well do U.S. twelfth graders do on the mathematics general knowledge assessment?

What were students asked to do on the mathematics general knowledge assessment?

How does U.S. twelfth-grade students' relative performance in mathematics compare to that of U.S. eighth-grade students?

Is there a gender gap in mathematics general knowledge at the twelfth grade?

Has the relative international standing of the United States in mathematics at the end of secondary school changed over time?

Science General Knowledge Assessment

How well do U.S. twelfth graders do on the science general knowledge assessment?

What were students asked to do on the science general knowledge assessment?

How does U.S. twelfth-grade students' relative performance in science compare to that of U.S. eighth-grade students?

Is there a gender gap in science general knowledge at the twelfth grade?

Has the relative international standing of the United States in science at the end of secondary school changed over time?

How does the performance of U.S. twelfth graders in science compare to their performance in mathematics?

CHAPTER 3: ACHIEVEMENT OF ADVANCED STUDENTS

Key Points

Advanced Mathematics Assessment

How do U.S. twelfth graders with advanced mathematics instruction compare to advanced mathematics students in other countries?

How do U.S. twelfth graders with calculus or Advanced Placement calculus compare to all advanced mathematics students in other countries?

How do U.S. students score in the different content areas of advanced mathematics?

What were students asked to do on the advanced mathematics assessment?

Is there a gender gap in advanced mathematics at the twelfth grade?

Physics Assessment

How do U.S. twelfth graders with physics instruction compare to advanced science students in other countries?

How do U.S. twelfth graders with Advanced Placement physics instruction compare to advanced science students in other countries?

How do U.S. students score in the different content areas of physics?

What were advanced science students asked to do on the physics assessment?

Is there a gender gap in physics at the twelfth grade?

How does U.S. student performance in physics compare to that in advanced mathematics?

CHAPTER 4: THE CONTEXT OF LEARNING

Key Points

The Context of Learning for Students Participating in the General Knowledge Assessments

How does secondary schooling in the other TIMSS countries resemble and differ from that in the United States?

How do U.S. twelfth-grade students compare internationally on factors associated with their lives inside and outside of school?

Which of these factors related to education systems and students are associated with the relatively poor performance of U.S. twelfth graders in TIMSS on the general knowledge assessments?

Why do U.S. students perform more poorly relative to the international average at the end of secondary schooling than in eighth grade?

The Context of Learning for Advanced Mathematics and Science Students in the Final Year of Secondary School

How do U.S. physics and advanced mathematics students compare internationally on factors associated with their lives in school?

Are any of these instructional experiences of physics and advanced mathematics students associated with U.S. relative performance?

Discussion

CONCLUSIONS

WORKS CITED

APPENDIX 1: Summary Of International Study Guidelines And Definition Of Eligible Students

A1.1: Nations' Definitions Of Eligible Students And Whether Met Sampling Standards: Mathematics And Science General Knowledge Assessments

A1.2: Nations' Definitions Of Eligible Students And Whether Met Sampling Standards: Advanced Mathematics Assessment

A1.3: Nations' Definitions Of Eligible Students And Whether Met Sampling Standards: Physics Assessment

APPENDIX 2: National Average Scores, Percentiles Of Achievement, And Standard Errors

A2.1: National Average Scores And Standard Errors: Mathematics And Science General Knowledge

A2.2: National Average Scores And Standard Errors: Physics And Advanced Mathematics

A2.3: Percentiles Of Achievement In Mathematics General Knowledge: Final Year Of Secondary School

A2.4: Percentiles Of Achievement In Science General Knowledge: Final Year Of Secondary School

A2.5: Percentiles Of Achievement In Advanced Mathematics: Final Year Of Secondary School

A2.6: Percentiles Of Achievement In Physics: Final Year Of Secondary School

APPENDIX 3: Performance on Assessment Item Examples By Country

A3.1: Performance On Assessment Items Examples By Country: Mathematics And Science General Knowledge

A3.2: Performance On Assessment Items Examples By Country: Physics And Advanced Mathematics

APPENDIX 4: Scores and Standard Errors for U.S. AP and Non-AP Physics and Calculus Students

A4.1: U.S. AP and Non-AP Calculus Students' Scores By Content Area

A4.2: U.S. AP and Non-AP Physics Students' Scores By Content Area

APPENDIX 5: Additional Supporting Materials

A5.1: Mathematics Performance At Eighth Grade And Final Year Of Secondary School For The 20 Countries That Participated In TIMSS At Both Grade Levels

A5.2: Mathematics Performance At Fourth Grade And Final Year Of Secondary School For The 12 Countries That Participated In TIMSS At Both Grade Levels

A5.3: Achievement In Mathematics General Knowledge By Gender For Students In Their Final Year Of Secondary School

A5.4: Science Performance At Eighth Grade And Final Year Of Secondary School For The 20 Countries That Participated In TIMSS At Both Grade Levels

A5.5: Science Performance At Fourth Grade And Final Year Of Secondary School For The 12 Countries That Participated In TIMSS At Both Grade Levels

A5.6: Achievement In Science General Knowledge By Gender For Students In Their Final Year Of Secondary School

A5.7: Advanced Mathematics And Advanced Science Students As A Proportion Of Age Cohort And Performance On Advanced Mathematics And On Physics Assessments Relative To The United States

A5.8: Gender Differences In Advanced Mathematics Achievement For Students In Their Final Year Of Secondary School Having Taken Advanced Mathematics

A5.9: Achievement In Advanced Mathematics Content Areas By Gender For Students Having Taken Advanced Mathematics

A5.10: Gender Differences In Physics Achievement For Students In Their Final Year Of Secondary School Having Taken Advanced Science

A5.11: Achievement In Physics Content Areas By Gender For Advanced Science Students

A5.12: Extent Of Differentiation In Secondary Education And Performance On TIMSS General Knowledge Assessments Relative To The United States

A5.13: Average Age Of Students Assessed And Grades Included In General Knowledge Assessments Compared To Performance On Mathematics General Knowledge Assessment Relative The United States

A5.14: Secondary Enrollment And Completion Compared To The United States

A5.15: Centralization Of Decision-Making About Curriculum Syllabi And Performance On Mathematics And Science General Knowledge Assessments Relative To The United States

A5.16: Gross National Product Per Capita And Public Expenditure On Elementary And Secondary Education Of TIMSS Nations Compared To Performance On The Mathematics General Knowledge Assessment Relative To The United States

A5.17: Average Age Of Participants In TIMSS Eighth-Grade Mathematics Assessment And Final Year Of Secondary School Mathematics General Knowledge Assessment And Nations' Relative Standing In Achievement In The Two Assessments

A5.18: Mathematics And Science Coursetaking And Change In Standing Relative To The International Average Between Eighth Grade And Final Year Of Secondary School

A5.19: Average Age Of Participants In TIMSS Eighth-Grade Science Assessment And Final Year Of Secondary School Science General Knowledge Assessment And Change In Nations' Standing Relative To The International Average From Eighth Grade To Final Year Of Secondary School

A5.20: Responses To Selected Student Questionnaire Items: Responses Of Students Participating In Mathematics And Science General Knowledge Assessments

A5.21: Responses To Selected Student Questionnaire Items: Responses of Students Participating In Advanced Mathematics Assessment

A5.22: Responses To Selected Student Questionnaire Items: Responses Of Students Participating In Physics Assessment

APPENDIX 6: Advisors To The U.S. TIMSS Study

APPENDIX 7: Additional TIMSS Reports

FIGURE 1: Mathematics General Knowledge Achievement.

FIGURE 2: Example 1: Mathematics General Knowledge Item

FIGURE 3: Example 2: Mathematics General Knowledge Item

FIGURE 4: Example 3: Mathematics General Knowledge Item

FIGURE 5: Science General Knowledge Achievement

FIGURE 6: Example 4: Science General Knowledge Item

FIGURE 7: Example 5: Science General Knowledge Item

FIGURE 8: Example 6: Science General Knowledge Item

FIGURE 9: Average Advanced Mathematics Performance Of Advanced Mathematics Students In All Countries

FIGURE 10: Average Advanced Mathematics Performance Of Advanced Mathematics Students In Other Countries Compared With U.S. Calculus And AP Calculus Students

FIGURE 11: Average Advanced Mathematics Performance Of Advanced Mathematics Students In Other Countries Compared With U.S. AP Calculus Students

FIGURE 12: Achievement In Advanced Mathematics Content Areas

FIGURE 13: Example 7: Geometry Item

FIGURE 14: Example 8: Probability And Statistics Item

FIGURE 15: Example 9: Calculus Item

FIGURE 16: Average Physics Performance Of Advanced Science Students In All Countries

FIGURE 17: Average Physics Performance Of Advanced Science Students In Other Countries Compared with U.S. AP Physics Students

FIGURE 18: Achievement In Physics Content Areas

FIGURE 19: Example 10: Mechanics Item

FIGURE 20: Example 11: Heat Item

FIGURE 21: Example 12: Wave Phenomena Item

FIGURE 22: Age Beginning Grade 1 And Grade(s) Marking End Of Secondary School in TIMSS Nations

FIGURE 23: U.S. Twelfth-Grade Students' Reports on Personal Safety at School In Comparison With The International Average

FIGURE 24: U.S. Twelfth-Grade Students' Reports On Hours On A Normal School Day Spent Working At A Paid Job In Comparison With The International Average

FIGURE 25: Relationship Between U.S. Relative Performance And Schooling And Student Factors: Mathematics General Knowledge

FIGURE 26: Relationship Between U.S. Relative Performance And Schooling And Student Factors: Science Knowledge Assessments

FIGURE 27: Relationship Between U.S. Relative Performance And Education System Factors: Grade Eight And End Of Secondary School

FIGURE 28: Advanced Mathematics Students' Reports On Connecting Mathematics To Everyday Problems

FIGURE 29: Relationship Between U.S. Relative Performance And Instructional Factors: Physics And Advanced Mathematics Students

The (NCES) is the primary federal entity for collecting, analyzing, and reporting data related to education in the United States and other nations. It fulfills a congressional mandate to collect, collate, analyze, and report full and complete statistics on the condition of education in the United States; conduct and publish reports and specialized analyses of the meaning and significance of such statistics; assist state and local education agencies in improving their statistical systems; and review and report on education activities in foreign countries.

NCES activities are designed to address high priority education data needs; provide consistent, reliable, complete, and accurate indicators of education status and trends; and report timely, useful, and high-quality data to the U.S. Department of Education, the Congress, the states, other education policy makers, practitioners, data users, and the general public.

We strive to make our products available in a variety of formats and in language that is appropriate to a variety of audiences. You, as our customer, are the best judge of our success in communicating information effectively. If you have any comments or suggestions about this or any other NCES product or report, we would like to hear from you. Please direct your comments to:

The authors wish to thank all those who contributed to the production of this report through their insightful suggestions. The invited reviewers who gave of their time and expertise included: Susan Fuhrman of the University of Pennsylvania; Henry Heikkinen of the University of Northern Colorado; Mary Lindquist of Columbus State University; Laura Lippman of NCES; and Robert Burton of NCES. We would also like to thank the many other individuals both within and outside the Department of Education who provided helpful comments during the development of this report.

The Third International Mathematics and Science Study (TIMSS) is the largest, most comprehensive, and most rigorous international study of schools and student achievement ever conducted. This report, Pursuing Excellence: A Study of U.S. Twelfth-Grade Mathematics and Science Achievement in International Context, compares the general mathematics and science knowledge of our students in their last year of secondary school with those of 20 other countries, as well as the achievement of our students taking physics and advanced mathematics courses with those in 15 other countries. It is the last of three major TIMSS reports by the (NCES) in its Pursuing Excellence series. The first report, outlining U.S. comparative eighth-grade results, was released in November 1996, and the second report, detailing fourth-grade results, was released in June 1997. Together, these three studies paint the most complete picture ever of how achievement in mathematics and science by U.S. students compares with that of other nations. The information is intended to help U.S. educators, parents, policymakers, and others evaluate the strengths and weaknesses of our schools from an international perspective. This comparative portrait can be used to examine our education system, scrutinize improvement plans, and evaluate proposed standards and curricula.

The scope of TIMSS is unprecedented in the annals of education research. The international project involved the testing of more than one-half million students in mathematics and science at three grade levels in 41 countries. In contrast to previous international comparative studies, TIMSS also goes beyond the traditional "horserace" data on student performance to explore possible causes for differences in achievement including questions on students' lives inside and outside of the classroom.

This wealth of data is being analyzed and published by NCES and others around the world. TIMSS has become the most accessible international education study ever by releasing information in a variety of new forms, including CD-ROM, videotape, and the World Wide Web (//timss). We invite everyone who is dedicated to enhancing the quality of our nation's mathematics and science education to make the fullest possible use of this rich resource.

Together, the various TIMSS reports constitute important tools that can improve the quality of primary and secondary education for all students. That is why the Center has worked cooperatively with other parts of the U.S. Department of Education to produce a multi-media resource kit designed for educators and those interested in using TIMSS data to improve teaching, curricula, and student achievement in states and local communities. We also will be conducting a follow-up study in 1999, when the students who took TIMSS in the fourth grade have reached the eighth grade, both to compare their performance with the 1995 eighth-grade results, and to assess the level of progress made by this group of students over the intervening four years.

The TIMSS data provide a reference point from which we can begin to clarify what we mean by "world-class" education. They give us tools by which we can benchmark not only the performance of our students but also the way in which we deliver instruction. Most importantly, they allow the U.S. to learn unique lessons from other members of the world community so that we may better pursue the goal of an excellent education for all students.

Pascal D. Forgione, Jr.
Commissioner of Education Statistics
February 1998

The Third International Mathematics and Science Study (TIMSS) was designed explicitly to enable educators and policy makers to compare achievement in science and mathematics of students in the United States with those in other countries at three levels of education, grades 4, 8, and the final year of secondary school (grade 12 in the U.S.). With this publication of the results of the 1995 assessment of the final year of secondary school, TIMSS has been successful. In addition, differences in student learning and characteristics of schooling, as measured by the TIMSS assessment instruments and questionnaires, enhance our understanding of the possible influences of such factors as school organization, teaching practices, student study habits, and family background. But the secrets of raising the level of student achievement beyond their current levels are not readily uncovered, and this study provides no easy answers or quick fixes.

The results of students in the final year of secondary school in the TIMSS science and mathematics general knowledge assessments found that our students performed less well than they did at grade 8, significantly below the international mean. In addition, U.S. most advanced students (those taking pre-calculus or calculus and those taking physics) performed at low levels in advanced mathematics and at especially low levels in physics when compared with similar students in other countries.

Once the results for all grades are considered, we see that U.S. students in the early school years have reasonable levels of achievement when compared with other countries--in science they are actually rated near the top--but performance lags by grade 8 and becomes even poorer at grade 12. The report's new information about advanced students should be reviewed carefully by college and university policy makers as well as those who influence coursetaking and career decisions made during the high school years.

Results of the advanced mathematics test reveal some unexpected weaknesses. Despite the fact that about one-quarter of the test related to calculus and that one-half of the U.S. advanced mathematics students were actually studying calculus, it was in geometry, not calculus, where U.S. students performed worst. This is consistent with performance in grades 4 and 8, but unexpected because these advanced students have all had formal geometry coursework. The results show that both geometry and algebra need to be key subjects of study throughout the curriculum.

For me, as a physicist with a keen interest in education, the science results are even more troubling. Students performed poorly in most sub-areas of physics, with the poorest performance coming on items on mechanics and electricity/magnetism (areas that account for about 75 percent of American physics textbooks). Even students who took an Advanced Placement physics course scored below the international norm.

These studies suggest that students appear to disengage from learning critical mathematics and science content as they progress through the school system. The sources of disengagement may include the classroom environment, the quality of instruction, and parental and community support for the value of science and mathematics to our children's future.

Improving achievement in mathematics and science subjects, whether in basic skills or advanced critical thinking, will require that students have, in combination, access to good teachers, good teaching materials, and agreement within the school on the goals of learning for all students. There are many efforts underway in states and localities throughout the United States to reform the process of teaching and learning mathematics and science. They are beginning to reveal mechanisms for obtaining gains in achievement. TIMSS also provides us with examples of nations with high performance at all grade levels, most notably Canada, the Netherlands, and Switzerland. American educators need to examine these successful efforts, learn from them, and effectively use all available resources to improve teaching and learning in mathematics and science at all grade levels.

Neal Lane, Director
National Science Foundation
February 1998

INTRODUCTION

• The Third International Mathematics and Science Study (TIMSS) is the largest, most comprehensive, and most rigorous international comparison of education ever undertaken. During 1995, the study assessed the mathematics and science knowledge of a half-million students from 41 nations at three levels of schooling.
• The information in this report is about students who were assessed at the end of twelfth grade in the United States and at the end of secondary education in other countries. It includes four areas of performance: mathematics general knowledge, science general knowledge, physics, and advanced mathematics.
• This report on students in the final year of secondary school is the last in a series of three public-audience reports titled Pursuing Excellence. The first report presented findings on student achievement at eighth grade. The second report presented findings from the fourth grade.
• TIMSS is a fair and accurate comparison of mathematics and science achievement in the participating nations. The students who participated in TIMSS were scientifically selected to accurately represent students in their respective nations. The entire assessment process was scrutinized by international technical review committees to ensure its adherence to established standards. Those nations in which irregularities arose, including the United States, are clearly noted in this and other TIMSS reports.
• Criticisms of previous international studies comparing students near the end of secondary school are not valid for TIMSS. Because the high enrollment rates for secondary education in the United States are typical of other TIMSS countries, our general population is not being compared to more select groups in other countries. Further, the strict quality controls ensured that the sample of students taking the general knowledge assessments was representative of all students at the end of secondary school, not just those in academically-oriented programs.
• This report consists of three parts: initial findings from the assessments of mathematics and of science general knowledge; initial findings from assessments of physics and of advanced mathematics; and initial findings about school systems and students' lives; and how those are associated with the relative performance of U.S. students compared to those in other cultures.

ACHIEVEMENT OF ALL STUDENTS

• A sample of all students at the end of secondary school (twelfth grade in the United States) was assessed in mathematics and science general knowledge. Mathematics general knowl-edge and science general knowledge are defined as the knowledge of mathematics and of science needed to function effectively in society as adults.
• U.S. twelfth graders performed below the international average and among the lowest of the 21 TIMSS countries on the assessment of mathematics general knowledge. U.S. students were outperformed by those in 14 countries, and outperformed those in 2 countries. Among the 21 TIMSS nations, our students' scores were not significantly different from those in 4 countries.
• U.S. twelfth graders also performed below the international average and among the lowest scoring of the 21 TIMSS countries on the assessment of science general knowledge. U.S. students were outperformed by students in 11 countries. U.S. students outperformed students in 2 countries. Our students' scores were not significantly different from those of 7 countries, including France, Germany, Italy, and the Russian Federation.
• The international standing of U.S. students was stronger at the eighth grade than at the twelfth grade in both mathematics and science among the countries that participated in the assessments at both grade levels.
• The U.S. international standing on the general knowledge component of TIMSS was higher in science than in mathematics. This pattern is similar to the findings at fourth and eighth grades in TIMSS.
• The U.S. was one of three countries that did not have a significant gender gap in mathematics general knowledge among students at the end of secondary schooling. While there was a gender gap in science general knowledge in the United States, as in every other TIMSS nation except one, the U.S. gender gap was one of the smallest.

ACHIEVEMENT OF ADVANCED STUDENTS

• The advanced mathematics assessment was administered to students who had taken or were taking pre-calculus, calculus, or AP calculus in the United States and to advanced mathematics students in other countries. The physics assessment was administered to students in the United States who had taken or were taking physics or AP physics and to advanced science students in other countries.
• Performance of U.S. physics and advanced mathematics students was among the lowest of the 16 countries which administered the physics and advanced mathematics assessments. In physics, 14 countries outperformed the United States; no countries performed more poorly. In advanced mathematics, 11 countries outperformed the United States and no countries performed more poorly.
• In all five content areas of physics and in all three content areas of advanced mathematics, U.S. physics and advanced mathematics students' performance was among the lowest of the TIMSS nations.
• In both physics and advanced mathematics, males outperformed females in the United States and most of the other TIMSS countries.
• More countries outperformed the United States in physics than in advanced mathematics. This differs from the results for mathematics and science general knowledge, as well as the results at grades 4 and 8, where more countries outperformed the United States in mathematics than in science.

CONTEXTS OF LEARNING

• It is too early in the process of data analysis to provide strong evidence to suggest factors that may be related to the patterns of performance at the end of secondary schooling described here.
• Although secondary education in the United States differs structurally in important dimensions from that in many of the other countries, in this first analysis, few of those structural differences are clearly related to the relatively poor performance of our twelfth graders on the TIMSS assessments.
• Although the lives of U.S. graduating students differ from those of their peers in other countries on several of the factors examined, few appear to be systematically related to our performance in twelfth grade compared to the other countries participating in TIMSS.
• Further analyses are needed to provide more definitive insights on these subjects.

CONCLUSIONS

• U.S. students' performance was among the lowest of the participating countries in mathematics and science general knowledge, physics, and advanced mathematics.
• TIMSS does not suggest any single factor or combination of factors that can explain why our performance at twelfth grade is low relative to other countries at the end of secondary education.
• From our initial analyses, it also appears that some factors commonly thought to be related to individual student performance are not strongly related to national averages of student performance at the end of secondary school in TIMSS.
• TIMSS provides a rich source of information about student performance in mathematics and science, and about education in other countries. These initial findings suggest that to use the study most effectively, we need to pursue the data beyond this initial report, taking the opportunity and time to look at interrelationships among factors in greater depth.