N ATIONAL C ENTER FOR E DUCATION S TATISTICS

INITIAL FINDINGS FROM THE

THIRD INTERNATIONAL MATHEMATICS AND SCIENCE STUDY

OFFICE OF EDUCATIONAL RESEARCH AND IMPROVEMENT

U.S. DEPARTMENT OF EDUCATION

NCES 98-049

PURSUING EXCELLENCE

A STUDY OF U.S. TWELFTH-GRADE

MATHEMATICS AND SCIENCE ACHIEVEMENT

IN INTERNATIONAL CONTEXT
Sayuri Takahira

Patrick Gonzales

Mary Frase

Laura Hersh Salganik

United States National Coordinating Committee:

Eugene Owen William Schmidt

Lois Peak Larry Suter

Contributors:

Nancy Caldwell Molly Soule 

Leland Cogan Brian Thompson

Margaret Cozzens Gilbert Valverde

Leslie Jocelyn Pamela Warner

David Kastberg Christine Welch

John Konstant Trevor Williams

David Nohara

PURSUING EXCELLENCE

A STUDY OF U.S. TWELFTH-GRADE

MATHEMATICS AND SCIENCE ACHIEVEMENT

IN INTERNATIONAL CONTEXT

INITIAL FINDINGS FROM THE

THIRD INTERNATIONAL MATHEMATICS AND SCIENCE STUDY
2

National Center for Education Statistics

The National Center for Education Statistics (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:

National Center for Education Statistics

Office of Educational Research and Improvement

U.S. Department of Education

555 New Jersey Avenue NW

Washington, DC 20208-5574

Phone: (202) 219-1333

e-mail: timss@ed.gov

Suggested Citation:

U.S. Department of Education. National Center for Education Statistics,

Pursuing Excellence: A Study of U.S. Twelfth-Grade 

Mathematics and Science Achievement in International Context, 

NCES 98-049. Washington, DC: U.S. Government Printing Office, 1998.

February 1998

REVISED August 1998

Available for downloading at http://nces.ed.gov/timss

U.S. Department of Education

Richard W. Riley

Secretary

Office of Educational Research and

Improvement

C. Kent McGuire

Assistant Secretary

National Center for 

Education Statistics

Pascal D. Forgione, Jr.

Commissioner 

Data Development and Longitudinal

Studies Group

Martin E. Orland

Associate Commissioner

International Activities Program

Eugene Owen

Director
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.

A CKNO WLEDGMENTS 

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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. TwelfthGrade 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 National Center for Education

Statistics (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 (http://nces.ed.gov/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. 

COMMISSIONER’S

S T A TEMENT
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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
7

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 onehalf 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

NSF DIRECT OR'S 

S T A TEMENT
8

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
9

ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

COMMISSIONER’S STATEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

NSF DIRECTOR’S STATEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

EXECUTIVE SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

CHAPTER I: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

WHAT IS TIMSS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

COMPARING THE UNITED STATES TO OTHER COUNTRIES. . . . . . . . . . . . . . . . . . . . . . . . 24

THE TIMSS RESEARCH TEAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

WHAT QUESTIONS DOES THIS REPORT ANSWER? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

CHAPTER 2: ACHIEVEMENT OF ALL STUDENTS. . . . . . . . . . . . . . . . . . . . . . 28

KEY POINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

MATHEMATICS GENERAL KNOWLEDGE ASSESSMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

How well do U.S. twelfth graders do on the mathematics 

general knowledge assessment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

What were students asked to do on the mathematics 

general knowledge assessment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

How does U.S. twelfth-grade students’ relative performance 

in mathematics compare to that of U.S. eighth-grade students?. . . . . . . . . . . 33

Is there a gender gap in mathematics general knowledge at the 

twelfth grade?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Has the relative international standing of the United States in 

mathematics at the end of secondary school changed over time? . . . . . . . . . 34

SCIENCE GENERAL KNOWLEDGE ASSESSMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

How well do U.S. twelfth graders do on the science 

general knowledge assessment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

What were students asked to do on the science 

general knowledge assessment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

How does U.S. twelfth-grade students’ relative performance in science 

compare to that of U.S. eighth-grade students? . . . . . . . . . . . . . . . . . . . . . . . 37

Is there a gender gap in science general knowledge at the twelfth grade? . . . . 38

Has the relative international standing of the United States in science 

at the end of secondary school changed over time? . . . . . . . . . . . . . . . . . . . . 39

How does the performance of U.S. twelfth graders in science 

compare to their performance in mathematics? . . . . . . . . . . . . . . . . . . . . . . . 39

CHAPTER 3: ACHIEVEMENT OF ADVANCED STUDENTS . . . . . . . . . . . . . . 40

KEY POINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

ADVANCED MATHEMATICS ASSESSMENT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

How do U.S. twelfth graders with advanced mathematics instruction 

compare to advanced mathematics students in other countries? . . . . . . . . . . 42

T ABLE OF CONTENTS
10

How do U.S. twelfth graders with calculus or Advanced 

Placement calculus compare to all advanced mathematics 

students in other countries?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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

advanced mathematics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

What were students asked to do on the advanced mathematics assessment? . . 47

Is there a gender gap in advanced mathematics at the twelfth grade? . . . . . . . 50

PHYSICS ASSESSMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

How do U.S. twelfth graders with physics instruction compare 

to advanced science students in other countries? . . . . . . . . . . . . . . . . . . . . . . 50

How do U.S. twelfth graders with Advanced Placement physics 

instruction compare to advanced science students in other countries? . . . . . 52

How do U.S. students score in the different content areas of physics? . . . . . . . 53

What were advanced science students asked to do on the 

physics assessment? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Is there a gender gap in physics at the twelfth grade? . . . . . . . . . . . . . . . . . . . . 57

How does U.S. student performance in physics compare 

to that in advanced mathematics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

CHAPTER 4: THE CONTEXT OF LEARNING . . . . . . . . . . . . . . . . . . . . . . . . . . 58

KEY POINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

THE CONTEXT OF LEARNING FOR STUDENTS PARTICIPATING IN THE

GENERAL KNOWLEDGE ASSESSMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

How does secondary schooling in the other TIMSS countries 

resemble and differ from that in the United States? . . . . . . . . . . . . . . . . . . . . 60

How do U.S. twelfth-grade students compare internationally 

on factors associated with their lives inside and outside of school? . . . . . . . . 64

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? . . . . . . . . . . . . . . . 67

Why do U.S. students perform more poorly relative to 

the international average at the end of secondary schooling 

than in eighth grade?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

THE CONTEXT OF LEARNING FOR ADVANCED MATHEMATICS AND SCIENCE

STUDENTS IN THE FINAL YEAR OF SECONDARY SCHOOL . . . . . . . . . . . . . . . . . . . . . . . 73

How do U.S. physics and advanced mathematics students compare 

internationally on factors associated with their lives in school? . . . . . . . . . . . 74

Are any of these instructional experiences of physics and advanced

mathematics students associated with U.S. relative performance? . . . . . . . . . 76

DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

WORKS CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
11

APPENDIX 1: Summary Of International Study Guidelines And 

Definition Of Eligible Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A1.1: Nations’ Definitions Of Eligible Students And Whether Met 

Sampling Standards: Mathematics And Science General 

Knowledge Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

A1.2: Nations’ Definitions Of Eligible Students And Whether Met 

Sampling Standards: Advanced Mathematics Assessment . . . . . . . . . . . 90

A1.3: Nations’ Definitions Of Eligible Students And Whether Met 

Sampling Standards: Physics Assessment . . . . . . . . . . . . . . . . . . . . . . . . 93 

APPENDIX 2: National Average Scores, Percentiles Of Achievement,

And Standard Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

A2.1: National Average Scores And Standard Errors: Mathematics 

And Science General Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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

Advanced Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

A2.3: Percentiles Of Achievement In Mathematics General Knowledge: 

Final Year Of Secondary School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

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

Year Of Secondary School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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

Of Secondary School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

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

Of Secondary School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

APPENDIX 3: Performance on Assessment Item Examples By Country. . . . . . . . . . . 105

A3.1: Performance On Assessment Items Examples By Country: 

Mathematics And Science General Knowledge . . . . . . . . . . . . . . . . . . 106

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

And Advanced Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

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

Calculus Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A4.1: U.S. AP and Non-AP Calculus Students’ Scores By Content Area . . . . 110

A4.2: U.S. AP and Non-AP Physics Students’ Scores By Content Area . . . . . 110

APPENDIX 5: Additional Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

A5.3: Achievement In Mathematics General Knowledge By Gender 

For Students In Their Final Year Of Secondary School . . . . . . . . . . . . 114
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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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

A5.6: Achievement In Science General Knowledge By Gender For 

Students In Their Final Year Of Secondary School . . . . . . . . . . . . . . . 117

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. . . . . . . . . . . . . . . . . 118

A5.8 Gender Differences In Advanced Mathematics Achievement For 

Students In Their Final Year Of Secondary School Having Taken

Advanced Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

A5.9: Achievement In Advanced Mathematics Content Areas By Gender 

For Students Having Taken Advanced Mathematics . . . . . . . . . . . . . . 120

A5.10: Gender Differences In Physics Achievement For Students In Their 

Final Year Of Secondary School Having Taken Advanced Science . . . 121

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

Science Students. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

A5.12: Extent Of Differentiation In Secondary Education And 

Performance On TIMSS General Knowledge Assessments Relative 

To The United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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 . . . . . . . . 125

A5.14: Secondary Enrollment And Completion Compared To The 

United States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

A5.15: Centralization Of Decision-Making About Curriculum Syllabi And

Performance On Mathematics And Science General Knowledge

Assessments Relative To The United States . . . . . . . . . . . . . . . . . . . . . 127

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. . . . . . . . . . . . . . . . . . . . . . 128

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. . . . . . . . . . . . . . . . . . . . . . . . . 129

A5.18: Mathematics And Science Coursetaking And Change In Standing 

Relative To The International Average Between Eighth Grade And 

Final Year Of Secondary School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A5.20: Responses To Selected Student Questionnaire Items: Responses Of

Students Participating In Mathematics And Science General 

Knowledge Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

A5.21: Responses To Selected Student Questionnaire Items: Responses 

of Students Participating In Advanced Mathematics Assessment. . . . . . 136

A5.22: Responses To Selected Student Questionnaire Items: Responses 

Of Students Participating In Physics Assessment . . . . . . . . . . . . . . . . . 138

APPENDIX 6: Advisors To The U.S. TIMSS Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

APPENDIX 7: Additional TIMSS Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

LIST OF FIGURES

FIGURE 1: Mathematics General Knowledge Achievement. . . . . . . . . . . . . . . . . . . 30

FIGURE 2: Example 1: Mathematics General Knowledge Item . . . . . . . . . . . . . . . . 32

FIGURE 3: Example 2: Mathematics General Knowledge Item . . . . . . . . . . . . . . . . 32

FIGURE 4: Example 3: Mathematics General Knowledge Item . . . . . . . . . . . . . . . . 33

FIGURE 5: Science General Knowledge Achievement . . . . . . . . . . . . . . . . . . . . . . . 36

FIGURE 6: Example 4: Science General Knowledge Item . . . . . . . . . . . . . . . . . . . . 36

FIGURE 7: Example 5: Science General Knowledge Item . . . . . . . . . . . . . . . . . . . . 37

FIGURE 8: Example 6: Science General Knowledge Item . . . . . . . . . . . . . . . . . . . . 38

FIGURE 9: Average Advanced Mathematics Performance

Of Advanced Mathematics Students In All Countries . . . . . . . . . . . . . . 43

FIGURE 10: Average Advanced Mathematics Performance

Of Advanced Mathematics Students In Other Countries

Compared With U.S. Calculus And AP Calculus Students. . . . . . . . . . . 44

FIGURE 11: Average Advanced Mathematics Performance

Of Advanced Mathematics Students In Other Countries

Compared With U.S. AP Calculus Students . . . . . . . . . . . . . . . . . . . . . . 45

FIGURE 12: Achievement In Advanced Mathematics Content Areas. . . . . . . . . . . . . 46

FIGURE 13: Example 7: Geometry Item. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

FIGURE 14: Example 8: Probability And Statistics Item. . . . . . . . . . . . . . . . . . . . . . . 48

13
FIGURE 15: Example 9: Calculus Item. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

FIGURE 16: Average Physics Performance Of 

Advanced Science Students In All Countries . . . . . . . . . . . . . . . . . . . . . 51

FIGURE 17: Average Physics Performance Of Advanced Science Students 

In Other Countries Compared with U.S. AP Physics Students. . . . . . . . 52

FIGURE 18: Achievement In Physics Content Areas . . . . . . . . . . . . . . . . . . . . . . . . . 54

FIGURE 19: Example 10: Mechanics Item . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

FIGURE 20: Example 11: Heat Item. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

FIGURE 21: Example 12: Wave Phenomena Item . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

FIGURE 22: Age Beginning Grade 1 And Grade(s) Marking

End Of Secondary School in TIMSS Nations. . . . . . . . . . . . . . . . . . . . . 62

FIGURE 23: U.S. Twelfth-Grade Students’ Reports on Personal Safety at 

School In Comparison With The International Average . . . . . . . . . . . . 67

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

FIGURE 25: Relationship Between U.S. Relative Performance And 

Schooling And Student Factors: Mathematics General Knowledge . . . . 69

FIGURE 26: Relationship Between U.S. Relative Performance And Schooling

And Student Factors: Science Knowledge Assessments . . . . . . . . . . . . . 70

FIGURE 27: Relationship Between U.S. Relative Performance And Education 

System Factors: Grade Eight And End Of Secondary School. . . . . . . . . 72

FIGURE 28: Advanced Mathematics Students’ Reports On Connecting 

Mathematics To Everyday Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

FIGURE 29: Relationship Between U.S. Relative Performance

And Instructional Factors: Physics And Advanced

Mathematics Students. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

14
15
16
17

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 knowledge 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 

EXECUTIVE

SUMMAR Y
18

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.
19

■ 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.
CHAPTER 1:

INTRODUCTION
The Third International Mathematics

and Science Study (TIMSS) is the largest

and most comprehensive comparative

international study of education that has

ever been undertaken. TIMSS in the

United States was coordinated by the

National Center for Education Statistics

(NCES) and the National Science Foundation (NSF). The study assessed a halfmillion students from 41 countries in 30

languages to compare their mathematics and science achievement. This report

focuses on the 23 countries that participated in the TIMSS study of students at

the end of secondary education.

TIMSS comes at a time when mathematics and science achievement has been

designated as an educational priority.

One of our eight current National Education Goals is that “by the year 2000,

the United States will be first in the

world in mathematics and science

achievement.” In addition, mathematics

and science experts have issued major

calls for reform in the teaching of their

subjects. The National Council of Teachers of Mathematics published Curriculum and Evaluation Standards for School

Mathematics1 in 1989, and Professional

Standards for Teaching Mathematics2 in

1991. In 1993, the American Association

for the Advancement of Science followed suit with Benchmarks for Science Literacy,

3 and in 1996, the National Academy of Sciences published National Science Education Standards.

4

This is the last of three reports in 

the Pursuing Excellence series. The first

report presented initial findings on the

eighth grade and was released in

November, 1996. The second report presented findings on the fourth grade and

was released in June, 1997. This report

presents initial findings about the international standing of the United States’

twelfth graders relative to students completing secondary school in other countries. It is based on the comparative data

published in the report, Mathematics and

Science Achievement in the Final Year of Secondary School: IEA’s Third International

Mathematics and Science Study.

5 The

TIMSS International Study Center at

Boston College will release complete

data files for the study later this year,

which will allow a more extensive examination of student performance in mathematics and science in the participating

countries. 

WHAT IS TIMSS?

TIMSS is the third comparison of

mathematics achievement and third

comparison of science achievement

carried out by the International

Association for the Evaluation of

Educational Achievement (IEA).

Previous IEA studies of mathematics and

science were conducted for each subject

separately at various times during the

1960s, 1970s, and 1980s. TIMSS is the

first IEA study that has assessed both

mathematics and science at the same

time. Comparative studies of other

subjects, including reading literacy

(1992)6 and computers in education

(1993),7 have also been published by the

IEA.

TIMSS was designed to focus on students

at three different stages of schooling:

midway through elementary school, midway through lower secondary school, and

at the end of upper secondary school. Initial findings for the 41 countries in the

lower secondary school component8 and

for the 26 countries that participated in

the elementary school component9 are

reported in earlier volumes of the

Pursuing Excellence series. This report presents initial findings for the 23 countries

21
22

A. The terms “mathematics general knowledge” and “science general knowledge” used throughout this

report are equivalent to the terms “mathematics literacy” and “science literacy” used in the international report on achievement in the final year of secondary school published by Boston College.

in the remaining component of TIMSS,

students at the end of secondary education. Findings are presented for four

broad areas of performance:

■ Mathematics general knowledgeA for

all students in the final year of secondary education, including those

who had taken advanced courses as

well as those who had not;

■ Science general knowledgeA for all

students in the final year of secondary education, including those

who had taken advanced science

courses as well as those who had not;

■ Advanced mathematics for students

in the final year of secondary education who had taken or were taking

advanced courses in mathematics;

and

■ Physics for students in the final year

of secondary education who had

taken or were taking physics.

For the assessments of mathematics

general knowledge and science general

knowledge, this report presents results

for 21 countries: Australia, Austria,

Canada, Cyprus, the Czech Republic,

Denmark, France, Germany, Hungary,

Iceland, Italy, Lithuania, the Netherlands, New Zealand, Norway, the

Russian Federation, Slovenia, South

Africa, Sweden, Switzerland, and the

United States.

For the assessment of advanced

mathematics, results are reported for 16

countries: Australia, Austria, Canada,

Cyprus, the Czech Republic, Denmark,

France, Germany, Greece, Italy, Lithuania, the Russian Federation, Slovenia,

Sweden, Switzerland, and the United

States.

For the physics assessment, results are

reported for 16 countries: Australia,

Austria, Canada, Cyprus, the Czech

Republic, Denmark, France, Germany,

Greece, Latvia, Norway, the 

Russian Federation, Slovenia, Sweden,

Switzerland, and the United States.

The elementary and middle school

components of TIMSS defined eligible

students primarily on the basis of age.

The elementary school group included

students enrolled in the pair of adjacent

grades that contained the most 9-yearolds, grades 3 and 4 in the United States

and most other countries. The middle

school students were in the pair of

grades that contained the most 13-yearolds, grades 7 and 8 in the United States

and most other countries.

A major goal of the end of secondary

school component of TIMSS was to

measure what students know by the time

they leave the secondary school system.

Because countries have different structures for secondary education, the final

grade of secondary education in the

countries participating in TIMSS may be

as low as 9 and as high as 14, depending

on the country and program in which

the student is enrolled. For the United

States, the final year of secondary education is grade 12, and twelfth-grade students were selected for the study. All

twelfth graders were eligible for the
23

mathematics and science general

knowledge portion of the study.

Advanced mathematics students in the

United States were defined as twelfth

graders who had taken or were taking a

full year of a high school course that

included the word “calculus” in the title,

including pre-calculus. Physics students

were twelfth graders who had taken or

were taking at least one full year of high

school physics. Appendix 1 provides

information about how other countries

identified students to participate in the

study.

Students in both public and private

schools were administered the

mathematics and science general

knowledge assessments, which together

were about 1.5 hours in length, and

included both multiple-choice and freeresponse items. In each country, the

items were translated into the primary

languages of instruction. In the United

States, all assessments were administered in English. Testing occurred 2 to 3

months before the end of the 1994-95

school year. Students with special needs

and disabilities that would make it difficult for them to take the assessments

were excused. Students were allowed to

use calculators for all assessments.

Like the other components of TIMSS,

participating countries collected data

beyond the student assessments.

Students completed questionnaires

about their experiences in and out of

school. School administrators completed questionnaires about school policies

and practices. An exploratory curriculum analysis compared mathematics and

science curriculum guides and textbooks. It studied subject-matter content,

sequencing of topics, and expectations

for student performance. Teacher questionnaires were not administered, as

some of the graduating students who

participated in the study were no longer

enrolled in mathematics and science. 

TIMSS is the most fair and accurate

international comparison of students

that has ever been undertaken. In each

nation, the students who participated in

TIMSS were to be randomly selected to

represent all students meeting the grade

level or age criteria for each of the three

populations. An international curriculum analysis was carried out prior to the

development of the assessments to

ensure that the items would reflect the

mathematics and science curricula in

the TIMSS countries. To further ensure

that the assessments measured knowledge that the world community considers important for students to know, the

items were developed by international

committees. International monitors

carefully checked the translations and

visited many classrooms while the assessments were being administered in each

of the participating countries to make

sure that the instructions were properly

followed. 

The quality standards for the sampling

process in TIMSS were higher than in

any previous international comparison

of education systems. Maintaining these

high standards provided challenges for

most of the countries that participated

in this portion of TIMSS. Most of the 

23 countries—including the United

States—experienced difficulties of various types. This is consistent with experience in the United States in conducting

assessments at the end of high school.

Areas of difficulty included minimizing

the extent to which students were

excluded from the population eligible

for the sample and gaining participation

of schools and students after they were

selected for the sample. 
24

While most countries had difficulties

meeting the sampling standards in this

portion of TIMSS, the nature of these

difficulties, and the students and schools

excluded, are generally well understood. Appendix 1 contains a summary

of the TIMSS study guidelines and provides information about sampling and

adherence to sampling and other standards in all the countries. All countries

in which difficulties arose are shown in

parentheses in the figures and tables in

this report. The United States is in

parentheses because its combined

school and student participation rate

was 64 percent, below the standard of 75

percent. It is most likely that as a group,

schools and students who were selected

for TIMSS but did not participate in the

assessments in the United States would

have had below average scores, thus lowering the U.S. average. This was probably the case as well in other countries

having similar difficulties. 

Full documentation of the data collection methodologies and statistical analyses used in all the participating countries is available in technical and quality

control reports published by the TIMSS

International Study Center at Boston

College.10 A list of additional TIMSS

reports published to date is contained in

Appendix 7.

COMPARING THE UNITED STATES

TO OTHER COUNTRIES

Some have argued that comparisons of

the performance of U.S. students with

students in other countries are inappropriate. One argument is that, in the

United States, larger portions of a given

age cohort are enrolled in the education

system—particularly at the secondary

level—than in other countries, resulting

in a comparison between our general

population and more select groups in

other countries. Another argument is

that in international comparisons, while

the United States tests a sample representative of our general student population, some countries test only those students in elite, college preparatory

schools or courses of study. Although

these arguments may have been valid in

previous studies, neither holds true in

TIMSS. 

As is discussed in more detail in Chapter

4, the most recent data indicate that in

most countries participating in TIMSS,

secondary school enrollment rates are

similar to that of the United States. Not

only do the TIMSS countries have most

of their secondary school-age population enrolled in school, the strict quality

controls discussed earlier ensured that

the sample of students taking the mathematics and science general knowledge

assessments were representative of the

entire population at the end of secondary school. Thus, for example, in

most countries with distinct education

“streams,” such as academic and vocational, students in all programs were

represented in the TIMSS sample. This

represents an improvement over previous studies of secondary school achievement, in which some countries only

assessed students in certain types of

schools or programs.

Of course, there are still many other differences between the secondary school

systems of the countries participating in

TIMSS. However, since a major goal of

this component of TIMSS was to assess

how well people entering adulthood

understand the mathematics and science needed to function effectively in

society, comparing students at the end

of secondary school is entirely appropriate. This is because the end of secondary
25

school represents the culmination of

each country’s attempts to prepare all

young people for living in society.

Rather than use differences between systems to argue against comparisons, or, at

the other extreme, ignore such differences, their relationship to mathematics

and science achievement should be

explored.

THE TIMSS RESEARCH TEAM

TIMSS was conducted by the IEA, which

is a Netherlands-based organization of

ministries of education and research

institutions from its member countries.

The IEA delegated responsibility for

overall coordination and management

of the TIMSS study to Albert Beaton at

the TIMSS International Study Center,

located at Boston College. Each of the

IEA member nations that made the decision to participate in TIMSS paid for

and carried out the data collection in its

own country according to the international guidelines. The cost of the international coordination was paid by the

National Center for Education Statistics

(NCES) of the U.S. Department of Education, the National Science Foundation

(NSF), and the Canadian Government.

The United States portion of TIMSS was

also funded by NCES and NSF. William

Schmidt of Michigan State University

was the U.S. National Research Coordinator. Policy decisions on the study were

made by the U.S. National Coordinating

Committee. NCES monitored the international and U.S. TIMSS projects. The

U.S. data collection was carried out by

Westat, a private survey research firm.

Trevor Williams and Nancy Caldwell

were Westat project co-directors. The

many advisors to the study are listed in

Appendix 6.

The U.S. TIMSS team also included the

approximately 10,000 twelfth-grade students who took the assessments, and

their principals in 210 schools nationwide. Their cooperation has made this

report possible.

WHAT QUESTIONS DOES THIS

REPORT ANSWER?

This report answers three basic questions:

■ How does the mathematics and science general knowledge of U.S.

twelfth graders compare to that of

students completing secondary

school in other nations?

■ How do U.S. high school seniors with

instruction in physics and advanced

mathematics perform in these subjects in comparison to advanced science and mathematics students in

other nations?

■ What factors might contribute to the

performance of the United States relative to other countries in mathematics and science at the end of secondary school?

Chapter 2 answers the first question.

This question is important because it

measures what our students know at the

end of secondary school compared to

similar students in other nations. The

findings in this chapter reveal how well

our students have been prepared by 12

years of formal schooling for their

future as adults in a world that increasingly relies on mathematics, science,

and technology.

Chapter 3 answers the second question.

Advanced students had taken or were

taking higher level mathematics and
26

science courses in secondary school,

such as calculus and physics. Many are

likely to become our nation’s next generation of professionals in fields related

to mathematics and science.

Chapter 4 answers the third question. It

examines a variety of factors related to

schooling and students’ lives to see if

any of them provide insight into why

U.S. students perform as they do relative

to students in other countries at the end

of secondary school.
27
CHAPTER 2:

ACHIEVEMENT OF

ALL STUDENTS

KEY POINTS:

U.S. twelfth graders scored below the

international average and among the lowest

of the 21 TIMSS nations in both mathematics and science general knowledge in the

final year of secondary school.

U.S. students’ international standing was

stronger at the eighth grade than at the

twelfth grade in both mathematics and

science.

The United States was one of three

countries that did not have a significant

gender gap in mathematics general

knowledge at the end of secondary

schooling. While there was a gender gap 

in science general knowledge in the United

States, as in all the other TIMSS countries

except one, the U.S. gender gap was one 

of the smallest.

The U.S. international standing on the

general knowledge component of TIMSS

was stronger in science than in

mathematics.This pattern is similar to the

findings at fourth and eighth grades in

TIMSS.
29

MATHEMATICS AND SCIENCE

GENERAL KNOWLEDGE

How well do young people understand

the basic mathematics and science

needed to function effectively in society? To answer this question, TIMSS

developed assessments of mathematics

and science general knowledge. These

assessments were designed to determine

students’ general level of knowledge of

fundamental scientific and mathematical concepts at the time they complete

secondary education. These assessments

were given to a random sample of all

students at the grade set by their nation

or program of studies as the end of their

secondary schooling, regardless of

whether or not they were currently taking mathematics or science at the time

of the study.

Because the assessments were designed

to examine how well students had

acquired the mathematical and scientific skills and knowledge judged by an

international committee of experts to

be necessary for all citizens in their daily

life, the questions asked of the students

were not tied to school curriculum.

Instead, they covered the students’

knowledge of mathematical and scientific concepts, reasoning, and practical

or “real world” applications. The results

provide a glimpse of how well-prepared

to function in the adult world are the

graduates of the education system in the

various TIMSS nations.

This report examines the performance

of U.S. students relative to students in

other participating countries. Tempting

though it may be, reporting U.S. scores

by rank alone would be incorrect. This is

because the average scores reported for

each country were based on a sample of

students in each country, and are therefore estimates of the “true” scores that

would have been achieved had all the

eligible students participated in the

assessments.

While many steps were taken to ensure

that the samples were representative of

the total population, each estimated

score has a margin of error associated

with it. The margin of error is expressed

as a “plus or minus” interval around the

estimated score, creating a range of

scores within which the true score is

likely to fall. Thus, while one score may

be higher than another, if the difference between the two is small enough, it

may fall within the margin of error and

not be statistically significant. Because

precise scores cannot be determined

with perfect accuracy, to fairly compare

the United States to other countries,

nations have been grouped into

broad bands according to whether

their performance was significantly

higher than, not significantly different from, or significantly lower than

the United States.

In TIMSS, we can say with 95 percent

confidence that comparisons of other

countries’ scores on the general

knowledge assessments to those of

the United States are accurate plus or

minus about 12 to 36 points, depending on the size and design of the samples in other countries. Comparisons

of the United States to the international average are accurate plus or

minus about 7 points. (Table A2.1 in

Appendix 2 contains a list of national

averages and standard errors.)
30

MATHEMATICS GENERAL

KNOWLEDGE ASSESSMENT

The mathematics general knowledge

assessment consists of about 80 percent

multiple choice items and 20 percent

free-response items. Items were chosen

based on their likelihood of arising in

real-life situations and not on their

connection to a particular curriculum.

However, they can be described in

terms of common mathematics curriculum topics, such as number sense,

including fractions, percentages, and

proportionality; algebraic sense;

measurement and estimation; and data

representation. On average, for the

countries participating in the TIMSS

assessment of mathematics general

knowledge, these topics are typically

covered in about the seventh grade.

How Well Do U.S. Twelfth Graders

Do On The Mathematics General

Knowledge Assessment?

On the mathematics portion of the

general knowledge assessment, U.S.

students scored below the international

average, and among the lowest of the 21

countries. Figure 1 shows how U.S.

students performed on the mathematics general knowledge assessment.

NATIONS WITH AVERAGE SCORES NOT

SIGNIFICANTLY DIFFERENT FROM THE U.S.

NATION AVERAGE

(ITALY) 476

(RUSSIAN FEDERATION) 471

(LITHUANIA) 469

CZECH REPUBLIC 466

(UNITED STATES) 461

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY LOWER THAN THE U.S.

NATION AVERAGE

(CYPRUS) 446

(SOUTH AFRICA) 356

FIGURE 1: 

MATHEMATICS GENERAL KNOWLEDGE ACHIEVEMENT

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses. See Appendix 1 

for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 2.1. Chestnut Hill, MA: Boston College.

INTERNATIONAL AVERAGE = 500

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY HIGHER THAN THE U.S.

NATION AVERAGE

(NETHERLANDS) 560

SWEDEN 552

(DENMARK) 547

SWITZERLAND 540

(ICELAND) 534

(NORWAY) 528

(FRANCE) 523

NEW ZEALAND 522

(AUSTRALIA) 522

(CANADA) 519

(AUSTRIA) 518

(SLOVENIA) 512

(GERMANY) 495

HUNGARY 483
31

In mathematics general knowledge, 

students in the final year of secondary

school in 14 countries scored above 

our twelfth graders (the Netherlands,

Sweden, Denmark, Switzerland, Iceland,

Norway, France, New Zealand, Australia,

Canada, Austria, Slovenia, Germany,

and Hungary). Students in 4 countries

were not significantly different from

ours (Italy, the Russian Federation,

Lithuania, and the Czech Republic).

Students in two countries (Cyprus and

South Africa) performed significantly

below students in the United States. 

One explanation for our low performance that has been suggested in the

past is that, because of our diverse population, there is a greater range of

scores among U.S. students, and the

difference between our lowest-scoring

students and our typical student is

greater than in many other countries.

These low-scoring students, it has been

argued, “bring down” the U.S. average.

Available information suggests that this

is not the case in TIMSS.A

Looking at the distribution of scores can

also illustrate the relatively low position

of the United States in TIMSS. The

entire distribution of U.S. scores is shifted downward from that of many of the

high performing countries. For example, while a quarter of U.S. students

scored 521 or higher, in many high-performing countries half or more of the

students had scores that high. Furthermore, the scores of U.S. students at the

95th percentile were similar to those of

students at the 75th percentile in some

countries. (See Table A2.3 in Appendix

2 for percentiles for mathematics general knowledge; see Tables A2.4, A2.5, and

A2.6 for percentiles for the other

assessments.)

What Were Students Asked To Do

On The Mathematics General

Knowledge Assessment?

Mathematics general knowledge assessment items were designed to measure

general knowledge and skills judged by an

international committee of experts to be

necessary for citizens in their daily life.

Three examples of mathematics general

knowledge assessment items are shown.

Table A3.1 in Appendix 3 shows the percentage of students responding correctly

to each example item in every country. 

The item shown in Figure 2 requires students to use complex procedures to

solve a percentage problem. Fifty-seven

percent of U.S. twelfth graders responded correctly to this item. The international average was 64 percent correct.

Some students who responded incorrectly chose “C,” which is simply the difference of the two percentages, rather

than correctly taking the product of the

percentages. 

The item shown in Figure 3 requires students to provide their response in an

open-ended format. Eighty-five percent

of U.S. students responded correctly on

this item. The international average was

74 percent. Students needed to be able

to read the line graph and use the

labeled information on the vertical axis

to provide the correct answer of 60

km/h as the car’s maximum speed. 

A. Specifically, the difference between students with a median score (fiftieth percentile) and those at

the fifth percentile is 129 points in the United States; looking at all countries, the average 

difference between fifth and fiftieth percentiles is 137 points. In addition, the difference between

the scores of students at the fifth and ninety-fifth percentiles is similar in most countries. In the

United States, 296 points separate these two groups of students, and the average difference is 292

for all 21 countries.
Correct Answer: B U.S. Average: 57 percent International Average: 64 percent

32

FIGURE 3:

EXAMPLE 2: MATHEMATICS GENERAL KNOWLEDGE ITEM

Kelly went for a drive in her car. During the drive, a cat ran in front of the car.

Kelly slammed on the brakes and missed the cat.

Slightly shaken, Kelly decided to return home by a shorter route. The graph

below is a record of the car’s speed during the drive.

What was the maximum speed, in kilometers per hour, of the car during the drive?

Correct Answer: 60 km/h U.S. Average: 85 percent International Average: 74 percent

72

60

48

36

24

12

0

Kelly's drive

Time

9:00 9:03 9:06 9:09 9:12

Speed

(km/h)

SOURCE: Third International Mathematics and Science Study, 1994-1995.

FIGURE 2: 

EXAMPLE 1: MATHEMATICS GENERAL KNOWLEDGE ITEM

Experts say that 25% of all serious bicycle accidents involve head injuries and that,

of all head injuries, 80% are fatal.

What percent of all serious bicycle accidents involve fatal head injuries?

A. 16%

B. 20%

C. 55%

D. 105%

SOURCE: Third International Mathematics and Science Study, 1994-1995.
33

How long a piece of ribbon does he need? 

A. 46 cm

B. 52 cm

C. 65 cm

D. 71 cm

E. 77 cm

Correct Answer: E U.S. Average: 32 percent International Average: 45 percent

FIGURE 4: 

EXAMPLE 3: MATHEMATICS GENERAL KNOWLEDGE ITEM

Stu wants to wrap some ribbon around a box as shown below and have 25

centimeters left to tie a bow.

SOURCE: Third International Mathematics and Science Study, 1994-1995.

The item in Figure 4 requires students

to use the dimensions of a figure to solve

a problem. Thirty-two percent of U.S.

twelfth graders answered this item

correctly. The international average was

45 percent. Some students who responded incorrectly forgot to take into

account in their calculations the sides of

the box that are not visible in the diagram or the 25 centimeters of 

ribbon needed to tie a bow.

How Does U.S. Twelfth-Grade 

Students’ Relative Performance In

Mathematics Compare To That Of

U.S. Eighth-Grade Students?

The group of countries participating in

each phase of TIMSS differed. However,

20 of the 21 countries participating in

the general knowledge assessments in

the final year of secondary schooling

also participated in the middle school

portion of TIMSS. We can calculate an

international average for mathematics

achievement of students in these 20

countries both for eighth grade and for
34

the final year of secondary schooling.

(This international average will differ

from that based on all countries participating in TIMSS at each grade level—41

in eighth grade and 21 for the final year

of secondary schooling. The average

U.S. eighth grade mathematics performance is below the international average when the international average is

based on all 41 countries participating

in TIMSS at eighth grade, but is similar

to the international average based on

those 20 countries that also participated

in the general knowledge assessments at

the end of secondary schooling.) Table

A5.1 in Appendix 5 shows the standing

of each country relative to the 

20-country international average for the

two grade levels and whether that relative standing was different at the two

grade levels. (See Table A5.2 in Appendix 5 for a similar comparison for the 12

countries that participated in TIMSS

both at fourth grade and in the general

mathematics knowledge assessment at

the end of secondary school.)

The relative standing of U.S. students in

mathematics was lower at twelfth grade

than at eighth grade. About half the

countries had a similar standing relative

to the international average at both

grade levels. The other half were about

equally divided between those with a

higher and a lower relative standing in

the final year of secondary schooling

than in eighth grade. The former group

was composed of Nordic countries plus

New Zealand, while the latter included

countries from the former Communist

Bloc and Australia, in addition to the

United States.

Is There A Gender Gap In

Mathematics General Knowledge 

At The Twelfth Grade?

In the United States and other countries, policy makers have made great

efforts to make mathematics and science

more accessible to females, and to

encourage gender equity in these subjects. Despite these efforts, students in

the final year of secondary school in

most TIMSS nations demonstrated a 

significant gender gap in the mathematics portion of the general knowledge

assessment, with males performing 

better than females. In the United States,

boys’ and girls’ scores in mathematics

general knowledge were not significantly

different. The United States was one of

three countries (in addition to South

Africa and Hungary) among the TIMSS

nations which did not have a significant

gender gap in mathematics performance

(see Table A5.3 in Appendix 5). 

Has The Relative International

Standing Of The United States In

Mathematics At The End Of

Secondary School Changed Over

Time?

International comparisons over time are

difficult. The first international studies

of mathematics and science achievement were conducted in the 1960s, and

there have been other assessments in

each subject since then. However, each

assessment has been done differently. A

different set of nations participated, different topics in mathematics and science were included in the assessments,

the age and type of students sampled in

each country changed slightly, and

indeed even the borders and names of

some of the nations have changed. Furthermore, the field of assessment has
35

matured greatly over the past 30 years,

having made many improvements upon

the methods of the then-revolutionary

early studies. These and other factors

complicate comparisons over time and

require that any conclusions be necessarily tentative. 

In TIMSS, we have seen that U.S. twelfth

graders scored below the international

average in mathematics general knowledge, and among the lowest of all

nations. This international standing was

similar to the one reported for U.S.

twelfth graders in the IEA First and Second International Mathematics Studies

conducted in the 1960s and 1980s.

Thus, relative to their international

counterparts completing secondary

school, it is unlikely that U.S. twelfth

graders’ standing has changed significantly in mathematics achievement over

the past 30 years.

SCIENCE GENERAL KNOWLEDGE

ASSESSMENT

The science portion of the general

knowledge assessment consisted of

about 60 percent multiple choice items

and 40 percent free-response items.

Items were chosen based on their

likelihood of arising in real-life situations and not on their connection to a

particular curriculum. Looked at in

terms of common science curriculum

topics, however, the items covered the

topics of earth science, life science, and

physical science. On average, for the

countries participating in the TIMSS

assessment of science general knowledge, these topics are typically covered

in about the ninth grade.

How Well Do U.S. Twelfth Graders

Do On The Science General

Knowledge Assessment?

On the science portion of the general

knowledge assessment, U.S. students

scored below the international average,

and among the lowest scoring of the 21

countries. Figure 5 shows how U.S. students performed on the science general

knowledge assessment.

On the assessment of science general

knowledge, students at the end of secondary school in 11 countries (Sweden,

the Netherlands, Iceland, Norway,

Canada, New Zealand, Australia,

Switzerland, Austria, Slovenia, and

Denmark) outperformed U.S. twelfth

graders. Students in 7 countries performed not significantly different from

those in the United States (Germany,

France, the Czech Republic, the Russian

Federation, Italy, Hungary, and

Lithuania). Students in Cyprus and

South Africa performed below students

in the United States.

What Were Students Asked To Do

On The Science General Knowledge

Assessment?

Three examples of TIMSS science general knowledge assessment items are

presented. Table A3.1 in Appendix 3

shows the percentage of students in

every participating country responding

correctly to each of these example

items.

The item shown in Figure 6 requires students to apply scientific principles to

develop explanations. Forty-two percent

of U.S. students responded correctly to

this item. The international average was

61 percent correct. Some students’
36

FIGURE 6:

EXAMPLE 4: SCIENCE GENERAL KNOWLEDGE ITEM

Some high-heeled shoes are claimed to damage floors. The base diameter of

these very high heels is about 0.5 cm and of ordinary heels about 3 cm. Briefly

explain why the very high heels may cause damage to floors. 

Correct Answer Examples:

• “The pressure from the heel is greater because the area is smaller.”

• “Because of the narrow diameter of very high heels, all the body weight is

spread over a smaller area. There is greater pressure exerted on the floor

with the higher heels because it is all placed on a small area. The pressure is

less on a wider heel because the weight is distributed over a greater area

causing less damage.”

U.S. Average: 42 percent International Average: 61 percent

SOURCE: Third International Mathematics and Science Study, 1994-1995.

NATIONS WITH AVERAGE SCORES NOT

SIGNIFICANTLY DIFFERENT FROM THE U.S.

NATION AVERAGE

(GERMANY) 497

(FRANCE) 487

CZECH REPUBLIC 487

(RUSSIAN FEDERATION) 481

(UNITED STATES) 480

(ITALY) 475

HUNGARY 471

(LITHUANIA) 461

FIGURE 5: 

SCIENCE GENERAL KNOWLEDGE ACHIEVEMENT

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses.

See Appendix 1 for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 2.2. Chestnut Hill, MA: Boston College.

INTERNATIONAL AVERAGE = 500

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY HIGHER THAN THE U.S.

NATION AVERAGE

SWEDEN 559

(NETHERLANDS) 558

(ICELAND) 549

(NORWAY) 544

(CANADA) 532

NEW ZEALAND 529

(AUSTRALIA) 527

SWITZERLAND 523

(AUSTRIA) 520

(SLOVENIA) 517

(DENMARK) 509 NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY LOWER THAN THE U.S.

NATION AVERAGE

(CYPRUS) 448

(SOUTH AFRICA) 349
37

incorrect responses, such as “because

they are sharper and poke into the

floor,” attributed the damage to sharpness rather than the effects of pressure

placed on a small surface area.

The item shown in Figure 7 requires an

understanding of causes of pollution.

Seventy-eight percent of U.S. twelfth

graders responded correctly on this

item. The international average was 77

percent.

The item shown in Figure 8 requires

knowledge of complex information

about the interdependence of life. The

U.S. average was 40 percent correct, and

the international average was 37

percent. Some students who responded

incorrectly to this item were not sufficiently explicit about how a species can

regulate the population of its prey. 

How Does U.S. Twelfth-Grade

Students’ Relative Performance In

Science Compare To That Of U.S.

Eighth-Grade Students?

As in mathematics, it is possible to compare the science performance of all U.S.

students at both eighth grade and in the

final year of secondary school to the

group of 20 countries that participated

in both of these portions of TIMSS.

Table A5.4 in Appendix 5 displays the

standing for each country relative to the

international average for science

achievement for the two grade levels

based on the 20 countries and whether

that relative standing was different at

the two grade levels. (See Table A5.5 in

Appendix 5 for a similar comparison for

the 12 countries that participated in

TIMSS both at fourth grade and in the

science general knowledge assessment

at the end of secondary school.)

FIGURE 7: 

EXAMPLE 5: SCIENCE GENERAL KNOWLEDGE ITEM

CFCs (chlorofluorocarbons) revolutionized personal and industrial life for 30 years.

They were the coolant in refrigerators and the propellants in aerosols, pressure

packs, and fire extinguishers. There are now very strong international moves to stop

the use of these substances because:

A they are chemically inert.

B. they contribute to the greenhouse effect.

C. they are poisonous to humans.

D. they destroy the ozone layer.

Correct Answer: D U.S. Average: 78 percent International Average: 77 percent

SOURCE: Third International Mathematics and Science Study, 1994-1995.
38

In science, the United States is one of 7

countries where the standing relative to

the international average was lower at

the end of secondary schooling than it

was at eighth grade. The others were former Communist Bloc countries plus

Australia and Germany. Eight countries

had a similar standing relative to the

international average at both grade levels and 5 had a higher relative standing

in the final year of secondary schooling

than in eighth grade. 

Is There A Gender Gap In Science

General Knowledge At The Twelfth

Grade?

In the United States, there was a gender

gap on the science portion of the

twelfth-grade general knowledge assessment. Excluding South Africa, in all

other TIMSS nations, including the

United States, males performed significantly better than females in science.

However, among those countries, the

U.S. gender gap in science was one of

the smallest (see Table A5.6 in

Appendix 5).

When an animal or plant species is introduced to an area where it has never

previously existed, it frequently creates a problem by multiplying out of control

and displacing established species. One way of fighting introduced species is

to poison them. This may be impractical, be very costly or carry heavy risks.

Another method, called biological control, involves the use of living organisms,

other than human beings, to control the pest species.

Give an actual example of a biological control.

Correct Answer Examples:

• “Have a house cat in your house to rid mice as a biological control.”

• “Ladybugs are introduced to eat aphids.”

U.S. Average: 40 percent International Average: 37 percent

SOURCE: Third International Mathematics and Science Study, 1994-1995.

FIGURE 8:

EXAMPLE 6: SCIENCE GENERAL KNOWLEDGE ITEM
39

Has The Relative International

Standing Of The United States In

Science At The End Of Secondary

School Changed Over Time? 

In TIMSS, we have seen that U.S. twelfth

graders scored below the international

average in science, and among the lowest of all nations. This is basically the

same relative international standing

reported for U.S. twelfth graders in the

IEA First and Second International Science Studies in the 1960s and 1980s.

Thus, relative to their international

counterparts in the final year of secondary school, it is unlikely that U.S.

twelfth graders’ standing has changed

significantly in science.

How Does The Performance Of 

U.S. Twelfth Graders In Science

Compare To Their Performance In

Mathematics?

Although U.S. students scored below

the international average and among

the lowest of TIMSS nations on both

portions of the general knowledge

assessments, the U.S. international

standing on the general knowledge

assessments was slightly higher in

science than it was in mathematics.

Fourteen countries were significantly

higher than the United States in the

mathematics general knowledge assessment, while 11 countries outperformed

the United States in science general

knowledge. This pattern is similar to the

fourth- and eighth-grade TIMSS results,

in which the U.S. relative international

standing was higher in science than it

was in mathematics.

Among the major trading partners of

the United States that participated in

TIMSS at the end of secondary school,

students in Canada outperformed the

U.S. in both mathematics and science

general knowledge. Students in France

and Germany outperformed U.S. students in mathematics general knowledge, and performed similar to U.S. students in science.

We have now examined what TIMSS

tells us about all students in their final

year of secondary school. Next, we turn

to an examination of how the advanced

students in the United States who were

taking or had taken advanced courses in

mathematics and science compared to

their counterparts in other TIMSS

nations.
CHAPTER 3:

ACHIEVEMENT OF

ADVANCED STUDENTS

KEY POINTS:

The performance of U.S. physics and

advanced mathematics students was among

the lowest of the 16 countries that

administered the physics and advanced

mathematics assessments.

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. This was true for 4 of the 5

content areas in physics and for all 3 of the

content areas in advanced mathematics.

More countries outperformed the United

States in physics than in advanced

mathematics.This differs from results for

mathematics and science general

knowledge, where more countries

outperformed the United States in

mathematics than in science.
Chapter 2 has shown us how U.S. twelfth

graders performed in mathematics and

science general knowledge in comparison to students at the close of their

secondary school studies in other countries. It shows us the level of general

mathematics and scientific knowledge

of the entire sampled student population. But because advances in science

and technology are playing a greater

role in shaping the future of our nation

and our world, it is useful to look

beyond the general levels of science and

mathematics general knowledge and

focus on the advanced levels of knowledge of those who are likely to become

our next generation of professionals in

fields related to mathematics and

science.

Therefore, in addition to the TIMSS

assessments of science and mathematics

general knowledge, other assessments

were created to compare the achievement of students taking advanced

science and mathematics courses.

Physics was selected by the participating

countries for the advanced science

assessment because “it is the branch of

science most closely associated with

mathematics,” and because it was viewed

as coming “closest to the essential elements of natural science.”11 Students

were allowed to use calculators on the

assessments and relevant formulas were

provided.

The numbers of students participating

in the physics and advanced

mathematics assessments were generally

much smaller (one-third to one-half as

many) than in the mathematics and

science general knowledge assessments.

As a result, estimates of a country’s

average scores in the physics and

advanced mathematics assessments have

larger margins of error than in the

mathematics and science general knowledge assessments. We can say with 95

percent confidence that comparisons of

other countries’ scores to those of the

United States are accurate plus or minus

20 to 40 points on advanced mathematics, and 15 to 65 points on physics,

depending on the size and design of the

samples in other countries. Comparisons of the United States with the international average are accurate plus or

minus about 12 points for advanced

mathematics and 7 points for physics.

(Table A2.2 in Appendix 2 contains a list

of national average scores and standard

errors.)

ADVANCED MATHEMATICS

ASSESSMENT 

An assessment of advanced mathematics

was given to a sample of students taking

advanced coursework in mathematics.

In the United States, these were students

who had taken or were taking a full year

of a high school course that included the

word “calculus” in the title. This included calculus, pre-calculus, Advanced

Placement calculus, and calculus and

analytic geometry. It should be noted,

however, that the advanced mathematics

assessment was not primarily a calculus

assessment. About one-quarter of the

items were in the content area of calculus. Other content areas included in the

assessment were: numbers, equations,

and functions; validation and structure;

probability and statistics; and geometry.

Sub-scales were created for the geometry; calculus; and numbers, equations,

and functions content areas. The

number of items in the other two

categories was too small to obtain

41
42

reliable scores so separate sub-scales

were not developed for them. On the

advanced mathematics assessment,

three-quarters of the items were multiple

choice and one-quarter free response. 

Fewer countries participated in the

advanced mathematics assessment than

in the general knowledge assessments.

Among the 21 countries which participated in the mathematics and science

general knowledge assessments, six

countries (Hungary, Iceland, the

Netherlands, New Zealand, Norway, and

South Africa) did not administer the

advanced mathematics assessment.

Greece, which did not participate in the

mathematics and science general knowledge assessments, participated in the

advanced mathematics assessment. As a

result, 16 countries participated in the

advanced mathematics assessment.

The goal of the advanced mathematics

assessment was to compare the mathematics performance of students in the

most advanced 10 to 20 percent of their

age cohort across nations. Countries

were asked to identify these students

using definitions appropriate for their

own education systems. In the United

States, in order to meet the criterion of

representing 10 to 20 percent of the age

cohort, students whose highest mathematics course was pre-calculus were

included along with students who had

studied or were studying calculus.

In two countries, the Russian Federation

and Lithuania, the advanced mathematics students constituted less than 5 percent of their age cohort; in Austria, Germany, and Slovenia, they constituted

more than 20 percent. In the remaining

11 countries—including the United

States—students in the advanced mathematics assessment were representative of

about 10 to 20 percent of their age

cohort. Table A5.7 in Appendix 5 contains the estimated percentages of the

age cohort in each country represented

by students who took the advanced

mathematics assessment.

How Do Our Twelfth Graders With

Advanced Mathematics Instruction

Compare To Advanced Mathematics

Students In Other Countries?

The performance of U.S. twelfth-grade

advanced mathematics students was

among the lowest of the 16 TIMSS

nations who administered the assessment to a comparable population of

their advanced mathematics students

and below the international average. 

Figure 9 shows that 11 nations outperformed the United States, while U.S.

scores were not significantly different

from those of 4 other nations. No

countries scored below the United

States on the assessment of advanced

mathematics.

U.S. advanced mathematics students

included those who had completed or

were completing pre-calculus, calculus,

calculus and analytic geometry, or

Advanced Placement calculus, representing about 14 percent of the schoolcompleting age cohort in the United

States. If we compared only those U.S.

students who had taken or were taking

calculus or Advanced Placement calculus

against all the advanced mathematics

students in other countries, how did our

calculus students perform? 
43

How Do U.S. Twelfth Graders With

Calculus Or Advanced Placement

Calculus Compare To All Advanced

Mathematics Students In Other

Countries?

U.S. twelfth graders with calculus or

Advanced Placement calculus instruction

represented about 7 percent of the U.S.

age cohort. These students did perform

better in the assessment than the larger

U.S. group that also included students

whose highest course was pre-calculus. 

Advanced mathematics students in 6

countries (France, the Russian

Federation, Switzerland, Denmark,

Cyprus, and Lithuania) outperformed

calculus and AP calculus students in the

U.S. Figure 10 shows that the

performance of U.S. twelfth graders

with calculus or Advanced Placement

calculus instruction was not significantly

different from the international average

and 7 of the 16 TIMSS nations that

administered the assessment to their

advanced mathematics students. Our

scores were significantly higher than

those of two other nations (Germany

and Austria). 

NATIONS WITH AVERAGE SCORES NOT

SIGNIFICANTLY DIFFERENT FROM THE U.S.

NATION AVERAGE

(ITALY) 474

CZECH REPUBLIC 469

(GERMANY) 465

(UNITED STATES) 442

(AUSTRIA) 436

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY LOWER THAN THE U.S.

NATION AVERAGE

NONE

FIGURE 9: 

AVERAGE ADVANCED MATHEMATICS PERFORMANCE OF ADVANCED MATHEMATICS STUDENTS

IN ALL COUNTRIES

INTERNATIONAL AVERAGE = 501

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY HIGHER THAN THE U.S.

NATION AVERAGE

FRANCE 557

(RUSSIAN FEDERATION) 542

SWITZERLAND 533

(AUSTRALIA) 525

(DENMARK) 522

(CYPRUS) 518

(LITHUANIA) 516

GREECE 513

SWEDEN 512

CANADA 509

(SLOVENIA) 475

NOTE: Nations not meeting international sampling or other guidelines are shown in parentheses.

See Appendix 1 for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 5.1. Chestnut Hill, MA: Boston College.
44

The performance of U.S. twelfth

graders with Advanced Placement

calculus instruction, who represent

about 5 percent of the U.S. age cohort

was significantly higher than the performance of advanced mathematics students in 5 other countries. Figure 11

shows that one nation (France) outperformed the United States, while our

scores were not significantly different

from 9 other countries and the international average. Thus, the most advanced

mathematics students in the United

States, about 5 percent of the total age

cohort, performed similarly to 10 to 20

percent of the age cohort in most of the

other countries.

How Do U.S. Students Score In 

The Different Content Areas Of

Advanced Mathematics?

Representing student achievement in

advanced mathematics as a total score is a

useful way to summarize achievement.

However, the advanced mathematics

assessment contained different content

areas, which are emphasized and sequenced differently in curricula around

the world. Based on national priorities,

some content areas have been studied

more than others in different countries

by the time these students are ready to

graduate from secondary school.

NATIONS WITH AVERAGE SCORES NOT

SIGNIFICANTLY DIFFERENT FROM THE U.S.

NATION AVERAGE

(AUSTRALIA)* 525

GREECE 513

SWEDEN 512

CANADA 509

(UNITED STATES) 492

(SLOVENIA) 475

(ITALY) 474

CZECH REPUBLIC 469

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY LOWER THAN THE U.S.

NATION AVERAGE

(GERMANY) 465

(AUSTRIA) 436

FIGURE 10: 

AVERAGE ADVANCED MATHEMATICS PERFORMANCE OF ADVANCED MATHEMATICS STUDENTS IN

OTHER COUNTRIES COMPARED WITH U.S. CALCULUS AND AP CALCULUS STUDENTS

INTERNATIONAL AVERAGE = 504

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY HIGHER THAN THE U.S.

NATION AVERAGE

FRANCE 557

(RUSSIAN FEDERATION) 542

SWITZERLAND 533

(DENMARK) 522

(CYPRUS) 518

(LITHUANIA) 516

*The placement of Australia may appear out of place; however, statistically its placement is correct.

NOTE: Nations not meeting international sampling or other guidelines are shown in parentheses.

See Appendix 1 for details for each country.

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 5.1. Chestnut Hill, MA: Boston College; and unpublished tabulations.
45

The TIMSS advanced mathematics

assessment included sets of items

designed to sample students’ ability to do

work in the following areas:

Numbers, Equations, and Functions:

Complex numbers and their properties; permutations and combinations; 

equations and formulas; and

patterns, relations, and functions.

Calculus: 

Infinite processes; and change.

Geometry: 

Basic geometry; coordinate geometry; polygons and circles; and threedimensional geometry.

Figure 12 shows that in all of the content

areas of advanced mathematics, U.S. students’ performance was among the lowest of the TIMSS nations. 

Among the content areas, U.S. students’

performance was relatively weakest in

NATIONS WITH AVERAGE SCORES NOT

SIGNIFICANTLY DIFFERENT FROM THE U.S.

NATION AVERAGE

(RUSSIAN FEDERATION) 542

SWITZERLAND 533

(AUSTRALIA) 525

(DENMARK) 522

(CYPRUS) 518

(LITHUANIA) 516

(UNITED STATES) 513

GREECE 513

SWEDEN 512

CANADA 509

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY LOWER THAN THE U.S.

NATION AVERAGE

(SLOVENIA) 475

(ITALY) 474

CZECH REPUBLIC 469

(GERMANY) 465

(AUSTRIA) 436

FIGURE 11:

AVERAGE ADVANCED MATHEMATICS PERFORMANCE OF ADVANCED MATHEMATICS STUDENTS IN

OTHER COUNTRIES COMPARED WITH U.S. AP CALCULUS STUDENTS

INTERNATIONAL AVERAGE = 505

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY HIGHER THAN THE U.S.

NATION AVERAGE

FRANCE 557

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses.

See Appendix 1 for details for each country.

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 5.1. Chestnut Hill, MA: Boston College; and unpublished tabulations.
46

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

HIGHER THAN THE U.S.

NATION AVERAGE

(CYPRUS) 561

FRANCE 560

GREECE 538

(RUSSIAN FEDERATION) 537

(AUSTRALIA) 530

(ITALY) 520

SWITZERLAND 512

(DENMARK) 508

(CANADA) 503

(LITHUANIA) 498

SWEDEN 480

NATIONS WITH AVERAGE

SCORES NOT SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

(SLOVENIA) 471

(GERMANY) 454

(UNITED STATES) 450

CZECH REPUBLIC 446

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

(AUSTRIA) 439

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

HIGHER THAN THE U.S.

NATION AVERAGE

(RUSSIAN FEDERATION) 548

SWITZERLAND 547

FRANCE 544

(DENMARK) 527

(CYPRUS) 517

(LITHUANIA) 515

(CANADA) 499

GREECE 498

(AUSTRALIA) 496

CZECH REPUBLIC 494

SWEDEN 492

(GERMANY) 487

(ITALY) 480

(SLOVENIA) 476

(AUSTRIA) 462

NATIONS WITH AVERAGE

SCORES NOT SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

(UNITED STATES) 424

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

NONE

FIGURE 12:

ACHIEVEMENT IN ADVANCED MATHEMATICS CONTENT AREAS

INTERNATIONAL AVERAGE = 501 INTERNATIONAL AVERAGE = 501 INTERNATIONAL AVERAGE = 500

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

HIGHER THAN THE U.S.

NATION AVERAGE

(RUSSIAN FEDERATION) 555

FRANCE 548

(LITHUANIA) 547

GREECE 539

SWEDEN 523

(AUSTRALIA) 517

SWITZERLAND 514

(CANADA) 512

(CYPRUS) 510

(DENMARK) 504

(SLOVENIA) 491

NATIONS WITH AVERAGE

SCORES NOT SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

CZECH REPUBLIC 460

(ITALY) 460

(UNITED STATES) 459

(GERMANY) 457

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

(AUSTRIA) 412

NUMBERS & EQUATIONS CALCULUS GEOMETRY

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses.

See Appendix 1 for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 6.1. Chestnut Hill, MA: Boston College.
47

geometry: no country scored similar to

or below the United States. In numbers,

equations, and functions, as well as in

calculus, fewer countries (11 countries)

scored above the United States. See

Table A4.1 in Appendix 4 for U.S. AP

and non-AP calculus students’ scores by

content area.

What Were Students Asked To Do

On The Advanced Mathematics

Assessment?

There are three examples of advanced

mathematics assessment items. Table

A3.2 in Appendix 3 shows the percentage of students in every country

responding correctly to each of these

example items.

An example of a geometry item is shown

in Figure 13. This item required

FIGURE 13: 

EXAMPLE 7: GEOMETRY ITEM

Correct Answer Example:

Correct proof proves that aB = aC, using the following facts:

• the sum of angles in any triangle is 180 ̊

• if two angles of a triangle are equal, the triangle is isosceles

also may include:

—vertically opposite angles are equal

—supplementary angles add to 180 ̊

A

M

B C

N

40 ̊

20 ̊

S

In the ∆ABC, shown below, the altitudes BN and CM intersect at point S. The measure

of the aMSB is 40 ̊ and the measure of aSBC is 20 ̊. Write a PROOF of the following

statement:

“∆ABC is isosceles.”

Give geometric reasons for statements in your proof. 

SOURCE: Third International Mathematics and Science Study, 1994-1995.

U.S. Average: 19 percent International Average: 48 percent
48

students to prove and justify the given

statement. The international average for

this item was 48 percent. Nineteen percent of U.S. students responded at least

partially correctly. Over one-third of

U.S. students did not receive credit for

this item due to incorrect argumentation and/or including more than one

incorrect geometric fact, step, or reason. 

Figure 14 is an example of a probability

and statistics item. Of U.S. students, 62

percent responded correctly. The

international average was 50 percent

correct. Some students who responded

incorrectly to this item chose “E,” 

perhaps simply counting all of the even

numbers between four and twenty-four,

rather than correctly counting only the

factors of 24 that are divisible by four or

six.

The calculus item shown in Figure 15,

that required students to demonstrate

their understanding of integrals, proved

to be a difficult item for most students,

including U.S. students. Twenty-seven

percent of U.S. students responded correctly to this item, and the international

A

B

C

D

E

1

6

5

24

1

4

1

3

5

12

FIGURE 14: 

EXAMPLE 8: PROBABILITY AND STATISTICS ITEM

A set of 24 cards is numbered with the positive integers from 1 to 24. If the cards

are shuffled and if only one is selected at random, what is the probability that

the number on the card is divisible by four or six?

Correct Answer: D U.S. Average: 62 percent International Average: 50 percent

SOURCE: Third International Mathematics and Science Study, 1994-1995.
49

FIGURE 15: 

EXAMPLE 9: CALCULUS ITEM

The figure above shows the graph of y = ƒ(x).

S1 is the area enclosed by the x-axis, x = a, and y = ƒ (x);

S2 is the area enclosed by the x-axis, x = b, and y = ƒ (x);

where a<b and 0<S2

<S1.

Correct Answer: C U.S. Average: 27 percent International Average: 35 percent

SOURCE: Third International Mathematics and Science Study, 1994-1995.

y

a

y = ƒ (x)

b x 0

S1

S2
50

average was about 35 percent. Many students who responded incorrectly apparently did not recognize that if a curve

lies above the x-axis, the integral represents the area under the curve, and if

the curve lies below the x-axis, the integral represents the negative of the area

between the curve and the x-axis.

Is There A Gender Gap In Advanced

Mathematics At The Twelfth Grade?

In the United States, twelfth-grade

males outperformed twelfth-grade

females in advanced mathematics. The

United States was one of the 11 TIMSS

nations in which a gender gap existed.

No significant gender gap existed in the

other 5 countries. For the United States

and 7 other countries, there was a significant gender gap existing in all 

3 advanced mathematics content areas.

(See Tables A5.8 and A5.9 in Appendix 5.)

PHYSICS ASSESSMENT

The TIMSS physics assessment included

questions about mechanics; electricity

and magnetism; particle, quantum and

other types of modern physics; heat;

and wave phenomena. In the United

States, the population that took the

assessment was twelfth graders 

who had taken or were taking at least

one year-long course in physics. This

included physics I, physics II, advanced

physics, and Advanced Placement

physics. 

Fewer countries participated in the

physics assessment than in the general

knowledge assessments. Among the 21

countries which participated in the

mathematics and science general knowledge assessments, 7 countries (Hungary,

Iceland, Italy, Lithuania, the Netherlands, New Zealand, and South Africa)

did not administer the physics assessment. Greece and Latvia, which did not

participate in the general knowledge

assessments, participated in the physics

assessment. As a result, 16 countries participated in the physics assessment.

In general, countries identified similar

percentages of an age cohort as appropriate for the physics assessment.

Although countries used their own

definitions to identify advanced science

students, for 11 of the 16 countries,

including the United States, these

students represented about 10 to 20 

percent of their age cohort. The only

exceptions to this pattern were Denmark, Latvia, and the Russian Federation, where physics students represented

less than 5 percent of the age cohort,

and Austria and Slovenia, where the students represented more than 20 percent

of the age cohort. (Table A5.7 in Appendix 5 contains the percentages of the

age cohort in each country represented

by students who took the physics assessment.)

How Do U.S. Twelfth Graders With

Physics Instruction Compare To

Advanced Science Students In Other

Countries?

The performance of U.S. twelfth-grade

physics students was among the lowest

of the 16 TIMSS nations that administered the assessment to a comparable

population of their students and below

the international average. Figure 16

shows that 14 nations outperformed the

United States, while our scores were not
51

significantly different from those of one

other nation. No countries scored below

the United States on the physics assessment. One interesting aspect of the

scores on the physics assessment is that

there was less variation in the scores

among U.S. students than in 13 of the

other 15 countries. The range of U.S.

students scores was relatively narrow—

189 points between the 5th and 95th percentile compared to an average difference of 293 points for all 16 countries.

In the United States, the population

that took the assessment were twelfth

graders who had completed or were

completing physics I, physics II,

advanced physics, or Advanced Placement physics, representing about 14

percent of the age cohort. If we

compared only those U.S. students who

had taken or were taking Advanced

Placement physics with all the advanced

science students in other countries, how

did U.S. AP physics students perform?

NATIONS WITH AVERAGE SCORES NOT

SIGNIFICANTLY DIFFERENT FROM THE U.S.

NATION AVERAGE

(AUSTRIA) 435

(UNITED STATES) 423

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY LOWER THAN THE U.S.

NATION AVERAGE

NONE

FIGURE 16:

AVERAGE PHYSICS PERFORMANCE OF ADVANCED SCIENCE STUDENTS IN ALL COUNTRIES

INTERNATIONAL AVERAGE = 501

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY HIGHER THAN THE U.S.

NATION AVERAGE

NORWAY 581

SWEDEN 573

(RUSSIAN FEDERATION) 545

(DENMARK) 534

(SLOVENIA) 523

(GERMANY) 522

(AUSTRALIA) 518

(CYPRUS) 494

(LATVIA) 488

SWITZERLAND 488

GREECE 486

(CANADA) 485

FRANCE 466

CZECH REPUBLIC 451

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses.

See Appendix 1 for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 8.1. Chestnut Hill, MA: Boston College.
How Do U.S. Twelfth Graders With

Advanced Placement Physics

Instruction Compare To Advanced

Science Students In Other

Countries?

U.S. twelfth graders with Advanced

Placement physics represented about 1

percent of the age cohort in the United

States. U.S. students who had taken or

were taking Advanced Placement

physics were outperformed by advanced

science students in fewer nations than

were the students in our larger group of

physics students. Figure 17 shows that

U.S. Advanced Placement physics students scored below the international

average and advanced science students

in 6 nations, while the average U.S.

score was significantly higher than that

of one other nation. The performance

of U.S. twelfth graders with Advanced

Placement physics instruction was no

different from the performance of 8 of

the 16 TIMSS nations that administered

the assessment to their advanced science

52

NATIONS WITH AVERAGE SCORES NOT

SIGNIFICANTLY DIFFERENT FROM THE U.S.

NATION AVERAGE

(SLOVENIA)* 523

(CYPRUS) 494

(LATVIA) 488

SWITZERLAND 488

GREECE 486

(CANADA) 485

(UNITED STATES) 474

FRANCE 466

CZECH REPUBLIC 451

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY LOWER THAN THE U.S.

NATION AVERAGE

(AUSTRIA) 435

FIGURE 17:

AVERAGE PHYSICS PERFORMANCE OF ADVANCED SCIENCE STUDENTS IN OTHER COUNTRIES

COMPARED WITH U.S. AP PHYSICS STUDENTS

INTERNATIONAL AVERAGE = 504

NATIONS WITH AVERAGE SCORES 

SIGNIFICANTLY HIGHER THAN THE U.S.

NATION AVERAGE

NORWAY 581

SWEDEN 573

(RUSSIAN FEDERATION) 545

(DENMARK) 534

(GERMANY) 522

(AUSTRALIA) 518

*The placement of Slovenia may appear out of place; however, statistically its placement is correct.

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses.

See Appendix 1 for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 8.1. Chestnut Hill, MA: Boston College.
53

students. However, U.S. Advanced Placement physics students represented a

much smaller proportion of the age

cohort in the United States than did the

advanced science students in most of

the other countries.

How Do U.S. Students Score In The

Different Content Areas Of Physics?

Representing student achievement in

physics as a total score is a useful way to

summarize achievement. However, the

physics assessment contained different

content areas, which are emphasized

and sequenced differently in curricula

around the world. Based on national

priorities, and sequencing of physics

instruction for advanced students at the

secondary level, some content areas

have been studied more than others in

various countries by the time these students graduate from secondary school.

The TIMSS physics assessment included

sets of items designed to sample students’

ability to do work in the following areas:

Mechanics: Dynamics of motion; time,

space and motion; types of forces;

and fluid behavior.

Electricity/magnetism: Electricity; and

magnetism.

Heat: Physical changes; energy types,

sources and conversions; heat and

temperature; and kinetic theory.

Wave phenomena: Sound and vibration;

light; and wave phenomena.

Modern physics: Nuclear chemistry;

quantum theory and fundamental

particles; astrophysics; subatomic

particles; and relativity theory.

Figure 18 shows that in all five physics

content areas, U.S. students’ performance

was among the lowest of the TIMSS

nations. In two content areas, one nation

scored below the United States. Students

in Austria scored below students in the

United States in the content area of heat

and students in Cyprus scored below U.S.

students in the area of modern physics.

Among the content areas, U.S. students

performed the poorest in the content

areas of mechanics and electricity/magnetism, in terms of the number of

countries outperforming the United

States. See Table A4.2 in Appendix 4 for

U.S. AP and non-AP physics students’

scores by content area.

What Were Advanced Science

Students Asked To Do On The 

Physics Assessment?

On pages 56 and 57, there are three

examples of physics assessment items.

Table A3.2 in Appendix 3 shows the percentage of students in every country

responding correctly to each of these

example items.

Figure 19 is an example of a mechanics

item. Forty-one percent of U.S. physics

students responded correctly to this

item. The international average was

about 70 percent. Some students who

responded incorrectly appear not to

have recognized that the pressure of the

water would cause the horizontal placement of the streams to differ. Figure 20

is an example of a heat item. Forty-nine

percent of U.S. physics students chose

the correct answer. The international

average on this item was 41 percent correct. Many students who responded

incorrectly chose “A.”
54

FIGURE 18: 

ACHIEVEMENT IN PHYSICS CONTENT AREAS

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY

HIGHER THAN THE U.S.

NATION AVERAGE

NORWAY 572

SWEDEN 563

(SLOVENIA) 552

(RUSSIAN FEDERATION) 537

(CYPRUS) 530

(DENMARK) 529

GREECE 514

(AUSTRALIA) 507

(GERMANY) 495

(LATVIA) 489

SWITZERLAND 482

(CANADA) 473

CZECH REPUBLIC 469

FRANCE 457

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY

HIGHER THAN THE U.S.

NATION AVERAGE

SWEDEN 570

NORWAY 565

(RUSSIAN FEDERATION) 549

GREECE 520

(DENMARK) 513

(AUSTRALIA) 512

(GERMANY) 512

(SLOVENIA) 509

(CYPRUS) 502

FRANCE 494

(CANADA) 485

(LATVIA) 485

SWITZERLAND 480

CZECH REPUBLIC 465

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY

HIGHER THAN THE U.S.

NATION AVERAGE

NORWAY 536

(RUSSIAN FEDERATION) 530

SWEDEN 522

(SLOVENIA) 521

(AUSTRALIA) 517

(DENMARK) 512

SWITZERLAND 509

(CANADA) 508

FRANCE* 491

NATIONS WITH 

AVERAGE SCORES NOT 

SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

(AUSTRIA) 420

(UNITED STATES) 420

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

NONE

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

NONE

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

(AUSTRIA) 445

NATIONS WITH 

AVERAGE SCORES NOT 

SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

(AUSTRIA) 432

(UNITED STATES) 420

NATIONS WITH 

AVERAGE SCORES NOT 

SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

(LATVIA) 504

(GERMANY) 496

CZECH REPUBLIC 488

GREECE 481

(UNITED STATES) 477

(CYPRUS) 476

MECHANICS ELECTRICITY/MAGNETISM HEAT

INTERNATIONAL AVERAGE = 501 INTERNATIONAL AVERAGE = 501 INTERNATIONAL AVERAGE = 501
55

FIGURE 18 (CONTINUED):

ACHIEVEMENT IN PHYSICS CONTENT AREAS

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY

HIGHER THAN THE U.S.

NATION AVERAGE

NORWAY 560

SWEDEN 560

(DENMARK) 537

(GERMANY) 530

(AUSTRALIA) 519

(RUSSIAN FEDERATION) 515

(SLOVENIA) 514

(CYPRUS) 507

SWITZERLAND 498

(CANADA) 488

NATIONS WITH 

AVERAGE SCORES NOT 

SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

(LATVIA)* 498

(AUSTRIA) 468

FRANCE 463

GREECE 453

(UNITED STATES) 451

CZECH REPUBLIC 447

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

NONE

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY 

LOWER THAN THE U.S.

NATION AVERAGE

(CYPRUS ) 434

NATIONS WITH 

AVERAGE SCORES NOT 

SIGNIFICANTLY 

DIFFERENT FROM THE U.S.

NATION AVERAGE

(LATVIA)* 488

(UNITED STATES) 456

CZECH REPUBLIC 453

GREECE 447

WAVE PHENOMENA MODERN PHYSICS

*The placement of Latvia on wave phenomena and modern physics, and France on heat, may appear out of place;

however, statistically their placement is correct.

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses. See Appendix 1

for details for each country.

SOURCE: Mullis et al. (1998). Mathematics Achievement in the Final Year of Secondary School. Table 9.1. Chestnut Hill,

MA: Boston College.

INTERNATIONAL AVERAGE = 500 INTERNATIONAL AVERAGE = 501

NATIONS WITH AVERAGE

SCORES SIGNIFICANTLY

HIGHER THAN THE U.S.

NATION AVERAGE

NORWAY 576

SWEDEN 560

(GERMANY) 545

(DENMARK) 544

(RUSSIAN FEDERATION) 542

(AUSTRALIA) 521

(SLOVENIA) 511

(CANADA) 494

SWITZERLAND 488

(AUSTRIA) 480

FRANCE 474
A jar of oxygen gas and a jar of hydrogen gas are at the same temperature. 

Which of the following has the same value for the molecules of both gases?

A. the average velocity

B. the average momentum

C. the average force

D. the average kinetic energy

56

FIGURE 19:

EXAMPLE 10: MECHANICS ITEM

The figure shows a common plastic bottle (1L) filled with water and with three

holes in it, so that the water runs out of the holes.

Explain what is wrong with the figure.

Correct Answer Example

• “The pressure will increase with depth due to water above, so the water jets

will have other paths.”

SOURCE: Third International Mathematics and Science Study, 1994-1995.

U.S.Average: 41 percent International Average: 70 percent

FIGURE 20:

EXAMPLE 11: HEAT ITEM

SOURCE: Third International Mathematics and Science Study, 1994-1995.

Correct Answer: D U.S.Average: 49 percent International Average: 41 percent
A third example of a physics item concerns wave phenomena, as shown in Figure 21. This proved to be a difficult item

for most students, including U.S. students. Twelve percent of U.S. physics

students received at least partial credit

for this item, and the international

average was approximately 37 percent correct. Some students who responded incorrectly to this item did not adequately distinguish between the loudness of the

sound and a change in the wave frequency.

Is There A Gender Gap In Physics At

The Twelfth Grade?

In the United States, as in all the other

TIMSS nations except Latvia, twelfthgrade males outperformed twelfth-grade

females in physics. In the United States,

this gender gap existed in 4 of the 5 content areas of physics included in the

TIMSS assessment (all except heat). More

than three-quarters of the countries had a

significant gender gap in the content

areas of mechanics, wave phenomena,

and modern physics. (See Tables A5.10

and A5.11 in Appendix 5.)

How Does U.S. Student Performance

In Physics Compare To That In

Advanced Mathematics?

Unlike our performance on the general

knowledge portion of the assessment

(where U.S. students’ relative performance was stronger in science than it was

in mathematics), U.S. performance on the

physics assessment was weaker relative to

other countries than on the advanced

mathematics assessment. Fourteen countries scored above the U.S. in the physics

assessment, while fewer countries (11

countries) outperformed the U.S. in the

advanced mathematics assessment.

The relationship between performance in

physics and advanced mathematics might

be more similar to the pattern in general

knowledge assessments (with students performing better in science than in mathematics) if TIMSS had assessed other content areas of science such as life science or

environmental issues and the nature of science, as was done in eighth grade. Among

the content areas of the science assessment

given to eighth graders, U.S. students’ performance was weakest in physics and

strongest in life science and in environmental issues and the nature of science.

57

FIGURE 21: 

EXAMPLE 12: WAVE PHENOMENA ITEM

A car moving at a constant speed with a siren sounding comes towards you and

then passes by. Describe how the frequency of the sound you hear changes. 

Correct Answer Examples

• “The pitch is higher as the car comes closer and lower after it goes by.”

• “When the car approaches, the wavelength of the sound is shorter than it is

when the car moves away.”

SOURCE: Third International Mathematics and Science Study, 1994-1995.

U.S.Average: 12 percent International Average: 37 percent
CHAPTER 4:

THE CONTEXT OF

LEARNING

KEY POINTS:

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 described here.

While secondary education in the United

States differs from that in many of the

other countries on important dimensions,

few of those differences are clearly related

to the relatively poor performance of our

twelfth graders on the TIMSS assessments.

The lives of United States graduating

students differ from those of their peers in

other countries on several of the factors

examined. Where there are differences,

few appear to be systematically related to

U.S. performance in twelfth grade

compared to the other countries

participating in TIMSS.

Further analyses are needed to provide

more definitive insights on these subjects.
59

Chapters 2 and 3 have portrayed how

U.S. high school students in the spring

of their senior year performed in

mathematics and science compared to

their peers at the end of secondary

school in many other countries.

Generally, the performance of these

U.S. students did not compare favorably

with that of students in the other countries participating in TIMSS. The results

from previous international assessments

have generally shown that U.S. performance relative to other countries was

lower at higher grade levels and a

similar pattern emerged in TIMSS, with

the strongest U.S. performance in

fourth grade and the poorest at the end

of secondary schooling.

This chapter uses data from TIMSS and

other sources to examine a number of

factors that could contribute to the poor

performance of U.S. twelfth graders.

Most of the factors examined in this

chapter are ones that previous research

has shown to be associated with variation in student performance within the

United States or which observers have

suggested could be associated with differences in performance between countries. (See Appendix 5 for details.)

Since we are primarily interested in

identifying factors that might account

for the relatively poor performance of

U.S. students, we did not use the

strategy of looking for factors that

account for variation across all the

countries. Instead, we used the

following two-step process: For each

potential explanatory factor, the first

step was to determine whether each of

the other TIMSS countries were

significantly higher or lower or were

similar to the United States on that

factor. The second step was to examine

whether the countries that outperformed the United States differed on

that factor from the United States and

from countries that performed similarly

to or below the United States.A

The first section of the chapter examines

factors that might be associated with the

performance of U.S. twelfth graders on

the general knowledge assessments

relative to students in other countries.

The second section examines factors that

might be associated with our relative performance on the physics and advanced

mathematics assessments. Both sections

are organized in the following manner.

First the factors are discussed, focusing on

how the United States compares to the

other countries on each one. Then, those

factors that seem to be related to the U.S.

performance compared to the other

countries are identified and discussed.

(At the end of the first section, there is

also a discussion of two factors that might

A. Such an approach to the data was chosen for this initial analysis in part because the data for individual

students were not yet available for any country except the United States. In addition, since the analysis

had to be conducted on country-level data, where there were at most 21 cases (i.e., the maximum

number of countries for any of the assessments), more sophisticated statistical analysis was unlikely

to detect any relationships unless the relationships were very pronounced. Two byproducts of using

such an approach should be noted. First, if there are any factors on which the United States differs

from all the other countries, those factors cannot explain the U.S. relative performance, since the

U.S. would differ on that factor both from the countries that outperformed us and the ones that did

not. Second, because the United States was outperformed by all the participating countries except

one (Austria) on the physics assessment, we are unlikely to find any factors on which the United

States (and Austria) differ from all the other countries. In a few cases, the analysis had only one step,

namely to calculate and compare the average for the factor in question (e.g., GNP per capita) for two

groups of countries: those that outperformed the United States and those that did not.
60

be related to the lower relative standing of

U.S. students in twelfth grade than in

eighth grade.) Figures 25-27 and 29 summarize the findings of these analyses.

To simplify the discussion, the analyses

about factors related to U.S. international standing on the general knowledge

assessments focused on the mathematics

general knowledge assessment, rather

than looking both at mathematics and at

science general knowledge performance.

More countries outperformed the

United States in mathematics than in science general knowledge and all the

countries that outperformed the United

States in science outperformed us in

mathematics general knowledge as well. 

THE CONTEXT OF LEARNING FOR

STUDENTS PARTICIPATING IN THE

GENERAL KNOWLEDGE

ASSESSMENTS 

The way in which countries structure

and provide secondary education, or

high school as it is known in the United

States, differs greatly around the world.

Among the nations participating in

TIMSS, different policy decisions, cultural beliefs about how best to develop

students’ potential, and other factors

result in differences in secondary education such as school types, enrollment,

the courses students take, course curricula, and financial support for schools. In

some cases, these differences are more

pronounced than in others. TIMSS provides an opportunity to examine

whether these differences in education

systems are related to what students

know in mathematics and science at the

end of their secondary schooling.

Some have argued in the past that

because the secondary education systems

in many other countries are quite different from those in the United States, it is

inappropriate to compare the performance of U.S. students with those in other

countries. The fact that other countries

differ in the decisions they have made

about the nature of secondary education

provides an opportunity to examine

whether these differences in education

systems are related to what students know

at the end of their secondary schooling in

mathematics and science. In addition,

understanding something about the differences between education systems provides important information for interpreting the findings about student

performance.

How Does Secondary Schooling In

The Other TIMSS Countries

Resemble And Differ From That In

The United States?

Structure of Secondary Education

One major way in which the organization of schooling in the United States

differs from that in many of the TIMSS

countries is the amount of differentiation within secondary education. This

differentiation can take at least two

forms. One involves the extent to which

students are separated into different

programs, either within schools or

between schools. The other is whether

the length of secondary schooling is the

same for all students—across all schools,

programs, and regions of the country.

The United States is atypical among

TIMSS countries in the lack of differentiation in secondary schooling on either

dimension. 

The United States was one of five countries in TIMSS (the others are also former English colonies—Australia,

Canada, New Zealand, and South

Africa) where most students attend com-
61

prehensive high schools, regardless of

their ability, prior academic performance, and career goals (see Table A5.12

in Appendix 5). Within those comprehensive high schools, students select

their courses each year. Although there

are graduation requirements in terms of

the number of courses students must

complete in specified fields, students

generally can enroll in any course for

which they meet the prerequisites.12

Most of the students in other TIMSS

countries attend either specialized or

mixed secondary schools. In specialized

schools, students of different abilities or

career goals attend separate types of

schools. Although in some of these

countries students have varying degrees

of choice regarding their school type or

program of study, once they enroll in a

particular school or program, the specific courses they will take are generally

fixed. In mixed secondary schools, students of different abilities or career

goals all attend the same school, but

based on ability or interest, students are

divided into one of several pre-set programs of coursework within the school.

In 6 of the TIMSS countries, including

the United States, secondary schooling

ends at the same grade for all students.

In the other 17 countries participating

in some facet of TIMSS at this level, the

length of schooling varies (Figure 22).

Generally, vocationally-oriented programs involve fewer years of secondary

schooling than do those with an academic focus. For example, in the Czech

Republic, there are three types of secondary schools—gymnasium (academic),

technical, and vocational—and depending on the school or program, students

complete secondary schooling at the

end of grades 10, 11, 12, or 13. Students

in technical schools and gymnasium usually complete their secondary education

at grade 12, but a few end at grade 13. In

the vocational schools, the end of secondary education can occur between

grades 10 and 13 depending on the type

of vocation. In some countries, after

completing one secondary vocational

program, students may enroll in a

second such program in another field.

In TIMSS, students were tested in the

final year of secondary education

regardless of their type of school or

program, so that within the same country, students who took TIMSS varied in

the number of years of schooling they

had completed. Thus, in the Czech

Republic, when TIMSS tested students

in the final year of secondary school in

each type of school, there were Czech

students taking TIMSS who were in

grades 10 to 13. Across all 21 countries

participating in the general knowledge

portions of TIMSS, students as low as

grade 10 and as high as grade 14 were

tested (Table A5.13 in Appendix 5).

Like the United States, every country

assessed students in grade 12 (except

the Russian Federation where students

complete general secondary school at

grade 11), but in the majority of countries students in at least one other grade

also participated in TIMSS.

Reflecting the differences in the structure

and organization of the education systems

in the various countries, the average age

of the students in each country taking the

general knowledge assessments also varied across countries, from about 17 to 21

(Table A5.13 in Appendix 5). The average

age of U.S. students was 18.1 years and the

international average for all 21 countries

in the general knowledge assessments was

18.7 years. Countries with relatively high

average ages (19.0 or above) tended to be

countries where primary school does not
62

AGE AT GRADE 1 GRADE

NATION

FIGURE 22

AGE BEGINNING GRADE 1 AND GRADE(S) MARKING END OF

SECONDARY SCHOOL IN TIMSS NATIONS

1 2 3 4 5 6 7 8 9 10 11 12 13 14

AUSTRALIA

AUSTRIA

CANADA

CYPRUS

CZECH REPUBLIC

DENMARK

FRANCE

GERMANY

GREECE

HUNGARY

ICELAND

ITALY

LATVIA

LITHUANIA

NETHERLANDS

NEW ZEALAND

NORWAY

RUSSIAN FEDERATION

SLOVENIA

SOUTH AFRICA

SWEDEN

SWITZERLAND

UNITED STATES

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Appendix A. Chestnut Hill, MA: Boston College.

NOTE: The width of the bar segments do not indicate the proportion of the cohort that complete school at the

end of the indicated grades.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

6

6

6

6

6

7

6

6

6

6

6

6

6

7

6

6

7

6/7

7

6

7

6/7

6
start until age 7 and/or where secondary schooling extends beyond grade 12.

Most of these countries have much higher proportions of 18-year-olds enrolled

in secondary school than the United

States and some have one-fourth to onethird of 20-year-olds still enrolled in secondary school (compared to 2 percent

of 20-year-olds in the United States). (See

Table A5.14 in Appendix 5.)

Secondary Enrollment and Completion

One possible explanation for the poor

performance of U.S. students might be

that a much higher proportion of the

U.S. population completes secondary

education than in the countries that outperformed the U.S. on TIMSS. If that

were the case, then the students participating in the TIMSS general knowledge

assessments would represent an elite

group within other countries while they

would represent nearly all the population in the United States. However, data

gathered as part of TIMSS and by the

Organization for Economic

Cooperation and Development (OECD)

on secondary enrollment and completion indicate that this is not the case.

While in the past, it was true that the

United States differed from many other

countries in educating most of its young

people through the end of secondary

school, that was no longer true in the

year TIMSS was conducted. In the

TIMSS countries as a whole, large proportions of the population now attend

and complete secondary school (Table

A5.14 in Appendix 5). In 1995, enrollment in secondary education represented, on average, over 90 percent of children of secondary school age among all

21 countries participating in the general

knowledge portion of TIMSS as well as

in the United States.

While current secondary enrollment in

the United States and the other TIMSS

countries is similar, the United States

still has an edge in secondary completions among a somewhat older age

group, reflecting differences in secondary enrollment in past years. Data collected by OECD reveal that in 1995 the

average proportion of the population

ages 25-34 who had completed high

school, while relatively high (78 percent) for the 14 TIMSS countries for

which the information was available, was

somewhat lower than in the United

States (87 percent).13

Curriculum

Although the general knowledge

assessments were not designed to match

secondary mathematics and science curricula, the content of the U.S. secondary

curriculum relative to the other TIMSS

countries might contribute to the poor

U.S. performance. A comparison of the

topics covered in the mathematics and

science general knowledge assessments

with curriculum frameworks did reveal

that both general knowledge assessments covered content that is introduced later in the U.S. curriculum than

it is introduced, on average, in the other

TIMSS countries as a whole.14

The content of the mathematics general

knowledge assessment represented

about a seventh-grade level of curriculum for most TIMSS nations, but was

most equivalent to the ninth-grade curriculum in the United States. The science general knowledge content was

most equivalent to ninth-grade curriculum internationally, and to eleventhgrade curriculum in the United States.

The higher grade-level equivalent of the

assessments in the United States reflects

the relatively late appearance of algebra

63
and many geometry topics in

mathematics, and of chemistry and

physics in science in the U.S. curriculum

compared to their appearance in the

curriculum of other countries.

Another aspect of curriculum that differs among the TIMSS countries is the

extent to which final approval about curriculum syllabi is centralized. In about

half of the TIMSS countries, decisions

about curriculum syllabi are centralized

at the national level. That is, the national level of government has exclusive

responsibility for or gives final approval

of the syllabi for courses of study. 

In a few countries, such curriculum

decisions are regionally centralized, and

in the remaining countries, including the

United States, final approval of curriculum syllabi are not centralized (Table

A5.15 in Appendix 5). 

Support for Education

One factor that may be associated with

both education system and student differences is the affluence of the countries, which may be translated into the

level of resources available to schools

and families. The United States was one

of the more affluent countries with a

GNP per capita of $25,860 compared to

$17,305 for all 21 countries participating in the general knowledge portion of

TIMSS (Table A5.16 in Appendix 5).

However, about one-third of the countries had GNP per capita similar to or

higher than the United States ($23,500

to $37,000). Similarly, the United States

had higher per capita public spending

on elementary/secondary education

than two-thirds of the other countries. It

should be noted that the U.S. performance resembled, on average, the economically less-affluent countries (those

with lower GNPs per capita and lower

per capita expenditures on elementary/secondary education) participating

in the general knowledge assessments,

while two of the less affluent countries

(Hungary and Slovenia) also outperformed the United States.

We now turn our attention to the extent

to which the United States is similar to

or differs from the other TIMSS nations

on factors related to the everyday lives of

students both within and outside of

school.

How Do U.S. Twelfth-Grade

Students Compare Internationally

On Factors Associated With Their

Lives Inside And Outside Of School? 

As discussed above, we know that upper

secondary education, or “high school”

as it is known in the United States, varies

greatly among the TIMSS nations.

Students in one country may attend a

school with a particular focus based on

their abilities or career goals, while students in another country may be

required to choose among several specialties as their “major” in a general

school. In other countries, students may

create their own program by choosing

among a variety of courses.

While we know much about the differences between school systems in the

TIMSS nations, we know less about students’ everyday lives in those schools,

and, in particular, how aspects of their

everyday lives may affect their performance. In order to learn more, TIMSS

asked all students about a number of

factors that are related to student performance within the United States and

many other countries. For a few countries, information is not available for

some of the factors.

64
Based on students’ reports, TIMSS finds

the following concerning those students

who took the general knowledge assessments. (See Table A5.20 in Appendix 5

for a detailed summary of these results.)

Mathematics and Science Coursetaking

Countries may vary in how much mathematics and science students take in secondary school and at what level.

Research has shown in the United States

that more years of science and mathematics coursetaking in high school are

associated with higher levels of performance.15 If a similar pattern holds in

other countries and greater proportions

of students in high-achieving countries

have studied mathematics and science

for more years or have taken advanced

courses than in the United States, that

could contribute to the relatively poor

performance of U.S. students. 

Because of the differences in the ways

the curriculum is delivered in the various countries, it is difficult to construct

comparable measures for the amount or

the level of mathematics and science

that students in different countries have

studied. Students were asked whether

they were currently taking mathematics

and science at the time they participated

in TIMSS, which at least indicates

whether they were still studying these

subjects in their final year of secondary

school. Countries did vary considerably

in the proportion of students reporting

they were currently taking mathematics

(from about half to all students) and science (from one-third to all students). 

U.S. graduating students were less likely

to be taking mathematics or science than

were their counterparts in other countries. While 66 percent of graduating

students in the U.S. were currently

taking mathematics, the average in all

the countries participating in the

general knowledge assessments was 79

percent. The same pattern was also true

for science (53 percent for the United

States and 67 percent for all the TIMSS

countries).

Homework

One factor that could be related to U.S.

students’ performance is the amount of

homework and studying they do. U.S.

students reported spending fewer hours

on homework and studying per day than

the international average for students in

the final year of secondary school (1.7

and 2.6 hours respectively). Students in

15 nations (out of 19) reported spending more hours, on average, studying or

doing homework per day than their U.S.

counterparts, while students in only one

nation, the Czech Republic, reported a

lower average number of hours studying

or doing homework per day. (See table

A5.20 in Appendix 5.)

Calculators and Computers

There is considerable discussion in the

U.S. about how and to what extent

calculators and computers should be

incorporated into classroom instruction

in mathematics and science. TIMSS

asked students about their usage of

calculators and computers in many settings—at home, school, and elsewhere.

U.S. students’ use of calculators was similar to that of students in other countries.

About half of U.S. twelfth-grade students

(52 percent) reported using a calculator

on a daily basis, which is similar to the

international average (55 percent).

65
66

In all nations, students were given the

opportunity to use calculators if they

wished to do so during the TIMSS mathematics and science general knowledge

assessments. While a majority of U.S. students reported taking advantage of the

opportunity to use calculators during the

mathematics and science general

knowledge assessments, a smaller proportion of U.S. students did so than the

international average (71 and 79 percent,

respectively). More students took advantage of the opportunity in 12 nations

than did students in the United States.

About three-quarters of U.S. twelfthgrade students reported using a computer at school, home, or elsewhere,

which is higher than the international

average (73 and 57 percent, respectively).

Attitudes Toward Mathematics and

Science

Perhaps U.S. students do less well

because they have less positive attitudes

toward mathematics and science. About

21 percent of U.S. twelfth graders said

they liked mathematics a lot, which was

higher than the international average of

15 percent.

Students were asked whether they liked

biology, chemistry, earth science, and

physics. For chemistry, earth science and

physics, the percentage of U.S. students

who said that they liked the subject or

who liked it a lot (49, 68, and 47 percent

respectively) was higher than the international average (42, 63, and 42 percent

respectively). The percentage of U.S.

students who said they liked biology or

who liked biology a lot was 67, the same

as the international average.

Personal Safety in School

The school environment should be conducive to learning. One factor that may

detract from the amount of learning that

takes place is a school environment where

students’ safety is somewhat problematic.

Students in TIMSS were asked about

thefts and threats in school. The United

States was above the international average

in both.

About one-quarter of U.S. twelfth-graders

had experienced theft of their property at

school in the month prior to the assessments, which was higher than the international average (Figure 23). Theft was

experienced by a smaller percentage of

students in 15 nations (out of 17). 

While less common than theft in most

nations around the world, approximately

one-tenth of U.S. twelfth-grade students

reported having been threatened at

school in the month prior to TIMSS,

which was higher than the international

average (Figure 23). In only one other

nation, South Africa, did a larger

percentage of students report having been

threatened than did students in the

United States. Threats of violence at

school were experienced by a smaller percentage of students in 10 nations (out of

16). 

Television and Video Watching

The amount of television students watch is

often mentioned as a factor related to

achievement. U.S. twelfth graders spent,

on average, the same amount of time

watching television or videos as the international average. U.S. students watched

an average of 1.7 hours of television or

videos on a normal school day, which was

the same amount of time as the average

for the 20 countries for which data were
67

available. 

Working at a Paid Job

Students at the end of secondary school

may spend their out-of-school time in a

variety of ways other than studying and

doing homework. If students work long

hours, at part-time jobs, that may leave

them with less time and energy to

devote to school. More U.S. twelfthgrade students reported that they

worked at a paid job, and worked longer

hours, on a normal school day, than did

students in any other TIMSS nation

(Figure 24). A little more than half of

U.S. students said that they worked 3 or

more hours on a normal school day at a

paid job compared with the international average of about one-fifth of all

graduating students. Moreover, U.S. students reported that they worked an average of 3.1 hours on a normal school day,

which was higher than for students in

any other TIMSS nation.

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?

Most of the factors described above do

not seem to account for U.S. students’

relatively poor performance. Among

the factors related to the education sys0

5

10

15

20

25

30

7

Had 

something 

stolen in the 

month prior 

to TIMSS

PERCENTAGE OF STUDENTS

11

International Average

United States

13

24

Were

threatened 

by another 

student in the 

month prior 

to TIMSS

FIGURE 23:

U.S. TWELFTH-GRADE STUDENTS’ REPORTS ON PERSONAL SAFETY AT SCHOOL IN COMPARISON

WITH THE INTERNATIONAL AVERAGE

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 4.21. Chestnut Hill, MA: Boston College.
68

tems, this is the case for differentiation

in the secondary education system, the

grade level of the students participating

in TIMSS, rates of secondary enrollment

and completion, and centralization of

decision-making about curriculum syllabi (Figures 25 and 26). Only the average age of the students taking the general knowledge assessments and the curricular-level equivalent of those assessments seem to be possible factors contributing to the relatively poor U.S. performance on these assessments.

While the average age of the students

participating in TIMSS in the countries

outperforming the United States ranged

from 17.5 to 21.2 years, countries with

an average age of 19.0 or above were

somewhat more likely to outscore the

United States than the countries in

which the average age was less than 19.0. 

The content of the general knowledge

assessments represented material covered at a higher grade level in the

United States than the other countries as

a whole. However, estimates for the

grade-level equivalents of the assessments for each of the other TIMSS

countries individually are not currently

available. Therefore, we cannot currently compare how the assessments correspond to the curriculum in the countries

0

10

20

30

40

50

60

70

80

Less

than

one

hour

One to

two

hours

Three to

five

hours

More

than

five

hours

PERCENTA

GE OF STUDENTS

39

27

9

28

9

International Average

United States 72

9 7

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

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 4.21. Chestnut Hill, MA: Boston College.
69

FIGURE 25:

RELATIONSHIP BETWEEN U.S. RELATIVE PERFORMANCE AND SCHOOLING AND STUDENT FACTORS:

MATHEMATICS GENERAL KNOWLEDGE

MATHEMATICS GENERAL KNOWLEDGE

FACTORS

U.S. COMPARED TO

INTERNATIONAL

AVERAGE OR MOST

COMMON 

PATTERN ON THE

FACTOR1

FACTOR ASSOCIATED

WITH U.S. RELATIVE 

PERFORMANCE2

APPENDIX TABLE WITH

SUPPORTING

INFORMATION

— Data not available.

1. Based on how the United States compares to the international average for the TIMSS countries for which data were available.

2. Based on whether the factor was associated with the relatively poor performance of the United States compared

to the other participating countries.

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut

Hill, MA: Boston College; and Organisation for Economic Cooperation and Development. (1997). Education at a

Glance: OECD Indicators 1997. Paris: OECD.

DIFFERENTIATION IN LESS NO A5.12

SCHOOLS/PROGRAMS

DIFFERENTIATION IN LENGTH LESS NO A5.12

OF SECONDARY EDUCATION

AVERAGE AGE OF STUDENTS BELOW YES A5.13

PARTICIPATING IN THE 

ASSESSMENT

GRADE OF STUDENTS ASSESSED SAME NO A5.13

CURRENT ENROLLMENT SAME NO A5.14

IN SECONDARY EDUCATION

SECONDARY COMPLETION ABOVE NO A5.14

AMONG 25-34 YEAR OLDS

CURRICULAR GRADE-LEVEL ABOVE — NONE

EQUIVALENT OF THE 

ASSESSMENT

CENTRALIZATION OF LESS NO A5.15

DECISION-MAKING ABOUT 

CURRICULUM SYLLABI

GNP PER CAPITA ABOVE NO A5.16

PUBLIC EXPENDITURE ON ABOVE NO A5.16

ELEMENTARY/SECONDARY

EDUCATION PER CAPITA

TAKING MATHEMATICS IN FINAL BELOW NO A5.20

YEAR OF SECONDARY SCHOOL

HOURS OF HOMEWORK BELOW NO A5.20

DAILY USE OF CALCULATORS SAME NO A5.20

CALCULATOR USE ON TIMSS BELOW YES A5.20

USE OF COMPUTERS ABOVE NO A5.20

POSITIVE ATTITUDES TOWARD ABOVE NO A5.20

MATHEMATICS

THEFT OF PROPERTY AT ABOVE NO A5.20

SCHOOL

PERSONAL THREATS AT ABOVE NO A5.20

SCHOOL

AVERAGE HOURS WATCHING SAME NO A5.20

TV OR VIDEOS

AVERAGE HOURS WORKING ABOVE NO A5.20

AT A PAID JOB ON A NORMAL

SCHOOL DAY
70

FIGURE 26:

RELATIONSHIP BETWEEN U.S. RELATIVE PERFORMANCE AND SCHOOLING AND STUDENT FACTORS:

SCIENCE GENERAL KNOWLEDGE

FACTORS

U.S. COMPARED TO

INTERNATIONAL 

AVERAGE ON THE 

FACTOR1

FACTOR 

ASSOCIATED WITH

U.S. RELATIVE 

PERFORMANCE2

APPENDIX TABLE

WITH

SUPPORTING 

INFORMATION

— Data not available.

1. Based on how the United States compares to the international average for the TIMSS countries for which data were available.

2. Based on whether the factor was associated with the relatively poor performance of the United States compared

to the other participating countries.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut

Hill, MA: Boston College.

CURRICULAR GRADE-LEVEL ABOVE — NONE

EQUIVALENT OF THE 

ASSESSMENT

TAKING SCIENCE IN FINAL BELOW NO A5.20

YEAR OF SECONDARY 

SCHOOL

POSITIVE ATTITUDES TOWARD ABOVE NO A5.20

CHEMISTRY

POSITIVE ATTITUDES TOWARD ABOVE NO A5.20

EARTH SCIENCE

POSITIVE ATTITUDES TOWARD ABOVE NO A5.20

PHYSICS

POSITIVE ATTITUDES TOWARD SAME NO A5.20

BIOLOGY

SCIENCE 

GENERAL KNOWLEDGE
71

that outperformed the United States to

how they correspond to the United

States and the countries that performed

similarly or worse than we did.

Most of the factors related to students’

lives do not seem to account for U.S.

students’ relatively poor performance

either. Among these factors, this is the

case for mathematics and science

coursetaking during the final year of

secondary school, hours spent on

homework or studying, the use of calculators, the use of computers, positive

attitudes toward mathematics and science, personal safety in school, television and video watching, and hours

spent working at a paid job. Only the

percentage of students using a calculator during the TIMSS mathematics general knowledge assessment is related to

the U.S. performance on the mathematics general knowledge assessment relative to the other TIMSS nations.

Countries in which a higher percentage

of students used a calculator on the

TIMSS mathematics general knowledge

assessment were more likely to outperform the United States than countries

with a similar or lower percentage of

student calculator use on the mathematics general knowledge assessment.

Eleven of the 12 countries with higher

student calculator use during the TIMSS

assessment than the United States performed better than the United States in

mathematics general knowledge.

Moreover, 5 of the 8 countries with similar or lower student calculator use during the assessment than the United

States performed similar to or lower

than the United States in mathematics

general knowledge. However, it is

unclear whether using a calculator

helped students score higher on the

TIMSS mathematics general knowledge

assessment, or whether more able students were more likely to use a calculator on the assessment.

While most of the factors examined

above do not appear to be associated

with the relatively poor performance of

the United States at twelfth grade in

comparison with other nations, we now

turn to the question of whether any of

these same factors can explain the differences in the relative performance of

U.S. students in TIMSS at eighth grade

and at twelfth grade. 

Why Do U.S. Students Perform

More Poorly Relative To The

International Average At The End Of

Secondary Schooling Than In Eighth

Grade?

The performance of all U.S. students

was poorer in twelfth grade than in

eighth grade relative to the other 19

countries which participated in TIMSS

at both levels. One factor that does seem

to be associated with whether countries’

relative position differed between the

eighth grade and the end of secondary

school general knowledge assessments is

the average age of the students

participating in the two assessments in

each country (Figure 27).

As indicated previously, there was

considerable variation across the

countries in the average age of students

participating in the general knowledge

assessments. This variation reflects two

factors: the age at which students begin

first grade (six in most countries, seven

in a few) and the highest grade in secondary education (ranging from 10 to

14, depending on the country and the

student’s program). In countries where

some of the students participating in the
72

FIGURE 27:

RELATIONSHIP BETWEEN U.S. RELATIVE PERFORMANCE AND EDUCATION SYSTEM FACTORS: 

GRADE EIGHT AND END OF SECONDARY SCHOOL

MATHEMATICS

FACTORS

U.S. COMPARED TO

INTERNATIONAL 

AVERAGE ON THE 

FACTOR1

FACTOR ASSOCIATED

WITH DIFFERENCE IN 

RELATIVE

PERFORMANCE IN

EIGHTH GRADE AND

END OF SCHOOL 

ASSESSMENTS2

APPENDIX TABLE WITH

SUPPORTING 

INFORMATION

SCIENCE

1. Based on how the United States compares to the international average for the TIMSS countries for which data

were available.

2. Based on whether the factor was associated with the lower relative standing of the United States compared to

the international average in twelfth grade than in eighth grade.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut

Hill, MA: Boston College.

AGE OF STUDENTS IN END BELOW YES A5.17

OF SECONDARY SCHOOL

ASSESSMENT

PROPORTION CURRENTLY BELOW NO A5.18

TAKING MATHEMATICS 

AT END OF 

SECONDARY SCHOOL

AGE OF STUDENTS IN END BELOW YES A5.19

OF SECONDARY SCHOOL

ASSESSMENT

PROPORTION CURRENTLY BELOW NO A5.18

TAKING SCIENCE 

AT END OF 

SECONDARY SCHOOL

end of secondary school assessment were

in grades above 12, the average age tended to be older. As a result, the average

age of students taking the end of secondary school assessment ranged from

16.9 to 21.2 years.

There was also variation, though less so,

in the average age of students participating in the middle school assessment.

The targeted population in that assessment was the two grades with the largest

number of 13-year olds at the beginning

of the school year. In most countries, the

grades were seven and eight, but in a few

countries—generally those in which first

grade begins at age seven—the grades

assessed were six and seven. The “eighth

grade” comparisons were based on

eighth graders for the former countries

and seventh graders for the latter.

Although the ages were generally comparable across countries, the average age

for each country was affected by factors

such as the exact timing of the assessment and the variation in age within

grades. The country averages for students in the eighth grade comparisons
73

ranged from 13.6 to 15.4 years.

In the countries whose standing relative

to the international average was more

favorable at the end of secondary

schooling than in eighth grade, the 

average age of the students participating

in TIMSS tended to be younger than the

international average in the “eighth

grade” assessment and older than the

international average in the end of

school assessment. In addition, in those

countries whose relative position was

less favorable in the end of school

assessment than it was in the eighth

grade assessment, the average age of the

students participating in the end of

school assessment tended to be below 

the average, which was the case for the

United States.

As a result of these patterns, the difference between the average age of the students participating in the two assessments was greater for countries whose

relative standing was more favorable at

the end of secondary schooling than for

countries whose relative standing was less

favorable at the end of secondary schooling than in eighth grade. On average, the

difference in age of the students participating in the two assessments was about 5

years 3 months in countries whose relative standing was more favorable at the

end of secondary schooling and 3 years 6

months in countries with a less-favorable

standing at the end of secondary school

(Tables A5.17 and A5.19 in Appendix 5). 

Countries where more students were taking mathematics in their final year of secondary school were not more likely to

have a higher relative standing in twelfth

grade compared to their standing in

eighth grade. In fact, for mathematics,

countries whose relative standing was less

favorable in twelfth grade had a higher

proportion of students enrolled in mathematics in the final year of secondary

schooling, on average, than did those

whose relative standing was higher in

twelfth grade, although this pattern did

not hold for the United States. The

United States was the only country whose

relative standing was lower in twelfth

grade where the proportion of students

currently taking mathematics was below

the international average.

We now turn our attention to examining

the context in which advanced mathematics and physics students learn.

THE CONTEXT OF LEARNING FOR

ADVANCED MATHEMATICS AND

SCIENCE STUDENTS IN THE FINAL

YEAR OF SECONDARY SCHOOL

Decisions made by nations in how they

structure and provide secondary education affect all students, including

advanced mathematics and science students. This section examines how differences in the delivery and implementation of advanced mathematics and science courses among the TIMSS nations

relate to the performance of advanced

mathematics and science students. In

particular, this section will focus on

advanced science and mathematics students’ everyday experiences in school

and the classroom to learn more about

how aspects of their school lives may be

related to performance in physics and

advanced mathematics. 
How Do U.S. Physics and Advanced

Mathematics Students Compare

Internationally on Factors

Associated With Their Lives In

School?

Unlike a number of their U.S. peers,

most advanced mathematics and

advanced science students continue to

take mathematics or science courses in

their final year of secondary school. To

take advantage of this fact, TIMSS asked

physics and advanced mathematics students for information about their classroom experiences in those subjects.

Results from TIMSS indicate the following information about students who

took the physics and advanced mathematics assessments. (See Tables A5.21

and A5.22 in Appendix 5 for detailed

summary information.)

Homework

Students enrolled in mathematics and in

physics in the last year of secondary

school were asked how frequently they

were assigned homework in these subjects. U.S. twelfth-grade physics and

advanced mathematics students more frequently reported being assigned homework three or more times per week than

the international average. Half of U.S.

twelfth-grade physics students (51 percent) reported being assigned physics

homework three or more times a week

compared to the international average of

forty percent for advanced science students. Among advanced mathematics students, 90 percent of U.S. students reported this much homework in mathematics,

while the international average was 65

percent.

Calculators

A higher percentage of U.S. physics and

advanced mathematics students reported

using a calculator on a daily basis than

their international counterparts.

Approximately 80 percent of both U.S.

advanced mathematics and physics students reported using a calculator on a

daily basis. The international average for

both subjects was about 70 percent. As

with the mathematics and science general knowledge assessments, students in

all TIMSS nations were provided the

opportunity to use calculators during

the physics and advanced mathematics

assessments. More U.S. students who

took the advanced mathematics assessment reported using a calculator during

the assessment (86 percent) than the

international average (76 percent).

Among U.S. students who took the

physics assessment, 81 percent of students reported using a calculator during

the assessment, similar to the international average (79 percent).

Hours of Instruction

TIMSS asked physics and advanced mathematics students to report on the number

of hours of mathematics or physics

instruction they received each week.

Among U.S. twelfth-grade advanced

mathematics students who were currently

taking a mathematics course, a much

lower percentage reported receiving five

or more hours of mathematics instruction

per week than the international average.

Twelve percent of U.S. advanced mathematics students stated that they received

five or more hours of mathematics

instruction per week, compared to an

international average of 37 percent. 

74
75

In physics, the pattern was the reverse.

A higher percentage of U.S. twelfthgrade physics students currently taking

physics reported receiving five or more

hours of physics instruction per week

than the international average. Seventeen

percent of U.S. physics students stated

that they received five or more hours of

physics instruction per week; the international average was 8 percent.

Computers

TIMSS queried students in advanced

mathematics or physics courses about

using computers to solve exercises or

problems in their lessons. U.S. students

were more likely to report using a computer in these subjects than the international average. Thirty-four percent of

U.S. advanced mathematics and 42 percent of U.S. physics students reported

being asked to use a computer to solve

exercises or problems during at least

some lessons, which is higher than the

international average for both groups,

28 percent and 29 percent respectively.

Reasoning Tasks

Among the many aspects of classroom

instruction that experts have targeted for

improvement is providing opportunities

for students to develop and improve

their reasoning skills. To obtain a measure of how often students are asked to

do reasoning tasks in class, TIMSS

queried students whether they have

been asked by their teachers to do any of

the following: explain their reasoning

behind an idea; represent and analyze

relationships using tables, charts, or

graphs; work on problems for which

there is no immediately obvious method

or solution; or write equations to represent relationships. Based on the

responses to these questions, U.S. students in both subjects were more likely

to report being asked to do reasoning

tasks than the international average.

Forty-three percent of U.S. twelfth-grade

advanced mathematics students reported that they were asked to do at least

one of these reasoning tasks in “every

mathematics lesson,” while the international average was 32 percent. Among

U.S. physics students, 36 percent

reported that they were asked to do at

least one of these reasoning tasks in

“every physics lesson,” compared to the

international average of approximately

23 percent.

Laboratory Experiments

Another area of education that has

received much attention is the use of

experiments to enhance students’

learning of concepts and knowledge in

science. When queried whether they

were asked to conduct laboratory

experiments during physics lessons, 96

percent of U.S. physics students replied

affirmatively, which was higher than the

international average (79 percent) of

advanced science students who replied

similarly. More U.S. physics students

stated that they were asked to conduct

laboratory experiments than students in

10 of the 15 other TIMSS nations that

participated in the physics assessment. 
76

Connecting Mathematics to Everyday

Problems

Some experts believe that one way to

improve students’ interest in mathematics

is to connect it to everyday, real-world

problems rather than just to abstract

concepts. U.S. advanced mathematics

students were more likely to report that

they were asked to connect mathematics

to everyday problems, than the

international average (85 and 68 percent

respectively) (Figure 28). More U.S.

advanced mathematics students reported

that they were asked to apply mathematics

to everyday problems in their

mathematics lessons than students in 13 of

the 15 other nations that participated in

the advanced mathematics assessment.

Are Any Of These Instructional

Experiences Of Physics And

Advanced Mathematics Students

Associated With U.S. Relative

Performance?

There does not appear to be a relationship between student performance in

physics or advanced mathematics and

most other instructional factors related

to advanced mathematics and physics

(see Figure 29 and Tables A5.21 and

A5.22 in Appendix 5). Only the percentage of advanced mathematics students who received five hours or more

of mathematics instruction per week was

related to the U.S. performance relative

to the other participating countries.

0

10

20

30

40

50

60

PERCENTA

GE OF STUDENTS

International Average

United States

Most

lessons

27

15

Every

lesson

16

5

Never/

almost

never

15

32

Some

lessons

48

42

FIGURE 28:

ADVANCED MATHEMATICS STUDENTS’ REPORTS ON CONNECTING MATHEMATICS TO

EVERYDAY PROBLEMS

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 7.4. Chestnut Hill, MA: Boston College.
77

FIGURE 29:

RELATIONSHIP BETWEEN U.S. RELATIVE PERFORMANCE AND INSTRUCTIONAL FACTORS: 

PHYSICS AND ADVANCED MATHEMATICS STUDENTS

ADVANCED MATHEMATICS

FACTORS

U.S. COMPARED TO

INTERNATIONAL 

AVERAGE ON THE 

FACTOR1

FACTOR

ASSOCIATED WITH

U.S. RELATIVE

PERFORMANCE2

APPENDIX TABLE

WITH SUPPORTING 

INFORMATION

PHYSICS

1. Based on how the United States compares to the international average for the TIMSS countries participating in

the assessment.

2. Based on whether the factor was associated with the relatively poor performance of the United States on the

assessment compared to the other participating countries.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut

Hill, MA: Boston College.

HOMEWORK ASSIGNMENTS ABOVE NO A5.21

DAILY USE OF CALCULATOR ABOVE NO A5.21

CALCULATOR USE ON TIMSS ABOVE NO A5.21

HOURS OF INSTRUCTION BELOW YES A5.21

USE OF COMPUTER IN ABOVE NO A5.21

LESSONS

ASKED TO DO REASONING ABOVE NO A5.21

TASKS IN LESSONS

CONNECT MATHEMATICS TO ABOVE NO A5.21

EVERYDAY PROBLEMS 

IN LESSONS

HOMEWORK ASSIGNMENTS ABOVE NO A5.22

DAILY USE OF CALCULATOR ABOVE NO A5.22

CALCULATOR USE ON TIMSS SAME NO A5.22

HOURS OF INSTRUCTION ABOVE NO A5.22

USE OF COMPUTER IN ABOVE NO A5.22

LESSONS

ASKED TO DO ABOVE NO A5.22

REASONING TASKS IN LESSONS

LABORATORY EXPERIMENTS ABOVE NO A5.22

IN LESSONS
78

Countries in which a higher percentage

of advanced mathematics students

received five or more hours of mathematics instruction per week were more

likely to outperform the U.S. than countries with a similar or lower percentage of

students receiving that amount of instruction. All seven countries in which a higher proportion of advanced mathematics

students received five or more hours of

mathematics instruction per week outperformed the United States on the

advanced mathematics assessment. Of

the seven countries in which the

advanced mathematics students were no

more likely than U.S. students to receive

five or more hours of mathematics

instruction per week, three performed

similar to and four outperformed the

United States.

A similar pattern was not found for the

amount of physics instruction that

advanced science students received per

week. However, it should be noted that

students were asked about the amount of

instruction they received in physics, not

in all science courses that they were taking. In many of the TIMSS countries, a

substantial proportion of students take

more than one science course in the final

year of secondary school.16

DISCUSSION

We have examined the early evidence

from TIMSS and other sources comparing the United States to the international average of TIMSS countries

on various factors that many experts

believe are related to educational performance. When appropriate, we have

examined whether these differences are

associated with the relatively low performance of the United States in the

TIMSS mathematics and science general

knowledge, advanced mathematics, and

physics assessments. Initial evidence

does not point definitively to any factor,

or group of factors, that would explain

U.S. students’ performance in comparison with their international peers.

We did note, however, that two factors—

the average age of students at the time of

the assessment and the percentage of

students who reported using a calculator

during the assessment—were associated

with U.S. students’ general knowledge of

mathematics compared to students in

other countries. Also, one factor—the

percentage of students who received at

least five hours of mathematics instruction per week—was associated with the

relative performance of the students in

advanced mathematics.

In addition, one factor that appears to be

associated with differences in countries’

relative position between eighth grade

and the end of secondary school is the

average age of the students participating

in the two assessments in each country. 
79

Further analyses may reveal underlying

patterns that are not apparent in these

initial results. For example, while the

factors we have examined may not

explain our performance relative to

most of the countries that outperformed us, some could be influential

relative to at least one of the countries.

Furthermore, many of these factors are -

inter-related and this analysis looked at

each factor separately.

It is important to note that while most of

the student characteristics that we examined did not explain U.S. performance

relative to other countries, many were

related to individual student performance within the United States and other

countries. For example, although country averages for television watching,

homework, and mathematics and science course-taking were not related to

average performance, individual students who watched less television, did

more homework, and took mathematics

and science during the final year of secondary school generally outperformed

their peers.17 While this may seem counter-intuitive, it can arise when there are

country-level factors that influence performance for all students in a similar

manner. Additional analyses are needed

to understand more fully the interrelationships among individual and countrylevel factors.
CONCLUSIONS
81

This report has presented highlights

from the initial analyses of the academic

performance of the U.S. twelfth graders

in comparison with performance of students from other countries at the end of

secondary education. The performance

of U. S. students in mathematics and science at the end of secondary school is

among the lowest of those countries participating in TIMSS. This is true for all

students as well as for students in

advanced mathematics and in physics.

The report has also presented the evidence available from early analyses concerning why U.S. students’ performance

is one of the lowest among the participating TIMSS countries. TIMSS does

not suggest any single factor or combination of factors that can explain why

our performance is so low. From our initial analyses, it also appears that some

factors commonly thought to influence

individual student performance are not

strongly related to performance when

comparing average student performance across countries.

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.
82

1. National Council of Teachers of

Mathematics. (1989). Curriculum and

Evaluation Standards for School

Mathematics. Reston, VA: National

Council of Teachers of Mathematics.

2. National Council of Teachers of

Mathematics. (1991). Professional

Standards for Teaching Mathematics.

Reston, VA: National Council of

Teachers of Mathematics. 

3. American Association for the

Advancement of Science. (1993).

Benchmarks for Science Literacy. New York:

Oxford Press.

4. National Academy of Sciences.

(1996). National Science Education

Standards. Washington, DC: National

Academy Press. 

5. Mullis, I.V.S., Martin, M.O., Beaton,

A.E., Gonzalez, E.J., Kelly, D.L., and

Smith, T.A. (1998). Mathematics and

Science Achievement in the Final Year of

Secondary School. Chestnut Hill, MA:

Boston College.

6. Elley, W.B. (1992). How in the World

Do Students Read? The Hague,

Netherlands: International Association

for the Evaluation of Educational

Achievement.

7. Pelgrum, H. and Plomp, T. (1993).

International IEA Computers in Education

Study. New York: Pergamon Press.

8. U.S. Department of Education,

National Center for Education Statistics.

(1996). Pursuing Excellence: A Study of

U.S. Eighth-Grade Mathematics and Science

Teaching, Learning, Curriculum, and

Achievement in International Context.

NCES 97-198. Washington, DC: National

Center for Education Statistics.

9. U.S. Department of Education,

National Center for Education Statistics.

(1997). Pursuing Excellence: A Study of

U.S. Fourth-Grade Mathematics and Science

Achievement in International Context.

NCES 97-255. Washington, DC: National

Center for Education Statistics.

10. Martin, M. and Kelly, D. (1996).

Third International Mathematics and

Science Study: Technical Report, Volume 1:

Design and Development. Chestnut Hill,

MA: Boston College; and Martin, M. and

Mullis, I.V.S. (1996). Third International

Mathematics and Science Study: Quality

Assurance in Data Collection. Chestnut

Hill, MA: Boston College.

11. Mullis, I.V.S., Martin, M.O., Beaton,

A.E., Gonzalez, E.J., Kelly, D.L., and

Smith, T.A. (1998). Mathematics and

Science Achievement in the Final Year of

Secondary School. Chestnut Hill, MA:

Boston College.

12. Carey, N., Farris, E., and Carpenter, J.

(1994). Curricular Differentiation in

Public High Schools. NCES 95-360.

Washington, DC: National Center for

Education Statistics.

13. Organisation for Economic

Cooperation and Development. (1997).

Education at a Glance: OECD Indicators

1997. Paris: OECD.

WORKS

CITED
14. Schmidt, W. (forthcoming). Facing

the Consequences: Using TIMSS for a Closer

Look at United States Mathematics and

Science Education. Hingham, MA: Kluwer.

15. Madigan, T. (1997). Science

Proficiency and Course Taking in High

School. NCES 97-838. Washington, DC:

National Center for Education Statistics;

Rock, D., and Pollack, J.(1995).

Mathematics Course-Taking and Gains in

Mathematics Achievement. NCES 95-714.

Washington, DC: National Center for

Education Statistics; Owings, J.A. and

Lee, R. (1994). Changes in Math

Proficiency between 8th and 10th Grade.

NCES 93-455. Washington, DC: National

Center for Education Statistics; and

Hoffer, T.B., Radinski, K.A., and Moore,

W. (1995). Social Background Differences

in High School Mathematics and Science

Coursetaking and Achievement. NCES 95-

206. Washington, DC: National Center

for Education Statistics.

16. Mullis, I.V.S., Martin, M.O., Beaton,

A.E., Gonzalez, E.J., Kelly, D.L., and

Smith, T.A. (1998). Mathematics and

Science Achievement in the Final Year of

Secondary School. Chestnut Hill, MA:

Boston College.

17. Ibid. (1998).

83
APPENDICES
85

Twenty-three nations participated in the

study. Twenty-one participated in the

general assessments, while two other

nations (Greece and Latvia) only participated in one or both of the advanced

assessments.

To identify comparable groups across

countries for the three assessments, 

TIMSS countries were asked to identify

eligible students in terms of common

definitions, after adapting the definitions

to country-specific situations. Students in

the mathematics and science general

knowledge assessments were to be 

in their final year of secondary school. 

For the advanced mathematics

assessment, eligible students were those

who had taken or were taking advanced

courses in mathematics. For the physics

assessment, students were those who 

had taken or were taking physics.

The international guidelines specified the

following sampling standards: 

■ the sample was to be representative of

at least 90 percent of students in the

total population eligible for the study.

Therefore, exclusion rates must be

under 10 percent. 

■ the school participation rate without

the use of replacement schools must

be at least 50 percent, and

■ the combined participation rate (the

product of school and student participation rates after replacements) must

be at least 75 percent, or school and

student participation rates must each

be 85 percent.

■ Countries were also required to submit

a sampling plan for approval by the

TIMSS International Study Center. 

Most of the TIMSS countries experienced

some deviation from international guidelines for execution of the study, at the

end of secondary school, in one or

more of the assessments. All deviations

from these guidelines are bolded in the

tables in Appendix 1. 

APPENDIX 1 

SUMMARY OF INTERNATIONAL STUDY GUIDELINES AND

DEFINITION OF ELIGIBLE STUDENTS
86

CZECH

REPUBLIC

Students in their final year of each type of

school. In technical schools and gymnasia,

students in Grades 12 and 13 were tested. In

vocational schools students in Grades 10, 11,

12 and 13 were tested, depending on their

vocation.

Exclusion rate: 6%

School participation rate

before replacement: 100%

Combined participation

rate: 92%

Nation Population and exclusion rate Whether met sampling

standards

(AUSTRALIA) Students in the final year of secondary

school, Grade 12, in government, Catholic,

and independent schools.

Exclusion rate: 6% 

School participation rate

before replacement: 49%, 

Combined participation

rate: 52% 

(AUSTRIA) Students in their final year of academic schools

(Grade 12), their final year of higher technical

and vocational school (Grade 13), their final

year of medium technical and vocational

school (Grades 10, 11, or 12 depending on the

vocational program of the student), and

students in their final year of apprenticeship

(Grades 12, 13, or 14).

Exclusion rate: 18% (students enrolled in

teacher training colleges and courses lasting

less than three years excluded).

School participation rate

before replacement: 36%,

Combined participation

rate: 73% 

(CANADA) Students in Grade 12 in all provinces except

in Grades 13 and 14 (depending on program) in Quebec; in Ontario, also students

completing the Ontario Academic Credits

(OAC) in Grade 13.

Exclusion rate: 9%

School participation rate

before replacement: 82%

Combined participation

rate: 68%

(CYPRUS) Students in Grade 12 of lycea and the technical schools. Vocational students in technical

schools were not tested. Students in the private

vocational schools were not included.

Exclusion rate: 22% (private and vocational

schools excluded) 

School participation rate

before replacement: 100%

Combined participation

rate: 98%

TABLE A1.1

NATIONS’ DEFINITIONS OF ELIGIBLE STUDENTS AND WHETHER MET SAMPLING STANDARDS:

MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE ASSESSMENTS
87

(DENMARK) Students in Grade 12 of the general secondary

and vocational schools were tested; however,

students finishing their formal schooling after

Folkeskole (Grade 9) were not tested.

Exclusion rate: 2% 

Did not follow sampling

procedures

School participation rate

before replacement: 55%

Combined participation

rate: 49%

(FRANCE) Students in their final year of preparation for all

types of the baccalauréat which includes students in Grade 12 or Grade 13 (depending on

the type of exam). Also tested were students in

the final year of preparation for the 

Brevet d’études professionnelles or the Certificat

d’aptitude professionnelle who will not continue

towards a baccalauréat (Grade 11).

Exclusion rate: 1% 

School participation rate

before replacement: 80% 

Combined participation

rate: 69%

(GERMANY) Students in their final year in the gymnasium

and the vocational education programs. This

corresponded to Grade 13 in the Laender of

the former West Germany and to Grade 12 in

the Laender of the former East Germany.

Exclusion rate: 11%

Did not follow sampling

procedures

School participation rate

before replacement: 89% 

Combined participation

rate: 80%

HUNGARY Students in their final year of academic secondary and vocational schools (Grade 12)

and students in the final in-school year of

trade school (Grade 10).

Exclusion rate: 0% 

School participation rate

before replacement: 100% 

Combined participation

rate: 98%

(ICELAND) Students who were to graduate that year

from an upper secondary school, that is, students in Grades 12, 13, and 14.

Exclusion rate: 0% 

School participation rate

before replacement: 100% 

Combined participation

rate: 74%

TABLE A1.1 (CONTINUED)

MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE ASSESSMENTS

Nation Population and exclusion rate Whether met sampling

standards
88

(RUSSIAN

FEDERATION)

Students in final year, Grade 11, of general

secondary school. Students in vocational

programs were not tested.

Exclusion rate: 43% (vocational schools and

non-Russian speaking students excluded).

School participation rate

before replacement: 93% 

Combined participation

rate: 90%

Nation Population and exclusion rate Whether met sampling

standards

(ITALY) Students in all types of schools in their final year

of secondary school. The final grade of school

depended on their focus of study within the

school type, ranging from Grade 11 to Grade

13. Students in private schools were not tested.

Exclusion rate: 30% (four regions of 20 were

excluded).

School participation rate

before replacement: 60% 

Combined participation

rate: 62%

(LITHUANIA) Students in final year, Grade 12 in vocational,

gymnasia, and secondary schools where

Lithuanian is the language of instruction.

Schools not under the authority of the Ministry

of Education or the Ministry of Science were

excluded.

Exclusion rate: 16% (schools where Lithuanian

was not the language of instruction).

School participation rate

before replacement: 97% 

Combined participation

rate: 85%

(NETHERLANDS) Students in final year, Grade 12 of 6-year preuniversity program; students in final year,

Grade 11, in 5-year senior general secondary

program; and students in the second year,

Grade 12, of a two to four year senior secondary vocational program. Students in

apprenticeship programs were not tested.

Exclusion rate: 22% (short senior vocational

and apprenticeship programs excluded).

Did not follow sampling

procedures

School participation rate

before replacement: 36% 

Combined participation

rate: 49%

NEW

ZEALAND

Students in Grade 12 and students in Grade 11

who were not returning to school for Grade 12.

Exclusion rate: 0% 

School participation rate

before replacement: 87% 

Combined participation rate:

81%

(NORWAY) Students in Grade 12 in all areas of study.

Exclusion rate: 4% 

School participation rate

before replacement: 74% 

Combined participation

rate: 71%

TABLE A1.1 (CONTINUED)

MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE ASSESSMENTS
89

Nation Population and exclusion rate Whether met sampling

standards

(SLOVENIA) Students in Grade 12 in gymnasia and in

technical secondary schools, and students

in Grade 11 in vocational schools. Students

finishing vocational school in Grades 9 and

10 were not tested.

Exclusion rate: 6% 

Did not follow sampling

procedures

School participation rate

before replacement: 46% 

Combined participation

rate: 42%

(SOUTH

AFRICA)

Students in Grade 12.

Exclusion rate: 0% 

Did not follow sampling

procedures

School participation rate

before replacement: 65% 

Combined participation

rate: 65%

SWEDEN Students in Grade 12 in schools with the new

three-year upper-secondary school system,

and in the former two- or three-year system,

students in the final year, Grade 11 or 12,

respectively.

Exclusion rate: 0% 

School participation rate

before replacement: 95% 

Combined participation

rate: 82%

SWITZERLAND Students in their final year of gymnasium, general education, teacher training, and vocational training. This corresponded to Grade 11

or 12 in gymnasium (final year depending on

canton), Grade 12 in the general track; Grade

12 in the teacher-training track; and Grade 11,

12, or 13 in the vocational track (final year

varies by occupation).

Exclusion rate: 3% 

School participation rate

before replacement: 87% 

Combined participation

rate: 85%

TABLE A1.1 (CONTINUED)

MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE ASSESSMENTS

(UNITED

STATES)

Students in Grade 12.

Exclusion rate: 4% 

School participation rate

before replacement: 77% 

Combined participation

rate: 64%

NOTE: Nations not meeting international sampling or other guidelines are shown in parentheses. Specific 

deviations from these guidelines are bolded.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Appendix A,Tables B.4 and B.10, and Figure B.4. Chestnut Hill, MA: Boston College.
90

CZECH

REPUBLIC

Gymnasium students in their final year of

study, Grade 12 or 13. 

Exclusion rate: 6%

School participation rate

before replacement: 100% 

Combined participation

rate: 92%

(DENMARK) Mathematics and physics students in the

gymnasium and mathematics students in

their final year, Grade 12, of the technical or

higher preparation tracks.

Exclusion rate: 2%

Did not follow sampling

procedures 

School participation rate

before replacement: 55% 

Combined participation

rate: 49%

Nation Population and exclusion rate* Whether met sampling

standards

(AUSTRALIA) Students in their final year of senior secondary,

Grade 12, enrolled in mathematics courses

(varies across states) preparing them for postsecondary study, and students in Grade 12

who took such mathematics courses during

Grade 11.

Exclusion rate: 6%

School participation rate

before replacement: 47% 

Combined participation

rate: 55%

(AUSTRIA) Students in their final year of the academic

(Grade 12) or higher technical (Grade 13)

track, taking courses in advanced mathematics.

Exclusion rate: 18% (students enrolled in

teacher training colleges and courses lasting

less than three years excluded).

School participation rate

before replacement: 37% 

Combined participation

rate: 81%

CANADA Students in their final year in mathematics

courses preparing them for postsecondary

study, Grade 12 or 13 (varies by province),

except in Quebec where students in the

two-year science program were tested.

Exclusion rate: 9%

School participation rate

before replacement: 85% 

Combined participation

rate: 77%

(CYPRUS) Students in their final year (Grade 12) in the

mathematics/science program of study at

the lyceum.

Exclusion rate: 22% (private and vocational

schools excluded).

School participation rate

before replacement: 100% 

Combined participation

rate: 96%

TABLE A1.2

NATIONS’ DEFINITIONS OF ELIGIBLE STUDENTS AND WHETHER MET SAMPLING STANDARDS:

ADVANCED MATHEMATICS ASSESSMENT
91

Nation Population and exclusion rate* Whether met sampling

standards

FRANCE Students in their final year of the scientific

track, Grade 12, preparing the baccalauréat

général.

Exclusion rate: 1%

School participation rate

before replacement: 90%

Combined participation rate:

77%

(GERMANY) Students in their final year, Grade 12 or 13

depending on the Laender, in advanced

mathematics courses (three to five periods per

week).

Exclusion rate: 11%

School participation rate

before replacement: 79% 

Combined participation rate:

78%

GREECE Students in their final year, Grade 12, of the

general (academic) Lyceum and of the multibranch Lyceum, taking advanced courses in

mathematics and/or science in preparation for

university disciplines requiring mathematics.

Exclusion rate: 0%

School participation rate

before replacement: 76% 

Combined participation rate:

87%

TABLE A1.2 (CONTINUED)

ADVANCED MATHEMATICS ASSESSMENT

(ITALY) Students in their final year of Liceo Scientifico

(classical schools), Grade 11, 12, or 13,

depending on the program of study, and

Instituti Technici (technical schools), Grade 13.

Exclusion rate: 30% (four regions of 20 were

excluded).

School participation rate

before replacement: 70% 

Combined participation rate:

68%

(LITHUANIA) Students in their final year, Grade 12, of the

mathematics and science gymnasia and students in secondary schools offering enhanced

curriculum in mathematics.

Exclusion rate: 16% (schools where Lithuanian

was not the language of instruction).

School participation rate

before replacement: 100% 

Combined participation

rate: 92%

(RUSSIAN

FEDERATION)

Students in their final year, Grade 11, in general secondary schools in advanced mathematics courses or advanced mathematics

and physics courses.

Exclusion rate: 43% (vocational schools and

non-Russian speaking students excluded).

School participation rate

before replacement: 98%

Combined participation

rate: 96%
92

Nation Population and exclusion rate* Whether met sampling

standards

SWEDEN Students in their final year, Grade 12, of the

Natural Science or Technology lines.

Exclusion rate: 0%

School participation rate

before replacement: 95%

Combined participation

rate: 89%

SWITZERLAND Students in their final year, Grade 12 or 13, of

the scientific track of the Maturitätsschule

(gymnasium) in schools and programs (A-E)

with federal recognition.

Exclusion rate: 3%

School participation rate

before replacement: 99% 

Combined participation

rate: 87%

(UNITED

STATES)

Students in Grade 12 who had taken or

were taking Advanced Placement calculus,

calculus, or pre-calculus.

Exclusion rate: 4%

School participation rate

before replacement: 76% 

Combined participation

rate: 67%

TABLE A1.2 (CONTINUED)

ADVANCED MATHEMATICS ASSESSMENT

(SLOVENIA) Students in their final year of gymnasium

and technical and professional schools,

Grade 12, all of whom were taking

advanced mathematics courses.

Exclusion rate: 6%

Did not follow sampling

procedures

School participation rate

before replacement: 46% 

Combined participation

rate: 42%

NOTE: Nations not meeting international sampling or other guidelines are shown in parentheses. Specific

deviations from these guidelines are bolded.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Appendix A,Tables B.4 and B.11, and Figure B.5. Chestnut Hill, MA: Boston College.

* Sample exclusion rates are based on all students in the final year of secondary school, not just those eligible to

participate in the advanced mathematics assessment.
93

Nation Population and exclusion rate* Whether met sampling

standards

(AUSTRALIA) Students in the final year of secondary school,

Grade 12, enrolled in Year 12 physics.

Exclusion rate: 6%

School participation rate

before replacement: 63%

Combined participation rate:

54%

(AUSTRIA) Students in their final year of the academic

(Grade 12) or higher technical (Grade 13)

track, taking courses in physics.

Exclusion rate: 18% (Students enrolled in

teacher training colleges and courses lasting

less than three years excluded).

School participation rate

before replacement: 37% 

Combined participation rate:

81%

(CANADA) Students in their final year in physics courses

preparing them for post-secondary study,

Grade 12 or 13 (varies by province), except in

Quebec where students in the two-year

science program were tested.

Exclusion rate: 9%

School participation rate

before replacement: 80%

Combined participation rate:

73%

(CYPRUS) Students in their final year (Grade 12) of the

mathematics/science program of study at the

lyceum.

Exclusion rate: 22% (private and vocational

schools excluded). 

School participation rate

before replacement: 100%

Combined participation rate:

96%

TABLE A1.3

NATIONS’ DEFINITIONS OF ELIGIBLE STUDENTS AND WHETHER MET SAMPLING STANDARDS:

PHYSICS ASSESSMENT

CZECH

REPUBLIC

Gymnasium students in their final year of

study, Grade 12 or 13.

Exclusion rate: 6%

School participation rate

before replacement: 100%

Combined participation rate:

92%

(DENMARK) Mathematics and physics students in the

gymnasium and physics students in their final

year, Grade 12, of the technical track.

Exclusion rate: 2%

Did not follow sampling 

procedures 

School participation rate

before replacement: 55%

Combined participation rate:

47%
94

Nation Population and exclusion rate* Whether met sampling

standards

FRANCE Students in their final year of the scientific

track, Grade 12, preparing for the baccalauréat général.

Exclusion rate: 1%

School participation rate

before replacement: 90% 

Combined participation rate:

77%

(GERMANY) Students in the final year, Grade 12 or 13

depending on the Laender, in physics courses

(3 to 5 periods per week). 

Exclusion rate: 11%

School participation rate

before replacement: 77% 

Combined participation rate:

82%

GREECE Students in their final year, Grade 12, of the general (academic) Lyceum and the multi-branch

Lyceum taking advanced courses in mathematics and/or science in preparation for

university disciplines requiring physics.

Exclusion rate: 0%

School participation rate

before replacement: 76% 

Combined participation rate:

87%

TABLE A1.3 (CONTINUED)

PHYSICS ASSESSMENT

(LATVIA) Students in Grade 12, enrolled in advanced

physics courses, in Latvian-speaking academic secondary schools.

Exclusion rate: 50% (non-Latvian-speaking

academic secondary schools).

School participation rate

before replacement: 84% 

Combined participation

rate: 77%

NORWAY Students in their final year, Grade 12, of the

three-year physics course in the general

academic branch.

Exclusion rate: 4%

School participation rate

before replacement: 78%

Combined participation

rate: 83%

(RUSSIAN

FEDERATION)

Students in their final year, Grade 11, in general

secondary schools in advanced physics courses

or advanced mathematics and physics courses.

Exclusion rate: 43% (vocational schools and

non-Russian-speaking students excluded).

School participation rate

before replacement: 98% 

Combined participation

rate: 95%

(SLOVENIA) Students in their final year of gymnasia,

Grade 12, taking the physics matura examination.

Exclusion rate: 6%

Did not follow sampling

procedures 

School participation rate

before replacement: 46% 

Combined participation

rate: 43%
95

Nation Population and exclusion rate* Whether met sampling

standards

SWEDEN Students in their final year, Grade 12, of the

Natural Science or Technology lines.

Exclusion rate: 0%

School participation rate

before replacement: 95% 

Combined participation rate:

89%

SWITZERLAND Students in their final year, Grade 12 or 13, of

the the Maturitätsschule (gymnasium) in schools

and programs (A-E) with federal recognition.

Exclusion rate: 3%

School participation rate

before replacement: 99%

Combined participation rate:

87%

(UNITED

STATES)

Students in Grade 12 who had taken

Advanced Placement physics or physics.

Exclusion rate: 4%

School participation rate

before replacement: 77% 

Combined participation

rate: 68%

TABLE A1.3 (CONTINUED)

PHYSICS ASSESSMENT

* Sample exclusion rates are based on all students in the final year of secondary school, not just those eligible to

participate in the physics assessment.

NOTE: Nations not meeting international sampling or other guidelines are shown in parentheses. Specific

deviations from these guidelines are bolded.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Appendix A,Tables B.4 and B.12, and Figure B.6. Chestnut Hill, MA: Boston College.
96
97

APPENDIX 2 

NATIONAL AVERAGE SCORES, PERCENTILES OF

ACHIEVEMENT, AND STANDARD ERRORS
98

MATHEMATICS SCIENCE

GENERAL KNOWLEDGE GENERAL KNOWLEDGE

NATION AVERAGE STANDARD AVERAGE STANDARD

ERROR ERROR

(AUSTRALIA) 522 9.3 527 9.8

(AUSTRIA) 518 5.3 520 5.6

(CANADA) 519 2.8 532 2.6

(CYPRUS) 446 2.5 448 3.0

CZECH REPUBLIC 466 12.3 487 8.8

(DENMARK) 547 3.3 509 3.6

(FRANCE) 523 5.1 487 5.1

(GERMANY) 495 5.9 497 5.1

HUNGARY 483 3.2 471 3.0

(ICELAND) 534 2.0 549 1.5

(ITALY) 476 5.5 475 5.3

(LITHUANIA) 469 6.1 461 5.7 

(NETHERLANDS) 560 4.7 558 5.3

NEW ZEALAND 522 4.5 529 5.2

(NORWAY) 528 4.1 544 4.1

(RUSSIAN FEDERATION) 471 6.2 481 5.7

(SLOVENIA) 512 8.3 517 8.2

(SOUTH AFRICA) 356 8.3 349 10.5

SWEDEN 552 4.3 559 4.4

SWITZERLAND 540 5.8 523 5.3

(UNITED STATES) 461 3.2 480 3.3

The 95 percent “plus or minus” confidence interval around each nation’s score is

two times the standard error.

MATHEMATICS GENERAL KNOWLEDGE INTERNATIONAL AVERAGE = 500

SCIENCE GENERAL KNOWLEDGE INTERNATIONAL AVERAGE = 500

NOTE: Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1

for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Tables 2.1 and

2.2. Chestnut Hill, MA: Boston College.

TABLE A2.1

NATIONAL AVERAGE SCORES AND STANDARD ERRORS:

MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE
99

PHYSICS ADVANCED MATHEMATICS

NATION AVERAGE STANDARD AVERAGE STANDARD

ERROR ERROR

(AUSTRALIA) 518 6.2 525 11.6

(AUSTRIA) 435 6.4 436 7.2

(CANADA)* 485 3.3 509 4.3

(CYPRUS) 494 5.8 518 4.3

CZECH REPUBLIC 451 6.2 469 11.2

(DENMARK) 534 4.2 522 3.4

FRANCE 466 3.8 557 3.9

(GERMANY) 522 11.9 465 5.6

GREECE 486 5.6 513 6.0

(ITALY) — — 474 9.6

(LATVIA) 488 21.5 — —

(LITHUANIA) — — 516 2.6

NORWAY 581 6.5 — —

(RUSSIAN FEDERATION) 545 11.6 542 9.2

(SLOVENIA) 523 15.5 475 9.2

SWEDEN 573 3.9 512 4.4

SWITZERLAND 488 3.5 533 5.0

(UNITED STATES) 423 3.3 442 5.9

PHYSICS INTERNATIONAL AVERAGE = 501

ADVANCED MATHEMATICS INTERNATIONAL AVERAGE = 501

— Data not available because nation did not participate in the assessment.

* Canada did not meet international sampling and other guidelines for the physics assessment, but did for the

advanced mathematics assessment. See Appendix 1 for details.

NOTE: Nations not meeting international sampling and other guidelines are shown in parentheses. See Appendix 1

for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Tables 5.1

and 8.1. Chestnut Hill, MA: Boston College.

The 95 percent “plus or minus” confidence interval around each nation’s score is

two times the standard error.

TABLE A2.2

NATIONAL AVERAGE SCORES AND STANDARD ERRORS:

PHYSICS AND ADVANCED MATHEMATICS
100

5th Percentile 25th Percentile 50th Percentile 75th Percentile 95th Percentile

AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.)

(AUSTRALIA) 357 (17.5) 459 (9.4) 523 (8.6) 585 (9.5) 684 (10.4)

(AUSTRIA) 393 (9.2) 461 (7.9) 515 (6.4) 573 (6.4) 653 (8.9)

(CANADA) 375 (5.8) 457 (4.6) 516 (4.5) 579 (3.8) 674 (5.3)

(CYPRUS) 329 (6.0) 395 (2.2) 442 (5.0) 493 (4.0) 572 (3.9)

CZECH REPUBLIC 328 (12.2) 394 (10.3) 450 (15.9) 530 (16.5) 648 (13.6)

(DENMARK) 406 (8.2) 487 (5.6) 548 (6.4) 609 (4.7) 689 (6.2)

(FRANCE) 392 (8.6) 468 (6.3) 523 (3.7) 578 (6.9) 655 (9.9)

(GERMANY) 347 (10.5) 432 (11.3) 494 (6.7) 554 (8.9) 652 (8.0)

HUNGARY 343 (3.8) 417 (3.1) 477 (3.8) 545 (3.5) 644 (6.6)

(ICELAND) 393 (5.3) 472 (4.0) 531 (3.0) 592 (3.2) 683 (6.6)

(ITALY) 336 (15.3) 417 (7.5) 475 (6.3) 534 (4.6) 619 (11.7)

(LITHUANIA) 329 (8.8) 412 (9.1) 470 (7.0) 529 (8.3) 606 (5.4)

(NETHERLANDS) 407 (5.7) 498 (7.1) 565 (6.1) 622 (5.2) 704 (16.0)

NEW ZEALAND 358 (7.4) 453 (7.0) 523 (6.3) 589 (5.2) 685 (6.7)

(NORWAY) 384 (7.7) 461 (6.1) 523 (4.1) 592 (4.5) 691 (6.8)

(RUSSIAN FEDERATION) 342 (6.4) 410 (4.8) 464 (6.0) 528 (7.8) 622 (16.6)

(SLOVENIA) 365 (13.7) 451 (8.5) 516 (7.4) 573 (6.6) 652 (5.7)

(SOUTH AFRICA) 264 (3.2) 304 (3.8) 337 (4.9) 380 (10.4) 532 (33.7)

SWEDEN 396 (6.4) 483 (5.1) 546 (4.8) 620 (4.1) 722 (6.8)

SWITZERLAND 395 (7.4) 478 (7.9) 539 (7.9) 601 (5.5) 684 (5.3)

(UNITED STATES) 325 (4.4) 395 (3.8) 454 (4.4) 521 (6.7) 621 (7.4)

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1

for details for each country.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table E.2. Chestnut Hill, MA: Boston College.

NATION

TABLE A2.3

PERCENTILES OF ACHIEVEMENT IN MATHEMATICS GENERAL KNOWLEDGE:

FINAL YEAR OF SECONDARY SCHOOL
101

5th Percentile 25th Percentile 50th Percentile 75th Percentile 95th Percentile

AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.)

(AUSTRALIA) 361 (14.5) 462 (12.2) 525 (8.5) 591 (13.6) 689 (4.0)

(AUSTRIA) 388 (5.6) 460 (8.3) 513 (7.3) 575 (9.6) 672 (23.5)

(CANADA) 396 (7.1) 475 (5.8) 529 (3.6) 588 (3.8) 673 (5.2)

(CYPRUS) 319 (8.7) 392 (11.6) 443 (5.6) 499 (7.5) 599 (10.8)

CZECH REPUBLIC 349 (9.5) 424 (9.2) 477 (11.6) 540 (12.1) 655 (12.8)

(DENMARK) 369 (6.1) 448 (4.9) 505 (5.6) 568 (7.0) 657 (5.4)

(FRANCE) 358 (7.9) 434 (5.4) 485 (8.4) 542 (7.9) 618 (5.6)

(GERMANY) 350 (12.2) 437 (7.4) 494 (6.7) 556 (6.3) 649 (11.1)

HUNGARY 342 (2.9) 410 (3.5) 463 (2.2) 524 (3.7) 624 (6.1)

(ICELAND) 429 (5.0) 497 (1.9) 545 (3.3) 598 (2.1) 680 (3.8)

(ITALY) 339 (11.4) 417 (6.5) 470 (4.6) 528 (6.0) 624 (17.2)

(LITHUANIA) 324 (13.5) 403 (7.5) 460 (7.4) 517 (4.6) 601 (9.1)

(NETHERLANDS) 421 (9.0) 498 (6.1) 556 (6.4) 616 (10.5) 702 (19.8)

NEW ZEALAND 369 (16.8) 467 (8.9) 530 (7.0) 592 (4.4) 683 (5.2)

(NORWAY) 404 (6.9) 480 (5.2) 539 (2.7) 600 (7.4) 706 (11.6)

(RUSSIAN FEDERATION) 338 (6.1) 418 (6.9) 476 (9.3) 541 (9.2) 638 (13.7)

(SLOVENIA) 384 (10.1) 459 (8.7) 514 (8.7) 571 (10.3) 662 (22.5)

(SOUTH AFRICA) 228 (4.8) 282 (4.3) 325 (6.3) 390 (18.2) 550 (22.1)

SWEDEN 420 (9.4) 495 (4.3) 551 (4.2) 617 (5.5) 724 (9.2)

SWITZERLAND 375 (10.6) 459 (6.9) 521 (5.0) 584 (4.9) 681 (9.2)

(UNITED STATES) 332 (8.0) 416 (4.6) 477 (3.3) 541 (4.9) 640 (8.0)

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1

for details for each country.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary

School. Table E.3. Chestnut Hill, MA: Boston College.

TABLE A2.4

PERCENTILES OF ACHIEVEMENT IN SCIENCE GENERAL KNOWLEDGE:

FINAL YEAR OF SECONDARY SCHOOL

NATION
102

TABLE A2.5

PERCENTILES OF ACHIEVEMENT IN ADVANCED MATHEMATICS:

FINAL YEAR OF SECONDARY SCHOOL

5th Percentile 25th Percentile 50th Percentile 75th Percentile 95th Percentile

AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.)

(AUSTRALIA) 337 (30.1) 456 (17.5) 530 (9.0) 597 (10.4) 692 (21.1)

(AUSTRIA) 283 (15.2) 379 (11.4) 443 (7.9) 497 (8.8) 577 (16.4)

CANADA 352 (7.1) 443 (5.4) 508 (4.8) 576 (7.2) 676 (10.1)

(CYPRUS) 371 (23.0) 465 (5.7) 523 (10.4) 574 (5.2) 651 (15.8)

CZECH REPUBLIC 320 (12.7) 399 (9.2) 454 (10.4) 524 (15.6) 665 (20.2)

(DENMARK) 403 (5.6) 474 (3.8) 523 (2.3) 572 (4.8) 643 (6.9)

FRANCE 439 (5.5) 511 (5.1) 558 (5.5) 603 (6.4) 673 (8.4)

(GERMANY) 328 (9.3) 408 (8.0) 463 (5.7) 522 (5.6) 605 (6.9)

GREECE 321 (35.1) 454 (11.6) 521 (6.4) 585 (5.1) 668 (12.7)

(ITALY) 314 (14.9) 419 (13.4) 477 (10.3) 534 (8.3) 622 (22.7)

(LITHUANIA) 388 (12.2) 461 (5.5) 512 (3.6) 567 (3.3) 666 (16.9)

(RUSSIAN FEDERATION) 360 (9.3) 465 (9.3) 539 (12.7) 618 (9.4) 730 (22.4)

(SLOVENIA) 330 (10.2) 408 (9.5) 473 (10.1) 537 (8.5) 630 (20.4)

SWEDEN 375 (7.9) 458 (10.5) 513 (11.4) 568 (7.0) 653 (13.6)

SWITZERLAND 401 (5.6) 473 (6.2) 525 (7.9) 587 (5.9) 691 (3.4)

(UNITED STATES) 292 (3.8) 375 (7.1) 437 (6.4) 504 (6.1) 609 (8.9)

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 

for details for each country.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table E.4. Chestnut Hill, MA: Boston College.

NATION
103

5th Percentile 25th Percentile 50th Percentile 75th Percentile 95th Percentile

NATION

AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.) AVERAGE (S.E.)

TABLE A2.6

PERCENTILES OF ACHIEVEMENT IN PHYSICS:

FINAL YEAR OF SECONDARY SCHOOL

(AUSTRALIA) 386 (11.8) 461 (3.3) 517 (6.6) 570 (8.5) 656 (11.9)

(AUSTRIA) 306 (11.9) 379 (11.3) 427 (5.9) 486 (10.1) 581 (22.3)

(CANADA) 346 (5.1) 429 (2.9) 482 (4.4) 539 (7.3) 633 (14.3)

(CYPRUS) 325 (8.0) 434 (10.9) 487 (4.9) 551 (9.0) 681 (28.8)

CZECH REPUBLIC 337 (4.5) 397 (6.2) 440 (6.6) 493 (12.3) 605 (29.5)

(DENMARK) 397 (8.4) 478 (4.3) 535 (5.9) 588 (6.1) 677 (15.2)

FRANCE 358 (9.4) 423 (6.8) 465 (4.1) 509 (3.1) 574 (8.3)

(GERMANY) 374 (13.2) 458 (16.2) 519 (12.0) 580 (19.1) 688 (10.1)

GREECE 333 (18.9) 431 (5.7) 495 (7.7) 545 (6.3) 619 (8.2)

(LATVIA) 348 (12.2) 418 (15.7) 474 (19.2) 540 (36.5) 687 (31.5)

NORWAY 432 (6.3) 517 (11.1) 578 (6.3) 646 (7.2) 727 (6.1)

(RUSSIAN FEDERATION) 368 (18.2) 468 (15.7) 544 (12.6) 619 (16.5) 722 (21.2)

(SLOVENIA) 332 (11.3) 457 (15.3) 528 (21.2) 598 (14.1) 689 (36.3)

SWEDEN 422 (12.2) 511 (8.9) 574 (6.6) 634 (6.6) 725 (6.7)

SWITZERLAND 353 (20.6) 430 (7.6) 479 (4.7) 540 (5.2) 648 (9.9)

(UNITED STATES) 331 (4.7) 384 (4.0) 420 (4.2) 458 (6.4) 520 (6.6)

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1

for details for each country.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table E.5. Chestnut Hill, MA: Boston College.
104
105

APPENDIX 3 

PERFORMANCE ON ASSESSMENT ITEM EXAMPLES BY COUNTRY
106

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

SOURCE: Third International Math and Science Study International Study Center, P-Value Almanac for Achievement

Items. Population 3 - Literacy. Chestnut Hill, MA: Boston College.

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH

REPUBLIC

(DENMARK)

(FRANCE)

(GERMANY)

HUNGARY

(ICELAND)

(ITALY)

(LITHUANIA)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(RUSSIAN

FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

SWEDEN

SWITZERLAND

(UNITED STATES)

INTERNATIONAL

AVERAGE

74.2

64.6

74.4

53.2

52.6

75.0

74.0

59.1

65.1

73.3

59.6

61.2

82.5

75.0

67.3

53.7

63.5

22.5

77.5

67.3

57.4

64.4

88.4

84.4

79.6

53.8

65.8

78.0

71.3

74.3

55.8

73.8

61.9

61.2

91.4

91.1

77.8

61.7

79.9

59.6

84.6

74.7

84.5

74.0

50.8

51.8

44.7

21.6

38.4

58.1

48.3

45.7

31.6

54.4

33.5

42.0

61.6

58.9

47.3

48.1

50.6

14.1

57.3

59.0

32.0

45.2

68.9

68.5

69.0

57.7

50.2

64.4

47.8

65.3

67.2

78.1

53.6

45.3

77.9

67.6

71.8

53.0

71.2

18.9

71.8

70.3

41.7

61.0

68.3

74.5

84.3

82.3

91.7

83.5

86.2

66.2

67.6

92.6

78.0

68.0

88.8

78.8

82.2

66.3

72.4

38.7

92.8

72.9

77.9

76.9

52.2

33.6

55.0

26.7

36.7

36.2

28.3

18.3

26.6

59.8

23.5

34.4

64.8

48.9

47.9

36.1

34.8

11.7

36.5

28.7

40.2

37.2

NATION

PERCENTAGE OF STUDENTS RESPONDING CORRECTLY

MATHEMATICS GENERAL

KNOWLEDGE ITEMS

SCIENCE GENERAL 

KNOWLEDGE ITEMS

FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 6 FIGURE 7 FIGURE 8

TABLE A3.1

PERFORMANCE ON ASSESSMENT ITEM EXAMPLES BY COUNTRY: 

MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE
107

— Did not participate in the assessment.

1. Canada did not meet international sampling or other guidelines for the physics assessment, but did for the

advanced mathematics assessment. See Appendix 1 for details.

2. Data not available.

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for details

for each country.

International average is the average of the national figures.

SOURCES: Third International Math and Science Study International Study Center, P-Value Almanac for Achievement

Items. Population 3 - Advanced Mathematics. Chestnut Hill, MA: Boston College;TIMSS International Study Center,

P-Value Almanac for Achievement Items. Population 3 - Physics. Chestnut Hill, MA: Boston College.

TABLE A3.2

PERFORMANCE ON ASSESSMENT ITEM EXAMPLES BY COUNTRY: 

PHYSICS AND ADVANCED MATHEMATICS

(AUSTRALIA)

(AUSTRIA)

(CANADA)1

(CYPRUS)

CZECH

REPUBLIC

(DENMARK)

FRANCE

(GERMANY)

GREECE

(ITALY)

(LATVIA)

(LITHUANIA)

NORWAY

(RUSSIAN

FEDERATION)

(SLOVENIA)

SWEDEN

SWITZERLAND

(UNITED STATES)

INTERNATIONAL

AVERAGE

60.0

22.9

55.4

62.9

44.2

39.9

64.5

31.1

65.5

45.5

—

48.1

—

61.7

39.8

50.0

62.9

18.9

48.3

76.1

36.6

60.9

35.1

42.9

66.9

61.9

46.0

29.1

33.7

—

48.9

—

35.4

39.9

64.4

62.5

62.4

50.2

34.5

19.0

28.4

51.2

24.6

38.7

38.6

26.5

32.0

41.8

—

31.1

—

42.9

25.2

48.0

43.6

27.4

34.6

51.1

73.1

54.5

91.5

70.3

77.1

52.5

83.2

—

66.4

—

81.8

72.0

82.8

75.3

71.3

40.8

69.6

60.5

47.9

45.1

33.0

29.4

33.7

16.9

42.6

52.8

—

39.3

—

44.4

43.2

49.1

31.5

43.2

49.0

41.4

53.3

50.6

22.0

67.9

3.5

40.9

17.9

59.6

40.1

—

42.9

—

44.5

29.2

53.8

19.8

29.7

12.0

36.7

NATION

PERCENTAGE OF STUDENTS RESPONDING CORRECTLY

ADVANCED

MATHEMATICS ITEMS PHYSICS ITEMS

FIGURE 13 FIGURE 14 FIGURE 15 FIGURE 19 FIGURE 20 FIGURE 21

(2)
108
109

APPENDIX 4 

SCORES AND STANDARD ERRORS FOR U.S. AP AND NON-AP

PHYSICS AND CALCULUS STUDENTS
110

417

416

474

448

453

418

2.6

3.0

3.0

2.3

2.2

3.1

460

463

507

487

497

474

8.4

8.9

7.1

6.1

10.4

11.2

MECHANICS

ELECTRICITY/

MAGNETISM

HEAT

WAVE 

PHENOMENA

MODERN

PHYSICS

OVERALL

NON-AP PHYSICS 

STUDENTS

AVERAGE STANDARD

ERROR

AP PHYSICS

STUDENTS

AVERAGE STANDARD

ERROR

NUMBERS AND

EQUATIONS

CALCULUS

GEOMETRY

OVERALL

NON-AP CALCULUS 

STUDENTS

AVERAGE STANDARD

ERROR

459

455

421

445

7.9

6.8

8.2

8.5

520

523

484

513

5.2

7.2

5.3

5.4

TABLE A4.1

U.S. AP AND NON-AP CALCULUS STUDENTS’ SCORES BY CONTENT AREA

SOURCE: Third International Mathematics and Science Study, unpublished tabulations.

SOURCE: Third International Mathematics and Science Study, unpublished tabulations.

AP CALCULUS

STUDENTS

AVERAGE STANDARD

ERROR

TABLE A4.2

U.S. AP AND NON-AP PHYSICS STUDENTS’ SCORES BY CONTENT AREA

CONTENT 

AREA

CONTENT 

AREA
111

APPENDIX 5

ADDITION AL SUPPOR TING MA TERIALS
112

NATION

(DENMARK)4

(ICELAND)

NEW ZEALAND6

(NORWAY)4

SWEDEN4

STANDING RELATIVE

TO THE INTERNATIONAL

AVERAGE1,2

EIGHTH

GRADE

FINAL

YEAR

ABOVE

ABOVE

ABOVE

BELOW

ABOVE

SAME

ABOVE

SAME

ABOVE

BELOW

BELOW

ABOVE

SAME

BELOW

ABOVE

ABOVE

BELOW

SAME

ABOVE

SAME3

SAME

ABOVE

ABOVE

BELOW

SAME

ABOVE

ABOVE

SAME

BELOW

ABOVE

BELOW

ABOVE

ABOVE

ABOVE

BELOW

SAME

BELOW

ABOVE

ABOVE

BELOW

TABLE 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

HIGHER IN FINAL YEAR OF

SECONDARY SCHOOL THAN IN

EIGHTH GRADE

(AUSTRIA)

(CANADA)

(CYPRUS)

(FRANCE)

(GERMANY)

(LITHUANIA)

(NETHERLANDS)

(SOUTH AFRICA)

SWITZERLAND5

SIMILAR IN FINAL YEAR OF

SECONDARY SCHOOL AS IN

EIGHTH GRADE

(AUSTRALIA)6

CZECH REPUBLIC

HUNGARY

(RUSSIAN FEDERATION)5

(SLOVENIA)

(UNITED STATES)

LOWER IN FINAL YEAR OF

SECONDARY SCHOOL THAN IN

EIGHTH GRADE

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(FRANCE) 

(GERMANY)

HUNGARY

(ICELAND)

(LITHUANIA)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(RUSSIAN FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

SWEDEN 

SWITZERLAND

(UNITED STATES)

1. Above: Nation's performance higher than the average at that grade for the twenty nations.

Same: Nation's performance not significantly different from the average at that grade for the twenty nations.

Below: Nation's performance lower than the average at that grade for the twenty nations.

2. International average is the average of the national figures for the twenty nations.

3. U.S. average performance is below the international average based on all 41 countries that participated in the

eighth grade portion of TIMSS.

4. Based on standing relative to the international average in seventh grade.

5. Based on standing relative to the international average in seventh or eighth grade, depending upon the system in

place in each canton (Switzerland) or age starting school (Russian Federation).

6. Based on standing relative to the international average in eighth or ninth grade, depending upon the system in

place in each state/territory (Australia) or age beginning primary school (New Zealand).

NOTE: Nations not meeting international sampling or other guidelines in the final year of secondary school assessment are shown in parentheses. See Appendix 1 for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 2 and

Figure 2.3. Chestnut Hill, MA: Boston College., Mullis et al. (1996). Mathematics Achievement in the Middle School Years.

Table 2. Chestnut Hill, MA: Boston College.

COMPARISON OF STANDING RELATIVE TO

THE INTERNATIONAL AVERAGE IN 

EIGHTH GRADE AND FINAL YEAR OF 

SECONDARY SCHOOL
113

NATION

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH REPUBLIC

HUNGARY

(ICELAND)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(SLOVENIA)

(UNITED STATES)

(ICELAND)

NEW ZEALAND4

(NORWAY)3

STANDING RELATIVE

TO THE INTERNATIONAL

AVERAGE1, 2

FOURTH

GRADE

FINAL

YEAR

ABOVE

ABOVE

SAME

BELOW

ABOVE

ABOVE

BELOW

ABOVE

BELOW

BELOW

ABOVE

ABOVE

SAME

SAME

SAME

BELOW

SAME

BELOW

ABOVE

ABOVE

SAME

SAME

SAME

BELOW

TABLE 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

HIGHER IN FINAL YEAR OF

SECONDARY SCHOOL THAN IN

FOURTH GRADE

(CANADA)

(CYPRUS)

(NETHERLANDS)

SIMILAR IN FINAL YEAR OF

SECONDARY SCHOOL AS IN

FOURTH GRADE

(AUSTRALIA)4

(AUSTRIA)

CZECH REPUBLIC

HUNGARY

(SLOVENIA)

(UNITED STATES)

LOWER IN FINAL YEAR OF

SECONDARY SCHOOL THAN IN

FOURTH GRADE

1. Above: Nation's performance higher than the average at that grade for the twelve nations.

Same: Nation's performance not significantly different from the average at that grade for the twelve nations.

Below: Nation's performance lower than the average at that grade for the twelve nations.

2. International average is the average of the national figures for the twelve nations.

3. Based on standing relative to international average in third grade.

4. Based on standing relative to international average in fourth or fifth grade, depending upon the system in place in

each state/territory (Australia) or age beginning primary school (New Zealand).

NOTE: Nations not meeting international sampling or other guidelines in the final year of secondary school 

assessment are shown in parentheses. See Appendix 1 for details for each country.

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 2.1.

Chestnut Hill, MA: Boston College; and Martin et al. (1997). Mathematics Achievement in the Primary School Years.

Tables 2 and 1.1. Chestnut Hill, MA: Boston College.

COMPARISON OF STANDING RELATIVE TO

THE INTERNATIONAL AVERAGE IN 

FOURTH GRADE AND FINAL YEAR OF

SECONDARY SCHOOL
1. Difference is calculated by subtracting average females’ score from average males’ score, based on 

unrounded averages.

2. Nations ordered based on size of difference between males’ and females’ scores, from lowest to highest.

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary

School. Table 2.4. Chestnut Hill, MA: Boston College.

TABLE A5.3

ACHIEVEMENT IN MATHEMATICS GENERAL KNOWLEDGE BY GENDER FOR

STUDENTS IN THEIR FINAL YEAR OF SECONDARY SCHOOL
115

NATION

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(FRANCE)

(GERMANY)

HUNGARY

(ICELAND)

(LITHUANIA)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(RUSSIAN FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

SWEDEN 

SWITZERLAND

(UNITED STATES)

(DENMARK)3

(FRANCE)

(ICELAND)

NEW ZEALAND4

SWITZERLAND5

STANDING RELATIVE

TO THE INTERNATIONAL

AVERAGE1, 2

EIGHTH

GRADE

FINAL

YEAR

ABOVE

ABOVE

ABOVE

BELOW

ABOVE

BELOW

BELOW

ABOVE

ABOVE

BELOW

BELOW

ABOVE

SAME

ABOVE

ABOVE

ABOVE

BELOW

ABOVE

SAME

ABOVE

SAME

ABOVE

ABOVE

BELOW

SAME

SAME

SAME

SAME

BELOW

ABOVE

BELOW

ABOVE

ABOVE

ABOVE

BELOW

SAME

BELOW

ABOVE

ABOVE

BELOW

TABLE 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

HIGHER IN FINAL YEAR OF SECONDARY

SCHOOL THAN IN EIGHTH GRADE

(AUSTRIA)

(CANADA)

(CYPRUS) 

(LITHUANIA)

(NETHERLANDS)

(NORWAY)3

(SOUTH AFRICA)

SWEDEN3

SIMILAR IN FINAL YEAR OF SECONDARY

SCHOOL AS IN EIGHTH GRADE

(AUSTRALIA)4

CZECH REPUBLIC

(GERMANY)

HUNGARY

(RUSSIAN FEDERATION)5

(SLOVENIA)

(UNITED STATES)

LOWER IN FINAL YEAR OF SECONDARY

SCHOOL THAN IN EIGHTH GRADE

1. Above: Nation's performance higher than the average at that grade for the twenty nations.

Same: Nation's performance not significantly different from the average at that grade for the twenty nations.

Below: Nation's performance lower than the average at that grade for the twenty nations.

2. International average is the average of the national figures for the twenty nations.

3. Based on standing relative to the international average in seventh grade.

4. Based on standing relative to the international average in eighth or ninth grade, depending upon the system in

place in each state/territory (Australia) or age beginning primary school (New Zealand).

5. Based on standing relative to the international average in seventh or eighth grade, depending upon the system in

place in each canton (Switzerland) or age starting school (Russian Federation).

NOTE: Nations not meeting international sampling or other guidelines in the final year of secondary school assessment are shown in parentheses. See Appendix 1 for details for each country.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 2 and

Figure 2.4. Chestnut Hill, MA: Boston College., Mullis et al. (1996). Mathematics Achievement in the Middle School Years. Table 2. Chestnut Hill, MA: Boston College.

COMPARISON OF STANDING RELATIVE TO

THE INTERNATIONAL AVERAGE IN 

EIGHTH GRADE AND FINAL YEAR OF

SECONDARY SCHOOL
116

NATION

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH REPUBLIC

HUNGARY

(ICELAND)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(SLOVENIA)

(UNITED STATES)

(CANADA)

(ICELAND)

(NORWAY)3

STANDING RELATIVE

TO THE INTERNATIONAL

AVERAGE1, 2

FOURTH

GRADE

FINAL

YEAR

ABOVE

ABOVE

SAME

BELOW

ABOVE

SAME

BELOW

ABOVE

SAME

SAME

SAME

ABOVE

SAME

SAME

ABOVE

BELOW

SAME

BELOW

ABOVE

ABOVE

SAME

ABOVE

SAME

BELOW

TABLE 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

HIGHER IN FINAL YEAR OF SECONDARY

SCHOOL THAN IN FOURTH GRADE

(CYPRUS) 

(NETHERLANDS)

NEW ZEALAND4

(SLOVENIA)

SIMILAR IN FINAL YEAR OF SECONDARY

SCHOOL AS IN FOURTH GRADE

(AUSTRALIA)4

(AUSTRIA)

CZECH REPUBLIC

HUNGARY

(UNITED STATES)

LOWER IN FINAL YEAR OF SECONDARY

SCHOOL THAN IN FOURTH GRADE

1. Above: Nation's performance higher than the average at that grade for the twelve nations.

Same: Nation's performance not significantly different from the average at that grade for the twelve nations.

Below: Nation's performance lower than the average at that grade for the twelve nations.

2. International average is the average of the national figures for the twelve nations.

3. Based on standing relative to the international average in third grade.

4. Based on standing relative to the international average in fourth or fifth grade, depending upon the system in

place in each state/territory (Australia) or age beginning primary school (New Zealand).

NOTE: Nations not meeting international sampling or other guidelines in the final year of secondary school 

assessment are shown in parentheses. See Appendix 1 for details for each country.

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 2.2.

Chestnut Hill, MA: Boston College; and Martin et al. (1997). Science Achievement in the Primary School Years. Table 1.1.

Chestnut Hill, MA: Boston College.

COMPARISON OF STANDING RELATIVE TO

THE INTERNATIONAL AVERAGE IN 

FOURTH GRADE AND FINAL YEAR OF

SECONDARY SCHOOL
117

1. Difference is calculated by subtracting average females’ score from average males’ score, based on

unrounded averages.

2. Nations ordered based on size of difference between males’ and females’ scores, from lowest to highest.

NOTES:

Nations not meeting international sampling and other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 2.5. Chestnut Hill, MA: Boston College.

TABLE A5.6

ACHIEVEMENT IN SCIENCE GENERAL KNOWLEDGE BY GENDER FOR STUDENTS IN

THEIR FINAL YEAR OF SECONDARY SCHOOL
118

TABLE 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

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

SOURCE: Mullis et. al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Figures 5.1

and 8.1,Tables 5.1 and 8.1. Chestnut Hill, MA: Boston College.

ADVANCED MATHEMATICS

PERFORMED ABOVE THE U.S.

NATION AND

PERFORMANCE

RELATIVE TO THE U.S.

PERCENTAGE OF

AGE COHORT

REPRESENTED

NATION AND

PERFORMANCE

RELATIVE TO THE U.S.

PERCENTAGE OF

AGE COHORT

REPRESENTED

ADVANCED SCIENCE/PHYSICS

(AUSTRALIA) 16 (AUSTRALIA) 13

CANADA 16 (CANADA) 14

(CYPRUS) 9 (CYPRUS) 9

(DENMARK) 21 CZECH REPUBLIC 11

FRANCE 20 (DENMARK) 3

GREECE 10 FRANCE 20

(LITHUANIA) 3 (GERMANY) 8

(RUSSIAN FEDERATION) 2 GREECE 10

(SLOVENIA) 75 (LATVIA) 3

SWEDEN 16 NORWAY 8

SWITZERLAND 14 (RUSSIAN FEDERATION) 2

(SLOVENIA) 39

SWEDEN 16

SWITZERLAND 14

AVERAGE 18 12

PERFORMED SAME AS THE U.S.

(AUSTRIA) 33 (AUSTRIA) 33

CZECH REPUBLIC 11

(GERMANY) 26

(ITALY) 14

AVERAGE 21 33

(UNITED STATES) 14 (UNITED STATES) 14

INTERNATIONAL

AVERAGE 19 14
1. Difference is calculated by subtracting average females’ score from average males’ score, based on

unrounded averages.

2. Nations ordered based on size of difference between males’ and females’ scores, from lowest to highest.

NOTES

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1

for details for each country.

International average is the average of the national figures.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary

School. Table 5.4. Chestnut Hill, MA: Boston College.

TABLE A5.8

GENDER DIFFERENCES IN ADVANCED MATHEMATICS ACHIEVEMENT FOR

STUDENTS IN THEIR FINAL YEAR OF SECONDARY SCHOOL

HAVING TAKEN ADVANCED MATHEMATICS
NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School.

Table 6.2. Chestnut Hill, MA: Boston College.

TABLE A5.9

ACHIEVEMENT IN ADVANCED MATHEMATICS CONTENT AREAS BY GENDER FOR

STUDENTS HAVING TAKEN ADVANCED MATHEMATICS

▲ = Males’ score is significantly higher than females’ score.
1. Difference is calculated by subtracting average females’ score from average males’ score, based on

unrounded averages.

2. Nations ordered based on size of difference between males’ and females’ scores, from lowest to highest.

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1

for details for each country.

International average is the average of the national figures.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary

School. Table 8.4. Chestnut Hill, MA: Boston College.

TABLE A5.10

GENDER DIFFERENCES IN PHYSICS ACHIEVEMENT FOR STUDENTS IN THEIR FINAL

YEAR OF SECONDARY SCHOOL HAVING TAKEN ADVANCED SCIENCE
TABLE A5.11

ACHIEVEMENT IN PHYSICS CONTENT AREAS BY GENDER FOR ADVANCED

SCIENCE STUDENTS

▲ = Males’ score is significantly higher than females’ score.
TABLE A5.11 (CONTINUED)

ACHIEVEMENT IN PHYSICS CONTENT AREAS BY GENDER FOR ADVANCED

SCIENCE STUDENTS

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for details

for each country.

International average is the average of the national figures.

“S.E.” is standard error.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 9.2.

Chestnut Hill, MA: Boston College.

▲ = Males’ score is significantly higher than females’ score.
124

TABLE A5.12

EXTENT OF DIFFERENTIATION IN SECONDARY EDUCATION AND PERFORMANCE ON TIMSS

GENERAL KNOWLEDGE ASSESSMENTS RELATIVE TO THE UNITED STATES

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

Bold: Nations that performed above the U.S. in both mathematics and science general knowledge.

Bold italic: Nations that performed above the U.S. in mathematics general knowledge only. Regular: Nations that performed similar to the U.S. in both mathematics and science general knowledge. Italic: Nations that performed below the U.S. in both mathematics and science general knowledge.

Greece and Latvia participated only in the physics and/or advanced mathematics assessments. For these 

countries:

Greece: Specialized/mixed schools and varying lengths of secondary schooling.

Latvia: Specialized/mixed schools and varying lengths of secondary schooling.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Appendix A.

Chestnut Hill, MA: Boston College.

EXTENSIVE DIFFERENTIATION

WITHIN AND BETWEEN

SCHOOLS IN PROGRAMS FOR

STUDENTS WITH DIFFERING

ABILITIES OR INTERESTS

DIFFERENTIATION IN LENGTH OF 

SECONDARY EDUCATION

YES NO

YES 

(SPECIALIZED AND 

MIXED SECONDARY

SCHOOLS)

(AUSTRIA)

CZECH REPUBLIC

(FRANCE)

(GERMANY)

HUNGARY

(ICELAND)

(ITALY)

(LITHUANIA)

(NETHERLANDS)

(RUSSIAN FEDERATION)

(SLOVENIA)

SWEDEN

SWITZERLAND

(CYPRUS)

(DENMARK)

(NORWAY)

NO 

(COMPREHENSIVE 

SECONDARY SCHOOLS) 

(CANADA)

NEW ZEALAND

(AUSTRALIA)

(SOUTH AFRICA)

(UNITED STATES)
125

TABLE A5.13

AVERAGE AGE OF STUDENTS ASSESSED AND GRADES INCLUDED IN

GENERAL KNOWLEDGE ASSESSMENTS COMPARED TO PERFORMANCE ON MATHEMATICS GENERAL

KNOWLEDGE ASSESSMENT RELATIVE TO THE UNITED STATES

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 1.1,

Figure 2.1, and Appendix A. Chestnut Hill, MA: Boston College.

PERFORMED ABOVE THE U.S.

NATION AND

PERFORMANCE

RELATIVE TO THE

U.S. IN 

MATHEMATICS

GENERAL

KNOWLEDGE

AVERAGE AGE 

OF STUDENTS

PARTICIPATING IN

GENERAL

KNOWLEDGE

ASSESSMENTS

(AUSTRALIA) 17.7 X 12

(AUSTRIA) 19.1 X X X X X 10-14

(CANADA) 18.6 X X X 12-14

(DENMARK) 19.1 X 12

(FRANCE) 18.8 X X X 11-13

(GERMANY) 19.5 X X 12-13

HUNGARY 17.5 X X 10,12

(ICELAND) 21.2 X X X 12-14

(NETHERLANDS) 18.5 X X 11-12

NEW ZEALAND 17.6 X X 11-12

(NORWAY) 19.5 X 12

(SLOVENIA) 18.8 X X 11-12

SWEDEN 18.9 X X 11-12

SWITZERLAND 19.8 X X X 11-13

AVERAGE 18.9

CZECH REPUBLIC 17.8 X X X X 10-13

(ITALY) 18.7 X X X 11-13

(LITHUANIA) 18.1 X 12

(RUSSIAN FEDERATION) 16.9 X 11

END OF SECONDARY GRADES

ASSESSED IN GENERAL KNOWLEDGE

ASSESSMENTS

10 11 12 13 14

(CYPRUS) 17.7 X 12

(SOUTH AFRICA) 20.1 X 12

AVERAGE 

(SAME AND BELOW) 18.2

(UNITED STATES) 18.1 X 12

INTERNATIONAL

AVERAGE 18.7

PERFORMED BELOW THE U.S.

PERFORMED SAME AS THE U.S.

RANGE
126

TABLE A5.14

SECONDARY ENROLLMENT AND COMPLETION COMPARED TO THE UNITED STATES

— Data not available.

* Percentage in secondary school represents gross enrollment of all ages at the secondary level as a percentage of

school-age children as defined by each country. This may be reported in excess of 100% if some pupils are younger or older than the country’s standard range of secondary school age.

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

Percentage in secondary school, 1995; Percentage 25-34 year olds completing secondary education from National Labor

Force surveys, 1995 or 1996; Percentage enrolled in secondary education by age refers to school year 1994/95 (except

for Austria where data is for 1992/93 school year).

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 4 and

Figure 2.1. Chestnut Hill, MA: Boston College; and Organisation for Economic Cooperation and Development.

(1997). Education at a Glance: OECD Indicators. Tables A2.2a and C3.3. Paris: OECD.

PERFORMED ABOVE THE U.S.

NATION AND

PERFORMANCE

RELATIVE TO THE

U.S. IN 

MATHEMATICS

GENERAL

KNOWLEDGE

PERCENTAGE

IN

SECONDARY

SCHOOL

PERCENTAGE

25-34-YEAR-OLDS

COMPLETING

SECONDARY

EDUCATION

(AUSTRALIA) 84 57 77 32 20 17

(AUSTRIA) 107 81 88 56 22 8

(CANADA) 88 84 69 34 10 —

(DENMARK) 114 69 82 71 52 31

(FRANCE) 106 86 91 60 34 15

(GERMANY) 101 89 93 82 57 31

HUNGARY 81 — 71 39 17 11

(ICELAND) 103 — 77 65 63 33

(NETHERLANDS) 93 70 91 69 47 32

NEW ZEALAND 104 64 74 33 17 13

(NORWAY) 116 88 90 83 33 19

(SLOVENIA) 85 — — — — —

SWEDEN 99 88 96 87 24 12

SWITZERLAND 91 88 82 75 52 23

AVERAGE 98 79 83 60 34 20

PERFORMED SAME AS THE U.S.

PERCENTAGE ENROLLED

IN SECONDARY EDUCATION

BY AGE

17 18 19 20

CZECH REPUBLIC 86 91 72 30 6 3

(ITALY) 81 49 — — — —

(LITHUANIA) 78 — — — — —

(RUSSIAN FEDERATION) 88 — — — — —

(CYPRUS) 95 — — — — —

(SOUTH AFRICA) 77 — — — — —

AVERAGE 84 — — — — —

(SAME AND BELOW)

(UNITED STATES) 97 87 75 22 4 2

INTERNATIONAL 94 78 82 56 31 18

AVERAGE

PERFORMED BELOW THE U.S.
127

TABLE A5.15 

CENTRALIZATION OF DECISION-MAKING ABOUT CURRICULUM SYLLABI AND

PERFORMANCE ON MATHEMATICS AND SCIENCE GENERAL KNOWLEDGE ASSESSMENTS

RELATIVE TO THE UNITED STATES

NOTES:

Countries are “Nationally Centralized” regarding curriculum if the highest level of decision-making authority within

the education system (e.g., ministry of education) has exclusive responsibility for or gives final approval of the syllabi

for courses of study. If curriculum syllabi are determined at the regional level (e.g., state, province, territory), a coun- try is “Regionally Centralized.” If syllabi for courses of study are not determined nationally or regionally, a country is

“Not Centralized.” 

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

Bold: Nations that performed above the U.S. in both mathematics and science general knowledge. Bold italic: Nations that performed above the U.S. in mathematics general knowledge only. Regular: Nations that performed similar to the U.S. in both mathematics and science general knowledge. Italic: Nations that performed below the U.S. in both mathematics and science general knowledge.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Figure 1.

Chestnut Hill, MA: Boston College.

EXTENT OF CENTRALIZATION

NATIONALLY CENTRALIZED

NATION

(AUSTRIA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(FRANCE)

(ITALY)

(LITHUANIA)

NEW ZEALAND

(NORWAY)

(SLOVENIA)

(SOUTH AFRICA)

SWEDEN

REGIONALLY CENTRALIZED

NOT CENTRALIZED

(CANADA)

(GERMANY)

SWITZERLAND

(AUSTRALIA)

HUNGARY

(ICELAND)

(NETHERLANDS)

(RUSSIAN FEDERATION)

(UNITED STATES)
128

TABLE 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

— Data not available.

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for

details for each country.

International average is the average of the national figures.

GNP per capita and public expenditure figures based on estimates for 1994 at current market prices in U.S. dollars,

except in Cyprus where GNP per capita figure is for 1993.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 5 and

Figure 2.1. Chestnut Hill, MA: Boston College.

PERFORMED ABOVE THE U.S.

NATION AND 

PERFORMANCE 

RELATIVE TO THE U.S.

IN MATHEMATICS 

GENERAL 

KNOWLEDGE

GNP PER CAPITA

(U.S. $) 

PUBLIC EXPENDITURE

ON ELEMENTARY/

SECONDARY 

EDUCATION

AS PERCENT OF GNP

PUBLIC EXPENDITURE

ON ELEMENTARY/

SECONDARY 

EDUCATION

PER CAPITA (U.S. $)

(AUSTRALIA) $17,980 3.69 $663

(AUSTRIA) 24,950 4.24 1,058

(CANADA) 19,570 4.62 904

(DENMARK) 28,110 4.80 1,349

(FRANCE) 23,470 3.61 847

(GERMANY) 25,580 2.43 622

HUNGARY 3,840 4.31 166

(ICELAND) 24,590 4.77 1,173

(NETHERLANDS) 21,970 3.30 725

NEW ZEALAND 13,190 3.15 415

(NORWAY) 26,480 5.26 1,393

(SLOVENIA) 7,140 4.20 300

SWEDEN 23,630 4.92 1,163

SWITZERLAND 37,180 3.72 1,383

AVERAGE 21,263 4.07 869

PERFORMED SAME AS THE U.S.

CZECH REPUBLIC 3,210 3.75 120

(ITALY) 19,270 2.89 557

(LITHUANIA) 1,350 2.18 29

(RUSSIAN FEDERATION) 2,650 — —

(CYPRUS) 10,380 3.60 374

(SOUTH AFRICA) 3,010 5.12 154

AVERAGE 

(SAME AND BELOW)

(UNITED STATES) 25,860 4.02 1,040

INTERNATIONAL 

AVERAGE

PERFORMED BELOW THE U.S.

17,305 3.93 722

6,645 3.51 247 
129

TABLE 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

1. Difference in average ages is calculated by subtracting the average age of the participants in the eighth grade mathematics

assessment from the average age of the participants in the final year of secondary school mathematics general knowledge

assessment.

2. Based on average age of participants in the seventh grade.

3. Based on average age of participants in eighth or ninth grade, depending upon the system in place in each state/territory

(Australia) or age beginning primary school (New Zealand).

4. Based on average age in seventh or eighth grade, depending upon the system in place in each canton (Switzerland) or age

beginning secondary school (Russian Federation).

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for details for each

country.

International average is the average of national figures.

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 1.1 and Figure 2.3.

Chestnut Hill, MA: Boston College; Mullis et al. (1996). Mathematics Achievement in the Middle School Years. Table 1.1.

Chestnut Hill, MA: Boston College.

NATION’S STANDING

RELATIVE TO THE

INTERNATIONAL

AVERAGE IN EIGHTH

GRADE COMPARED TO

FINAL YEAR OF

SECONDARY SCHOOL

NATION

AVERAGE AGE OF 

PARTICIPANTS IN 

ASSESSMENT

EIGHTH

GRADE

FINAL YEAR

OF 

SECONDARY

SCHOOL

DIFFERENCE IN 

AVERAGE AGE OF 

PARTICIPANTS IN THE

TWO ASSESSMENTS1

HIGHER IN FINAL 

YEAR OF 

SECONDARY SCHOOL 

AVERAGE

(DENMARK)

(ICELAND)

NEW ZEALAND

(NORWAY)

SWEDEN

13.9 2

13.6 3

14.0 3

13.9 2

13.9 2

19.1

21.2

17.6

19.5

18.9

13.9 19.3

5.2

7.6

3.6

5.6

5.0

SAME IN BOTH

(AUSTRIA)

(CANADA)

(CYPRUS)

(FRANCE)

(GERMANY)

(LITHUANIA)

(NETHERLANDS)

(SOUTH AFRICA)

SWITZERLAND

14.3

14.1

13.7

14.3

14.8

14.3

14.3

15.4

14.2 4

19.1

18.6

17.7

18.8

19.5

18.1

18.5

20.1

19.8

4.8

4.5

4.0

4.5

4.7

3.8

4.2

4.7

5.6

LOWER IN FINAL 

YEAR OF 

SECONDARY SCHOOL

(AUSTRALIA)

CZECH REPUBLIC

HUNGARY

(RUSSIAN FEDERATION)

(SLOVENIA)

(UNITED STATES)

14.2 3

14.4

14.3

14.0 4

14.8

14.2

17.7

17.8

17.5

16.9

18.8

18.1

3.5

3.4

3.2

2.9

4.0

3.9

5.4

AVERAGE 14.4 18.9 4.5

AVERAGE 14.3 17.8 3.5

INTERNATIONAL AVERAGE 14.2 18.7 4.4
130

TABLE A5.18

MATHEMATICS AND SCIENCE COURSETAKING AND CHANGE IN STANDING RELATIVE TO THE

INTERNATIONAL AVERAGE BETWEEN EIGHTH GRADE AND FINAL YEAR OF SECONDARY SCHOOL

COMPARISON TO THE 

UNITED STATES ON

COURSETAKING

PERCENTAGE OF STUDENTS 

CURRENTLY TAKING 

MATHEMATICS

PERCENTAGE OF STUDENTS 

CURRENTLY TAKING 

SCIENCE

NATION ABOVE 

U.S.

NATION SAME AS 

U.S.

NATION BELOW 

U.S.

(UNITED STATES)

INTERNATIONAL AVERAGE

DATA NOT AVAILABLE

(AUSTRALIA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(FRANCE)

HUNGARY

(LITHUANIA)

(RUSSIAN FEDERATION)

(SLOVENIA)

(AUSTRIA)

(ICELAND)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(SOUTH AFRICA)

SWEDEN

SWITZERLAND

(CANADA)

66%★

79%★

(GERMANY)

(AUSTRALIA)

(AUSTRIA)

(CYPRUS)

(FRANCE)

HUNGARY

(ICELAND)

(LITHUANIA)

NEW ZEALAND

(RUSSIAN FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

(CANADA)

(NETHERLANDS)

SWITZERLAND

CZECH REPUBLIC

(DENMARK)

(NORWAY)

SWEDEN

53%★

67%★

(GERMANY)

NOTES:

Nations not meeting international sampling or other guidelines for the end of secondary assessment are shown in

parentheses. See Appendix 1 for details for each country.

Bold: Nations that have a higher relative standing compared to the international average in eighth grade than at

the end of secondary school in that subject.

Regular Nations in which the relative standing compared to the international average is similar in eighth grade and

at the end of secondary school in that subject.

Italic Nations that have a lower relative standing compared to the international average in eighth grade than at

the end of secondary school in that subject.

International average is the average of the national figures.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Tables 4.2,

4.4, and Figures 2.3 and 2.4. Chestnut Hill, MA: Boston College.

★ U.S. average is significantly different from the international average.
131

TABLE 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 NATION’S STANDING RELATIVE TO THE INTERNATIONAL AVERAGE FROM

EIGHTH GRADE TO FINAL YEAR OF SECONDARY SCHOOL

1. Difference in average ages is calculated by subtracting the average age of the participants in the eighth grade mathematics

assessment from the average age of the participants in the final year of secondary school mathematics general knowledge

assessment.

2. Based on average age of participants in the seventh grade.

3. Based on average age of participants in eighth or ninth grade, depending upon the system in place in each state/territory

(Australia) or age beginning primary school (New Zealand).

4. Based on average age in seventh or eighth grade, depending upon the system in place in each canton (Switzerland) or age

beginning secondary school (Russian Federation).

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for details for each

country.

International average is the average of national figures.

SOURCES: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Table 1.1 and Figure 2.4.

Chestnut Hill, MA: Boston College; Mullis et al. (1996). Science Achievement in the Middle School Years. Table 1.1. Chestnut Hill, MA:

Boston College.

CHANGE IN NATION’S

STANDING RELATIVE TO

THE INTERNATIONAL

AVERAGE FROM EIGHTH

GRADE TO FINAL YEAR

OF SECONDARY

SCHOOL

NATION

AVERAGE AGE OF 

PARTICIPANTS IN 

ASSESSMENT

EIGHTH

GRADE

FINAL YEAR

OF 

SECONDARY

SCHOOL

DIFFERENCE IN 

AVERAGE AGE OF 

PARTICIPANTS IN THE

TWO ASSESSMENTS1

HIGHER IN FINAL 

YEAR OF 

SECONDARY SCHOOL 

AVERAGE

(DENMARK)

(FRANCE)

(ICELAND)

NEW ZEALAND

SWITZERLAND

13.9 2

14.33

13.63

14.0 3

14.2 4

19.1

18.8

21.2

17.6

19.8

14.0 19.3

5.2

4.5

7.6

3.6

5.6

SAME IN BOTH

(AUSTRIA)

(CANADA)

(CYPRUS)

(LITHUANIA)

(NETHERLANDS)

(NORWAY)

(SOUTH AFRICA)

SWEDEN

14.33

14.13

13.73

14.33

14.33

13.9 2

15.43

13.9 2

19.1

18.6

17.7

18.1

18.5

19.5

20.1

18.9

4.8

4.5

4.0

3.8

4.2

5.6

4.7

5.0

LOWER IN FINAL 

YEAR OF 

SECONDARY SCHOOL

(AUSTRALIA)

CZECH REPUBLIC

(GERMANY)

HUNGARY

(RUSSIAN FEDERATION)

(SLOVENIA)

(UNITED STATES)

14.2 3

14.43

14.83

14.33

14.0 4

14.83

14.2

17.7

17.8

19.5

17.5

16.9

18.8

18.1

3.5

3.4

4.7

3.2

2.9

4.0

3.9

5.3

AVERAGE 14.2 18.8 4.6

AVERAGE 14.4 18.0 3.7

INTERNATIONAL AVERAGE 14.2 18.7 4.4
132

TABLE A5.20

RESPONSES TO SELECTED STUDENT QUESTIONNAIRE ITEMS:

RESPONSES OF STUDENTS PARTICIPATING IN MATHEMATICS AND SCIENCE GENERAL

KNOWLEDGE ASSESSMENTS

NATION

ABOVE U.S.

ON THIS 

FACTOR

NATION 

SAME AS U.S.

ON THIS 

FACTOR

NATION

BELOW U.S. 

ON THIS 

FACTOR

DATA NOT

AVAILABLE

(UNITED STATES)

INTERNATIONAL

AVERAGE

PERCENTAGE OF

STUDENTS 

CURRENTLY TAKING 

MATHEMATICS

PERCENTAGE OF

STUDENTS CURRENTLY

TAKING SCIENCE

AVERAGE HOURS OF

HOMEWORK 

PER DAY

PERCENTAGE WHO

USE A CALCULATOR

“DAILY” 

(AUSTRALIA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(FRANCE)

HUNGARY

(ITALY)

(LITHUANIA)

(RUSSIAN FEDERATION)

(SLOVENIA)

(AUSTRIA)

(ICELAND)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(SOUTH AFRICA)

SWEDEN

SWITZERLAND

(CANADA)

(GERMANY)

66%★

79%

(AUSTRALIA)

(AUSTRIA)

(CYPRUS)

(FRANCE)*

HUNGARY*

(ICELAND)

(ITALY)

(LITHUANIA)

NEW ZEALAND

(RUSSIAN FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

(CANADA)

(NETHERLANDS)

SWITZERLAND

CZECH REPUBLIC

(DENMARK)

(NORWAY)

SWEDEN

(GERMANY)*

53%★

67%

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

(DENMARK)

(FRANCE)

HUNGARY

(ICELAND)

(ITALY)

(LITHUANIA)

NEW ZEALAND

(RUSSIAN FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

SWITZERLAND

(NETHERLANDS)

(NORWAY)

SWEDEN

CZECH REPUBLIC

(GERMANY)

1.7 HOURS★

2.6 HOURS

(AUSTRALIA)

(CANADA)

(CYPRUS)

(DENMARK)

(FRANCE)

HUNGARY

(ICELAND)

(NETHERLANDS)

NEW ZEALAND 

(SOUTH AFRICA)

(AUSTRIA)

(ITALY)

(LITHUANIA)

(NORWAY)

(SLOVENIA)

SWITZERLAND

CZECH REPUBLIC

(RUSSIAN FEDERATION)

SWEDEN

(GERMANY)

52%

55%

COMPARISON

TO THE U.S. ON

THE FACTOR

Notes for this table can be found at the end of table.

How to read this table: Columns represent responses to particular questionnaire items. The first three rows

show how each nation's students responded in comparison with U.S. students on that item. The style of the font for

the country names indicates how students in that country performed on the general knowledge assessment relative to the U.S. For example, the first column represents student responses to whether they were currently taking math- ematics. The first row in the first column lists the 10 countries in which a higher percentage of students than in the

U.S. reported that they were currently taking mathematics. The second row in the first column lists the 8 nations in

which a similar percentage of students as the U.S. reported that they were currently taking mathematics. The third

row in the first column lists the one nation in which a lower percentage of students than in the U.S. reported that

they were currently taking mathematics.
133

TABLE A5.20—(CONTINUED)

NATION

ABOVE U.S.

ON THIS 

FACTOR

NATION 

SAME AS U.S.

ON THIS 

FACTOR

NATION 

BELOW U.S. 

ON THIS 

FACTOR

(UNITED STATES)

INTERNATIONAL

AVERAGE

DATA NOT

AVAILABLE

PERCENTAGE WHO

USED A 

CALCULATOR ON 

THE TIMSS 

MATHEMATICS

GENERAL

KNOWLEDGE 

ASSESSMENT

PERCENTAGE WHO

USE A COMPUTER AT

SCHOOL, HOME, OR

ELSEWHERE

PERCENTAGE WHO

LIKE MATHEMATICS

“A LOT”

PERCENTAGE WHO

“LIKE” CHEMISTRY

OR LIKE IT “A LOT” 

(AUSTRALIA)

(AUSTRIA)

(CANADA)

CZECH REPUBLIC

(DENMARK)

(FRANCE)

(GERMANY)

HUNGARY

(NETHERLANDS)

NEW ZEALAND

SWEDEN

SWITZERLAND

(CYPRUS)

(ICELAND)

(ITALY)

(NORWAY)

(SLOVENIA)

(LITHUANIA)

(RUSSIAN FEDERATION)

(SOUTH AFRICA)

71%★

79%★

(DENMARK)

(ICELAND)

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(NETHERLANDS)

NEW ZEALAND

SWEDEN

(CYPRUS)

CZECH REPUBLIC

(FRANCE)

HUNGARY

(ITALY)

(LITHUANIA)

(NORWAY)

(RUSSIAN FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

SWITZERLAND

73%★

57%★

(GERMANY)

(DENMARK)

(SOUTH AFRICA)

(CYPRUS)

(ICELAND)

(ITALY)

SWITZERLAND

(AUSTRALIA) 

(AUSTRIA)

(CANADA)

CZECH REPUBLIC

(FRANCE)

HUNGARY

(LITHUANIA)

NEW ZEALAND

(NORWAY)

(RUSSIAN FEDERATION)

(SLOVENIA)

SWEDEN

21%★

15%★

(GERMANY)

(NETHERLANDS)

(ICELAND)

(SOUTH AFRICA)

(CANADA)

(CYPRUS)

(FRANCE)*

(ITALY)

(NORWAY)

(RUSSIAN FEDERATION)

SWEDEN

SWITZERLAND

(AUSTRALIA)

(AUSTRIA)

CZECH REPUBLIC

(DENMARK)

HUNGARY*

(LITHUANIA)

NEW ZEALAND

(SLOVENIA)

49%★

42%★

(GERMANY)*

(NETHERLANDS)

COMPARISON

TO THE U.S. ON

THE FACTOR
134

TABLE A5.20—(CONTINUED)

NATION

ABOVE U.S.

ON THIS 

FACTOR

NATION 

SAME AS U.S.

ON THIS 

FACTOR

NATION 

BELOW U.S. 

ON THIS 

FACTOR

INTERNATIONAL

AVERAGE

(UNITED STATES)

DATA NOT

AVAILABLE

PERCENTAGE WHO

“LIKE” EARTH 

SCIENCE OR LIKE IT

“A LOT” 

PERCENTAGE WHO

“LIKE” PHYSICS OR

LIKE IT “A LOT”

PERCENTAGE WHO

“LIKE” BIOLOGY OR

LIKE IT “A LOT”

PERCENTAGE WHO

HAD SOMETHING

STOLEN AT SCHOOL

IN THE MONTH

PRIOR TO TIMSS

(LITHUANIA)

(AUSTRIA) 

(CANADA)

CZECH REPUBLIC

(ICELAND)

(ITALY)

(RUSSIAN FEDERATION)

(SLOVENIA)

(SOUTH AFRICA)

SWEDEN

SWITZERLAND

(AUSTRALIA)

(CYPRUS)

(DENMARK)

(FRANCE)*

HUNGARY*

NEW ZEALAND

(NORWAY)

63%

68%★

(GERMANY)*

(NETHERLANDS)

(SOUTH AFRICA)

(CANADA)

(CYPRUS)

(DENMARK)

(FRANCE)*

(ICELAND)

(ITALY)

(NORWAY)

(RUSSIAN FEDERATION)

SWEDEN

SWITZERLAND

(AUSTRALIA)

(AUSTRIA)

CZECH REPUBLIC

HUNGARY*

(LITHUANIA)

NEW ZEALAND

(SLOVENIA)

42%

47%★★

(GERMANY)*

(NETHERLANDS)

(ICELAND)

(RUSSIAN FEDERATION)

(SOUTH AFRICA)

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

(DENMARK)

(FRANCE)*

HUNGARY*

(ITALY)

(LITHUANIA)

NEW ZEALAND

SWEDEN

SWITZERLAND

CZECH REPUBLIC

(NORWAY)

(SLOVENIA)

67%

67%★

(GERMANY)*

(NETHERLANDS)

(SOUTH AFRICA)

NEW ZEALAND

(AUSTRALIA) 

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

HUNGARY

(ICELAND)

(ITALY)

(LITHUANIA)

(NORWAY)

(RUSSIAN FEDERATION)

(SLOVENIA)

SWEDEN

SWITZERLAND 

13%

24%★★

(FRANCE)

(GERMANY)

(NETHERLANDS)

COMPARISON

TO THE U.S. ON

THE FACTOR
135

TABLE A5.20—(CONTINUED)

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for details for each country.

International average is the average of the national figures.

Bold: Nations that performed above the U.S. in both mathematics and science general knowledge. Bold italic: Nations that performed above the U.S. in mathematics general knowledge only. Regular: Nations that performed similar to the U.S. in mathematics and science general knowledge. Italic: Nations that performed below the U.S. in both mathematics and science general knowledge. * Because this factor concerns science general knowledge, and because these nations performed similar

to the U.S. in science, they are not bolded for this factor.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut

Hill, MA: Boston College.

★ U.S. average is significantly different from the international average.

ABOVE U.S.

ON THIS 

FACTOR

SAME AS U.S.

ON THIS 

FACTOR

BELOW U.S. 

ON THIS 

FACTOR

(UNITED STATES)

INTERNATIONAL

AVERAGE

DATA NOT

AVAILABLE

PERCENTAGE WHO

WERE THREATENED 

AT SCHOOL IN THE

MONTH PRIOR TO

TIMSS

AVERAGE HOURS OF

TV OR VIDEO

WATCHING ON A

NORMAL SCHOOL

DAY

AVERAGE HOURS 

AT A PAID 

JOB ON A NORMAL

SCHOOL DAY

PERCENTAGE WHO

WORK ONE OR

MORE HOURS AT A

PAID JOB ON A

NORMAL 

SCHOOL DAY

(SOUTH AFRICA)

(AUSTRALIA) 

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

NEW ZEALAND

(AUSTRIA)

(CANADA) 

(ICELAND)

(ITALY)

(LITHUANIA) 

(NORWAY) 

(RUSSIAN FEDERATION)

(SLOVENIA) 

SWEDEN

SWITZERLAND

11%★

7%★

(FRANCE)

(GERMANY)

HUNGARY

(NETHERLANDS)

CZECH REPUBLIC

HUNGARY

(LITHUANIA)

(NETHERLANDS)

NEW ZEALAND

(RUSSIAN FEDERATION)

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(CYPRUS)

(DENMARK)

(ICELAND)

(NORWAY)

SWEDEN

(FRANCE)

(ITALY)

(SLOVENIA)

(SOUTH AFRICA) 

SWITZERLAND

1.7 HOURS

1.7 HOURS

(GERMANY)

NONE

NONE

(AUSTRALIA) 

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(FRANCE)

(ICELAND)

(ITALY)

(LITHUANIA)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(RUSSIAN FEDERATION)

(SLOVENIA) 

(SOUTH AFRICA)

SWEDEN

SWITZERLAND

3.1 HOURS★

1.2 HOURS

(GERMANY)

HUNGARY

NONE

NONE

(AUSTRALIA) 

(AUSTRIA)

(CANADA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(FRANCE)

(ICELAND)

(ITALY)

(LITHUANIA)

(NETHERLANDS)

NEW ZEALAND

(NORWAY)

(RUSSIAN FEDERATION)

(SLOVENIA) 

(SOUTH AFRICA)

SWEDEN

SWITZERLAND

61%★

28%★

(GERMANY)

HUNGARY

COMPARISON

TO THE U.S. ON

THE FACTOR
136

TABLE A5.21

RESPONSES TO SELECTED STUDENT QUESTIONNAIRE ITEMS:

RESPONSES OF STUDENTS PARTICIPATING IN ADVANCED MATHEMATICS ASSESSMENT

NATION

ABOVE U.S.

ON THIS 

FACTOR

NATION

SAME AS U.S.

ON THIS 

FACTOR

NATION 

BELOW U.S. 

ON THIS 

FACTOR

(UNITED STATES)

INTERNATIONAL

AVERAGE

DATA NOT

AVAILABLE

PERCENTAGE WHO

ARE ASSIGNED

MATHEMATICS

HOMEWORK 3 OR

MORE TIMES PER

WEEK1

PERCENTAGE WHO

USE A CALCULATOR

AT SCHOOL, HOME

OR ANYWHERE ELSE

“DAILY”

PERCENTAGE WHO

USED A

CALCULATOR ON

THE TIMSS

ADVANCED

MATHEMATICS

ASSESSMENT

PERCENTAGE WHO

RECEIVE 5 HOURS

OR MORE OF 

MATHEMATICS

INSTRUCTION PER

WEEK1

(CYPRUS)

(AUSTRALIA)

CANADA

GREECE

(RUSSIAN FEDERATION)

(AUSTRIA)

CZECH REPUBLIC

(DENMARK)

(ITALY)

(LITHUANIA)

(SLOVENIA)

SWEDEN

SWITZERLAND

90%★

65%★

FRANCE

(GERMANY)

(AUSTRALIA)

(DENMARK)

SWEDEN

CANADA

(CYPRUS)

FRANCE

(AUSTRIA)

CZECH REPUBLIC

(GERMANY)

GREECE

(ITALY)

(LITHUANIA)

(RUSSIAN FEDERATION)

(SLOVENIA)

SWITZERLAND

82%★

70%★

CANADA

(DENMARK)

SWEDEN

SWITZERLAND

(AUSTRALIA)

(AUSTRIA)

CZECH REPUBLIC

FRANCE

(GERMANY)

(CYPRUS)

GREECE

(ITALY)

(LITHUANIA)

(RUSSIAN FEDERATION)

(SLOVENIA)

86%★

76%★

(AUSTRALIA)

CANADA

(CYPRUS)

FRANCE

GREECE

(LITHUANIA)

(RUSSIAN FEDERATION)

(AUSTRIA)

SWITZERLAND

CZECH REPUBLIC

(DENMARK)

(ITALY)

(SLOVENIA)

SWEDEN

12%★

37%★

(GERMANY)

How to read this table: Columns represent responses to particular questionnaire items. The first three rows show how each nation's students responded in comparison with U.S. students on that item. The style of the font for

the country names indicates how students in that country performed on the general knowledge assessment relative to the U.S. For example, the first column represents student responses to whether they were assigned mathematics

homework 3 or more times per week. The first row in the first column lists the one country in which a higher percentage of students than in the U.S. reported that they were assigned mathematics homework 3 or more times a week. The second row in the first column lists the 4 nations in which a similar percentage of students as the U.S. reported that they were assigned mathematics homework 3 or more times a week. The third row in the first column

lists the 8 nations in which a lower percentage of students than in the U.S. reported that they were assigned mathematics homework 3 or more times a week.

COMPARISON

TO THE U.S. ON

THE FACTOR

Notes for this table can be found at the end of table.
137

TABLE A5.21 – (CONTINUED)

NATION

ABOVE U.S.

ON THIS 

FACTOR

NATION

SAME AS U.S.

ON THIS 

FACTOR

NATION

BELOW U.S. 

ON THIS 

FACTOR

(UNITED STATES)

INTERNATIONAL

AVERAGE

DATA NOT

AVAILABLE

PERCENTAGE WHO ARE ASKED

TO USE COMPUTERS TO SOLVE

MATHEMATICS EXERCISES OR

PROBLEMS IN AT LEAST SOME

MATHEMATICS CLASSES2

PERCENTAGE WHO ARE

ASKED TO DO AT LEAST ONE

REASONING TASK 

IN “EVERY MATHEMATICS

LESSON”2

PERCENTAGE WHO ARE

ASKED TO APPLY 

MATHEMATICS TO EVERYDAY

PROBLEMS IN THEIR

MATHEMATICS LESSONS2

(CYPRUS)

(ITALY)

(SLOVENIA)

(AUSTRALIA)

(DENMARK)

GREECE

(AUSTRIA)

CANADA

CZECH REPUBLIC

FRANCE

(GERMANY)

(LITHUANIA)

(RUSSIAN FEDERATION)

SWEDEN

SWITZERLAND

34%★

28%★

(CYPRUS)

GREECE

(AUSTRALIA)

CZECH REPUBLIC

(ITALY)

SWEDEN

(AUSTRIA)

CANADA

(DENMARK)

FRANCE

(GERMANY)

(LITHUANIA)

(RUSSIAN FEDERATION)

(SLOVENIA)

SWITZERLAND

43%★

32%★

NONE

(AUSTRALIA)

CANADA

(AUSTRIA)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

FRANCE

(GERMANY)

GREECE

(ITALY)

(LITHUANIA)

(RUSSIAN FEDERATION)

(SLOVENIA)

SWEDEN

SWITZERLAND

85%★

68%★

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for details for each country.

International average is the average of the national figures.

Bold: Nations that performed above the U.S. advanced mathematics students on the advanced mathematics 

assessment.

Regular: Nations that performed similar to the U.S. advanced mathematics students on the advanced 

mathematics assessment.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut

Hill, MA: Boston College.

COMPARISON

TO THE U.S. ON

THE FACTOR

★ U.S. average is significantly different from the international average.

1. Percentage based only on those students who reported that they were currently taking mathematics.

2. Percentage is based on all students concerning the current or the most recent mathematics course taken.
138

TABLE A5.22

RESPONSES TO SELECTED STUDENT QUESTIONNAIRE ITEMS: 

RESPONSES OF STUDENTS PARTICIPATING IN PHYSICS ASSESSMENT

NATION 

ABOVE U.S.

ON THIS 

FACTOR

NATION 

SAME AS U.S.

ON THIS 

FACTOR

NATION 

BELOW U.S. 

ON THIS 

FACTOR

(UNITED STATES)

INTERNATIONAL

AVERAGE

DATA NOT

AVAILABLE

PERCENTAGE WHO

RECEIVE PHYSICS

HOMEWORK 3 OR

MORE TIMES PER

WEEK*

PERCENTAGE WHO

USE A CALCULATOR

AT SCHOOL, HOME

OR ANYWHERE ELSE

“DAILY”

PERCENTAGE WHO

USED A 

CALCULATOR ON 

THE TIMSS PHYSICS

ASSESSMENT

PERCENTAGE WHO

CURRENTLY RECEIVE

5 HOURS OR MORE

OF PHYSICS

INSTRUCTION PER

WEEK*

(CANADA)

(CYPRUS)

GREECE

NORWAY

(RUSSIAN FEDERATION)

(AUSTRALIA)

(DENMARK)

(AUSTRIA)

CZECH REPUBLIC

(GERMANY)

(LATVIA)

(SLOVENIA)

SWEDEN

SWITZERLAND

51%★

40%★

FRANCE

(AUSTRALIA)

(CANADA)

(CYPRUS)

(DENMARK)

NORWAY

SWEDEN

FRANCE

(GERMANY)

(SLOVENIA)

SWITZERLAND

(AUSTRIA)

CZECH REPUBLIC

GREECE

(LATVIA)

(RUSSIAN FEDERATION)

79%★

73%★

(AUSTRALIA)

(CANADA)

(DENMARK)

NORWAY

SWEDEN

SWITZERLAND

(CYPRUS)

CZECH REPUBLIC

FRANCE

(GERMANY)

(SLOVENIA)

(AUSTRIA)

GREECE 

(LATVIA)

(RUSSIAN FEDERATION)

81%

79%

(CANADA)

(AUSTRALIA)

(LATVIA)

(RUSSIAN FEDERATION)

(CYPRUS)

CZECH REPUBLIC

(DENMARK)

(GERMANY)

GREECE

NORWAY

(SLOVENIA)

SWEDEN

SWITZERLAND

17%★

8%★

(AUSTRIA)

FRANCE

How to read this table: Columns represent responses to particular questionnaire items. The first three rows show how each nation's students responded in comparison with U.S. students on that item. The style of the font for the

country names indicates how students in that country performed on the general knowledge assessment relative to the

U.S. For example, the first column represents student responses to whether they were assigned physics homework 3 or more times per week. The first row in the first column lists the 5 countries in which a higher percentage of stu- dents than in the U.S. reported that they were assigned physics homework 3 or more times a week. The second row in the first column lists the 2 nations in which a similar percentage of students as the U.S. reported that they were assigned physics homework 3 or more times a week. The third row in the first column lists the 7 nations in which a

lower percentage of students than in the U.S. reported that they were assigned physics homework 3 or more times a

week.

COMPARISON

TO THE U.S. ON

THE FACTOR

Notes for this table can be found at the end of table.
139

TABLE A5.22–(CONTINUED)

NATION

ABOVE U.S.

ON THIS 

FACTOR

NATION

SAME AS U.S.

ON THIS 

FACTOR

NATION

BELOW U.S. 

ON THIS 

FACTOR

(UNITED STATES)

INTERNATIONAL

AVERAGE

DATA NOT

AVAILABLE

PERCENTAGE WHO ARE

ASKED TO USE COMPUTERS

TO SOLVE PHYSICS 

EXERCISES OR PROBLEMS IN

SOME LESSONS*

PERCENTAGE WHO ARE

ASKED TO DO AT LEAST ONE

REASONING TASK IN “EVERY

PHYSICS LESSON”*

PERCENTAGE WHO ARE

ASKED TO CONDUCT

LABORATORY EXPERIMENTS

DURING SOME PHYSICS

LESSONS*

(SLOVENIA)

(CANADA)

(CYPRUS)

(DENMARK)

FRANCE

GREECE

(AUSTRALIA)

(AUSTRIA)

CZECH REPUBLIC

(GERMANY)

(LATVIA)

NORWAY

(RUSSIAN FEDERATION)

SWEDEN

SWITZERLAND

42%★

29%★

(CYPRUS)

CZECH REPUBLIC

FRANCE

GREECE

(AUSTRALIA)

(AUSTRIA)

(CANADA)

(DENMARK)

(GERMANY)

(LATVIA)

NORWAY

(RUSSIAN FEDERATION)

(SLOVENIA)

SWEDEN 

SWITZERLAND 

36%★

23%★

NONE

(CYPRUS)

(DENMARK)

FRANCE

NORWAY

SWEDEN

(AUSTRALIA)

(AUSTRIA)

(CANADA)

CZECH REPUBLIC

(GERMANY)

GREECE

(LATVIA)

(RUSSIAN FEDERATION)

(SLOVENIA)

SWITZERLAND

96%★

79%★

NOTES:

Nations not meeting international sampling or other guidelines are shown in parentheses. See Appendix 1 for details for each country.

International average is the average of national figures.

Bold: Nations that performed above the U.S. physics students on the physics assessment.

Regular: Nations that performed similar to the U.S. physics students on the physics assessment.

SOURCE: Mullis et al. (1998). Mathematics and Science Achievement in the Final Year of Secondary School. Chestnut

Hill, MA: Boston College.

COMPARISON

TO THE U.S. ON

THE FACTOR

★ U.S. average is significantly different from the international average.

* Percentage based only on those students who reported that they were currently taking physics.
140
141

APPENDIX 6

ADVISORS TO THE U.S. TIMSS STUDY
142

William Schmidt—Chair

U.S. TIMSS National Research

Coordinator 

Michigan State University

Gordon Ambach

Council of Chief State School Officers

Deborah Ball

University of Michigan

Audrey Champagne

SUNY University at Albany

David Cohen

University of Michigan 

John Dossey

Illinois State University

Emerson Elliott

National Council for Accreditation of

Teacher Education

Sheldon Glashow

Harvard University

Larry Hedges

University of Chicago

Henry Heikkinen

University of Northern Colorado

Jeremy Kilpatrick

University of Georgia

Mary Lindquist

Columbus State University

Marcia Linn

University of California at Berkeley

Robert Linn

University of Colorado

Paul Sally

The University of Chicago

Richard Shavelson

Stanford University

Bruce Spencer

Northwestern University

Elizabeth Stage

University of California at Berkeley

James Taylor

Global M

Kenneth Travers

University of Illinois

Paul Williams

University of Wisconsin
143

APPENDIX 7

ADDITIONAL TIMSS REPORTS 
144

Ordering information for each of the

following publications is located at the

end of this appendix.

Asterisks indicate that the publication is

included in Attaining Excellence: A TIMSS

Resource Kit.

HOW CAN EDUCATORS,

PRACTITIONERS, POLICYMAKERS,

AND CONCERNED CITIZENS

REFLECT UPON THEIR OWN

LOCAL PRACTICES IN LIGHT OF

TIMSS FINDINGS?

Attaining Excellence: A TIMSS Resource

Kit, September 1997 -This comprehensive package includes four modules

which contain the following items:

reports on the TIMSS findings; videotapes of classroom teaching in the

United States, Japan, and Germany;

guides for discussion leaders; presentation overheads with talking points for

speakers; checklists, leaflets, and flyers.

Note that the Kit’s twelve publications

and two videos include several items

that are available individually elsewhere

on this list. Those publications are

denoted by an asterisk in the margin.

$94. GPO Stock #065-000-01013-5.

To order, contact: Superintendent of

Documents. Also may be downloaded

from http://timss.enc.org.

WHERE CAN I FIND A GOOD

SUMMARY OF TIMSS FINDINGS

THAT PUTS U.S. EDUCATION IN

COMPARATIVE PERSPECTIVE?

*Pursuing Excellence: A Study of U.S.

Fourth-Grade Mathematics and Science

Achievement in International Context, June

1997 -This report summarizes the most

important findings concerning U.S.

achievement and schooling in the fourth

grade, Paperback, 68 pp. $4.75. GPO

Stock #065-000-01018-6.

To order, contact: Superintendent of

Documents. Also may be downloaded

from: http://nces.ed.gov/timss.

*Pursuing Excellence: A Study of U.S. EighthGrade Mathematics and Science Teaching,

Learning, Curriculum, and Achievement in

International Context, November 1996 -

This report draws from the assessments,

surveys, video, and case studies of

TIMSS to summarize the most important

findings concerning U.S. achievement

and schooling in the eighth grade.

Paperback, 80 pp. $9.50. GPO Stock

#065-000-00959-5.

To order, contact: Superintendent of

Documents. Also may be downloaded

from http://nces.ed.gov/timss.

WHERE CAN I FIND A DETAILED

INTERNATIONAL COMPARISON OF

FOURTH-GRADE STUDENTS?

Mathematics Achievement in the Primary

School Years: IEA’s Third International

Mathematics and Science Study (TIMSS),

June 1997 - This report focuses on thirdand fourth-grade mathematics achievement in 26 countries, including background information about students and

teachers. Paperback, 184 pp. + 52 pp.

Appendix. $20.00 (+ $5.00 shipping &

handling, if international).

To order, contact: TIMSS International

Study Center. Also may be downloaded

from: http://wwwcsteep.bc.edu/TIMSS1/

TIMSSPublications.html#International.
145

Science Achievement in the Primary School

Years: IEA’s Third International Mathematics and Science Study (TIMSS), June 1997 -

This report focuses on third- and fourthgrade science achievement in 26

countries, including background information about students and teachers.

Paperback, 148 pp. + 52 pp. Appendix.

$20.00 (+ $5.00 shipping & handling if

international).

To order, contact: TIMSS International

Study Center. Also may be downloaded

from: http://wwwcsteep.bc.edu/TIMSS1/

TIMSSPublications.html#International.

WHERE CAN I FIND A DETAILED

INTERNATIONAL COMPARISON

OF EIGHTH-GRADE STUDENTS?

*Mathematics Achievement in the Middle

School Years: IEA’s Third International

Mathematics and Science Study (TIMSS),

November 1996 - This report focuses on

seventh- and eighth-grade mathematics

achievement in 41 countries, including

background information about students

and teachers. Paperback, 176 pp. + 60

pp. Appendix. $30 (+$5.00 shipping and

handling if international). GPO Stock

#065-000-01023-2.

To order, contact: TIMSS International

Study Center or Superintendent of Documents. Also may be downloaded from:

http://wwwcsteep.bc.edu/TIMSS1/TI

MSSPublications.html#International.

*Science Achievement in the Middle School

Years: IEA’s Third International

Mathematics and Science Study (TIMSS),

November 1996 - This report focuses on

seventh- and eighth-grade science

achievement in 41 countries, including

background information about students

and teachers. Paperback, 168 pp. + 62

pp. Appendix. $30 (+$5.00 shipping

and handling if international). GPO

Stock #065-000-01023-2.

To order, contact: TIMSS International

Study Center or Superintendent of

Documents. Also may be downloaded

from: http://wwwcsteep.bc.edu/TIMSS1/

TIMSSPublications.html#International.

WHERE CAN I FIND A DETAILED

INTERNATIONAL COMPARISON

OF TWELFTH-GRADE STUDENTS?

Mathematics and Science Achievement in

the Final Year of Secondary School: IEA’s

Third International Mathematics and

Science Study (TIMSS) February 1998 -

This report focuses on mathematics and

science achievement in 24 countries at

the end of secondary school, including

background information about students

and teachers. Paperback, 236 pp. + 105

pp. Appendix. $30 (+$5.00 shipping and

handling if international).

To order, contact: TIMSS International

Study Center. Also may be downloaded

from: http://wwwcsteep.bc.edu/TIMSS1/

TIMSSPublications.html#International.

WHERE CAN I OBTAIN THE

COMPLETE TIMSS INTERNATIONAL

DATABASE IN ORDER TO

PERFORM SECONDARY ANALYSIS?

TIMSS International Database - The database contains achievement scores in

mathematics and science for those countries that participated in TIMSS at the

third- and fourth grades (Population 1)

and the seventh- and eighth grades

(Population 2), and questionnaire

results for students, teachers, and principals. The database can be used with
146

either SAS or SPSS software.

Accompanied by User Guidebook.

The TIMSS International Database is

available on CD-ROM from the IEA

Secretariat. It is provided in ASCII format and may also be downloaded from:

http://wwwcsteep.bc.edu/timss1/database.html

The Population 3 Database and User

Guide will be available June 1998.

WHERE CAN I COMPARE

STUDENTS’ PERFORMANCE ON A

SERIES OF PRACTICAL TASKS IN

BOTH MATHEMATICS AND

SCIENCE?

Performance Assessment in IEA’s Third

International Mathematics and Science

Study, 1997 - The regular TIMSS assessments were supplemented by hands-on

performance assessments which measured 4th- and 8th-grade students’ content and procedural knowledge, as well

as their ability to use that knowledge in

reasoning and problem solving.

Students in 21 countries participated,

making it the largest international performance assessment yet conducted.

This report includes findings from the

21 countries and descriptions of the performance tasks. Paperback, 128 pp. +

45 pp. Appendix. 

To order, contact: TIMSS International

Study Center. Also may be downloaded

from http://wwwcsteep.bc.edu/TIMSS1

/PAreport.html.

HOW CAN I GET A FIRST-HAND

GLIMPSE OF ACTUAL CLASSROOM

LESSONS IN THE U.S., GERMANY,

AND JAPAN?

*Eighth-Grade Mathematics Lessons: United

States, Japan, and Germany - An 80-

minute VHS tape with abbreviated versions of six eighth-grade mathematics

lessons: one algebra and one geometry

lesson each from the United States,

Japan, and Germany, GPO Stock #065-

000-01025-9, $20.

To order, contact: Superintendent of

Documents.

CD-ROM Video Examples from the

TIMSS Videotape Classroom Study:

Eighth-Grade Mathematics in Germany,

Japan, and the United States - Actual

episodes in eighth-grade mathematics

classes let viewers see an abbreviated

geometry and algebra lesson in each of

three countries: Germany, Japan, and

the U.S.

To order, contact: Superintendent of

Documents.

Minimum System Requirements:

IBM PC or 100% compatible, MS

Windows® (Windows 95® recommended), Pentium® (16 MB of RAM, 256

color SVGA or better, 2x or higher CDROM drive, Sound Card.

HOW CAN I LEARN MORE ABOUT

THE LIVES OF STUDENTS AND

TEACHERS IN THE U.S., JAPAN,

AND GERMANY?

Contemporary Research in the United

States, Germany, and Japan on Five

Education Issues: Structure of the

Education System; Standards in Education;

The Role of School in Adolescents’ Lives;
147

Individual Differences Among Students’

and Teachers’ Lives. 802 pp. $50.

The Education System in Germany: Case

Study Findings. 406 pp. $25.

The Education System in Japan: Case Study

Findings. 412 pp. $25.

The Education System in the United States:

Case Study Findings. 341 pp. $20.

To Sum It Up: Case Studies of Education in

Germany, Japan, and the United States. 166

pp. $10. (Shipping and handling, $5)

To order, contact: University of Michigan.

WHERE CAN I FIND OUT WHAT

TIMSS HAS LEARNED ABOUT

CURRICULUM?

A Splintered Vision: An Investigation of U.S.

Science and Mathematics Education, 1997 -

This book enunciates the argument that

math and science curricula in U.S.

schools suffer from a lack of focus. The

authors contend that in their effort to

canvas as many topics as possible, both

teachers and textbook publishers fail to

delve into the most important subjects

with sufficient depth. 176 pp. Hardback

ISBN: 0-7923-4440-5, $87; Paperback

ISBN: 0-7923-4441-3, $49 

To order, contact: Kluwer Academic

Publishers Group.

Many Visions, Many Aims: Volume 1, A

Cross-National Exploration of Curricular

Intentions in School Mathematics, 1997 - An

analysis of mathematics curriculum

guides and textbooks in 50 countries.

This report looks at the sequence and the

topics covered from kindergarten

through the end of secondary school, analyzed in a comparative framework. 286

pp. Hardback ISBN: 0-7923-4436-7, $120;

Paperback ISBN: 0-7923-4437-5, $55 .

To order, contact: Kluwer Academic

Publishers Group.

Characterizing Pedagogical Flow: An

Investigation of Mathematics and Science

Teaching in Six Countries, 1996 -

Describes the results of the Study of

Mathematics and Science Opportunity

(SMSO) survey, which investigated curriculum content and instructional methods in France, Japan, Norway, Spain,

Switzerland, and the United States,

using case studies in each participating

country. 229 pp. Hardback ISBN:

07923-42720, $110; Paperback ISBN:

07923-42739, $49 

To order, contact: Kluwer Academic

Publishers Group.

TIMSS Monograph Series No. 3

Mathematics Textbooks: A Comparative

Study of Grade 8 Texts, 1995 - An examination of eight mathematics textbooks

for 13-year-olds for their pedagogical

and philosophical similarities and differences. Texts are from the United

States, the Netherlands, the United

Kingdom, Norway, Spain, France,

Switzerland, and Japan. Paperback, 96

pp. ISBN: 1-895766-03-6. $16.95.

To order, contact: Pacific Educational

Press.

WHERE CAN I FIND OUT MORE

ABOUT THE METHODOLOGY 

OF TIMSS?

Third International Mathematics and

Science Study: Quality Assurance in Data

Collection, 1996 - A report on the quality

assurance program which ensured the

comparability of results across partici-
148

pating countries. The program emphasized instrument translation and adaptation, sampling response rates, test

administration and data collection, the

reliability of the coding process, and the

integrity of the database. Paperback, 93

pp. + 91 pp. Appendix.

To order, contact: TIMSS International

Study Center. Also may be downloaded

from: http://wwwcsteep.bc.edu/TIMSS1/

TIMSSPublications.html#International.

Third International Mathematics and

Science Study: Technical Report, Volume 1

Design and Development, 1996 - This

report describes the study, design, and

the development of TIMSS up to, but

not including, the operational stage of

main data collection. Paperback, 149

pp. + 40 pp. Appendix.

To order, contact: TIMSS International

Study Center. Also may be downloaded

from: http://wwwcsteep.bc.edu/TIMSS1/

TIMSSPublications.html#International.

TIMSS Monograph Series No. 1, Curriculum Frameworks for Mathematics and

Science, 1993 - This monograph explains

the study’s foci and its key first step - the

development of the curriculum frameworks that served as the guide for

designing the study’s achievement tests.

The frameworks are included in the

appendices. Paperback, 102 pp. ISBN:

0-88865-090-6. $16.95.

To order, contact: Pacific Educational

Press.

TIMSS Monograph Series No. 2 Research

Questions and Study Design, 1996 - This

monograph presents the study’s research

objectives along with discussions that

include: the impact of prior studies on the

design of TIMSS; how the research questions were derived from TIMSS’ conceptual framework; and how the research

questions and test items were tailored to

meet the contexts of the participating

countries. Paperback, 112 pp. ISBN: 1-

895766-02-8. $17.95.

To order, contact: Pacific Educational

Press.

WHERE CAN I READ THE ACTUAL

TEST ITEMS GIVEN TO STUDENTS?

TIMSS Mathematics Items Released Set for

Population 1 (Third and Fourth Grades) -

All publicly released items used to assess

third- and fourth-grade students in the

TIMSS study. Paperback, 98 pp. $20.00

(+ $5.00 shipping & handling, if

international).

TIMSS Science Items Released Set for

Population 1 (Third and Fourth Grades) -

All publicly released items used to assess

third- and fourth-grade students in the

TIMSS study. Paperback, 84 pp. $20.00

(+ $5.00 shipping & handling, if

international).

TIMSS Mathematics Items Released Set for

Population 2 (Seventh and Eighth Grades)

- All publicly released items used to

assess seventh- and eighth-grade students in the TIMSS study. Paperback,

142 pp. $20.00 (+ $5.00 shipping & handling, if international).

TIMSS Science Items Released Set for

Population 2 (Seventh and Eighth Grades)

- All publicly released items used to

assess seventh- and eighth-grade students in the TIMSS study. Paperback,

127 pp. $20.00 (+ $5.00 shipping & handling, if international).

TIMSS Mathematics and Science Items

Released Set for Population 3 (End of

Secondary School) - All publicly released

items used to assess students in their
149

final year of schooling in the TIMSS

study. Paperback.

To order, contact: TIMSS International

Study Center. Also may be downloaded

from: http://wwwcsteep.bc.edu/TIMSS1/

TIMSSPublications.html#International. 

HOW CAN I FIND OUT MORE

ABOUT EDUCATION IN VARIOUS

TIMSS COUNTRIES?

National Contexts for Mathematics and

Science Education: An Encyclopedia of the

Education Systems Participating in TIMSS,

1997 - Each participating country’s education system is discussed in a separate

chapter, considering geographic and

economic influences, school governance, teacher education, and curriculum. Hardback, 423 pp. $75.

To order, contact: Pacific Educational

Press.

CONTACT INFORMATION:

Superintendent of Documents

P.O. Box 371954

Pittsburgh, PA 15250-7954

Telephone: (202) 512-1800

Fax: (202) 512-2250.

TIMSS International Study Center 

Center for the Study of Testing,

Evaluation, and Educational Policy

(CSTEEP) Campion Hall Room 323

School of Education, Boston College

Chestnut Hill, MA 02167; 

Telephone: (617) 552-4521; 

Fax: (617) 552-8419; 

Email: timss@bc.edu; 

Internet: http://wwwcsteep.bc.edu.

The IEA Secretariat 

Herengracht 487 

1017 BT Amsterdam

The Netherlands; 

Telephone: +31 20 625 36 25; 

Fax: +31 20 420 71 36; 

E-mail: Department@IEA.nl.

Kluwer Academic Publishers Group

Order Department

P.O. Box 358, Accord Station

Hingham, MA 02018-0358; 

Telephone: (617) 871-6600; 

Fax (617) 871-6528; 

Email: kluwer@wkap.com; 

Internet: http://www.wkap.nl or

http://ustimss.msu.edu/publicat.htm.

Pacific Educational Press 

Faculty of Education

University of British Columbia

Vancouver, Canada V6T 1Z4; 

Telephone: (604) 822-5385; 

Fax: (604) 822-6603; 

Email: cedwards@interchange.ubc.ca.

University of Michigan

Attn: Suyin Liang

Center for Human Growth and

Development

300 N. Ingalls, 10th Floor

Ann Arbor, MI 48109-0406

Telephone: (734) 764-2443

(Please make checks payable to “The

University of Michigan.”)