Highlights From TIMSS 2007:

Mathematics and Science Achievement of U.S. Fourthand Eighth-Grade Students in an International Context

September 2009

Patrick Gonzales

Project Officer 

National Center for Education Statistics

Trevor Williams

Leslie Jocelyn

Stephen Roey

David Kastberg

Summer Brenwald

Westat

NCES 2009-001 REVISED

U.S. DEPARTMENT OF EDUCATION
U.S. Department of Education

Margaret Spellings

Secretary

Institute of Education Sciences

Sue Betka

Acting Director

National Center for Education Statistics

Stuart Kerachsky

Acting Commissioner

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Suggested Citation

Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Kastberg, D., and Brenwald, S. (2008). Highlights From TIMSS 2007: 

Mathematics and Science Achievement of U.S. Fourth- and Eighth-Grade Students in an International Context (NCES 2009–001 

Revised). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, 

DC.

For ordering information on this report, write to 

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Content Contact

Patrick Gonzales

(415) 920-9229

patrick.gonzales@ed.gov
iii

Executive Summary

 HIGHLIGHTS FROM TIMSS 2007 EXECUTIVE SUMMARY

The 2007 Trends in International Mathematics and Science 

Study (TIMSS) is the fourth administration since 1995 of this 

international comparison. Developed and implemented at 

the international level by the International Association for 

the Evaluation of Educational Achievement (IEA)—an 

international organization of national research institutions and 

governmental research agencies—TIMSS is used to measure 

over time the mathematics and science knowledge and skills 

of fourth- and eighth-graders. TIMSS is designed to align 

broadly with mathematics and science curricula in the 

participating countries. 

This report focuses on the performance of U.S. students 

relative to that of their peers in other countries in 2007, 

and on changes in mathematics and science achievement 

since 1995.1 Thirty-six countries or educational jurisdictions 

participated at grade four in 2007, while 48 participated at 

grade eight.2 This report also describes additional details 

about the achievement of U.S. student subpopulations. 

All differences described in this report are statistically 

significant at the .05 level. No statistical adjustments 

to account for multiple comparisons were used.

Key findings from the report include the following:

• In 2007, the average mathematics scores of both U.S. 

fourth-graders (529) and eighth-graders (508) were higher 

than the TIMSS scale average (500 at both grades).3

The average U.S. fourth-grade mathematics score 

was higher than those of students in 23 of the 35 other 

countries, lower than those in 8 countries (all located in 

Asia or Europe), and not measurably different from those 

in the remaining 4 countries.4 At eighth grade, the average 

U.S. mathematics score was higher than those of students 

in 37 of the 47 other countries, lower than those in 5 

countries (all of them located in Asia), and not measurably 

different from those in the other 5 countries.

• Compared to 1995, the average mathematics scores for 

both U.S. fourth- and eighth-grade students were higher in 

2007. At fourth grade, the U.S. average score in 2007 was 

529, 11 points higher than the 1995 average of 518. At 

eighth grade, the U.S. average mathematics score in 2007 

was 508, 16 points higher than the 1995 average of 492. 

• In 2007, 10 percent of U.S. fourth-graders and 6 percent 

of U.S. eighth-graders scored at or above the advanced 

international benchmark in mathematics.5 At grade four, 

seven countries had higher percentages of students 

performing at or above the advanced international 

mathematics benchmark than the United States: 

Singapore, Hong Kong SAR, Chinese Taipei, Japan, 

Kazakhstan, England, and the Russian Federation. 

Fourth-graders in these seven countries were also found 

to outperform U.S. fourth-graders, on average, on the 

overall mathematics scale. At grade eight, a slightly 

different set of seven countries had higher percentages 

of students performing at or above the advanced 

mathematics benchmark than the United States: Chinese 

Taipei, Korea, Singapore, Hong Kong SAR, Japan, 

Hungary, and the Russian Federation. These seven 

countries include the five countries that had higher 

average overall mathematics scores than the United 

States, as well as Hungary and the Russian Federation.

• In 2007, the average science scores of both U.S. fourthgraders (539) and eighth-graders (520) were higher 

than the TIMSS scale average (500 at both grades). 

The average U.S. fourth-grade science score was higher 

than those of students in 25 of the 35 other countries, 

lower than those in 4 countries (all of them in Asia), 

and not measurably different from those in the remaining 

6 countries. At eighth grade, the average U.S. science 

score was higher than the average scores of students 

in 35 of the 47 other countries, lower than those in 9 

countries (all located in Asia or Europe), and not 

measurably different from those in the other 3 countries.

1At grade four, a total of 257 schools and 10,350 students participated in the United States in 2007. At grade eight, 239 schools and 9,723 students participated. 

The overall weighted school response rate in the United States was 70 percent at grade four before the use of substitute schools. The final weighted student 

response rate at grade four was 95 percent. At grade eight, the overall weighted school response rate before the use of substitute schools was 68 percent. 

The final weighted student response rate at grade eight was 93 percent. 2The total number of countries reported here differs from the total number reported in the international TIMSS reports (Mullis et al. 2008; Martin et al. 2008). 

In addition to the 36 countries at grade four and 48 countries at grade eight, 8 other educational jurisdictions, or “benchmarking” entities, participated: the states 

of Massachusetts and Minnesota; the Canadian provinces of Alberta, British Columbia, Ontario, and Quebec; Dubai, United Arab Emirates; and the Basque region 

of Spain.

3TIMSS provides two overall scales—mathematics and science—as well as several content and cognitive domain subscales for each of the overall scales. 

The scores are reported on a scale from 0 to 1,000, with the TIMSS scale average set at 500 and standard deviation set at 100. 4TIMSS is open to countries and subnational entities, or educational jurisdictions, which are part of larger countries. For example, Hong Kong is a Special 

Administrative Region (SAR) of the People’s Republic of China. For convenience, this report uses the term “country” or “nation” to refer to all participating entities.

5TIMSS reports on four benchmarks to describe student performance in mathematics and science. Each benchmark is associated with a score on the achievement 

scale and a description of the knowledge and skills demonstrated by students at that level of achievement. The advanced international benchmark indicates that 

students scored 625 or higher. More information on the benchmarks can be found in the main body of the report and appendix A.
iv

• The average science scores for both U.S. fourth- and 

eighth-grade students in 2007 were not measurably 

different from those in 1995. The U.S. fourth-grade 

average science score in 2007 was 539 and in 1995 

was 542. The U.S. eighth-grade average science score 

in 2007 was 520 and in 1995 was 513.

• In 2007, 15 percent of U.S. fourth-graders and 10 percent 

of U.S. eighth-graders scored at or above the advanced 

international benchmark in science. At grade four, two 

countries had higher percentages of students performing 

at or above the advanced international science 

benchmark than the United States: Singapore and 

Chinese Taipei. Fourth-graders in these two countries 

were also found to outperform U.S. fourth-graders, on 

average, on the overall science scale. At grade eight, six 

countries had higher percentages of students performing 

at or above the advanced science benchmark than the 

United States: Singapore, Chinese Taipei, Japan, 

England, Korea, and Hungary. These six countries also 

had higher average overall eighth-grade science scores 

than the United States.

EXECUTIVE SUMMARY HIGHLIGHTS FROM TIMSS 2007
v

Acknowledgments

 HIGHLIGHTS FROM TIMSS 2007 Acknowledgments

The authors wish to thank all those who assisted with TIMSS 

2007, from its design to the reporting of findings. Most 

importantly, the authors wish to thank the many principals, 

teachers, and students who participated in the study.
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vii

Contents

 HIGHLIGHTS FROM TIMSS 2007 CONTENTS

 Page

Executive Summary .................................................................................................................................................................. iii

Acknowledgments .....................................................................................................................................................................v

List of Tables ............................................................................................................................................................................. viii

List of Figures ..............................................................................................................................................................................ix

List of Exhibits .............................................................................................................................................................................xi

Introduction .................................................................................................................................................................................1

TIMSS in brief............................................................................................................................................................................1

Design and administration of TIMSS .....................................................................................................................................1

Reporting TIMSS results...........................................................................................................................................................3

Nonresponse bias in the U.S. TIMSS samples .......................................................................................................................4

Further information.................................................................................................................................................................4

Mathematics Performance in the United States and Internationally

The TIMSS mathematics assessment ....................................................................................................................................5

Average scores in 2007..........................................................................................................................................................6

Trends in scores since 1995....................................................................................................................................................8

Content and cognitive domain scores in 2007 ................................................................................................................10

Performance on the TIMSS international benchmarks....................................................................................................13

Performance within the United States...............................................................................................................................15

Effect size of the difference in average scores................................................................................................................28

Science Performance in the United States and Internationally

The TIMSS science assessment............................................................................................................................................31

Average scores in 2007........................................................................................................................................................31

Trends in scores since 1995..................................................................................................................................................33

Content and cognitive domain scores in 2007 ................................................................................................................35

Performance on the TIMSS international benchmarks....................................................................................................38

Performance within the United States...............................................................................................................................41

Effect size of the difference in average scores................................................................................................................51

References .................................................................................................................................................................................55

Appendix A: Technical Notes.................................................................................................................................................A-1

Appendix B: Example Items ................................................................................................................................................... B-1

Appendix C: TIMSS-NAEP Comparison................................................................................................................................. C-1

Appendix D: Online Resources and Publications.................................................................................................................D-1
viii

APPENDNDIX B HIGHLIGHTS FROM TIMSS 2007 IX C HIGHLIGHTS FROM TIMSS 2007

List of Tables

 HIGHLIGHTS FROM TIMSS 2007 LIST OF TABLES

Table Page

1. Participation in the TIMSS fourth- and eighth-grade assessments, by grade and country: 

1995, 1999, 2003, and 2007................................................................................................................................................ 2

2. Percent of fourth- and eighth-grade TIMSS mathematics assessment devoted to content and cognitive 

domains: 2007..................................................................................................................................................................... 5

3. Average mathematics scores of fourth- and eighth-grade students, by country: 2007 ........................................... 7

4. Trends in average mathematics scores of fourth- and eighth-grade students, by country: 1995 to 2007.............. 8 

5. Description of TIMSS mathematics cognitive domains: 2007 ...................................................................................... 10

6. Average mathematics content and cognitive domain scores of fourth-grade students, 

by country: 2007 ............................................................................................................................................................... 11

7. Average mathematics content and cognitive domain scores of eighth-grade students, 

by country: 2007 ............................................................................................................................................................... 12

8. Description of TIMSS international mathematics benchmarks, by grade: 2007........................................................ 13

9. Mathematics scores of fourth- and eighth-grade students defining 10th and 90th percentiles, 

by country: 2007 ............................................................................................................................................................... 17

10. Percent of fourth- and eighth-grade TIMSS science assessment devoted to content 

and cognitive domains: 2007 ......................................................................................................................................... 31

11. Average science scores of fourth- and eighth-grade students, by country: 2007................................................... 32

12. Trends in average science scores of fourth- and eighth-grade students, by country: 1995 to 2007 ..................... 33

13. Description of TIMSS science cognitive domains: 2007................................................................................................ 35

14. Average science content and cognitive domain scores of fourth-grade students, by country: 2007 ................. 36

15. Average science content and cognitive domain scores of eighth-grade students, by country: 2007 ................ 37

16. Description of TIMSS international science benchmarks, by grade: 2007 ................................................................ 38

17. Science scores of fourth- and eighth-grade students defining 10th and 90th percentiles, 

by country: 2007 ............................................................................................................................................................... 42

A-1. Coverage of target populations and participation rates, by grade and country: 2007 ...................................... A-5

A-2. Total number of schools and students, by grade and country: 2007....................................................................... A-7

A-3. Number of new and trend mathematics and science items in the TIMSS grade four and grade eight 

assessments, by type: 2007.......................................................................................................................................... A-12

A-4. Number of mathematics and science items in the TIMSS grade four and grade eight assessments, 

by type and content domain: 2007........................................................................................................................... A-13

A-5. Within-country constructed-response scoring reliability for TIMSS grade four and grade eight 

mathematics and science items, by exact percent score 

agreement and country: 2007.................................................................................................................................... A-16

A-6. Weighted response rates for unimputed variables for TIMSS grade four and grade eight: 2007 ....................... A-20

A-7. Difference between average scores, standard deviations, pooled standard deviations, 

and effect sizes of mathematics and science scores of fourth- and eighth-grade students, 

by country, sex, race/ethnicity, and school poverty level: 2007............................................................................ A-24
ix

Figure Page

1. Countries that participated in TIMSS 2007 ....................................................................................................................... 3

2. Difference between average mathematics scores of U.S. fourth-and eighth-grade students 

and the TIMSS scale average: 1995, 1999, 2003, and 2007 ........................................................................................... 9

3. Percentage of US fourth- and eighth-grade students who reached each TIMSS international 

mathematics benchmark compared with the international median percentage: 2007....................................... 14

4. Percentage of fourth- and eighth-grade students who reached the TIMSS advanced international 

benchmark in mathematics, by country: 2007............................................................................................................. 16

5. Cutpoints at the 10th and 90th percentile for mathematics content domain scores of U.S. fourthand eighth-grade students: 2007 ................................................................................................................................... 18

6. Trends in 10th and 90th percentile mathematics scores of U.S. fourth- and eighth-grade students: 

1995, 1999, 2003, and 2007.............................................................................................................................................. 19

7. Difference in average mathematics scores of fourth- and eighth-grade students, 

by sex and country: 2007................................................................................................................................................. 20

8. Average mathematics scores of U.S. fourth- and eighth-grade students, by content domain 

and sex: 2007 .................................................................................................................................................................... 21

9. Trends in sex differences in average mathematics scores of U.S. fourth- and eighth-grade students: 

1995, 1999, 2003, and 2007.............................................................................................................................................. 22

10. Average mathematics scores of U.S. fourth- and eighth-grade students, by race/ethnicity: 2007....................... 23

11. Trends in differences in average mathematics scores of U.S. fourth- and eighth-grade students, 

by selected race/ethnicity: 1995, 1999, 2003 and 2007............................................................................................... 24

12. Average mathematics scores of U.S. fourth- and eighth-grade students, by percentage of students 

in public school eligible for free or reduced-price lunch: 2007 .................................................................................. 25

13. Trends in differences in average mathematics scores of U.S. fourthand eighth-grade students, by school poverty level: 1999, 2003, and 2007............................................................. 26

14. Effect size of difference in average mathematics achievement 

of fourth- and eighth-grade students, by country, sex, race/ethnicity, and school poverty level: 2007 .............. 29

15. Difference between average science scores of U.S. fourth- and eighth-grade students 

and the TIMSS scale average: 1995, 1999, 2003, and 2007 ......................................................................................... 34

16. Percentage of U.S. fourth- and eighth-grade students who reached each TIMSS international science 

benchmark compared with the international median percentage: 2007............................................................... 39

17. Percentage of fourth- and eighth-grade students who reached the TIMSS advanced international 

benchmark in science, by country: 2007 ...................................................................................................................... 40

18. Cutpoints at the 10th and 90th percentile for science content domain scores of U.S. fourthand eighth-grade students: 2007 ................................................................................................................................... 43

19. Trends in 10th and 90th percentile science scores of U.S. fourth- and eighth-grade students: 

1995, 1999, 2003, and 2007.............................................................................................................................................. 44

20. Difference in average science scores of fourth- and eighth-grade students, by sex and country: 2007............. 45

21. Average science scores of U.S. fourth- and eighth-grade students, by content domain and sex: 2007.............. 46

 HIGHLIGHTS FROM TIMSS 2007 LIST OF FIGURES

List of Figures
x

Figure Page

22. Trends in sex differences in average science scores of U.S. fourth- and eighth-grade students: 

1995, 1999, 2003, and 2007.............................................................................................................................................. 47

23. Average science scores of U.S. fourth- and eighth-grade students, 

by race/ethnicity: 2007.................................................................................................................................................... 48

24. Trends in differences in average science scores of U.S. fourth- and eighth-grade students, 

by selected race/ethnicity: 1995, 1999, 2003, and 2007.............................................................................................. 49

25. Average science scores of U.S. fourth- and eighth-grade students, by percentage of students 

in public school eligible for free or reduced-price lunch: 2007 .................................................................................. 50

26. Trends in differences in average science scores of U.S. fourth- and eighth-grade students, 

by school poverty level: 1999, 2003, and 2007.............................................................................................................. 51

27. Effect size of difference in average science achievement of fourth- and eighth-grade students, 

by country, sex, race/ethnicity, and school poverty level: 2007................................................................................ 53

LIST OF FIGURES HIGHLIGHTS FROM TIMSS 2007
xi

Exhibit Page

B1. Example fourth-grade mathematics item: 2007..........................................................................................................B-2

B2. Example fourth-grade mathematics item: 2007..........................................................................................................B-3

B3. Example fourth-grade mathematics item: 2007..........................................................................................................B-4

B4. Example eighth-grade mathematics item: 2007.........................................................................................................B-5

B5. Example eighth-grade mathematics item: 2007.........................................................................................................B-6

B6. Example eighth-grade mathematics item: 2007.........................................................................................................B-7

B7. Example eighth-grade mathematics item: 2007.........................................................................................................B-8

B8. Example fourth-grade science item: 2007 ...................................................................................................................B-9

B9. Example fourth-grade science item: 2007 .................................................................................................................B-10

B10. Example fourth-grade science item: 2007 .................................................................................................................B-11

B11. Example eighth-grade science item: 2007 ................................................................................................................B-12

B12. Example eighth-grade science item: 2007 ................................................................................................................B-13

B13. Example eighth-grade science item: 2007 ................................................................................................................B-14

B14. Example eighth-grade science item: 2007 ...............................................................................................................B-15

 HIGHLIGHTS FROM TIMSS 2007 LIST OF EXHIBITS

List of Exhibits
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1

Introduction

 HIGHLIGHTS FROM TIMSS 2007 INTRODUCTION

TIMSS in brief 

The Trends in International Mathematics and Science 

Study (TIMSS) 2007 is the fourth time since 1995 that this 

international comparison of student achievement has been 

conducted. Developed and implemented at the international 

level by the International Association for the Evaluation of 

Educational Achievement (IEA), an international organization 

of national research institutions and governmental research 

agencies, TIMSS is used to measure over time the 

mathematics and science knowledge and skills of fourthand eighth-graders. 

TIMSS is designed to align broadly with mathematics and 

science curricula in the participating countries. The results, 

therefore, suggest the degree to which students have learned 

mathematics and science concepts and skills likely to have 

been taught in school. TIMSS also collects background 

information on students, teachers, and schools to allow 

cross‐national comparison of educational contexts that may 

be related to student achievement. In 2007, there were 58 

countries and educational jurisdictions1 that participated 

in TIMSS, at the fourth- or eighth-grade level, or both.2

This report presents the performance of U.S. students 

relative to their peers in other countries, and on changes in 

mathematics and science achievement since 1995. Most of 

the findings in the report are based on the results presented 

in two reports published by the IEA and available online at 

http://www.timss.org:

• TIMSS 2007 International Mathematics Report: 

Findings From IEA’s Trends in International Mathematics 

and Science Study at the Fourth and Eighth Grades

(Mullis et al. 2008); and

• TIMSS 2007 International Science Report: Findings 

From IEA’s Trends in International Mathematics 

and Science Study at the Fourth and Eighth Grades

(Martin et al. 2008).

For a number of participating countries, changes in 

achievement can be documented over the last 12 years, 

from 1995 to 2007. For other countries, changes can be 

documented over a shorter period of time. Table 1 and 

figure 1 show the countries that participated in TIMSS 2007 

as well as their participation status in the earlier TIMSS data 

collections. The TIMSS fourth-grade assessment was 

implemented in 1995, 2003, and 2007, while the eighth-grade 

assessment was implemented in 1995, 1999, 2003, and 2007.

This report describes additional details about the achievement 

of U.S. students that are not available in the international 

reports, such as trends in the achievement of students of 

different racial and ethnic and socioeconomic backgrounds. 

Design and administration of TIMSS 

TIMSS 2007 is sponsored by the IEA and carried out under 

a contract with the TIMSS & PIRLS3 International Study Center 

at Boston College. The National Center for Education 

Statistics (NCES), in the Institute of Education Sciences 

at the U.S. Department of Education, is responsible for the 

implementation of TIMSS in the United States. Data collection 

in the United States was carried out under contract to 

Windwalker Corporation and its subcontractors, Westat 

and Pearson Educational Measurement. 

Participating countries administered TIMSS to two national 

probability samples of students and schools, based on a 

standardized definition. Countries were required to draw 

samples of students who were nearing the end of their fourth 

year or eighth year of formal schooling, beginning with the 

International Standard Classification of Education (ISCED) 

Level 1.4 In most countries, including the United States, these 

students were in the fourth and eighth grades. Details on the 

grades assessed in each country are included in appendix A. 

In the United States, TIMSS was administered between April 

and June 2007. The U.S. sample included both public and 

private schools, randomly selected and weighted to be 

representative of the nation.5 In total, 257 schools and 10,350 

students participated at grade four, and 239 schools and 

9,723 students participated at grade eight. The overall 

weighted school response rate in the United States was 70 

1TIMSS is open to countries and subnational entities, or educational jurisdictions, which are part of larger countries. For example, Hong Kong is a Special 

Administrative Region (SAR) of the People’s Republic of China. For convenience, this report uses the term “country” or “nation” to refer to all participating entities.

2Data from two nations were judged problematic by the IEA. Morocco failed to meet the required school participation rates in grade eight because of a procedural 

difficulty with some schools. Also, the quality of the data from Mongolia was not well documented at either grade level. In the international reports, Morocco is 

included in the fourth-grade tables but is shown “below the line” in the eighth-grade tables to indicate a problem in data quality. Data on Mongolia are reported 

in an appendix. For the purposes of the present report, statistics relating to Moroccan eighth-graders and to Mongolian students in both grades are not reported. 3The international study center takes its name from the two main IEA studies it coordinates; the Trends in International Mathematics and Science Study (TIMSS) 

and the Progress in International Reading Literacy Study (PIRLS).

4The ISCED was developed by the United Nations Educational, Scientific, and Cultural Organization (UNESCO) to assist countries in providing comparable, 

cross-national data. ISCED Level 1 is termed primary schooling, and in the United States is equivalent to the first through sixth grades (Matheson et al. 1996).

5The sample frame data for public schools in the United States was based on the 2006 National Assessment of Educational Progress (NAEP) sampling frame. 

This was done because recruitment of districts and schools began at the end of the 2005-06 school year to maximize response rates. The 2006 NAEP sampling 

frame was based on the 2003-04 Common Core of Data (CCD), and the data for private schools were from the 2003-04 Private School Universe Survey (PSS). 

Any school containing at least one grade four or one grade eight class was included in the school sampling frame.
2

APPENDIX B HIGHLIGHTS FROM TIMSS 2007 INTRODUCTION HIGHLIGHTS FROM TIMSS 2007

Grade four Grade eight

Country 1995 2003 2007 1995 1999 2003 2007

Total 26 25 36 41 38 46 48

Algeria  

Armenia    

Australia1       

Austria   

Bahrain  

Belgium (Flemish)    

Belgium (French) 

Bosnia and Herzegovina 

Botswana  

Bulgaria    

Canada   

Chile  

Chinese Taipei     

Colombia   

Cyprus      

Czech Republic     

Denmark  

Egypt  

El Salvador  

England2       

Estonia 

Finland 

France 

Georgia  

Germany  

Ghana  

Greece  

Hong Kong SAR3       

Hungary       

Iceland  

Indonesia   

Iran, Islamic Rep. of       

Ireland  

Israel4     

Italy4     

Japan       

Jordan   

Kazakhstan 

Grade four Grade eight

Country 1995 2003 2007 1995 1999 2003 2007

Total 26 25 36 41 38 46 48

Korea, Rep. of     

Kuwait    

Latvia5      

Lebanon  

Lithuania      

Macedonia, Rep. of  

Malaysia   

Malta 

Moldova, Rep. of   

Morocco4    

Netherlands      

New Zealand      

Norway      

Oman 

Palestinian Nat'l Auth.  

Philippines   

Portugal  

Qatar  

Romania    

Russian Federation      

Saudi Arabia  

Scotland      

Serbia  

Singapore       

Slovak Republic    

Slovenia1       

South Africa6   

Spain 

Sweden    

Switzerland 

Syrian Arab Republic 

Thailand    

Tunisia     

Turkey  

Ukraine  

United States       

Yemen 

1Because of national-level changes in the starting age/date for school, 1999 data for Australia and Slovenia cannot be compared to 2003 data. 2England collected data at grade eight in 1995, 1999, and 2003, but due to problems with meeting the minimum sampling requirements for 2003, its eighth-grade 

data are not shown in this report.

3Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

4Because of changes in the population tested, 1995 data for Israel and Italy, and 1999 data for Morocco are not shown. 5Only Latvian-speaking schools were included in 1995 and 1999. For trend analyses, only Latvian-speaking schools are included in the estimates. 6Because within-classroom sampling was not accounted for, 1995 data are not shown for South Africa.

NOTE: No fourth-grade assessment was conducted in 1999. Only countries that completed the necessary steps for their data to appear in the reports from the 

International Study Center are listed. In addition to the countries listed above, eight separate jurisdictions participated in the Trends in International Mathematics 

and Science Study (TIMSS) 2007: the provinces of Alberta, British Columbia, Ontario, and Quebec in Canada; the Basque region of Spain; Dubai, UAE, and the 

states of Massachusetts and Minnesota. Information on these eight jurisdictions can be found in the international TIMSS 2007 reports. Morocco participated in 

TIMSS 2007 at both the fourth and eighth grades, but due to sampling difficulties, its grade eight data are not shown in this report. Mongolia also participated in 

TIMSS 2007 but could not complete the steps necessary to have its data included in the report. Countries could participate at either grade level. Countries were 

required to sample students enrolled in the grade corresponding to the fourth and eighth year of schooling, beginning with International Standard Classification 

of Education (ISCED) level 1, providing that the mean age at the time of testing was at least 9.5 years and 13.5 years, respectively. In the United States and most 

countries, this corresponds to grade four and grade eight. See table A1 in appendix A for details.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1995, 

1999, 2003 and 2007.

Table 1. Participation in the TIMSS fourth- and eighth-grade assessments, by grade and country: 

1995, 1999, 2003, and 2007
3

HIGHLIGHTS FROM TIMSS 2007 HIGHLIGHTS FROM TIMSS 2007 INTRAPPE ODUCTI NDIX B ON

percent at grade four before the use of substitute schools and 

89 percent with the inclusion of substitute schools.6 At grade 

eight, the overall weighted school response rate before the 

use of substitute schools was 68 percent and 83 percent with 

the inclusion of substitute schools. The final weighted student 

response rate at grade four was 95 percent and at grade eight 

was 93 percent. Student response rates are based on a 

combined total of students from both sampled and substitute 

schools. Detailed information on sampling, administration, 

response rates, and other technical issues are included 

in appendix A.

Reporting TIMSS results

Achievement results from TIMSS are reported on a scale from 

0 to 1,000, with a TIMSS scale average of 500 and standard 

deviation of 100. Even though the countries participating in 

TIMSS have changed across the four assessments between 

1995 and 2007, comparisons between the 2007 results and 

prior results are still possible because the achievement scores 

in each of the TIMSS assessments are placed on a scale which 

is not dependent on the list of participating countries in any 

particular year. A brief description of the assessment equating 

and scaling is presented in appendix A to this volume. A more 

detailed presentation can be found in the TIMSS 2007 

Technical Report (Olson, Martin, and Mullis 2008).

In addition to numerical scale results, TIMSS also includes 

international benchmarks. The TIMSS international benchmarks 

provide a way to interpret the scale scores and to understand 

how students’ proficiency in mathematics and science varies 

along the TIMSS scale. The TIMSS benchmarks describe four 

levels of student achievement in each subject, based on the 

kinds of skills and knowledge students at each score cutpoint 

would need to successfully answer the mathematics and 

science items. In general, the score cutpoints for the TIMSS 

benchmarks were set based on the distribution of students 

Lithuania

Latvia

Romania

Ukraine

Sweden Bulgaria

Bosnia &

Herzegovina

Hungary Norway

Denmark

Germany Netherlands

Scotland

England

El Salvador

United States

Colombia

Czech Republic

Austria

Slovenia

Italy

Morocco

Malta

Ghana

Israel

Jordan

Serbia

Egypt

Turkey

Saudi

Arabia Qatar

Thailand

Malaysia

Singapore

Australia

Indonesia

New Zealand

Bahrain

Kuwait

Oman

Yemen

Cyprus

GeorgiaKazakhstan

Russian Federation

Armenia

Syrian Arab

Republic

Lebanon Hong Kong

Korea

Chinese Taipei

Japan

Algeria

Botswana

Tunisia

Palestinian

National

Authority

Slovak Republic

Iran,

 Islamic

 Rep. of

Figure 1. Countries that participated in TIMSS 2007

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

6NCES standards advise that substitute schools should not be included in the calculation of response rates (standard 1-3-8; National Center for Education 

Statistics 2002). Response rates calculated “before replacement” are consistent with this standard. Response rates calculated “after replacement” include 

substitute schools and hence are not consistent with NCES standards. Both kinds of response rates are reported here in the interests of comparability with 

the TIMSS international reports which report response rates before and after replacement.
4

along the TIMSS scale. More information on the development 

of the benchmarks and the procedures used to set the score 

cutpoints can be found in the TIMSS 2007 Technical Report

(Olson, Martin, and Mullis 2008). 

All differences described in this report are statistically 

significant at the .05 level. No statistical adjustments to 

account for multiple comparisons were used. Differences that 

are statistically significant are discussed using comparative 

terms such as “higher” and “lower.” Differences that are not 

statistically significant are either not discussed or referred to 

as “not measurably different” or “not statistically significant.” 

In this latter case, failure to find a difference as statistically 

significant does not necessarily mean that there was no 

difference. It simply means that, given the precision of the 

estimates, there is a larger than five percent chance that the 

difference was zero. In addition, because the results of tests 

of statistical significance are, in part, influenced by sample 

sizes, statistically significant results may not identify those 

findings that have policy or practical importance. For this 

reason, this report includes effect sizes to provide the reader 

with a sense of the magnitude of statistically significant 

differences. Further information about effect sizes and about 

the tests conducted to determine statistical significance can 

be found in appendix A. Supplemental tables providing all 

estimates and standard errors discussed in this report are 

available online at http://nces.ed.gov/pubsearch/pubsinfo.

asp?pubid=2009001. 

All data presented in this report are used to describe 

relationships between variables. These data are not intended, 

nor can they be used, to imply causality. Student performance 

can be affected by a complex mix of educational and other 

factors that are not examined here.

Nonresponse bias in the U.S. 

TIMSS samples

NCES standards require a nonresponse bias analysis if 

school-level response rates fall below 85 percent, as they 

did for both the fourth- and eighth-grade school samples 

in TIMSS 2007.7 As a consequence, a nonresponse bias 

analysis was undertaken, similar to that used for TIMSS 

2003 (Ferraro and Van De Kerckhove 2006). 

These analyses examined whether the participation status 

of schools (participant/non-participant) was related to seven 

school characteristics: the region of the country in which the 

school was located (Northeast, Southeast, Central, West); 

the type of community served by the school (central city, 

urban fringe/large town, rural/small town); whether the school 

was public or private; percentage of students eligible for free 

or reduced-price lunch; number of students enrolled in fourth 

or eighth grade; total number of students; and percentage of 

students from minority backgrounds. Details are provided in 

appendix A.8

The findings indicate some potential for bias in the data 

arising from regional and community-type differences in 

participation, along with the fact that schools with higher 

percentages of minority students were less likely to 

participate. Specifically, grade 4 schools in the central region 

were more likely to participate than schools in the other 

regions, and schools in rural/small towns were more likely 

to participate than schools in central cities. However with 

the inclusion of substitute schools there were no measurable 

differences by region and differences by community type were 

substantially reduced. At grade 8, after substitution, the results 

of the analyses indicated that schools in central cities were 

still more likely to participate than schools in urban/fringe/large 

towns. At both grades, schools with higher percentages 

of minority students were less likely to participate, but 

the measurable differences were small after substitution 

especially at grade 8. Since TIMSS is conducted under a 

set of standard rules designed to facilitate international 

comparisons, the U.S. nonresponse bias analysis results 

were not used to adjust the U.S. data for this source of bias. 

While this may be possible at some later date, at present the 

variables identified above remain as potential sources of bias 

in the published estimates. 

Further information

To assist the reader in understanding how TIMSS relates 

to the National Assessment of Educational Progress (NAEP), 

the primary source of national- and state-level data on U.S. 

students’ mathematics and science achievement, NCES 

compared the form and content of the TIMSS and NAEP 

mathematics and science assessments. A summary of 

the results of this comparison is included in appendix C. 

Appendix D includes a list of TIMSS publications and 

resources published by NCES and the IEA. Standard errors 

for the estimates discussed in the report are available online 

at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=

2009001. Detailed information on TIMSS can also be found 

on the NCES website (http://nces.ed.gov/timss) and the 

international TIMSS website (http://www.timss.org). 

7Standard 2-2-2 found in National Center for Education Statistics 2002.

8The full text of the nonresponse bias analysis conducted for TIMSS 2007 will be included in a technical report released with the U.S. national dataset. 

See appendix A for a description of the analyses undertaken and additional details on the findings.

INTRODUCTION HIGHLIGHTS FROM TIMSS 2007
5

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Mathematics Performance in the United States

and Internationally

The TIMSS mathematics 

assessment

The TIMSS mathematics assessment is designed along two 

dimensions: the mathematical topics or content that students 

are expected to learn and the cognitive skills students are 

expected to have developed. The topical or content domains 

(as they are called in TIMSS) covered at grade four are 

number, geometric shapes and measures, and data display

(table 2). At grade eight, the content domains are number, 

algebra, geometry, and data and chance. The cognitive 

domains in each grade are knowing, applying, and reasoning. 

Example items from the TIMSS mathematics assessment are 

included in appendix B (see items B1 through B7).

The proportion of items devoted to a domain, and, therefore, 

the contribution of the domain to the overall mathematics 

scale score differs somewhat across grades. For example, 

in 2007 at grade four, 52 percent of the TIMSS mathematics 

assessment focused on the number domain, while the 

analogous percentage at grade eight was 29 percent. 

The proportion of items devoted to each cognitive domain 

was similar across grades.

Also, within a content or cognitive domain, the makeup of 

items, in terms of difficulty and form of knowledge and skills 

addressed, differs across grade levels to reflect the nature, 

difficulty, and emphasis of the subject matter encountered in 

school at each grade. TIMSS 2007 Assessment Frameworks

(Mullis et al. 2005) provides a more detailed description 

of the content and cognitive domains assessed in TIMSS. 

The development and validation of the cognitive domains 

is detailed in IEA’s TIMSS 2003 International Report on 

Achievement in the Mathematics Cognitive Domains: 

Findings From a Developmental Project (Mullis, Martin, 

and Foy 2005).

TIMSS provides an overall mathematics scale score as well 

as content and cognitive domain scores at each grade level. 

The TIMSS mathematics scale is from 0 to 1,000 and the 

international mean score is set at 500, with a standard deviation 

of 100. The scaling of data is conducted separately for each 

grade and each content domain. Thus, a score of 500 on the 

grade four scale is not equivalent to a score of 500 on the 

grade eight scale. While the scales were created to each have 

a mean of 500 and a standard deviation of 100, the subject 

matter and the level of difficulty of items necessarily differ 

between the assessments at both grades. Therefore, direct 

comparisons between scores across grades should not be 

made. See appendix A for more details.

Table 2. Percentage of fourth- and eighth-grade TIMSS mathematics assessment 

devoted to content and cognitive domains: 2007

Grade four

Content domains

Percent of 

assessment

Number 52

Geometric shapes and measures 34

Data display 15

Cognitive domains

Percent of 

assessment

Knowing 39

Applying 39

Reasoning 22

Grade eight

Content domains

Percent of 

assessment

Number 29

Algebra 30

Geometry 22

Data and chance 19

Cognitive domains

Percent of 

assessment

Knowing 38

Applying 41

Reasoning 21

NOTE: The content and cognitive domains are the foundation of the Trends in International Mathematics and Science Study (TIMSS) 

assessment. The content domains define the specific mathematics subject matter covered by the assessment, and the cognitive 

domains define the sets of behaviors expected of students as they engage with the mathematics content. Each mathematics content 

domain has several topic areas. Each topic area is presented as a list of objectives covered in a majority of participating countries, 

at either grade four or grade eight. However, the cognitive domains of mathematics are defined by the same three sets of expected 

behaviors—knowing, applying, and reasoning. Detail may not sum to totals because of rounding.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and 

Science Study (TIMSS), 2007.
6

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Scores within a subject and grade are comparable over time. 

The TIMSS scale was established originally to have a mean 

of 500 based on the average of all of the countries that 

participated in TIMSS 1995 at the fourth and eighth grades. 

Successive TIMSS assessments since then (TIMSS 1999, 

2003, and 2007) have scaled the achievement data so that 

scores are equivalent from assessment to assessment. 

That is, a score of 500 in eighth-grade mathematics in 2007 

is equivalent to a score of 500 in eighth-grade mathematics 

in 2003, in 1999, and in 1995. The same is true for the fourthgrade scale: a score of 500 in fourth-grade mathematics 

in 2007 is equivalent to a score of 500 in fourth-grade 

mathematics in 2003 and 1995. More information on how 

the TIMSS scale was created can be found in appendix A. 

Average scores in 2007

The average mathematics scores for both U.S. fourth- and 

eighth-graders were higher than the TIMSS scale average 

(table 3). In 2007, the average score of U.S. fourth-graders 

was 529 and the average score of U.S. eighth-graders was 

508, compared with the TIMSS scale average of 500 at each 

grade level.

At grade four, the average U.S. mathematics score was higher 

than those in 23 of the 35 other countries, lower than those in 

8 countries (all 8 were in Asia or Europe), and not measurably 

different from the average scores in the remaining 4 countries.

At grade eight, the average U.S. mathematics score was higher 

than those in 37 of the 47 other countries, lower than those in 

5 countries (all of them located in Asia), and not measurably 

different from the average scores in the other 5 countries.
7

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

 Average score is higher than U.S. average score (p < .05)

 Average score is not measurably different from the U.S. average score (p < .05)

 Average score is lower than the U.S. average score (p < .05) 1Hong Kong is a Special Administrative Region (SAR) of the People's Republic 

of China.

2National Target Population does not include all of the International Target 

Population defined by the Trends in International Mathematics and Science 

Study (TIMSS) (see appendix A).

3Nearly satisfied guidelines for sample participation rates only after substitute 

schools were included (see appendix A).

4Met guidelines for sample participation rates only after substitute schools were 

included (see appendix A).

5National Defined Population covers 90 percent to 95 percent of National 

Target Population (see appendix A).

6Kuwait tested the same cohort of students as other countries, but later 

in 2007, at the beginning of the next school year. 7National Defined Population covers less than 90 percent of National Target 

Population (but at least 77 percent, see appendix A).

NOTE: Countries are ordered by 2007 average score. The tests for significance 

take into account the standard error for the reported difference. Thus, a small 

difference between the United States and one country may be significant while 

a large difference between the United States and another country may not be 

significant. The standard errors of the estimates are shown in tables E-1 and E-2 

available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 2007.

Table 3. Average mathematics scores 

of fourth- and eighth-grade students, 

by country: 2007

Grade four

Country

Average 

score

TIMSS scale average 500

Hong Kong SAR1 607

Singapore 599

Chinese Taipei 576

Japan 568

Kazakhstan2 549

Russian Federation 544

England 541

Latvia2 537

Netherlands3 535

Lithuania2 530

United States4,5 529

Germany 525

Denmark4 523

Australia 516

Hungary 510

Italy 507

Austria 505

Sweden 503

Slovenia 502

Armenia 500

Slovak Republic 496

Scotland4 494

New Zealand 492

Czech Republic 486

Norway 473

Ukraine 469

Georgia2 438

Iran, Islamic Rep. of 402

Algeria 378

Colombia 355

Morocco 341

El Salvador 330

Tunisia 327

Kuwait6 316

Qatar 296

Yemen 224

Grade eight

Country

Average 

score

TIMSS scale average 500

Chinese Taipei 598

Korea, Rep. of 597

Singapore 593

Hong Kong SAR1,4 572

Japan 570

Hungary 517

England4 513

Russian Federation 512

United States4,5 508

Lithuania2 506

Czech Republic 504

Slovenia 501

Armenia 499

Australia 496

Sweden 491

Malta 488

Scotland4 487

Serbia2,5 486

Italy 480

Malaysia 474

Norway 469

Cyprus 465

Bulgaria 464

Israel7 463

Ukraine 462

Romania 461

Bosnia and Herzegovina 456

Lebanon 449

Thailand 441

Turkey 432

Jordan 427

Tunisia 420

Georgia2 410

Iran, Islamic Rep. of 403

Bahrain 398

Indonesia 397

Syrian Arab Republic 395

Egypt 391

Algeria 387

Colombia 380

Oman 372

Palestinian Nat'l Auth. 367

Botswana 364

Kuwait6 354

El Salvador 340

Saudi Arabia 329

Ghana 309

Qatar 307
8

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Trends in scores since 1995

Several countries participated in both the first TIMSS in 1995 

and the most recent TIMSS in 2007 and therefore the average 

scores can be compared over a 12-year period. At grade four, 

16 countries, including the United States, participated in both 

the first and most recent TIMSS administrations. Comparing 

2007 mathematics scores with those from 1995, one-half of 

the countries (8 of 16), including the United States, showed 

improvement in average scores and one-quarter of the 

countries (4 of 16) showed declines (table 4). In 2007, the U.S. 

fourth-grade average mathematics score of 529 was 11 scale 

score points higher than the 1995 average of 518. 

The gain in the U.S. fourth-grade average mathematics score 

(11 scale score points) was greater than the difference in six 

countries (the four countries with declines in average scores, 

as well as two other countries) and less than the gain of four 

countries (England, Hong Kong SAR, Slovenia, and Latvia). 

There was no measurable difference between the 11 score 

point gain in the United States and the gains or declines in 

score points experienced in the other countries.

At grade eight, 20 countries, including the United States, 

participated in TIMSS in both 1995 and 2007. About onequarter of the countries (6 of 20), including the United States, 

had higher average mathematics scores in 2007 than in 1995 

and students in one-half of the countries (10 of 20) showed 

declines in their average scores. The U.S. eighth-grade 

average mathematics score of 508 was 16 scale score points 

higher than the 1995 average of 492.

The gain in the U.S. eighth-grade mathematics score 

(16 scale score points) was greater than the difference 

Grade eight

Average score Difference1

Country 1995 2007 2007–1995

Colombia 332 380 47*

Lithuania3 472 506 34*

Korea, Rep. of 581 597 17*

United States4,5 492 508 16*

England4 498 513 16*

Slovenia 494 501 7*

Hong Kong SAR2,4 569 572 4

Cyprus 468 465 -2

Scotland4 493 487 -6

Hungary 527 517 -10*

Japan 581 570 -11*

Russian Federation 524 512 -12

Romania 474 461 -12*

Australia 509 496 -13*

Iran, Islamic Rep. of 418 403 -15*

Singapore 609 593 -16*

Norway 498 469 -29*

Czech Republic 546 504 -42*

Sweden 540 491 -48*

Bulgaria 527 464 -63*

Table 4. Trends in average mathematics scores of fourth- and eighth-grade students, by country: 

1995 to 2007

Grade four

Average score Difference1

Country 1995 2007 2007–1995

England 484 541 57*

Hong Kong SAR2 557 607 50*

Slovenia 462 502 40*

Latvia3 499 537 38*

New Zealand 469 492 23*

Australia 495 516 22*

Iran, Islamic Rep. of 387 402 15*

United States4,5 518 529 11*

Singapore 590 599 9

Scotland4 493 494 1

Japan 567 568 1

Norway 476 473 -3

Hungary 521 510 -12*

Netherlands6 549 535 -14*

Austria 531 505 -25*

Czech Republic 541 486 -54*

 Country difference in average scores between 1995 and 2007 is greater than analogous U.S. difference (p < .05)

 Country difference in average scores between 1995 and 2007 is not measurably different from analogous U.S. difference (p < .05)

 Country difference in average scores between 1995 and 2007 is less than analogous U.S. difference (p < .05)

*p < .05. Within-country difference between 1995 and 2007 average scores is significant. 1Difference calculated by subtracting 1995 from 2007 estimate using unrounded numbers.

2Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

3In 2007, National Target Population did not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

4In 2007, met guidelines for sample participation rates only after substitute schools were included (see appendix A). 5In 2007, National Defined Population covered 90 percent to 95 percent of National Target Population (see appendix A). 6In 2007, nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A).

NOTE: Countries are ordered based on the difference in 1995 and 2007 average scores. All countries met international sampling and other guidelines in 2007, 

except as noted. Data are not shown for some countries, because comparable data from previous cycles are not available. The tests for significance take into 

account the standard error for the reported difference. Thus, a small difference between averages for one country may be significant while a large difference for 

another country may not be significant. Detail may not sum to totals because of rounding. The standard errors of the estimates are shown in tables E-1 and E-2 

available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1995 

and 2007.
9

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Figure 2. Difference between average 

mathematics scores of U.S. fourthand eighth-grade students and the 

TIMSS scale average: 1995, 1999, 

2003, and 2007

19991 1995 2003 2007

18* 18*

29*

19991 2003 2007

-8 4 2

8*

1995

-80

-60

-40

-20

0

20

40

60

80

Year

U.S. difference from TIMSS scale average

-80

-60

-40

-20

0

20

40

60

80

Year

U.S. difference from TIMSS scale average

Grade four

Grade eight

*p < .05. Difference between U.S. average and Trends in International 

Mathematics and Science Study (TIMSS) scale average is statistically significant. 1No fourth-grade assessment was conducted in 1999.

NOTE: In 2007, the United States met guidelines for sample participation rates 

only after substitute schools were included. The National Defined Population 

covered 90 percent to 95 percent of National Target Population (see appendix A). 

Difference calculated by subtracting the TIMSS scale average (500) from the 

U.S. average mathematics score. The standard errors of the estimates are shown 

in table E-39 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=

2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 1995, 1999, 2003, and 2007.

in 13 countries (including the 10 countries with declining scores 

and 3 others) and less than the gain of 2 countries (Colombia 

and Lithuania). There was no measurable difference between 

the 16 score point gain in the United States and the gains 

or declines in score points experienced in the other countries.

The size of the difference in scores between the U.S. fourthgraders’ and TIMSS scale averages was larger in 2007 at 29 

scale score points than it was in 1995 at 18 scale score points 

(figure 2). U.S. fourth-graders’ average mathematics scores 

were higher than the TIMSS scale average in each of the 3 

data collection years: 1995, 2003, and 2007. 

U.S. eighth-graders’ average mathematics scores showed no 

measurable difference from the TIMSS scale average in 3 of 

the 4 data collection years between 1995 and 2007. However, 

the 2007 U.S. score was higher than the U.S. score in 1995, 

with the U.S. score in 1995 some 8 points below the TIMSS 

scale average, but 8 points above the average in 2007.
10

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Table 5. Description of TIMSS mathematics cognitive domains: 2007

Cognitive domain Description

Knowing

Knowing addresses the facts, procedures, and concepts that students need to know to function mathematically. The key skills of 

this cognitive domain include recalling definitions, terminology, number properties, geometric properties, and notation; recognizing 

mathematical objects, shapes, numbers, and expressions; recognizing mathematical entities that are mathematically equivalent; 

computing algorithmic procedures for basic functions with whole numbers, fractions, decimals, and integers; approximating 

numbers to estimate computations; carrying out routine algebraic procedures; retrieving information from graphs, tables, and 

charts; reading simple scales; using appropriate units of measure and measuring instruments; estimating measures; classifying 

or grouping objects, shapes, numbers, and expressions according to common properties; making correct decisions about class 

membership; and ordering numbers and objects by attributes.

Applying

Applying focuses on students’ abilities to apply knowledge and conceptual understanding to solve problems or answer questions. 

The key skills of this cognitive domain include selecting appropriate operations, methods, or strategies for solving problems where 

there is a known algorithm or method of solution; representing mathematics information and data in diagrams, tables, graphs, 

and charts; generating equivalent representations for a given mathematical entity or relationship; generating an appropriate 

mathematical model, such as an equation or diagram for solving a routine problem; following and executing a set of mathematical 

instructions; drawing figures and shapes given specifications; solving routine problems (i.e., problems similar to those students are 

likely to have encountered in class); comparing and matching different representations of data (grade eight) and using data from 

charts, tables, graphs, and maps to solve routine problems.

Reasoning

Reasoning goes beyond the cognitive processes involved in solving routine problems to include unfamiliar situations, complex 

contexts, and multistep problems. The key skills of this cognitive domain include determining and describing relationships between 

variables or objects in mathematical situations; using proportional reasoning (grade four); decomposing geometric figures to simplify 

solving a problem; drawing the net of a given unfamiliar solid; visualizing transformations of three-dimensional figures; comparing 

and matching different representations of the same data (grade four); making valid inferences from given information; generalizing 

mathematical results to wider applications; combining mathematical procedures to establish results and combining results to 

produce a further result; making connections between different elements of knowledge and related representations; making linkages 

between different elements of knowledge and related representations; making linkages between related mathematical ideas; 

providing a justification for the truth or falsity of a statement by reference to mathematical results or properties; solving problems 

set in mathematical or real life contexts that students are unlikely to have encountered before; applying mathematical procedures 

in unfamiliar or complex contexts; and using geometric properties to solve non-routine problems.

NOTE: The descriptions of the cognitive domains are the same for grades four and eight, except where noted.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Content and cognitive domain 

scores in 2007

In addition to an overall mathematics score, TIMSS provides 

scores for content domains and cognitive domains (see table 

5 for a description of the cognitive domains). U.S. fourthgraders scored higher than the TIMSS scale average across 

the mathematics content domains in 2007 (table 6). U.S. 

fourth-graders’ average scores in number, geometric shapes 

and measures, and data display were between 22 and 43 

scale score points above the TIMSS scale average of 500 

in each content domain. 

U.S. fourth-graders performed better on average in the data

display domain than in the number and geometric shapes

and measures domains, at least in terms of comparisons 

with other countries. That is, there were fewer countries that 

outperformed the United States in data display than in the 

other two domains. U.S. fourth-graders outperformed their 

peers in 22 countries in the number domain, 20 countries 

in the geometric shapes and measures domain, and 28 

countries in the data display domain. They were outperformed 

by their peers in 9 countries in the number domain, 10 

countries in the geometric shapes and measures domain, 

and 4 countries in the data display domain. 

In the three cognitive domains, U.S. fourth-graders scored 

higher than the TIMSS scale average in 2007. U.S. fourthgraders’ average scores in the knowing, applying, and 

reasoning domains were between 23 and 41 scale score 

points higher than the TIMSS scale average of 500.

In terms of comparisons with other countries, U.S. fourthgraders performed relatively better on average in the knowing 

domain than the applying and reasoning domains. U.S. fourthgraders outperformed students in 16 to 27 countries across 

the three cognitive domains and were outperformed by their 

peers in 5 to 11 countries across the three cognitive domains. 

At the eighth-grade level, U.S. students scored higher, on 

average, than the TIMSS scale average in two of the four 

mathematics content domains in 2007 (table 7). U.S. eighthgraders’ average scores in number and data and chance were 

10 and 31 scale score points above the TIMSS scale score 

average of 500, respectively. On the other hand, U.S. eighthgraders’ average score in the geometry domain was lower than 

the TIMSS scale score average by 20 scale score points. There 

was no measurable difference between U.S. eighth-graders’ 

average score in algebra and the TIMSS scale score average. 

U.S. eighth-graders performed relatively better, on average, 

in the data and chance domain than in the number, algebra, 
11

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Table 6. Average mathematics content and cognitive domain scores of fourth-grade students, 

by country: 2007

Content domain Cognitive domain

Country Number

Geometric shapes 

and measures Data display Knowing Applying Reasoning

TIMSS scale average 500 500 500 500 500 500

Hong Kong SAR1 606 599 585 617 599 589

Singapore 611 570 583 620 590 578

Chinese Taipei 581 556 567 584 569 566

Japan 561 566 578 565 566 563

Kazakhstan2 556 542 522 559 547 539

Russian Federation 546 538 530 538 547 540

England 531 548 547 544 540 537

Latvia2 536 532 536 530 540 537

Netherlands3 535 522 543 525 540 534

Lithuania2 533 518 530 520 539 526

United States4,5 524 522 543 541 524 523

Germany 521 528 534 514 531 528

Denmark4 509 544 529 513 528 524

Australia 496 536 534 509 523 516

Hungary 510 510 504 511 507 509

Italy 505 509 506 514 501 509

Austria 502 509 508 505 507 506

Sweden 490 508 529 482 508 519

Slovenia 485 522 518 497 504 505

Armenia 522 483 458 518 493 489

Slovak Republic 495 499 492 492 498 499

Scotland4 481 503 516 489 500 497

New Zealand 478 502 513 482 495 503

Czech Republic 482 494 493 473 496 493

Norway 461 490 487 461 479 489

Ukraine 480 457 462 472 466 474

Georgia2 464 415 414 450 433 437

Iran, Islamic Rep. of 398 429 400 410 405 410

Algeria 391 383 361 384 376 387

Colombia 360 361 363 360 357 372

Morocco 353 365 316 354 346 —

El Salvador 317 333 367 312 339 356

Tunisia 352 334 307 343 329 —

Kuwait6 321 316 318 326 305 —

Qatar 292 296 326 293 296 —

Yemen — — — — — —

Average score is higher than the U.S. average score (p < .05)

Average score is not measurably different from the U.S. average score (p < .05)

Average score is lower than the U.S. average score (p < .05) 

— Not available. Average achievement could not be accurately estimated.

1Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

2National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

3Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A). 4Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 5National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year.

NOTE: Countries are ordered by 2007 overall mathematics average scale score. The tests for significance take into account the standard error for the reported 

difference. Thus, a small difference between the United States and one country may be significant while a large difference between the United States and 

another country may not be significant. The standard errors of the estimates are shown in table E-3 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?

pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
12

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Table 7. Average mathematics content and cognitive domain scores of eighth-grade students, 

by country: 2007

Content domain Cognitive domain

Country Number Algebra Geometry

Data and 

chance Knowing Applying Reasoning

TIMSS scale average 500 500 500 500 500 500 500

Chinese Taipei 577 617 592 566 594 592 591

Korea, Rep. of 583 596 587 580 596 595 579

Singapore 597 579 578 574 581 593 579

Hong Kong SAR1,2 567 565 570 549 574 569 557

Japan 551 559 573 573 560 565 568

Hungary 517 503 508 524 518 513 513

England2 510 492 510 547 503 514 518

Russian Federation 507 518 510 487 521 510 497

United States2,3 510 501 480 531 514 503 505

Lithuania4 506 483 507 523 508 511 486

Czech Republic 511 484 498 512 502 504 500

Slovenia 502 488 499 511 500 503 496

Armenia 492 532 493 427 507 493 489

Australia 503 471 487 525 487 500 502

Sweden 507 456 472 526 478 497 490

Malta 496 473 495 487 490 492 475

Scotland2 489 467 485 517 481 489 495

Serbia3,4 478 500 486 458 500 478 474

Italy 478 460 490 491 476 483 483

Malaysia 491 454 477 469 477 478 468

Norway 488 425 459 505 458 477 475

Cyprus 464 468 458 464 468 465 461

Bulgaria 458 476 468 440 477 458 455

Ukraine 460 464 467 458 471 464 445

Romania 457 478 466 429 470 462 449

Israel5 469 470 436 465 473 456 462

Bosnia and Herzegovina 451 475 451 437 478 440 452

Lebanon 454 465 462 407 464 448 429

Thailand 444 433 442 453 436 446 456

Turkey 429 440 411 445 439 425 441

Jordan 416 448 436 425 432 422 440

Tunisia 425 423 437 411 421 423 425

Georgia4 421 421 409 373 427 401 389

Iran, Islamic Rep. of 395 408 423 415 403 402 427

Bahrain 388 403 412 418 395 403 413

Indonesia 399 405 395 402 397 398 405

Syrian Arab Republic 393 406 417 387 393 401 396

Egypt 393 409 406 384 392 393 396

Algeria 403 349 432 371 371 412 —

Colombia 369 390 371 405 364 384 416

Oman 363 391 387 389 372 368 397

Palestinian Nat'l Auth. 366 382 388 371 365 371 381

Botswana 366 394 325 384 376 351 —

Kuwait6 347 354 385 366 347 361 —

El Salvador 355 331 318 362 336 347 —

Saudi Arabia 309 344 359 348 308 335 —

Ghana 310 358 275 321 313 297 —

Qatar 334 312 301 305 307 305 —

Average score is higher than the U.S. average score (p < .05)

 Average score is not measurably different from the U.S. average score (p < .05)

 Average score is lower than the U.S. average score (p < .05) 

— Not available. Average achievement could not be accurately estimated.

1Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

2Met guidelines for sample participation rates only after substitute schools were included (see appendix A).

3National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A).

4National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study (TIMSS) 

(see appendix A).

5National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year.

NOTE: Countries are ordered by 2007 overall mathematics average scale score. The tests for significance take into account the standard error for the reported 

difference. Thus, a small difference between the United States and one country may be significant while a large difference between the United States and another 

country may not be significant. The standard errors of the estimates are shown in table E-4 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
13

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

and geometry domains and relatively worse, on average, 

in geometry than the other three content domains, at least 

in terms of comparisons with other countries. U.S. eighthgraders outperformed students in 38 countries in the data 

and chance domain, 35 countries in the number domain, 

37 countries in the algebra domain, and 29 countries in the 

geometry domain. They were outperformed by their peers 

in 6 countries in the data and chance domain, 5 countries 

in the number domain, 7 countries in the algebra domain, 

and 14 countries in the geometry domain. 

In two of the three cognitive domains, the U.S. eighth-grade 

average score was higher than the TIMSS scale average 

in 2007. U.S. eighth-graders’ scores in the knowing and 

reasoning domains were 14 and 5 scale score points above 

the TIMSS scale score average of 500, respectively. On the 

other hand, U.S. eighth-graders’ average score in the applying

domain was not measurably different from the TIMSS scale 

score average. 

Like their fourth-grade counterparts, U.S. eighth-graders 

performed relatively better in the knowing domain than in the

applying and reasoning domains in terms of comparisons with 

other countries. U.S. eighth-graders outperformed students 

in 30 to 38 countries across the three cognitive domains. 

They were outperformed by their peers in 5 to 8 countries 

across the three cognitive domains. 

Performance on the TIMSS 

international benchmarks

The TIMSS international benchmarks provide a way to 

understand how students’ proficiency in mathematics varies 

along the TIMSS scale (table 8). TIMSS defines four levels 

of student achievement: advanced, high, intermediate, and 

low. The benchmarks can then be used to describe the kinds 

of skills and knowledge students at each score cutpoint would 

need to successfully answer the mathematics items included 

in the assessment. The descriptions of the benchmarks differ 

between the two grade levels, as the mathematical skills and 

knowledge needed to respond to the assessment items reflect 

the nature, difficulty, and emphasis at each grade.

Table 8. Description of TIMSS international mathematics benchmarks, by grade: 2007

Benchmark

(score cutpoint) Grade four

Advanced

(625)

Students can apply their understanding and knowledge in a variety of relatively complex situations and explain their reasoning. 

They can apply proportional reasoning in a variety of contexts. They demonstrate a developing understanding of fractions and 

decimals. They can select appropriate information to solve multistep word problems. They can formulate or select a rule for a 

relationship. Students can apply geometric knowledge of a range of two- and three-dimensional shapes in a variety of situations. 

They can organize, interpret, and represent data to solve problems.

High

(550)

Students can apply their knowledge and understanding to solve problems. Students can solve multistep word problems involving 

operations with whole numbers. They can use division in a variety of problem situations. They demonstrate understanding of place 

value and simple fractions. Students can extend patterns to find a later specified term and identify the relationship between ordered 

pairs. Students show some basic geometric knowledge. They can interpret and use data in tables and graphs to solve problems.

Intermediate

(475)

Students can apply basic mathematical knowledge in straightforward situations. Students at this level demonstrate an understanding 

of whole numbers. They can extend simple numeric and geometric patterns. They are familiar with a range of two-dimensional 

shapes. They can read and interpret different representations of the same data.

Low

(400)

Students have some basic mathematical knowledge. Students can demonstrate an understanding of adding and subtracting with 

whole numbers. They demonstrate familiarity with triangles and informal coordinate systems. They can read information from 

simple bar graphs and tables.

Grade eight

Advanced

(625)

Students can organize and draw conclusions from information, make generalizations, and solve nonroutine problems. They can 

solve a variety of ratio, proportion, and percent problems. They can apply their knowledge of numeric and algebraic concepts 

and relationships. Students can express generalizations algebraically and model situations. They can apply their knowledge 

of geometry in complex problem situations. Students can derive and use data from several sources to solve multistep problems.

High

(550)

Students can apply their understanding and knowledge in a variety of relatively complex situations. They can relate and compute with 

fractions, decimals, and percents, operate with negative integers, and solve word problems involving proportions. Students can work 

with algebraic expressions and linear equations. Students use knowledge of geometric properties to solve problems, including area, 

volume, and angles. They can interpret data in a variety of graphs and table and solve simple problems involving probability.

Intermediate

(475)

Students can apply basic mathematical knowledge in straightforward situations. They can add and multiply to solve one-step 

word problems involving whole numbers and decimals. They can work with familiar fractions. They understand simple algebraic 

relationships. They demonstrate understanding of properties of triangles and basic geometric concepts. They can read and 

interpret graphs and tables. They recognize basic notions of likelihood.

Low (400) Students have some knowledge of whole numbers and decimals, operations, and basic graphs.

NOTE: Score cutpoints for the international benchmarks are determined through scale anchoring. Scale anchoring involves selecting benchmarks (scale points) 

on the achievement scales to be described in terms of student performance, and then identifying items that students scoring at the anchor points can answer 

correctly. The score cutpoints are set at equal intervals along the achievement scales. The score cutpoints were selected to be as close as possible to the 

standard percentile cutpoints (i.e., 90th, 75th, 50th, and 25th percentiles). More information on the setting of the score cutpoints can be found in appendix A

and Martin et al. (2008).

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
14

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

In 2007, there were higher percentages of U.S. fourth-graders 

performing at or above each of the four TIMSS international 

benchmarks than the international medians9 of the percentages 

performing at each level (figure 3). For example, 10 percent 

of U.S. fourth-graders performed at or above the advanced 

benchmark (625) compared to the international median of 5 

percent. These students demonstrated an ability to apply 

their understanding and knowledge to a variety of relatively 

complex mathematical situations (see description in table 8). 

At the other end of the scale, 95 percent of U.S. fourthgraders performed at or above the low benchmark (400) 

compared with the international median of 90 percent. These 

students showed at least some basic mathematical skills by 

demonstrating an understanding of adding and subtracting 

with whole numbers, showing familiarity with triangles and 

informal coordinate systems, and reading information from 

simple bar graphs and tables.

Similar to their fourth-grade counterparts, there were higher 

percentages of U.S. eighth-graders performing at or above 

each of the four TIMSS international benchmarks than the 

international medians of the percentage performing at each 

level (figure 3). For example, 6 percent of U.S. eighth-graders 

performed at or above the advanced benchmark (625) 

compared to the international median of 2 percent. These 

students demonstrated an ability to organize information, 

make generalizations, solve nonroutine problems, and draw 

and justify conclusions from data (see description in table 8). 

At the other end of the scale, 92 percent of U.S. eighthgraders performed at or above the low benchmark (400) 

compared with the international median of 75 percent. 

These students showed at least a basic mathematical 

understanding of whole numbers and decimals, could 

perform simple computations, and complete a basic graph.

Figure 3. Percentage of U.S. fourth- and eighthgrade students who reached each 

TIMSS international mathematics 

benchmark compared with the 

international median percentage: 

2007

Advanced

0

10

20

30

40

50

60

70

80

90

100

90

26

67

Benchmark

Percent

Percent

United States

International median

Grade four

5

Low Intermediate High

95*

77*

40*

10*

Grade eight

Advanced

0

10

20

30

40

50

60

70

80

90

100

75

15

46

Benchmark

United States

International median

2

Low Intermediate High

92*

67*

31*

6*

*p < .05. U.S. percentage is significantly different from the Trends in International 

Mathematics and Science (TIMSS) international median percentage.

NOTE: The United States met guidelines for sample participation rates only 

after substitute schools were included and the National Defined Population 

covers 90 percent to 95 percent of National Target Population (see appendix 

A). The TIMSS international median represents all participating TIMSS 

jurisdictions, including the United States. The international median represents 

the percentage at which half of the participating countries have that percentage 

of students at or above the median and half have that percentage of students 

below the median. The standard errors for the estimates are shown in table E-5 

available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement 

(IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

9The international median at each benchmark represents the percentage at which half of the participating countries have that percentage of students at or above 

the median and half have that percentage of students below the median. For example, the low international benchmark median of 90 percent at grade four 

indicates that half of the countries have 90 percent or more of their students who met the low benchmark, and half have less than 90 percent of their students 

who met the low benchmark.
15

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

At grade four, seven countries had higher percentages of 

students performing at or above the advanced international 

mathematics benchmark than the United States (figure 4). 

Fourth-graders in these seven countries were also found 

to outperform U.S. fourth-graders, on average, on the overall 

mathematics scale (see table 3). At grade eight, a slightly 

different set of seven countries had higher percentages of 

students performing at or above the advanced mathematics 

benchmark than the United States (figure 4). These seven 

countries include the five countries that had higher average 

overall mathematics scores than the United States (see table 

3), as well as Hungary and the Russian Federation.

At grade four in 2007, higher percentages of U.S. students 

performed at or above the intermediate and low international 

benchmarks than in 1995 (intermediate: 77 v. 71 percent; low: 

95 v. 92 percent; data not shown). There were no measurable 

differences in the percentage of U.S. fourth-graders 

performing at or above either the high or advanced 

international benchmarks between 1995 and 2007 (high: 37 v. 

40 percent; advanced: 9 v. 10 percent). At grade eight, higher 

percentages of U.S. students performed at or above the high, 

intermediate, and low international benchmarks in 2007 than 

in 1995 (high: 31 v. 26 percent; intermediate: 67 v. 61 percent; 

low: 92 v. 86 percent; data not shown). There was no 

measurable difference in the percentage of U.S. eighthgraders performing at or above the advanced international 

benchmark in 2007 than in 1995 (6 v. 4 percent).

Performance within 

the United States

TIMSS not only provides a measure of mathematics 

performance of the nation as a whole, but also of the 

performance of student subpopulations. For this report, 

TIMSS data were analyzed to investigate the performance 

of students grouped in four ways: higher and lower 

performing students; males and females; racial and ethnic 

groups; and public schools serving students with different 

low‐income concentrations. 

Scores of lower and higher 

performing students

To examine the mathematics performance of each participating 

country’s higher and lower performing students, cutpoint 

scores were calculated for students performing at or above 

the 90th percentile (that is, the top 10 percent of students) and 

those performing at or below the 10th percentile (the bottom 

10 percent of students). The cutpoint scores were calculated 

for each country, rather than across all countries combined. 

In 2007, the highest-performing U.S. fourth-graders (those 

performing at or above the 90th percentile) scored 625 or 

higher (table 9). This was higher than the 90th percentile 

scores for fourth-graders in 23 countries and lower than the 

90th percentile score for students in 7 countries. The countries 

in which the 90th percentile cutpoint score was higher than 

the cutpoint score for U.S. are the same as those that 

outperformed the United States as a whole (table 3), with 

the exception of Latvia where the 90th percentile score of 

628 is not significantly different from 625 in the United States. 

The 90th percentile scores ranged between 371 (Yemen) 

and 702 (Singapore). The difference in the 90th percentile 

score between Singapore, the highest performing country, 

and the United States was 77 score points. 

The lowest-performing U.S. fourth-graders (those performing 

at or below the 10th percentile) scored 430 or lower in 2007 

(table 9). This was higher than the 10th percentile score 

in 23 countries and lower than the 10th percentile score in 

6 countries: Singapore, Hong Kong SAR, Japan, Chinese 

Taipei, Latvia, and the Netherlands. The score at the 10th 

percentile ranged between 81 (Yemen) and 520 (Hong Kong 

SAR). The difference in the cutpoint scores between the 

lowest-performing students in Hong Kong SAR and the 

United States was 90 score points.
16

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Figure 4. Percentage of fourth- and eighth-grade students who reached the TIMSS advanced 

international benchmark in mathematics, by country: 2007

Grade four Grade eight

0 10 20 30 40 50

0 10 20 30 40 50

2

2

2

2

3

3

3

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

6*

6*

8*

8*

10*

26*

31*

40*

40*

45*

4*

4*

4*

4*

4*

5*

5*

5*

6*

6*

6*

1*

1*

1*

1*

1*

1*

International median

Algeria

Saudi Arabia

Ghana

El Salvador

Botswana

Kuwait6

Qatar

Oman

Tunisia

Syrian Arab Republic

Bahrain

Colombia

Palestinian Nat'l Auth.

Norway

Indonesia

Egypt

Georgia2

Lebanon

Iran, Islamic Rep. of

Bosnia and Herzegovina

Jordan

Sweden

Cyprus

Malaysia

Italy

Ukraine

Thailand

Scotland3

Romania

Israel7

Slovenia

Bulgaria

Serbia2,4

Malta

Turkey

Czech Republic

Armenia

Australia

United States3,4

Lithuania2

Russian Federation

England3

Hungary

Japan

Hong Kong SAR1,3

Singapore

Korea, Rep. of

Chinese Taipei

5

5

5

6

6

#

#

#

#

#

#

#

#

#

41*

40*

24*

23*

19*

16*

16*

11*

10*

10*

9*

9*

8*

7*

7*

4*

3*

3*

3*

2*

2*

2*

1*

International median

Yemen

Qatar

Kuwait6

El Salvador

Tunisia

Algeria

Iran, Islamic Rep. of

Morocco

Colombia

Georgia2

Norway

Czech Republic

Ukraine

Sweden

Austria

Slovenia

Scotland3

Slovak Republic

New Zealand

Germany

Netherlands5

Denmark3

Armenia

Australia

Hungary

Lithuania2

United States3,4

Latvia2

Russian Federation

England

Kazakhstan2

Japan

Chinese Taipei

Hong Kong SAR1

Singapore

Italy

Percent

Percent

 Percentage is higher than U.S. percentage (p < .05)

 Percentage is not measurably different from U.S. percentage (p < .05)

 Percentage is lower than U.S. percentage (p < .05)

*p < .05. Percentage is significantly different from the international median percentage.

# Rounds to zero.

1Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

2National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

3Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year. 7National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A).

NOTE: The TIMSS international median represents all participating TIMSS jurisdictions, including the United States. The international median represents the 

percentage at which half of the participating countries have that percentage of students at or above the median and half have that percentage of students below 

the median. The tests for significance take into account the standard error for the reported difference. Thus, a small difference between the United States and one 

country may be significant while a large difference between the United States and another country may not be significant. The standard errors for the estimates are 

shown in table E-41 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
17

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Grade four

Country 90th percentile 10th percentile

International average 576 366

Singapore 702 487

Hong Kong SAR1 691 520

Japan 663 471

Chinese Taipei 663 488

Kazakhstan2 653 435

England 647 429

Russian Federation 647 436

Latvia2 628 444

United States3,4 625 430

Lithuania2 624 430

Hungary 620 389

Australia 620 408

Armenia 617 385

Netherlands5 612 454

Denmark3 611 431

Germany 607 440

Italy 601 406

New Zealand 598 377

Slovak Republic 597 389

Scotland3 592 389

Austria 590 416

Slovenia 589 408

Sweden 586 417

Czech Republic 576 392

Ukraine 573 356

Norway 566 372

Georgia2 549 322

Iran, Islamic Rep. of 508 290

Algeria 493 261

Colombia 470 238

Tunisia 469 178

Morocco 466 223

El Salvador 448 212

Kuwait6 443 184

Qatar 413 179

Yemen 371 81

Grade eight

Country 90th percentile 10th percentile

International average 559 339

Chinese Taipei 721 448

Korea, Rep. of 711 475

Singapore 706 463

Hong Kong SAR1,3 681 438

Japan 677 460

Hungary 624 405

England3 618 400

Russian Federation 617 402

Lithuania2 609 402

United States3,4 607 408

Armenia 601 390

Australia 600 394

Czech Republic 599 408

Malta 597 359

Serbia2,4 597 368

Slovenia 594 409

Scotland3 590 381

Romania 587 328

Bulgaria 586 324

Israel7 584 328

Sweden 582 399

Turkey 581 297

Malaysia 578 372

Cyprus 575 347

Italy 574 381

Ukraine 572 346

Thailand 562 327

Jordan 556 290

Norway 552 382

Bosnia and Herzegovina 552 352

Lebanon 549 354

Georgia2 532 280

Egypt 521 258

Iran, Islamic Rep. of 516 295

Indonesia 509 286

Tunisia 508 336

Bahrain 505 289

Syrian Arab Republic 502 290

Palestinian Nat'l Auth. 498 233

Oman 492 245

Colombia 477 281

Algeria 465 311

Botswana 460 264

Kuwait6 455 252

El Salvador 433 248

Saudi Arabia 429 231

Ghana 428 192

Qatar 427 186

Table 9. Mathematics scores of fourth- and eighth-grade students defining 10th and 90th 

percentiles, by country: 2007

 Percentile cutpoint score is higher than U.S. cutpoint score (p < .05)

 Percentile cutpoint score is not measurably different from U.S. cutpoint score (p < .05)

 Percentile cutpoint score is lower than U.S. cutpoint score (p < .05) 1Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

2National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS, see appendix A).

3Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year. 7National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A).

NOTE: Countries are ordered based on the 90th percentile cutpoint for mathematics scores. Cutpoints are calculated based on distribution of student scores within 

each country. The international average is the average of the cutpoint scores for all reported countries. The standard errors of the estimates are shown in tables 

E-6 and E-7 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
18

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Figure 5. Cutpoints at the 10th and 90th percentile for mathematics content domain scores 

of U.S. fourth- and eighth-grade students: 2007 

Mathematics score Mathematics score

Content domain

Total score

Content domain

Total score

625

430

632

413

428

615

621

464

Number

Geometric shapes

and measures

Data display

Grade four

90th percentile

10th percentile

Grade eight

90th percentile

10th percentile

Number

Algebra

Geometry

Data and chance

0 300 400 500 600 700 1,000 0 300 400 500 600 700 1,000

607

408

615

406

405

598

572

643

388

418

NOTE: The United States met guidelines for sample participation rates only after substitute schools were included. The National Defined Population covered 90 

percent to 95 percent of National Target Population (see appendix A). Cutpoints are calculated based on distribution of U.S. student scores. The standard errors 

of the estimates are shown in table E-8 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

On the three mathematics content domains at grade four, 

the highest-performing U.S. fourth-graders (90th percentile 

or higher) scored 632 or higher on the number domain, 615 

or higher on the geometric shapes and measures domain, 

and 621 or higher on the data display domain (figure 5). 

The lowest-performing U.S. students (10th percentile or lower) 

scored 413 or lower on the number domain, 428 or lower on 

the geometric shapes and measures domain, and 464 or 

lower on the data display domain in 2007. 

At grade eight, the highest-performing U.S. students (90th 

percentile or higher) in mathematics scored 607 or higher 

(table 9). The U.S. 90th percentile score was higher than 

that of 34 countries and lower than the 90th percentile score 

in 6 countries: Chinese Taipei, Korea, Singapore, Hong Kong 

SAR, Japan, and Hungary. The range at the eighth grade 

in 90th percentile scores was between 427 (Qatar) and 721 

(Chinese Taipei). The difference in average scores between 

the 90th percentile in Chinese Taipei and the United States 

was 114 score points. 

The lowest-performing U.S. eighth-graders (10th percentile 

or lower) scored 408 or less in 2007 (table 9). The 10th 

percentile score for U.S. eighth-graders in mathematics 

was higher than the 10th percentile score in 34 countries 

and lower than the 10th percentile score in 4 countries: 

Chinese Taipei, Korea, Singapore, and Japan. The range 

in 10th percentile scores was between 186 (Qatar) and 475 

(Korea). The difference in the cutpoint scores between the 

lowest-performing students in Korea and the United States 

was 66 score points.

On the four mathematics content domains at grade eight, 

the highest-performing U.S. eighth-graders (90th percentile 

or higher) scored 615 or higher on the number domain, 

598 or higher on the algebra domain, 572 or higher on the 

geometry domain, and 643 or higher on the data and chance

domain (figure 5). The same general pattern appears to hold 

among the lowest-performing U.S. students (10th percentile 

or lower) who scored 406 or lower on the number domain, 405 

or lower on the algebra domain, 388 or lower on the geometry

domain, and 418 or lower on the data and chance domain. 
19

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Figure 6. Trends in 10th and 90th percentile 

mathematics scores of U.S. fourthand eighth-grade students: 1995, 

1999, 2003, and 2007 

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

1999 2003 2007

Year

1995

Mathematics score

594* 611 608 607

400 408

380* 387*

19991 2003 2007

Year

Grade four

Grade eight

1995

Mathematics score

619 614* 625

430 408* 417*

90th percentile

10th percentile

90th percentile

10th percentile

*p < .05. Percentile cutpoint score is significantly different from 2007 percentile 

cutpoint score.

1No fourth-grade assessment was conducted in 1999.

NOTE: In 2007, the United States met guidelines for sample participation rates 

only after substitute schools were included. The National Defined Population 

covered 90 percent to 95 percent of National Target Population (see appendix A). 

Cutpoints are calculated based on distribution of U.S. student scores. The 

standard errors of the estimates are shown in table E-9 available at http://nces.

ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 1995, 1999, 2003, and 2007.

A comparison of 1995, when TIMSS was first administered, 

and 2007 shows no measurable change in the cutpoint score 

at the 90th percentile for U.S. fourth graders, the point marking 

the top 10 percent of students (figure 6). In 2007, the 90th 

percentile score for U.S. fourth-graders was 625; the 90th 

percentile score for 1995 was 619. However, a comparison 

of data from 2003 and 2007 shows there was an increase in 

the 90th percentile score defining the top-performing students: 

from 614 to 625. On the other hand, the lowest-performing U.S. 

fourth graders’ showed statistically significant improvement 

in mathematics: the 10th percentile score increased from 408 

in 1995 and 417 in 2003 to 430 in 2007.

At grade eight, both the 90th and 10th percentile scores were 

higher in 2007 than in 1995 (figure 6). Though the 90th 

percentile score has been relatively stable over the last three 

administrations of TIMSS, the 2007 score of 607 was higher 

than the 1995 score of 594, showing improvement among top 

students. The 10th percentile score for eighth-graders was 

higher in 2007 than in 1995 or 1999.

Average scores of male and female students

In 2007, U.S. fourth-grade males outperformed females by 6 

score points on average in mathematics (figure 7). In addition 

to the United States, of the 35 other countries participating at 

grade four, 20 showed a significant difference in the average 

mathematics scores of males and females: 12 in favor of 

males and 8 in favor of females. The difference in average 

scores between males and females ranged from 37 score 

points in Kuwait (in favor of females) to 17 score points in 

Colombia (in favor of males).
20

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Figure 7. Difference in average mathematics scores of fourth- and eighth-grade students, by sex 

and country: 2007 

 Male-female difference in average mathematics scores favors males and is statistically significant (p < .05)

 Male-female difference in average mathematics scores is not measurably different (p < .05)

 Male-female difference in average mathematics scores favors females and is statistically significant (p < .05)

# Rounds to zero.

1Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A). 2Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 3National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 4Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

5National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study (TIMSS) 

(see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year (see appendix A). 7National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A).

NOTE: The standard errors of the estimates are shown in tables E-10 and E-11 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Grade four

Difference in favor 

of females

Difference in 

favor of males

Difference in favor 

of females

Difference in 

favor of males

Grade eight

1

2

3

3

4

7

9

7

6

5

6

6

7

9

10

12

14

15

17

37

22

22

18

14

9

8

6

6

6

3

3

5

#

#

#

#

Kuwait6

Qatar

Yemen

Tunisia

Iran, Islamic Rep. of

Armenia

Kazakhstan5

Russian Federation

Singapore

Algeria

Georgia5

Latvia5

Ukraine

Lithuania5

England

Japan

New Zealand

Chinese Taipei

Morocco

Hungary

Hong Kong SAR4

Slovenia

Australia

United States2,3

Czech Republic

Sweden

Slovak Republic

Denmark2

Norway

Scotland2

El Salvador

Netherlands1

Germany

Austria

Italy

Colombia

Difference in average mathematics score

Oman

Qatar

Palestinian Nat'l Auth.

Bahrain

Thailand

Saudi Arabia

Kuwait6

Jordan

Cyprus

Romania

Botswana

Singapore

Bulgaria

Egypt

Hong Kong SAR2,4

Malaysia

Iran, Islamic Rep. of

Lithuania5

Serbia3,5

Ukraine

Russian Federation

Georgia5

Armenia

Indonesia

Norway

Sweden

Israel7

Czech Republic

Bosnia and Herzegovina

Chinese Taipei

Turkey

Malta

Hungary

Slovenia

Scotland2

Korea, Rep. of

Japan

Algeria

England2

Italy

Lebanon

Australia

Syrian Arab Republic

El Salvador

Tunisia

Ghana

Colombia

Difference in average mathematics score

United States2,3

80 60 40 20 0 20 40 60 80

80 60 40 20 0 20 40 60 80

4

4

6

6

13

1

2

3

4

4

4

4

4

5

5

6

7

11

1

32

22

21

21

16

15

5

7

11

13

15

15

15

38

54

36

32

23

23

22

20

20

18

1

#

1

2

3

4
21

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Figure 8. Average mathematics scores of U.S. fourth- and eighth-grade students, by content domain 

and sex: 2007 

Average mathematics score Average mathematics score

Content domain

Total score

Content domain

Total score

532*

526

528*

520

522

523

544

543

Number

Geometric shapes

and measures

Data display

Grade four

Males

Females

Grade eight

Males

Females

Number

Algebra

Geometry

Data and chance

0 300 400 500 600 700 1000 0 300 400 500 600 700 1,000

510

507

515*

506

503

498

483*

535*

477

527

,

*p < .05. Difference between average mathematics scores for males and females is statistically significant and favors males.

NOTE: The United States met guidelines for sample participation rates only after substitute schools were included. The National Defined Population covered 

90 percent to 95 percent of National Target Population (see appendix A). The standard errors of the estimates are shown in table E-12 available at http://nces.ed.gov/

pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007

The higher average for U.S. male fourth graders on the total 

mathematics scale reflects higher average performance on one 

content area: males outscored females 528 to 520, on average, 

in number (figure 8). There were no measurable sex differences 

detected in the average scores in either the geometric shapes 

and measures domain or the data display domain.

At grade eight, there was no measurable difference in the 

average mathematics scores of U.S. males and females 

in 2007 (figure 7). Among the 47 other countries participating 

in TIMSS at grade eight, 24 showed a difference in the 

average mathematics scores of males and females: 8 in favor 

of males and 16 in favor of females. The difference in average 

scores between males and females ranged from 54 score 

points in Oman (in favor of females) to 32 score points in 

Colombia (in favor of males).

Though there was no measurable difference detected in the 

average mathematics scores of U.S. eighth-grade males and 

females, U.S. males outperformed U.S. females in three of four 

mathematics content domains: number (515 v. 506), geometry

(483 v. 477), and data and chance (535 v. 527; figure 8). 
22

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Figure 9. Trends in sex differences in average 

mathematics scores of U.S. fourthand eighth-grade students: 1995, 

1999, 2003, and 2007 

Score

gap 5 7 6 4

Score

gap 3 8 6

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

1999 2003 2007

Year

1995

Average mathematics score

495* 505 507 510

502 507 490* 498

19991 2003 2007

Year

Grade four

Grade eight

1995

Average mathematics score

520* 522* 532

526 516* 514*

Males

Females

Males

Females

*p < .05. Significantly different from 2007. 1No fourth-grade assessment was conducted in 1999.

NOTE: In 2007, the United States met guidelines for sample participation rates 

only after substitute schools were included. The National Defined Population 

covered 90 percent to 95 percent of National Target Population (see appendix A). 

The standard errors of the estimates are shown in table E-13 available at http://

nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 1995, 1999, 2003 and 2007.

Both U.S. males and females’ average scores, at the fourth 

and eighth grades, were higher in 2007 than in 1995 (figure 

9). At grade four, the 2007 average scores of both males and 

females were higher than their average scores in both 1995 

and 2003. U.S. fourth-grade males scored 12 points higher 

on average in mathematics in 2007 than in 1995 (532 v. 520), 

and U.S. fourth-grade females scored 10 points higher, on 

average (526 v. 516).

At grade eight in 2007, U.S. males and females had higher 

scores, on average, compared to their scores in 1995: by 

15 scale score points among males (510 v. 495) and by 17 

scale score points among females (507 v. 490; figure 9). 
23

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Figure 10. Average mathematics scores of U.S. 

fourth- and eighth-grade students, 

by race/ethnicity: 2007

0

300

400

500

600

700

1,000

Race/ethnicity

Grade four

White Black Hispanic Asian Multiracial U.S.

average

TIMSS scale

average

Average mathematics score

550

482 504

582

534 529

500

533

457 475

549

506 508 500

0

300

400

500

600

700

1,000

Race/ethnicity

Grade eight

White Black Hispanic Asian Multiracial U.S.

average

TIMSS scale

average

Average mathematics score

NOTE: Reporting standards were not met for American Indian/Alaska Native 

and Native Hawaiian/Other Pacific Islander. Black includes African American. 

Racial categories exclude Hispanic origin. Students who identified themselves 

as being of Hispanic origin were classified as Hispanic, regardless of their race. 

Although data for some race/ethnicities are not shown separately because the 

reporting standards were not met, they are included in the U.S. totals shown 

throughout the report. The United States met guidelines for sample participation 

rates only after substitute schools were included. The National Defined 

Population covered 90 percent to 95 percent of the National Target Population 

(see appendix A). See appendix A in this report for more information. The 

standard errors of the estimates are shown in table E-14 available at http://nces.

ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 2007.

Average scores of students of different 

races and ethnicities

In 2007 U.S. non-Hispanic White, non-Hispanic Asian and 

multiracial fourth-graders scored higher on average than 

the TIMSS scale average in mathematics, while U.S. nonHispanic Black fourth-graders scored lower (figure 10).10

U.S. Hispanic fourth-graders’ average score showed 

no measurable difference from the TIMSS scale average. 

In comparison to the U.S. national average, U.S. White 

and Asian fourth-graders scored higher, on average, while 

U.S. Black and Hispanic fourth-graders scored lower. U.S. 

multiracial fourth-graders did not score measurably different 

from the U.S. national average in mathematics.

At grade eight, U.S. White, and Asian students scored higher, 

on average, than both the TIMSS scale average and the U.S. 

national average in mathematics. On the other hand, U.S. 

Black and Hispanic eighth-graders scored lower, on average, 

than the TIMSS scale average and U.S. national average. U.S. 

multiracial eighth-graders did not score measurably different 

from either the TIMSS scale average or the U.S. national 

average score in mathematics.

Over time, U.S. White, Black, Hispanic, and Asian students, 

in both fourth and eighth grades, have generally shown overall 

improvement in mathematics (figure 11). At grade four, U.S. 

White, Black, and Asian students had higher scores in 2007 

than in 1995 or 2003; Hispanic students improved their average 

mathematics score over a shorter period of time, between 2003 

and 2007, but not over the 12-year period since 1995.11 Though 

in each of the data collection years the differences in the 

average scores of White fourth-graders and their Black peers 

were statistically significant, the gap in scores decreased 

between 1995 and 2007 (84 points v. 67 points). On the other 

hand, the difference in average scores between White and 

Asian fourth-graders has reversed and grown over the same 

period of time, from being in favor of Whites in 1995 (541 v. 525) 

to being in favor of Asians in 2007 (550 v. 582). There has been 

no detectable change in the size of the gap in scores between 

White fourth-graders and their Hispanic classmates.

At grade eight, U.S. White, Black, Hispanic, and Asian 

students improved in mathematics, on average, when 2007 

scores are compared to those from 1995 (figure 11). Black 

and Hispanic eighth-graders also showed an increase in scores 

over a shorter period of time, when 2007 is compared to 1999. 

Though in each of the data collection years the differences 

in the average scores of White eighth-graders and their Black 

and Hispanic peers were statistically significant, the sizes of 

the gap in scores between these groups of students were 

smaller in 2007 than they were 12 years earlier in 1995 (White 

v. Black: 76 points v. 97 points; White v. Hispanic: 58 points v. 

73 points). There has been no detectable change in the size 

of the gap in scores between White eighth-graders and their 

Asian peers. 

10Black includes African American and Hispanic includes Latino. Race categories exclude Hispanic origin.

11The large apparent difference is not statistically significant because of relatively large standard errors.
24

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Score

gap

Score

gap 16* 8* 33 2 15 11 16

67 Score

gap

Score

gap 48 50 46 73* 60 58

81 Score

gap 84* 70 67 97* 78 76 Scoregap

0

300

400

500

600

700

1,000

19991 2003 2007

Year

Grade four

1995

Average mathematics score

541* 542* 550

482 457* 471*

1999 2003 2007

Year

Grade eight

Grade four Grade eight

Grade four Grade eight

1995

Average mathematics score

Average mathematics score Average mathematics score

Average mathematics score Average mathematics score

516*

444*

525 525 533

447 457

419*

516*

457*

525 525 533

475 465 443*

516* 539

525 525 533

549 537

514*

19991 2003 2007

Year

1995

541* 542* 550

504 493 492*

19991 2003 2007

Year

1995

541* 550*

582

542* 550 525*

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

1999 2003 2007

Year

1995

1999 2003 2007

Year

1995

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

0

300

400

500

600

700

White 1,000

Black

White

Black

White

Hispanic

White

Hispanic

White

Asian

White

Asian

Figure 11. Trends in differences in average mathematics scores of U.S. fourth- and eighth-grade 

students, by selected race/ethnicity: 1995, 1999, 2003, and 2007 

*p < .05. Significantly different from 2007. 1No fourth-grade assessment was conducted in 1999.

NOTE: Only the four numerically largest racial categories are shown. Multiracial data were not collected in 1995 and 1999. Reporting standards were not met for American 

Indian/Alaska Native and Native Hawaiian/Other Pacific Islander. Black includes African American. Racial categories exclude Hispanic origin. Students who identified 

themselves as being of Hispanic origin were classified as Hispanic, regardless of their race. Although data for some race/ethnicities are not shown separately because the 

reporting standards were not met, they are included in the U.S. totals shown throughout the report. In 2007, the United States met guidelines for sample participation rates 

only after substitute schools were included. The National Defined Population covered 90 percent to 95 percent of National Target Population (see appendix A). The tests for 

significance take into account the standard error for the reported difference. Thus, a small difference between averages for one student group may be significant while a large 

difference for another student group may not be significant. See appendix A in this report for more information. The standard errors of the estimates are shown in table E-15 

available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1995, 1999, 2003, 

and 2007.
25

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Figure 12. Average mathematics scores of U.S. 

fourth- and eighth-grade students, 

by percentage of students in public 

school eligible for free or reducedprice lunch: 2007

0

300

400

500

600

700

1,000

Percentage of students eligible for free or reduced-price lunch

Grade four

Less

than 10

percent

10 to 

24.9

percent

25 to 

49.9

percent

50 to 

74.9

percent

75 

percent

or more

U.S.

average

TIMSS

scale

average

Average mathematics score

583

553 537

510

479

529

500

0

300

400

500

600

700

1,000

Percentage of students eligible for free or reduced-price lunch

Grade eight

Less

than 10

percent

10 to 

24.9

percent

25 to 

49.9

percent

50 to 

74.9

percent

75 

percent

or more

U.S.

average

TIMSS

scale

average

Average mathematics score

557 543

514

482 465

508 500

NOTE: Analyses are limited to public schools only, based on school reports 

of the percentage of students in public school eligible for the federal free or 

reduced-price lunch program. The United States met guidelines for sample 

participation rates only after substitute schools were included. The National 

Defined Population covered 90 percent to 95 percent of the National Target 

Population (see appendix A). The standard errors of the estimates are shown 

in table E-16 available at http://nces.ed.gov/pubsearch/pubsinfo.

asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 2007.

Average scores of students attending 

public schools of various poverty levels

The U.S. results are also arrayed by the concentration of lowincome enrollment in the public schools, as measured by 

eligibility for free or reduced-price lunch, and shown in relation 

to the TIMSS scale average and the U.S. national average. 

In comparison to the TIMSS scale average, the average 

mathematics score of U.S. fourth graders in the highest 

poverty public schools (at least 75 percent of students eligible 

for free or reduced-price lunch) in 2007 was lower (479 v. 500); 

the average scores of fourth-graders in each of the other 

categories of school poverty was higher than the TIMSS 

scale average (figure 12). In comparison to the U.S. national 

average score, fourth-graders in schools with 50 percent 

or more students eligible for free or reduced-price lunch 

scored lower, on average, while those in schools with lower 

proportions of poor students scored higher, on average, 

than the U.S. national average.

On average, U.S. eighth-graders in public schools with at 

least 50 percent eligible for free and reduced price lunch 

scored lower than the TIMSS scale average in 2007 (482 

and 465 v. 500). U.S. eighth-graders attending public schools 

with fewer than 50 percent of students eligible for the free or 

reduced-price lunch program scored higher than the TIMSS 

scale average in mathematics. In comparison to the U.S. 

national average, U.S. eighth-graders in public schools with 

fewer than 25 percent of students eligible scored higher in 

mathematics, on average, while students in public schools 

with at least 50 percent eligible scored lower, on average.
26

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Score

gap 33 46

23 29 Score

gap

2007

Year

Grade four

2003

Average mathematics score

Grade four

Grade four

Grade four

566* 583

553 543*

566* 583

533 537

Less than 10 percent

10-24.9 percent

Year

2003 2007

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

Score

gap 96 103

67 72 Score

gap

2007

Year

2003

Average mathematics score

Average mathematics score Average mathematics score

566* 583

499* 510

566* 583

471 479

Less than 10 percent

50-74.9 percent

Less than 10 percent

25-49.9 percent

Less than 10 percent

75 percent or more

Year

2003 2007

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

Figure 13. Trends in differences in average mathematics scores of U.S. fourth- and eighth-grade 

students, by school poverty level: 1999, 2003, and 2007

See notes at end of table.

Comparisons of scores in 2007 to 2003 showed an 

inconsistent pattern of improvement in mathematics among 

U.S. fourth-graders in public schools serving students from 

various levels of poverty (figure 13).12 On the one hand, fourth 

graders in public schools with relatively lower levels of poverty 

(less than 10 percent to 24.9 percent eligible) and in public 

schools with relatively higher levels of poverty (50 to almost 

75 percent eligible) had higher average mathematics scores 

in 2007 than in 2003. On the other hand, there was no 

measurable difference detected in the average scores of 

students in public schools serving students from medium

and the highest level of poverty. Moreover, though the 

average mathematics scores were higher in 2007, the score 

gaps evident in the earlier data collections did not appear 

to diminish over time.13

Consistent with the lack of significant change between 

1999 and 2007 in eighth-grade mathematics scores overall, 

students in different types of public schools categorized by 

poverty also did not show detectable change in performance 

generally. And, as at grade four, the score gaps evident in 

earlier data collections did not appear to diminish over time.

12Information on the percentage of students eligible for the federal free or reduced-price lunch program was not collected in 1995 for either grade. Thus, comparisons 

over time on this measure are limited to an 8-year period. 

13Large apparent differences are not statistically significant because of relatively large standard errors.
27

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Score

gap

13 16 14

51 42 43 97 103 92

70 67 75 Score

gap

Year

Grade eight

Average mathematics score

Grade eight

Grade eight

Grade eight

546 557

543

547

533 531

546 557

514

547

505 495*

546 557

465

547

449 444

546 557

482

547

476 480

Less than 10 percent

10-24.9 percent

Year

1999 2003 2007

1999 2003 2007

1999 2003 2007

1999 2003 2007

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

Score

gap

Score

gap

Year

Average mathematics score

Average mathematics score Average mathematics score

Less than 10 percent

50-74.9 percent

Less than 10 percent

25-49.9 percent

Less than 10 percent

75 percent or more

Year

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

Figure 13. Trends in differences in average mathematics scores of U.S. fourth- and eighth-grade 

students, by school poverty level: 1999, 2003, and 2007—Continued

*p < .05. Significantly different from 2007. 

NOTE: Information on the percentage of students in school eligible for free or reduced-price lunch was not collected in 1995. No fourth-grade assessment was conducted 

in 1999. Analyses are limited to public schools only, based on school reports of the percentage of students in public school eligible for the federal free or reduced-price 

lunch program. In 2007, the United States met guidelines for sample participation rates only after substitute schools were included. The National Defined Population 

covered 90 percent to 95 percent of the National Target Population (see appendix A). The standard errors of the estimates are shown in table E-17 available at http://nces.

ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1999, 2003, 

and 2007.
28

MATHEMATICS HIGHLIGHTS FROM TIMSS 2007

Effect size of the difference 

in average scores

As noted in the introduction, this report includes effect sizes 

to provide the reader with a sense of the magnitude of the 

statistically significant differences reported thus far. Statistically 

significant results do not necessarily indicate those findings that 

are important or large enough to consider as informing policy or 

practice. Small differences may be statistically significant, but 

may not have much practical import. 

One way of looking at within-country differences in 

achievement between groups of students is to ask how large 

these differences are relative to across-country differences 

between the U.S. national average and an international 

benchmark, such as the national average for the country 

with the highest estimated score. As shown previously, the 

countries with the highest scores outpaced the United States 

on a number of measures. For example, the difference at 

grade four between the U.S. average mathematics score 

(529) and Hong Kong SAR average score (607) was 78 

score points (see table 3). The gap between the United States 

and Hong Kong SAR is also apparent in the percentage of 

students scoring at the advanced level: 10 percent of U.S. 

fourth-graders met the advanced international benchmark 

compared with 40 percent in Hong Kong SAR (see figure 4). 

Are differences within the United States between groups

of students (e.g., by race/ethnicity or poverty concentration 

in schools) bigger or smaller than these international 

differences? Effect sizes help make these comparisons. 

Figure 14 shows the effect size of the difference only for those 

groups with statistically significant score differences. Appendix 

A provides a discussion of how effect sizes were calculated.

As shown in figure 14, in grade four mathematics, the effect 

size of the difference between U.S. White and Black students 

is roughly the same as the effect size between the United 

States and Hong Kong SAR, the country with the highest 

estimated score, while the effect size between U.S. White 

and Hispanic students is roughly three-fifths the effect size 

between the United States and Hong Kong SAR. The largest 

effect size, between U.S. fourth-graders in schools with the 

lowest and highest poverty levels, is 1.4 times the effect size 

between the United States and Hong Kong SAR.

At grade eight, the effect size of the difference in mathematics 

scores between U.S. White and Black students is 1.1 times 

the effect size between the United States and Chinese Taipei, 

the country with the highest estimated score. The effect size 

between U.S. White and Hispanic students is four-fifths the 

effect size between the United States and Chinese Taipei. 

The largest effect size, between U.S. eighth-graders in schools 

with the lowest and highest poverty levels, is 1.3 times the 

effect size between the United States and Chinese Taipei.
29

HIGHLIGHTS FROM TIMSS 2007 MATHEMATICS

Figure 14. Effect size of difference in average mathematics achievement 

of fourth- and eighth-grade, by country, sex, race/ethnicity, 

and school poverty level: 2007

Groups compared

Grade four

United States

v. Hong Kong

SAR1

U.S. males

v.

U.S. females

U.S. White

students v.

U.S. Black

students

U.S. White

students v.

U.S. Hispanic

students

U.S. White

students v.

U.S. Asian

students

U.S. White

students v.

U.S. multiracial

students

U.S. public

schools with

lowest levels

of poverty v.

U.S. public

schools with highest

levels of poverty

Effect size

1.1

0.1

1.0

0.7

0.5

0.2

1.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Groups compared

Grade eight

United States

v.

Chinese Taipei

U.S. White

students v.

U.S. Black

students

U.S. White

students v.

U.S. Hispanic

students

U.S. White

students v.

U.S. Asian

students

U.S. White

students v.

U.S. multiracial

students

U.S. public

schools with

lowest levels

of poverty v.

U.S. public

schools with highest

levels of poverty

Effect size

1.0

1.1

0.8

0.2

0.4

1.3

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China. 

NOTE: Effect size is shown only for statistically significant differences between group means. Effect size is calculated 

by dividing the raw difference between group means by the pooled standard deviation (see appendix A). Black includes 

African American. Racial categories exclude Hispanic origin. Students who identified themselves as being of Hispanic 

origin were classified as Hispanic, regardless of their race. High-poverty schools are those in which 75 percent or more 

of students are eligible for the federal free or reduced-price lunch program. Low-poverty schools are those in which less 

than 10 percent of students are eligible. The United States met guidelines for sample participation rates only after 

substitute schools were included. The National Defined Population covered 90 percent to 95 percent of the National 

Target Population. See table E-18 (available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001) for standard 

deviations of the U.S. and other countries’ student populations. See table E-19 (available at http://nces.ed.gov/

pubsearch/pubsinfo.asp?pubid=2009001) for standard deviations of U.S. student subpopulations.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International 

Mathematics and Science Study (TIMSS), 2007.
Page intentionally left blank
31

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

The TIMSS science assessment

Like the TIMSS mathematics assessment, the TIMSS science 

assessment is designed along two dimensions: the science 

topics or content that students are expected to learn and the 

cognitive skills students are expected to have developed. 

The content domains covered at grade four are life science, 

physical science, and Earth science (see table 10). At grade 

eight, the content domains are biology, chemistry, physics, 

and Earth science. The cognitive domains in each grade are 

knowing, applying, and reasoning. Example items from the 

TIMSS science assessment are included in appendix B (see 

items B8 through B14).

The proportion of items devoted to a domain, and therefore 

the contribution of the domain to the overall science scale 

score, differs somewhat across grades. For example, at grade 

four in 2007, 37 percent of the TIMSS science assessment 

focused on the physical science domain, while at grade eight, 

46 percent of the assessment focused on the analogous 

chemistry and physics domains. The proportion of items 

devoted to each cognitive domain is similar across grades.

Also, within a content or cognitive domain, the makeup of 

items, in terms of difficulty and form of knowledge and skills 

addressed, differs across grade levels to reflect the nature, 

difficulty, and emphasis of the subject matter encountered in 

school at each grade. The TIMSS 2007 Assessment 

Frameworks (Mullis et al. 2005) provides a more detailed 

description of the content and cognitive domains assessed 

in TIMSS. The development and validation of the science 

cognitive domains is based on the same processes used 

in the development of the mathematics cognitive domains. 

Details of the development of the mathematics cognitive 

domains can be found in IEA’s TIMSS 2003 International 

Report on Achievement in the Mathematics Cognitive 

Domains: Findings From a Developmental Project (Mullis, 

Martin, and Foy 2005).

TIMSS provides an overall science scale score as well 

as content and cognitive domain scores at each grade level. 

As with the mathematics scale, the TIMSS science scale is 

from 0 to 1,000, and the international mean score is set at 500, 

with an international standard deviation of 100. The scaling of 

data is conducted separately for each grade and each content 

domain. While the scales were created to each have a mean 

of 500 and a standard deviation of 100, the subject matter 

and the level of difficulty of items necessarily differ between 

the assessments at both grades. Therefore, direct 

comparisons between scores across grades should not be 

made. Comparability over time is established by linking the 

data from each assessment to the data from the assessment 

that preceded it. More information on how the TIMSS scale 

was created can be found in appendix A.

Average scores in 2007

The average science scores for both U.S. fourth- and eighthgraders were higher than the TIMSS scale average (table 11). 

Table 10. Percentage of fourth- and eighth-grade TIMSS science assessment devoted 

to content and cognitive domains: 2007

Grade four

Content domains

Percent of 

assessment

Life science 43

Physical science 37

Earth science 21

Cognitive domains

Percent of 

assessment

Knowing 44

Applying 36

Reasoning 20

Grade eight

Content domains

Percent of 

assessment

Biology 36

Chemistry 20

Physics 26

Earth science 19

Cognitive domains

Percent of 

assessment

Knowing 39

Applying 40

Reasoning 21

NOTE: The content and cognitive domains are the foundation of the Trends in International Mathematics and Science Study (TIMSS) 

assessment. The content domains define the specific science subject matter covered by the assessment, and the cognitive domains 

define the sets of behaviors expected of students as they engage with the science content. Each science content domain has several 

topic areas. Each topic area is presented as a list of objectives covered in a majority of participating countries, at either grade four or 

grade eight. However, the cognitive domains of science are defined by the same three sets of expected behaviors—knowing, applying, 

and reasoning. Detail may not sum to totals because of rounding.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and 

Science Study (TIMSS), 2007.

Science Performance in the United States

and Internationally
32

SCIENCE HIGHLIGHTS FROM TIMSS 2007

 Average score is higher than the U.S. average score (p < .05)

 Average score is not measurably different from the U.S. average score (p < .05)

 Average score is lower than the U.S. average score (p < .05) 1Hong Kong is a Special Administrative Region (SAR) of the People's Republic 

of China.

2National Target Population does not include all of the International Target 

Population defined by the Trends in International Mathematics and Science 

Study (TIMSS) (see appendix A).

3Met guidelines for sample participation rates only after substitute schools were 

included (see appendix A).

4National Defined Population covers 90 percent to 95 percent of National 

Target Population (see appendix A).

5Nearly satisfied guidelines for sample participation rates only after substitute 

schools were included (see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 

2007, at the beginning of the next school year.

7National Defined Population covers less than 90 percent of National Target 

Population (but at least 77 percent, see appendix A).

NOTE: Countries are ordered by 2007 average score. The tests for significance 

take into account the standard error for the reported difference. Thus, a small 

difference between the United States and one country may be significant while 

a large difference between the United States and another country may not be 

significant. The standard errors of the estimates are shown in tables E-20 and 

E-21 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 2007.

Table 11. Average science scores of fourthand eighth-grade students, 

by country: 2007

Grade four

Country

Average 

score

TIMSS scale average 500

Singapore 587

Chinese Taipei 557

Hong Kong SAR1 554

Japan 548

Russian Federation 546

Latvia2 542

England 542

United States3,4 539

Hungary 536

Italy 535

Kazakhstan2 533

Germany 528

Australia 527

Slovak Republic 526

Austria 526

Sweden 525

Netherlands5 523

Slovenia 518

Denmark3 517

Czech Republic 515

Lithuania2 514

New Zealand 504

Scotland3 500

Armenia 484

Norway 477

Ukraine 474

Iran, Islamic Rep. of 436

Georgia2 418

Colombia 400

El Salvador 390

Algeria 354

Kuwait6 348

Tunisia 318

Morocco 297

Qatar 294

Yemen 197

Grade eight

Country

Average 

score

TIMSS scale average 500

Singapore 567

Chinese Taipei 561

Japan 554

Korea, Rep. of 553

England3 542

Hungary 539

Czech Republic 539

Slovenia 538

Hong Kong SAR1,3 530

Russian Federation 530

United States3,4 520

Lithuania2 519

Australia 515

Sweden 511

Scotland3 496

Italy 495

Armenia 488

Norway 487

Ukraine 485

Jordan 482

Malaysia 471

Thailand 471

Serbia2,4 470

Bulgaria7 470

Israel7 468

Bahrain 467

Bosnia and Herzegovina 466

Romania 462

Iran, Islamic Rep. of 459

Malta 457

Turkey 454

Syrian Arab Republic 452

Cyprus 452

Tunisia 445

Indonesia 427

Oman 423

Georgia2 421

Kuwait6 418

Colombia 417

Lebanon 414

Egypt 408

Algeria 408

Palestinian Nat'l Auth. 404

Saudi Arabia 403

El Salvador 387

Botswana 355

Qatar 319

Ghana 303

In 2007, the average score of U.S. fourth-graders was 539 and 

the average score of U.S. eighth-graders was 520, compared 

to the TIMSS scale average of 500 at each grade level.

At grade four, the average U.S. science score was higher than 

those in 25 of the 35 other countries, lower than the average 

scores in 4 countries (all of them in Asia), and not measurably 

different from the average scores of students in the remaining 

6 countries. 

At grade eight, the average U.S. science score was higher 

than those in 35 of the 47 other countries, lower than in 9 

countries (all located in Asia or Europe), and not measurably 

different from the average scores in the other 3 countries.
33

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Trends in scores since 1995

At grade four, 16 countries, including the United States, 

participated in both the first TIMSS in 1995 and the most 

recent TIMSS in 2007 and therefore can be compared over 

a 12-year period. Comparing 2007 with 1995, 7 of the 16 

countries showed improvement in average science scores, 

5 countries showed declines, and 4 countries, including the 

United States, had no measurable difference in average 

scores (table 12). In 2007, the U.S. fourth-grade average 

science score was 539, compared with 542 in 1995.

Grade eight

Average score Difference1

Country 1995 2007 2007–1995

Lithuania2 464 519 55*

Colombia 365 417 52*

Slovenia 514 538 24*

Hong Kong SAR3,4 510 530 20*

England4 533 542 8

United States4,5 513 520 7

Korea, Rep. of 546 553 7*

Russian Federation 523 530 7

Hungary 537 539 2

Australia 514 515 1

Cyprus 452 452 #

Japan 554 554 -1

Iran, Islamic Rep. of 463 459 -4

Scotland4 501 496 -5

Romania 471 462 -9

Singapore 580 567 -13

Czech Republic 555 539 -16*

Norway 514 487 -28*

Sweden 553 511 -42*

Grade four

Average score Difference1

Country 1995 2007 2007–1995

Singapore 523 587 63*

Latvia2 486 542 56*

Iran, Islamic Rep. of 380 436 55*

Slovenia 464 518 54*

Hong Kong SAR3 508 554 46*

Hungary 508 536 28*

England 528 542 14*

Australia 521 527 6

New Zealand 505 504 -1

United States4,5 542 539 -3

Japan 553 548 -5*

Netherlands6 530 523 -7

Austria 538 526 -12*

Scotland 514 500 -14*

Czech Republic 532 515 -17*

Norway 504 477 -27*

 Country difference in average scores between 1995 and 2007 is greater than analogous U.S. difference (p < .05)

 Country difference in average scores between 1995 and 2007 is not measurably different from analogous U.S. difference (p < .05)

 Country difference in average scores between 1995 and 2007 is less than analogous U.S. difference (p < .05)

# Rounds to zero.

*p < .05. Within-country difference between 1995 and 2007 average scores is significant. 1Difference calculated by subtracting 1995 from 2007 estimate using unrounded numbers. 

2In 2007, National Target Population did not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

3Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

4In 2007, met guidelines for sample participation rates only after substitute schools were included (see appendix A). 5In 2007, National Defined Population covered 90 percent to 95 percent of National Target Population (see appendix A). 6In 2007, nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A).

NOTE: Bulgaria collected data in 1995 and 2007, but due to a structural change in its education system, comparable science data from 1995 are not available. 

Countries are ordered by the difference between 1995 and 2007 overall average scores. All countries met international sampling and other guidelines in 2007, 

except as noted. Data are not shown for some countries, because comparable data from previous cycles are not available. The tests for significance take into 

account the standard error for the reported difference. Thus, a small difference between the United States and one country may be significant while a large 

difference between the United States and another country may not be significant. Detail may not sum to totals because of rounding. The standard errors of the 

estimates are shown in tables E-20 and E-21 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1995 

and 2007.

Table 12. Trends in average science scores of fourth- and eighth-grade students, by country: 

1995 to 2007
34

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Figure 15. Difference between average science 

scores of U.S. fourth- and eighthgrade students and the TIMSS scale 

average: 1995, 1999, 2003, and 2007

19991 2003 2007

-80

-60

-40

-20

0

20

40

60

80

Year

U.S. difference from TIMSS scale average

1995

42*

36* 39*

19991 2003 2007

-80

-60

-40

-20

0

20

40

60

80

13*

27*

15*

Year

U.S. difference from TIMSS scale average

20*

1995

Grade four

Grade eight

*p < .05. Difference between U.S. average and Trends in International 

Mathematics and Science Study (TIMSS) scale average is statistically 

significant.

1No fourth-grade assessment was conducted in 1999.

NOTE: The United States met guidelines for sample participation rates only after 

substitute schools were included. The National Defined Population covers 90 

percent to 95 percent of National Target Population (see appendix A). Difference 

calculated by subtracting the TIMSS scale average (500) from the U.S. average 

science score. The standard errors of the estimates are shown in table E-40 

available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 1995, 1999, 2003 and 2007.

At grade eight, 19 countries, including the United States, 

participated in TIMSS in both 1995 and 2007. Five countries 

had higher average science scores in 2007 than in 1995, 

3 countries showed declines in their average scores, 

and 11 countries, including the United States, had no 

measurable difference between average scores in 1995 

and 2007. The U.S. eighth-grade average science score 

was 520, compared with 513 in 1995.

Figure 15 shows the difference between the average U.S. 

science scores and the TIMSS scale average at grades four 

and eight for each of the TIMSS administrations. The average 

size of difference in science scores between the U.S. fourthgraders and the TIMSS scale average shows no significant 

change across the data collection years, from 36 to 42 scale 

score points above the TIMSS scale average. Similarly, at 

grade eight, there has been no measurable change in the size 

of the difference, on average, across the data collection years.
35

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Table 13. Description of TIMSS science cognitive domains: 2007

Cognitive Domain Description

Knowing

Knowing addresses the facts, information, concepts, tools, and procedures that students need to know to function scientifically. 

The key skills of this cognitive domain include making or identifying accurate statements about science facts, relationships, 

processes, and concepts; identifying the characteristics or properties of specific organisms, materials, and processes; providing 

or identifying definitions of scientific terms; recognizing and using scientific vocabulary, symbols, abbreviations, units, and scales 

in relevant contexts; describing organisms, physical materials, and science processes that demonstrate knowledge of properties, 

structure, function, and relationships; supporting or clarifying statements of facts or concepts with appropriate examples; 

identifying or providing specific examples to illustrate knowledge of general concepts; and demonstrating knowledge of the use 

of scientific apparatus, tools, equipment, procedures, measurement devices, and scales. 

Applying

Applying focuses on students’ ability to apply knowledge and conceptual understanding to solve problems or answer questions. 

The key skills of this cognitive domain include identifying or describing similarities and differences between groups of organisms, 

materials, or processes; distinguishing, classifying, or ordering individual objects, materials, organisms, and processes based on 

given characteristics and properties; using a diagram or model to demonstrate understanding of a science concept, structure, 

relationship, process, or biological or physical system or cycle; relating knowledge of an underlying biological or physical concept 

to an observed or inferred property, behavior, or use of objects, organisms, or materials; interpreting relevant textual, tabular, or 

graphical information in light of a science concept or principle; identifying or using a science relationship, equation, or formula to 

find a quantitative or qualitative solution involving the direct application or demonstration of a concept; providing or identifying an 

explanation for an observation or natural phenomena, demonstrating understanding of the underlying science concept, principle, 

law, or theory.

Reasoning

Reasoning goes beyond the cognitive processes involved in solving routine problems to include more complex tasks. The key 

skills of this cognitive domain include analyzing problems to determine the relevant relationships, concepts, and problem-solving 

steps; developing and explaining problem-solving strategies; providing solutions to problems that require consideration of a 

number of different factors or related concepts; making associations or connections between concepts in different areas of science; 

demonstrating understanding of unified concepts and themes across the domains of science; integrating mathematical concepts 

or procedures in the solutions to science problems; combining knowledge of science concepts with information from experience or 

observation to formulate questions that can be answered by investigation; formulating hypotheses as testable assumptions using 

knowledge from observation or analysis of scientific information and conceptual understanding; making predictions about the effects 

of changes in biological or physical conditions in light of evidence and scientific understanding; designing or planning investigations 

appropriate for answering scientific questions or testing hypotheses; detecting patterns in data; describing or summarizing data 

trends; interpolating or extrapolating from data or given information; making valid inferences based on evidence; drawing appropriate 

conclusions; demonstrating understanding of cause and effect; making general conclusions that go beyond the experimental 

or given conditions; applying conclusions to new situations; determining general formulas for expressing physical relationships; 

evaluating the impact of science and technology on biological and physical systems; evaluating alternative explanations and 

problem-solving strategies; evaluating the validity of conclusions through examination of the available evidence; and constructing 

arguments to support the reasonableness of solutions to problems.

NOTE: The descriptions of the cognitive domains are the same for grades four and eight.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 2007.

Content and cognitive domain 

scores in 2007

As in mathematics, TIMSS also provides scores for science 

content and cognitive domains (see table 13 for a description 

of the science cognitive domains). U.S. fourth-graders scored 

higher than the TIMSS scale average across the science 

content domains in 2007 (table 14). U.S. fourth-graders’ 

average scores in life science, physical science, and Earth 

science were between 33 and 40 scale score points above 

the TIMSS scale average of 500 in each content domain. 

U.S. fourth-graders outperformed their peers in 25 countries 

in the life science domain, 24 countries in the physical science

domain, and 21 countries in the Earth science domain. They 

were outperformed by their peers in 3 countries in the life

science and Earth science domains, and 7 countries in the 

physical science domain. 

U.S. fourth-graders’ average scores in the cognitive domains of 

knowing, applying, and reasoning were, on average, between 

33 and 41 scale score points higher than the TIMSS scale 

average of 500. U.S. fourth-graders outperformed students 

in 22 to 26 countries across the three cognitive domains. U.S. 

fourth-graders were outperformed by their peers in 1 country 

in the knowing domain, and 5 countries in the applying and 

reasoning domains. 

At the eighth-grade level, U.S. students scored higher than 

the TIMSS scale average in three of the four science content 

domains and the three cognitive domains in 2007 (table 15). 

U.S. eighth-graders’ average score in biology, chemistry, and 

Earth science was, on average, 10 to 30 scale score points 

above the TIMSS scale score average of 500. On the other 

hand, U.S. eighth-graders’ average score in the physics

domain was not measurably different from the TIMSS scale 

score average. 

U.S. eighth-graders outperformed students in 36 countries 

in the biology and Earth science domains, 35 countries in the 

chemistry domain, and 32 countries in the physics domain. 

They were outperformed by their peers in 5 countries in the 

biology and Earth science domains, 9 countries in the 

chemistry domain, and 10 countries in the physics domain. 
36

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Table 14. Average science content and cognitive domain scores of fourth-grade students, 

by country: 2007

Content domain Cognitive domain

Country Life science Physical science Earth science Knowing Applying Reasoning

TIMSS scale average 500 500 500 500 500 500

Singapore 582 585 554 587 579 568

Chinese Taipei 541 559 553 536 556 571

Hong Kong SAR1 532 558 560 546 549 561

Japan 530 564 529 528 542 567

Russian Federation 539 547 536 542 546 542

Latvia2 535 544 536 540 535 551

England 532 543 538 543 536 537

United States3,4 540 534 533 541 533 535

Hungary 548 529 517 540 531 529

Italy 549 521 526 530 539 526

Kazakhstan2 528 528 534 534 536 519

Germany 529 524 524 527 526 525

Australia 528 522 534 529 523 530

Slovak Republic 532 513 530 527 527 513

Austria 526 514 532 529 526 513

Sweden 531 508 535 526 521 527

Netherlands5 536 503 524 518 525 525

Slovenia 511 530 517 511 525 527

Denmark3 527 502 522 516 515 525

Czech Republic 520 511 518 520 516 510

Lithuania2 516 514 511 511 515 524

New Zealand 506 498 515 511 500 505

Scotland3 504 499 508 511 494 501

Armenia 489 492 479 486 487 484

Norway 487 469 497 485 478 480

Ukraine 482 475 474 476 477 478

Iran, Islamic Rep. of 442 454 433 437 451 436

Georgia2 427 414 432 434 424 388

Colombia 408 411 401 409 404 409

El Salvador 410 392 393 410 393 376

Algeria 351 377 365 350 379 357

Kuwait6 353 345 363 360 338 331

Tunisia 323 340 325 316 329 349

Morocco 292 324 293 291 311 318

Qatar 291 303 305 304 283 293

Yemen — — — — — —

Average score is higher than the U.S. average score (p < .05)

 Average score is not measurably different from the U.S. average score (p < .05)

 Average score is lower than the U.S. average score (p < .05)

— Not available. Average achievement could not be accurately estimated.

1Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

2National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

3Met guidelines for sample participation rates only after substitute schools were included (see appendix A).

4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A).

5Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year.

NOTE: Countries are ordered by 2007 overall science average scale score. The tests for significance take into account the standard error for the reported 

difference. Thus, a small difference between averages for the United States and one country may be significant while a large difference between averages for the 

United States and another country may not be significant. The standard errors of the estimates are shown in table E-22 available at http://nces.ed.gov/pubsearch/

pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
37

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Table 15. Average science content and cognitive domain scores of eighth-grade students, 

by country: 2007

Content domain Cognitive domain

Country Biology Chemistry Physics Earth Science Knowing Applying Reasoning

TIMSS scale average 500 500 500 500 500 500 500

Singapore 564 560 575 541 554 567 564

Chinese Taipei 549 573 554 545 565 560 541

Japan 553 551 558 533 534 555 560

Korea, Rep. of 548 536 571 538 543 547 558

England1 541 534 545 529 530 538 547

Hungary 534 536 541 531 524 549 530

Czech Republic 531 535 537 534 533 539 534

Slovenia 530 539 524 542 533 533 538

Hong Kong SAR1,2 527 517 528 532 532 522 533

Russian Federation 525 535 519 525 534 527 520

United States1,3 530 510 503 525 512 516 529

Lithuania4 527 507 505 515 513 512 527

Australia 518 505 508 519 501 510 530

Sweden 515 499 506 510 505 509 517

Scotland1 495 497 494 498 480 495 511

Italy 502 481 489 503 494 498 493

Armenia 490 478 503 475 493 502 459

Norway 487 483 475 502 486 486 491

Ukraine 477 490 492 482 477 488 488

Jordan 478 491 479 484 491 485 471

Malaysia 469 479 484 463 458 473 487

Thailand 478 462 458 488 473 472 473

Serbia3,4 474 467 467 466 485 469 455

Bulgaria5 467 472 466 480 489 471 448

Israel5 472 467 472 462 456 472 481

Bahrain 473 468 466 465 469 468 469

Bosnia and Herzegovina 464 468 463 469 486 463 452

Romania 459 463 458 471 451 470 460

Iran, Islamic Rep. of 449 463 470 476 468 454 462

Malta 453 461 470 456 436 462 473

Turkey 462 435 445 466 462 450 462

Syrian Arab Republic 459 450 447 448 474 445 440

Cyprus 447 452 458 457 438 456 460

Tunisia 452 458 432 447 441 445 458

Indonesia 428 421 432 442 426 425 438

Oman 414 416 443 439 428 423 428

Georgia4 423 418 416 425 440 422 394

Kuwait6 419 418 438 410 430 417 411

Colombia 434 420 407 407 418 417 428

Lebanon 405 447 431 389 403 422 420

Egypt 406 413 413 426 434 404 395

Algeria 411 414 397 413 409 410 414

Palestinian Nat'l Auth. 402 413 414 408 407 412 396

Saudi Arabia 407 390 408 423 417 403 395

El Salvador 398 377 380 400 394 388 384

Botswana 359 371 351 361 361 358 362

Qatar 318 322 347 312 325 322 —

Ghana 304 342 276 294 316 291 —

Average score is higher than the U.S. average score (p < .05)

 Average score is not measurably different from the U.S. average score (p < .05)

 Average score is lower than the U.S. average score (p < .05)

— Not available. Average achievement could not be accurately estimated.

1Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 2Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

3National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 4National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

5National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year.

NOTE: Countries are ordered by 2007 overall science average scale score. The tests for significance take into account the standard error for the reported 

difference. Thus, a small difference between averages for the United States and one country may be significant while a large difference between averages for the 

United States and another country may not be significant. The standard errors of the estimates are shown in table E-23 available at http://nces.ed.gov/pubsearch/

pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
38

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Table 16. Description of TIMSS international science benchmarks, by grade: 2007

Benchmark

(score cutpoint) Grade four

Advanced

(625)

Students can apply knowledge and understanding of scientific processes and relationships in beginning scientific inquiry. Students 

communicate their understanding of characteristics and life processes of organisms as well as of factors relating to human health. 

They demonstrate understanding of relationships among various physical properties of common materials and have some practical 

knowledge of electricity. Students demonstrate some understanding of the solar system and Earth’s physical features and processes. 

They show a developing ability to interpret the results of investigations and draw conclusions as well as a beginning ability to evaluate 

and support an argument.

High

(550)

Students can apply knowledge and understanding to explain everyday phenomena. Students demonstrate some understanding of 

plant and animal structure, life processes, and the environment and some knowledge of properties of matter and physical phenomena. 

They show some knowledge of the solar system, and of Earth’s structure, processes, and resources. Students demonstrate beginning 

scientific inquiry knowledge and skills, and provide brief descriptive responses combining knowledge of science concepts with 

information from everyday experience of physical and life processes.

Intermediate

(475)

Students can apply basic knowledge and understanding to practical situations in the sciences. Students recognize some basic 

information related to characteristics of living things and their interaction with the environment, and show some understanding of 

human biology and health. They also show some understanding of familiar physical phenomena. Students know some basic facts 

about the solar system and have a developing understanding of Earth’s resources. They demonstrate some ability to interpret 

information in pictorial diagrams and apply factual knowledge to practical situations.

Low

(400)

Students have some elementary knowledge of life science and physical science. Students can demonstrate knowledge of some 

simple facts related to human health and the behavioral and physical characteristics of animals. They recognize some properties 

of matter, and demonstrate a beginning understanding of forces. Students interpret labeled pictures and simple diagrams, complete 

simple tables, and provide short written responses to questions requiring factual information.

Grade eight

Advanced

(625)

Students can demonstrate a grasp of some complex and abstract concepts in biology, chemistry, physics, and Earth science.

They have an understanding of the complexity of living organisms and how they relate to their environment. They show understanding 

of the properties of magnets, sound, and light, as well as demonstrating understanding the structure of matter and physical and 

chemical properties and changes. Students apply knowledge of the solar system and of Earth’s features and processes, and apply 

understanding of major environmental issues. They understand some fundamentals of scientific investigation and can apply basic 

physical principles to solve some quantitative problems. They can provide written explanations to communicate scientific knowledge.

High

(550)

Students can demonstrate conceptual understanding of some science cycles, systems, and principles. They have some 

understanding of biological concepts including cell processes, human biology and health, and the interrelationship of plants and 

animals in ecosystems. They apply knowledge to situations related to light and sound, demonstrate elementary knowledge of heat 

and forces, and show some evidence of understanding the structure of matter, and chemical and physical properties and changes. 

They demonstrate some understanding of the solar system, Earth’s processes and resources, and some basic understanding of 

major environmental issues. Students demonstrate some scientific inquiry skills. They combine information to draw conclusions, 

interpret tabular and graphical information, and provide short explanations conveying scientific knowledge.

Intermediate

(475)

Students can recognize and communicate basic scientific knowledge across a range of topics. They demonstrate some 

understanding of characteristics of animals, food webs, and the effect of population changes in ecosystems. They are acquainted 

with some aspects of sound and force and have elementary knowledge of chemical change. They demonstrate elementary 

knowledge of the solar system, Earth’s processes, and resources and the environment. Students extract information from tables 

and interpret pictorial diagrams. They can apply knowledge to practical situations and communicate their knowledge through brief 

descriptive responses.

Low (400) Students can recognize some basic facts from the life and physical sciences. They have some knowledge of the human body, 

and demonstrate some familiarity with everyday physical phenomena. Students can interpret pictorial diagrams and apply 

knowledge of simple physical concepts to practical situations.

NOTE: Score cutpoints for the international benchmarks are determined through scale anchoring. Scale anchoring involves selecting benchmarks (scale points) 

on the achievement scales to be described in terms of student performance, and then identifying items that students scoring at the anchor points can answer 

correctly. The score cutpoints are set at equal intervals along the achievement scales. The score cutpoints were selected to be as close as possible to the 

standard percentile cutpoints (i.e., 90th, 75th, 50th, and 25th percentiles). More information on the setting of the score cutpoints can be found in appendix A 

and Martin et al. (2008).

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

In the three cognitive domains, the average U.S. score 

at eighth grade was higher than the TIMSS scale average. 

In 2007, U.S. eighth-graders’ average scores in the knowing, 

applying, and reasoning domains were between 12 and 29 

scale score points higher than the TIMSS scale average of 

500. U.S. eighth-graders outperformed students in 33 to 35 

countries across the three cognitive domains. U.S. eighthgraders were outperformed by their peers in 6 to 10 countries 

across the three cognitive domains. 

Performance on the TIMSS 

international benchmarks

The TIMSS international benchmarks distinguish four levels 

of student achievement: advanced, high, intermediate, 

and low, and provide a way to understand how students’ 

proficiency in science varies along the TIMSS scale (table 16). 

The descriptions of the benchmarks differ between the two 

grade levels, as the science skills and knowledge needed to 

respond to the assessment items reflect the nature, difficulty, 

and emphasis at each grade.
39

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Figure 16. Percentage of U.S. fourth- and eighthgrade students who reached each 

TIMSS international science 

benchmark compared with the 

international median percentage: 

2007

Advanced

0

10

20

30

40

50

60

70

80

90

100 93

34

74

Benchmark

Percent

Percent

United States

International median

Grade four

7

Low Intermediate High

94

78*

47*

15*

Grade eight

Advanced

0

10

20

30

40

50

60

70

80

90

100

78

17

49

Benchmark

United States

International median

3

Low Intermediate High

92*

71*

38*

10*

*p < .05. U.S. percentage is significantly different from the Trends in International 

Mathematics and Science (TIMSS) international median percentage.

NOTE: The United States met guidelines for sample participation rates only after 

substitute schools were included. The National Defined Population covered 90 

percent to 95 percent of National Target Population (see appendix A). The TIMSS 

international median represents all participating TIMSS jurisdictions, including the 

United States. The international median represents the percentage at which half 

of the participating countries have that percentage of students at or above the 

median and half have that percentage of students below the median. The 

standard errors for the estimates are shown in table E-24 available at http://nces.

ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement 

(IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

14The international median at each benchmark represents the percentage at which half of the participating countries have that percentage of students at or above the 

median and half have that percentage of students below the median. For example, the low international benchmark median of 93 percent at grade four indicates that half 

of the countries have 93 percent or more of their students who met the low benchmark, and half have less than 93 percent of their students who met the low benchmark.

In 2007, there were higher percentages of U.S. fourth-graders 

performing at or above three of the four TIMSS international 

benchmarks than the international median percentage 

(figure 16).14 For example, 15 percent of U.S. fourth-graders 

performed at or above the advanced benchmark (625) in 

science compared to the international median of 7 percent. 

These students demonstrated an ability to apply their 

knowledge and understanding of scientific processes and 

relationships in beginning scientific inquiry (see description 

in table 16). At the other end of the scale, 94 percent of U.S. 

fourth-graders performed at or above the low benchmark 

(400) which was not measurably different from the international 

median of 93 percent. These students showed at least some 

elementary knowledge of life science and physical science.

At the eighth grade, there were higher percentages of U.S. 

students performing at or above each of the four TIMSS 

international science benchmarks than the international 

median (figure 16). For example, 10 percent of U.S. eighthgraders performed at or above the advanced benchmark 

(625) compared to the international median of 3 percent. 

These students demonstrated a grasp of some complex 

and abstract concepts in biology, chemistry, physics, and 

Earth science (see description in table 14). At the other end 

of the scale, 92 percent of U.S. eighth-graders performed 

at or above the low benchmark (400) compared with the 

international median of 78 percent. These students recognized 

some basic facts from the life science and physical science.

At grade four, two countries had higher percentages of students 

performing at or above the advanced international science 

benchmark than the United States (figure 17). Fourth-graders 

in these two countries, Singapore and Chinese Taipei, were also 

found to outperform U.S. fourth-graders, on average, on the 

overall science scale (see table 11). At grade eight, six countries 

had higher percentages of students performing at or above the 

advanced science benchmark than the United States (figure 

17). These six countries also had higher average overall eighthgrade science scores than the United States (see table 11).

In comparison with earlier data collections, a lower percentage 

of U.S. fourth-graders performed at or above the advanced 

benchmark in 2007 than in 1995 (15 v. 19 percent; data 

not shown). There were no measurable differences in the 

percentage of U.S. fourth-graders performing at or above the 

high, intermediate, or low international science benchmarks 

between 1995 and 2007 (high: 50 v. 47 percent; intermediate: 

78 v. 78 percent; low: 92 v. 94 percent). At grade eight, there 

were fewer U.S. students performing at or above the advanced 

benchmark than in 1999 (10 v. 12 percent), but not between 

1995 and 2007 (data not shown). On the other hand, there 

were more U.S. eighth-graders performing at or above the low 

science benchmark in 2007 than in 1995 (92 v. 87 percent). 

There was no measurable difference in the percentage of U.S. 

eighth-graders performing at or above the high or intermediate 

international benchmarks in 2007 than in 1995. 
40

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Grade four Grade eight

0 10 20 30 40 50

0 10 20 30 40 50

3

2*

2

3

3

3

3

1*

1*

1*

1*

1*

#

#

#

#

#

#

#

#

#

#

10*

11*

11*

11*

13*

17*

17*

17*

25*

32*

4

5*

5*

5*

5*

5*

6*

8*

8*

8*

10*

2*

2*

2*

2*

1*

1*

7 International median

7

8

8

9*

1*

1*

#

#

#

#

#

#

#

36*

19*

16*

15*

14*

14*

13*

13*

12*

12*

11*

10*

10*

10*

10

7

6

4*

4*

3*

2*

2*

1*

International median

Percent

Percent

Yemen

Qatar

Tunisia

Algeria

Morocco

Kuwait6

El Salvador

Georgia4

Colombia

Norway

Iran, Islamic Rep. of

Ukraine

Lithuania4

Netherlands5

Scotland2

Slovenia

Denmark2

Czech Republic

New Zealand

Sweden

Austria

Kazakhstan4

Germany

Latvia4

Australia

Slovak Republic

Armenia

Japan

Italy

Hungary

Hong Kong SAR3

England

United States1,2

Russian Federation

Chinese Taipei

Singapore

Algeria

Botswana

El Salvador

Ghana

Qatar

Saudi Arabia

Tunisia

Indonesia

Georgia4

Kuwait6

Colombia

Oman

Egypt

Syrian Arab Republic

Lebanon

Palestinian Nat'l Auth.

Cyprus

Bosnia and Herzegovina

Norway

Romania

Serbia1,4

Bahrain

Iran, Islamic Rep. of

Malaysia

Thailand

Ukraine

Turkey

Israel7

Italy

Scotland2

Bulgaria7

Malta

Jordan

Sweden

Lithuania4

Australia

Armenia

United States1,2

Hong Kong SAR2,3

Russian Federation

Slovenia

Czech Republic

Hungary

Korea, Rep. of

England2

Japan

Chinese Taipei

Singapore

Figure 17. Percentage of fourth- and eighth-grade students who reached the TIMSS advanced 

international benchmark in science, by country: 2007

 Percentage is higher than U.S. percentage (p < .05)

 Percentage is not measurably different from U.S. percentage (p < .05)

 Percentage is lower than U.S. percentage (p < .05)

# Rounds to zero.

*p < .05. Percentage is significantly different from the international median percentage. 1National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 2Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 3Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

4National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

5Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year. 7National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A).

NOTE: The Trends in International Mathematics and Science Study (TIMSS) international median represents all participating TIMSS jurisdictions, including the 

United States. The international median represents the percentage at which half of the participating countries have that percentage of students at or above the 

median and half have that percentage of students below the median. The tests for significance take into account the standard error for the reported difference. 

Thus, a small difference between the United States and one country may be significant while a large difference between the United States and another country 

may not be significant. The standard errors for the estimates are shown in table E-42 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
41

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Performance within

the United States

As with mathematics, the TIMSS science data were analyzed 

to investigate the performance of students grouped in four 

ways: the highest and lowest performing students; males and 

females; racial and ethnic groups; and public schools serving 

students with different low-income concentrations. 

Scores of lower and higher 

performing students

To examine the science performance of each participating 

country’s higher and lower performing students, cutpoint 

scores were calculated for students performing at or above 

the 90th percentile (the top 10 percent of students) and those 

performing at or below the 10th percentile (the bottom 10 

percent of students). The 10th and 90th percentiles cutpoint 

scores were calculated for each country, rather than across 

all countries combined. 

In 2007, the highest-performing U.S. fourth-graders (those 

performing at or above the 90th percentile) scored 643 or 

higher in science (table 17). This was higher than the 90th 

percentile score for fourth-graders in 27 countries and lower 

than 2 of the 35 other countries. Of the 4 countries that 

outperformed the United States, on average, in science 

at grade four (see table 11), 2 had higher 90th percentile 

cutpoint scores than the United States: Singapore and 

Chinese Taipei. Scores at the 90th percentile ranged between 

379 (Yemen) and 701 (Singapore). The difference in scores 

between the highest-performing students in Singapore and 

the United States was 58 score points.

The lowest-performing U.S. fourth-graders in science (those 

performing at or below the 10th percentile) scored 427 or less 

in 2007 (table 17). The 10th percentile score for U.S. fourthgraders was higher than the 10th percentile score in 17 

countries and lower than that in 7 countries: Singapore, 

Chinese Taipei, the Russian Federation, Hong Kong SAR, 

Japan, Latvia, and the Netherlands. The range in scores at 

the 10th percentile was between 20 (Yemen) and 466 (Hong 

Kong SAR). The difference in scores between the lowestperforming students in Hong Kong SAR and the United States 

was 39 score points.
42

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Grade four

Country 90th percentile 10th percentile

International average 586 359

Singapore 701 464

Chinese Taipei 653 457

Russian Federation 646 443

United States1,2 643 427

England 641 438

Armenia 640 336

Hungary 637 425

Hong Kong SAR3 637 466

Italy 636 429

Japan 633 459

Slovak Republic 627 416

Australia 626 423

Latvia4 625 454

Kazakhstan4 623 433

Germany 623 427

Austria 620 423

Sweden 617 429

New Zealand 614 382

Denmark1 610 417

Slovenia 610 416

Czech Republic 610 416

Netherlands5 598 445

Lithuania4 595 428

Scotland1 593 400

Ukraine 576 364

Norway 570 374

Iran, Islamic Rep. of 558 304

Georgia4 524 306

Colombia 522 271

El Salvador 507 267

Kuwait6 505 182

Tunisia 497 119

Algeria 483 220

Morocco 465 139

Qatar 464 121

Yemen 379 20

Grade eight

Country 90th percentile 10th percentile

International average 573 352

Singapore 694 421

Chinese Taipei 665 439

England1 649 427

Japan 648 454

Korea, Rep. of 646 452

Hungary 635 437

Czech Republic 630 447

Slovenia 628 442

Russian Federation 627 427

Hong Kong SAR3 625 419

United States1,2 623 410

Australia 617 410

Lithuania4 616 414

Armenia 612 366

Sweden 608 405

Jordan 601 349

Scotland1 597 388

Bulgaria7 595 330

Malta 595 298

Israel7 591 329

Italy 590 393

Ukraine 588 374

Malaysia 581 357

Norway 578 389

Thailand 578 363

Turkey 577 336

Bahrain 575 351

Romania 572 345

Serbia2,4 571 359

Iran, Islamic Rep. of 566 355

Bosnia and Herzegovina 565 359

Cyprus 556 339

Syrian Arab Republic 546 355

Palestinian Nat'l Auth. 543 255

Oman 541 293

Lebanon 539 284

Egypt 537 275

Kuwait6 530 298

Georgia4 527 309

Tunisia 524 367

Indonesia 520 330

Colombia 514 319

Saudi Arabia 503 300

Algeria 488 327

Qatar 480 146

Botswana 478 220

El Salvador 477 298

Ghana 445 163

 Percentile cutpoint score is higher than U.S. cutpoint score (p < .05)

 Percentile cutpoint score is not measurably different from U.S. cutpoint score (p < .05)

 Percentile cutpoint score is lower than U.S. cutpoint score (p < .05) 1Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 2National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 3Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

4National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study 

(TIMSS) (see appendix A).

5Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year. 7National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A).

NOTE: Countries are ordered based on the 90th percentile cutpoint for science scores. Cutpoints are calculated based on distribution of student scores within 

each country. The international average is the average of the cutpoint scores for all reported countries. The standard errors of the estimates are shown in tables 

E-25 and E-26 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Table 17. Science scores of fourth- and eighth-grade students defining 10th and 90th percentiles, 

by country: 2007
43

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Figure 18. Cutpoints at the 10th and 90th percentile for science content domain scores of U.S. 

fourth- and eighth-grade students: 2007 

Science score Science score

Content domain

Total score

Content domain

Total score

643

427

641

433

433

630

630

433

Life Science

Physical Science

Earth Science

Grade four

90th percentile

10th percentile

Grade eight

90th percentile

10th percentile

Biology

Chemistry

Physics

Earth Science

0 300 400 500 600 700 1,000 0 300 400 500 600 700 1,000

623

410

633

421

410

607

603

634

399

410

NOTE: The United States met guidelines for sample participation rates only after substitute schools were included. The National Defined Population covered 90 

percent to 95 percent of National Target Population (see appendix A). The standard errors of the estimates are shown in table E-27 available at http://nces.ed.gov/

pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

On the three science content domains at grade four in 2007, 

the highest-performing U.S. students (90th percentile or 

higher) scored 641 or higher on the life science domain and 

630 or higher on both the physical science or Earth science

domains (figure 18). The lowest-performing U.S. students 

(10th percentile or lower) scored 433 or lower on the life

science, physical science, and Earth science domains. 

At grade eight, the highest-performing U.S. students (90th 

percentile or higher) in science scored 623 or higher in 2007 

(table 17). This was higher than the 90th percentile score 

in 34 countries and lower than in 6 countries: Singapore, 

Chinese Taipei, England, Japan, Korea, and Hungary. The 

range in 90th percentile scores was between 445 (Ghana) 

and 694 (Singapore). The difference in scores between the 

highest-performing students in Singapore and the United 

States was 71 score points. 

At the other end of the scale, the lowest-performing U.S. 

eighth-graders (10th percentile or lower) scored 410 or 

lower in science in 2007 (table 17). The 10th percentile score 

for U.S. eighth-graders was higher than the 10th percentile 

score in 34 countries and lower than in 8 countries: Chinese 

Taipei, England, Japan, Korea, Hungary, the Czech Republic, 

Slovenia, and the Russian Federation. The range in 10th 

percentile scores was between 163 (Ghana) and 454 (Japan). 

The difference in scores between the lowest-performing 

students in Japan and the United States was 44 score points.

On the four science content domains at grade eight, the 

highest-performing U.S. eighth-graders (90th percentile 

or higher) scored 633 or higher on the biology domain, 

607 or higher on the chemistry domain, 603 or higher on 

the physics domain, and 634 or higher on the Earth science

domain (figure 18). The lowest-performing U.S. students 

(10th percentile or lower) scored 421 or lower on the biology

domain, 410 or lower on the chemistry and Earth science

domains, and 399 or lower on the physics domain in 2007. 
44

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Figure 19. Trends in 10th and 90th percentile 

science scores of U.S. fourthand eighth-grade students: 

1995, 1999, 2003, and 2007 

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

1999 2003 2007

Year

1995

Science score

628 636* 628 623

419 410 384* 386*

19991 2003 2007

Year

Grade four

Grade eight

1995

Science score

654* 636 643

419 426 427

90th percentile

10th percentile

90th percentile

10th percentile

*p < .05. Percentile cutpoint score is significantly different from 2007 percentile 

cutpoint score.

1No fourth-grade assessment was conducted in 1999.

NOTE: In 2007, the United States met guidelines for sample participation rates 

only after substitute schools were included. The National Defined Population 

covered 90 percent to 95 percent of National Target Population (see appendix A). 

Cutpoints are calculated based on distribution of U.S. student scores. The 

standard errors of the estimates are shown in table E-28 available at http://nces.

ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 1995, 1999, 2003, and 2007.

A comparison of 1995 and 2007 shows a decline in the 90th 

percentile cutpoint score for U.S. fourth graders in science, the 

point marking the top 10 percent of students (figure 19). In 

2007, the 90th percentile score was 643, 11 score points lower 

than the analogous score of 654 in 1995. A comparison of the 

10th percentile science scores for U.S. fourth-graders in 1995 

and 2007 and 2003 and 2007 shows no measurable difference.

At grade eight, the data suggest a different picture. The 90th 

percentile cutpoint score in science showed no measurable 

differences in comparisons of 2007 to 1995 or 2003, but 

showed a decrease when the 2007 score was compared to 

the 1999 score (636 v. 623). The score identifying the lowestperforming U.S. eighth-graders in science was higher in 2007 

than in 1995 (410 v. 384) and in 1999 (410 v. 386).

Average scores of male and female students

In 2007, U.S. fourth-grade males and females showed no 

measurable difference in their average science performance 

(figure 20). Fourteen of the 35 other countries participating at 

grade four showed a significant difference in average science 

scores of males and females: 8 countries in favor of males 

and 6 in favor of females. The largest differences were 64 

score points in Kuwait (in favor of females) and 15 score 

points in Colombia (in favor of males).
45

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Figure 20. Difference in average science scores of fourth- and eighth-grade students, by sex 

and country: 2007 

 Male-female difference in average science scores favors males and is statistically significant (p < .05)

 Male-female difference in average science scores is not measurably different (p < .05)

 Male-female difference in average science scores favors females and is statistically significant (p < .05)

# Rounds to zero.

1Nearly satisfied guidelines for sample participation rates only after substitute schools were included (see appendix A). 2Met guidelines for sample participation rates only after substitute schools were included (see appendix A). 3National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 4Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.

5National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study (TIMSS) 

(see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year (see appendix A). 7National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent, see appendix A).

NOTE: The standard errors of the estimates are shown in tables E-29 and E-30 available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Grade four

Difference in favor

of females

Difference in 

favor of males

Difference in favor 

of females

Difference in 

favor of males

Grade eight

1

1

#

#

2

6

11

10

10

2

5

5

7

8

13

13

13

15

15

64

31

26

21

17

14

10

2

3

3

4

4

6

2

2

3

4

Difference in average science score

Difference in average science score

80 60 40 20 0 20 40 60 80

80 60 40 20 0 20 40 60 80

8

8

9

9

12

2

2

2

1

1

1

2

3

5

5

8

8

9

2

35

29

22

19

18

12

9

8

9

12

12

16

17

62

70

61

49

43

36

34

22

22

18

3

4

5

5

6

7

Qatar

Bahrain

Oman

Kuwait6

Saudi Arabia

Palestinian Nat'l Auth.

Jordan

Georgia5

Botswana

Thailand

Egypt

Cyprus

Iran, Islamic Rep. of

Bulgaria7

Israel7

Malaysia

Romania

Armenia

Singapore

Turkey

Hong Kong SAR2,4

Serbia3,5

Sweden

Norway

Algeria

Lithuania5

Indonesia

Ukraine

Slovenia

Malta

Bosnia and Herzegovina

Japan

Chinese Taipei

Scotland2

Russian Federation

Lebanon

Korea, Rep. of

Italy

England2

Czech Republic

Syrian Arab Republic

Hungary

United States2,3

Australia

Tunisia

El Salvador

Ghana

Colombia

Kuwait6

Tunisia

Qatar

Yemen

Armenia

Iran, Islamic Rep. of

Georgia5

Algeria

Morocco

Latvia5

New Zealand

Lithuania5

Russian Federation

England

Ukraine

Sweden

Kazakhstan5

Japan

Slovenia

Singapore

Scotland2

Chinese Taipei

Norway

Hungary

Hong Kong SAR4

Australia

United States2,3

Denmark2

Czech Republic

Slovak Republic

Netherlands1

Italy

El Salvador

Austria

Germany

Colombia
46

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Figure 21. Average science scores of U.S. fourth- and eighth-grade students, by content domain 

and sex: 2007 

Average science score Average science score

Content domain

Total score

Content domain

Total score

541

536

541

538

532

536

536*

531

Life science

Physical science

Earth science

Grade four

Male

Female

Grade eight

Male

Female

Biology

Chemistry

Physics

Earth science

0 300 400 500 600 700 1,000 0 300 400 500 600 700 1,000

526*

514

533*

527

508

512

514*

534*

491

516

*p < .05. Difference between average science scores for males and females is statistically significant and favors males.

NOTE: The United States met guidelines for sample participation rates only after substitute schools were included. The National Defined Population covered 90 

percent to 95 percent of National Target Population (see appendix A). The standard errors of the estimates are shown in table E-31 available at http://nces.ed.gov/

pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Although there was no measurable sex difference on the 

total average science score, U.S. males outperformed U.S. 

females in one content area: Earth science (536 v. 531; figure 

21). There was no measurable difference detected in the 

average scores of U.S. fourth-grade males and females 

in either the life science or physical science domains.

Unlike their fourth-grade counterparts, U.S. eighth-grade 

males outperformed their female classmates in science in 

2007 (figure 20). Among the 47 other countries participating in 

TIMSS, 24 showed a difference in the average science scores 

of males and females: 10 countries in favor of males and 14 in 

favor of females. The largest differences were 70 score points 

in Qatar (in favor of females) and 35 score points in Colombia 

and Germany (in favor of males).

Like the overall science scale at grade eight, U.S. males 

scored higher, on average, than their female classmates 

in three of the four science content domains: biology (533 

v. 527), physics (514 v. 491), and Earth science (534 v. 516; 

figure 21). There was no measurable difference detected in 

the average science scores of U.S. eighth-grade males and 

females in the chemistry domain. 
47

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Figure 22. Trends in sex differences in average 

science scores of U.S. fourthand eighth-grade students: 

1995, 1999, 2003, and 2007 

Score

gap 14 19 16 12

Score

gap 12* 5 5

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

1999 2003 2007

Year

1995

Average science score

520 524 536* 526

505 505 519 514

19991 2003 2007

Year

Grade four

Grade eight

1995

Average science score

548 538 541

536 533 536

Males

Females

Males

Females

*p < .05. Significantly different from 2007. 1No fourth-grade assessment was conducted in 1999.

NOTE: In 2007, the United States met guidelines for sample participation rates 

only after substitute schools were included. The National Defined Population 

covered 90 percent to 95 percent of National Target Population (see appendix A). 

Detail may not sum to totals due to rounding. The standard errors of the 

estimates are shown in table E-32 available at http://nces.ed.gov/pubsearch/

pubsinfo.asp?pubid=2009001. 

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 1995, 1999, 2003, and 2007.

There was no measurable change in the average scores of 

either U.S. males or females at grade four when 2007 scores 

were compared to those from 1995 and 2003 (figure 22). 

However, the advantage for males decreased, from 12 scale 

score points in 1995 to 5 scale score points in 2003 and 2007. 

At grade eight, there was also no measurable change in the 

average science scores of U.S. males and females or the gap 

between them when 2007 scores were compared to 1995 

(figure 22). However, the average science score for males 

was lower in 2007 than it was in 2003 (526 v. 536). 
48

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Figure 23. Average science scores of U.S.

fourth- and eighth-grade students, 

by race/ethnicity: 2007

0

300

400

500

600

700

1,000

Race/ethnicity

Grade four

White Black Hispanic Asian Multiracial U.S.

average

TIMSS scale

average

Average science score

567

488 502

573 550 539

500

551

455

480

543 522 520 500

0

300

400

500

600

700

1,000

Race/ethnicity

Grade eight

White Black Hispanic Asian Multiracial U.S.

average

TIMSS scale

average

Average science score

NOTE: Reporting standards were not met for American Indian/Alaska Native 

and Native Hawaiian/Other Pacific Islander. Black includes African American. 

Racial categories exclude Hispanic origin. Students who identified themselves 

as being of Hispanic origin were classified as Hispanic, regardless of their race. 

Although data for some race/ethnicities are not shown separately because the 

reporting standards were not met, they are included in the U.S. totals shown 

throughout the report. The United States met guidelines for sample participation 

rates only after substitute schools were included. The National Defined 

Population covered 90 percent to 95 percent of the National Target Population 

(see appendix A). See appendix A in this report for more information. The 

standard errors of the estimates are shown in table E-33 available at http://nces.

ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational 

Achievement (IEA), Trends in International Mathematics and Science Study 

(TIMSS), 2007.

Average scores of students of different 

races and ethnicities

In 2007, in comparison to the TIMSS scale average, U.S. 

White, Asian, and multiracial fourth-graders scored higher in 

science, on average, while U.S. Black fourth-graders scored 

lower (figure 23). U.S. Hispanic fourth-graders’ average score 

showed no measurable difference from the TIMSS scale 

average. In comparison to the U.S. national average, U.S. 

White and Asian fourth-graders scored higher in science, on 

average, while U.S. Black and Hispanic fourth-graders scored 

lower. U.S. multiracial fourth-graders’ average score showed 

no measurable difference from the U.S. national average.

At grade eight, U.S. White, Asian, and multiracial students 

scored higher, on average, than the TIMSS scale average in 

science and U.S. Black and Hispanic eighth-graders scored 

lower, on average (figure 23). In comparison to the U.S. 

national average, U.S. White and Asian eighth-graders scored 

higher in science, on average, while U.S. Black and Hispanic 

eighth-graders scored lower. U.S. multiracial eighth-graders’ 

average score showed no measurable difference from the 

U.S. national average.

Examination of performance over time shows that U.S. Black 

and Asian fourth-graders, and U.S. Black, Hispanic, and Asian 

eighth-graders had an overall pattern of improvement in 

science, on average (figure 24). There was no measurable 

change in the average science scores of White and Hispanic 

fourth-graders, and White eighth-graders when 2007 scores 

were compared to those from the earlier assessments. 

Moreover, though significant differences remain in the 

average scores of White students compared with most of their 

classmates, the score gap between White students and their 

counterparts decreased from 1995, at both grades. The 

exception is the score gap in science between White and 

Hispanic fourth-graders, which showed no measurable 

change over the data collection years. 
49

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Score

gap

Score

gap 47* 22* 6 38* 20 17 7

85 Score

gap

Score

gap 69 66 65 98* 70 71

109 Score

gap 110* 78 79 122* 91 96 Scoregap

0

300

400

500

600

700

1,000

19991 2003 2007

Year

Grade four

1995

Average science score

572 565 567

486 488

462*

1999 2003 2007

Year

Grade eight

Grade four Grade eight

Grade four Grade eight

1995

Average science score

Average science score Average science score

Average science score Average science score

438*

461 455

422*

462* 482 480

446*

544 547

527 536 543

552 551

506*

19991 2003 2007

Year

1995

572 565 567

498 502 503

19991 2003 2007

Year

1995

573

567 543* 525*

0

300

400

500

600

700

1,000

1999 2003 2007

Year

1995

1999 2003 2007

Year

1995

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

0

300

400

500

600

700

White 1,000

Black

White

Black

White

Asian

544 547 552 551

544 547 552 551

572 565

0

300

400

500

600

700

1,000 White

Asian

White

Hispanic

White

Hispanic

Figure 24. Trends in differences in average science scores of U.S. fourth- and eighth-grade students, 

by selected race/ethnicity: 1995, 1999, 2003, and 2007 

*p < .05. Significantly different from 2007. 1No fourth-grade assessment was conducted in 1999.

NOTE: Only the four numerically largest racial categories are shown. Multiracial data were not collected in 1995 and 1999. Reporting standards were not met for American 

Indian/Alaska Native and Native Hawaiian/Other Pacific Islander. Black includes African American. Racial categories exclude Hispanic origin. Students who identified 

themselves as being of Hispanic origin were classified as Hispanic, regardless of their race. Although data for some race/ethnicities are not shown separately because the 

reporting standards were not met, they are included in the U.S. totals shown throughout the report. In 2007, the United States met guidelines for sample participation rates 

only after substitute schools were included. The National Defined Population covered 90 percent to 95 percent of National Target Population (see appendix A). The tests for 

significance take into account the standard error for the reported difference. Thus, a small difference between averages for one student group may be significant while a large 

difference for another student group may not be significant. See appendix A in this report for more information. The standard errors of the estimates are shown in table E-34 

available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1995, 1999, 2003, 

and 2007.
50

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Figure 25. Average science scores of U.S. 

fourth- and eighth-grade students, 

by percentage of students in public 

school eligible for free or reducedprice lunch: 2007

0

300

400

500

600

700

1,000

Percentage of students eligible for free or reduced-price lunch

Grade four

Less

than 10

percent

10 to 

24.9

percent

25 to 

49.9

percent

50 to 

74.9

percent

75 

percent

or more

U.S.

average

TIMSS

scale

average

Average science score

590 567 550

520

477

539

500

0

300

400

500

600

700

1,000

Percentage of students eligible for free or reduced-price lunch

Grade eight

Less

than 10

percent

10 to 

24.9

percent

25 to 

49.9

percent

50 to 

74.9

percent

75 

percent

or more

U.S.

average

TIMSS

scale

average

Average science score

572 559

528

495

466

520 500

NOTE: Analyses are limited to public schools only, based on school reports of the 

percentage of students in public school eligible for the federal free or reducedprice lunch program. The United States met guidelines for sample participation 

rates only after substitute schools were included. The National Defined 

Population covered 90 percent to 95 percent of the National Target Population 

(see appendix A). The standard errors of the estimates are shown in table E-35 

available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement 

(IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Average scores of students attending public 

schools of various poverty levels

The U.S. results are also arrayed by the concentration of 

low‐income enrollment in the public schools, as measured by 

eligibility for free or reduced-price lunch, and shown in relation 

to the TIMSS scale average and the U.S. national average. 

In comparison to the TIMSS scale average, the average 

science score of U.S. fourth graders in the highest poverty 

public schools (at least 75 percent of students eligible for 

free or reduced-price lunch) in 2007 was lower; the average 

scores of fourth-graders in each of the other categories of 

school poverty was higher than the TIMSS scale average 

(figure 25). In comparison to the U.S. national average score, 

fourth-graders in schools with 50 percent or more students 

eligible for free or reduced-price lunch scored lower in 

science, on average, while those in schools with lower 

proportions of poor students scored higher, on average, 

than the U.S. national average.

In comparison to the TIMSS scale average, U.S. eighth-graders 

attending public schools with fewer than 50 percent of students 

eligible for the free or reduced-price lunch program scored 

higher in science, on average (figure 25). On the other hand, 

U.S. eighth-graders in public schools with 75 percent or more 

of students eligible scored lower in science, on average, than 

the TIMSS scale average. In comparison to the U.S. national 

average, U.S. eighth-graders in public schools with fewer than 

25 percent of students eligible scored higher in science, on 

average, while students in public schools with at least 50 

percent eligible scored lower, on average.
51

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Score

gap 29 40

13 23 Score

gap

2007

Year

Grade four

2003

Average science score

Grade four

Grade four

Grade four

580 590

567 567

551 550

Less than 10 percent

10-24.9 percent

Year

2003 2007

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

Score

gap 100 113

60 70 Score

gap

2007

Year

2003

Average science score

Average science score Average science score

519 520

480 477

Less than 10 percent

50-74.9 percent

Less than 10 percent

25-49.9 percent

Less than 10 percent

75 percent or more

Year

2003 2007

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

580 590

580 590 580 590

Figure 26. Trends in differences in average science scores of U.S. fourth- and eighth-grade students, 

by school poverty level: 1999, 2003, and 2007

See notes at end of table.

Comparisons of the 2007 average science scores to 

those for the earlier years within each school poverty level 

revealed no measurable change in the average science 

scores at either grade four or eight, with one exception 

(figure 26).15 At grade eight, students in public schools 

with the highest poverty levels (75 percent or more) had 

a higher average science score in 2007 than in 1999 

(466 v. 440). 

In addition, the size of the difference in average scores, 

or the score gap, between U.S. fourth- and eighth-graders 

in public schools with the lowest poverty level (less than 

10 percent) and their peers attending public schools with 

higher poverty levels showed no measurable change 

(figure 26). 

Effect size of the difference 

in average scores

As noted in the mathematics section of this report, statistically 

significant results do not necessarily indicate those findings 

that are important or large enough to consider as informing 

policy or practice. Small differences may be statistically 

significant, but may not have much practical import. 

As discussed earlier, the highest scoring countries outpaced 

the United States on a number of measures. The difference at 

grade four between the U.S. average science score (539) and 

the Singapore average score (587) was 48 score points (see 

table 11). The gap between the United States and Singapore 

is also apparent in the percentage of students scoring at the 

advanced level: 15 percent of U.S. fourth-graders met the 

advanced international benchmark compared with 36 percent 

15Information on the percentage of students eligible for the federal free or reduced-price lunch program was not collected in 1995 for either grade. Thus, 

comparisons over time on the poverty measure are limited to a 8-year period.
52

SCIENCE HIGHLIGHTS FROM TIMSS 2007

Score

gap

12 16 13

55 42 44 128 110 105

85 67 76 Score

gap

Year

Grade eight Grade eight

Average science score

Grade eight Grade eight

568 572

559

571

556 554

529 528 513

461 466 440*

495 504 484

Less than 10 percent

10-24.9 percent

Year

1999 2003 2007

1999 2003 2007

1999 2003 2007

1999 2003 2007

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

Score

gap

Score

gap

Year

Average science score

Average science score Average science score

Less than 10 percent

50-74.9 percent

Less than 10 percent

25-49.9 percent

Less than 10 percent

75 percent or more

Year

0

300

400

500

600

700

1,000

0

300

400

500

600

700

1,000

568 571 572

568 571 572

568 571 572

Figure 26. Trends in differences in average science scores of U.S. fourth- and eighth-grade students, 

by school poverty level: 1999, 2003, and 2007—Continued

*p < .05. Significantly different from 2007. 

NOTE: Information on the percentage of students in school eligible for free or reduced-price lunch was not collected in 1995. No fourth-grade assessment was conducted 

in 1999. Analyses are limited to public schools only, based on school reports of the percentage of students in school eligible for the federal free or reduced-price lunch 

program. In 2007, the United States met guidelines for sample participation rates only after substitute schools were included. The National Defined Population covered 90 

percent to 95 percent of National Target Population (see appendix A). The standard errors of the estimates are shown in table E-36 available at http://nces.ed.gov/

pubsearch/pubsinfo.asp?pubid=2009001.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1999, 2003, 

and 2007.

in Singapore (see figure 17). Are differences within the United 

States between groups of students (e.g., by race/ethnicity or 

poverty concentration in schools) bigger or smaller than these 

international differences? Effect sizes help make these 

comparisons. Figure 27 shows the effect size of the difference 

in science only for those groups with statistically significant 

score differences. Appendix A includes a discussion of how 

effect sizes were calculated.

As shown in figure 27, and as observed in mathematics, the 

effect sizes between groups vary considerably. For example, 

in grade four science, the effect size of the difference between 

U.S. White and Black students is 2.2 times and between U.S. 

White and Hispanic students is 1.6 times the effect size 

between the United States and Singapore, the country with 

the highest estimated score. The largest observed effect size, 

between U.S. fourth-graders in schools with the lowest and 

highest poverty levels, is 3 times the effect size between the 

United States and Singapore.

At grade eight, the effect size of the difference in science 

scores between U.S. White and Black students is 2.6 times 

and between U.S. White and Hispanic students is 2 times 

the effect size between the United States and Singapore, 

the country with the highest estimated score. The largest 

observed effect size, between U.S. eighth-graders in schools 

with the lowest and highest poverty levels, is 2.8 times the 

effect size between the United States and Singapore.
53

HIGHLIGHTS FROM TIMSS 2007 SCIENCE

Figure 27. Effect size of difference in average science achievement 

of fourth- and eighth-grade students, by country, sex, 

race/ethnicity, and school poverty level: 2007

Groups compared

Grade four

United States

v. Singapore

U.S. White

students v.

U.S. Black

students

U.S. White

students v.

U.S. Hispanic

students

U.S. White

students v.

U.S. multiracial

students

U.S. public

schools with

lowest levels

of poverty v.

U.S. public

schools with highest

levels of poverty

Effect size

0.5

1.1

0.8

0.2

1.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Groups compared

Grade eight

United States

v. Singapore

U.S. males v.

U.S. females

U.S. White

students v.

U.S. Black

students

U.S. White

students v.

U.S. Hispanic

students

U.S. White

students v.

U.S. multiracial

students

U.S. public

schools with

lowest levels

of poverty v.

U.S. public

schools with highest

levels of poverty

Effect size

0.5

0.1

1.3

1.0

0.4

1.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

NOTE: Effect size is shown only for statistically significant differences between group means. Effect size is calculated 

by dividing the raw difference between group means by the pooled standard deviation (see appendix A). Black includes 

African American. Racial categories exclude Hispanic origin. Students who identified themselves as being of Hispanic 

origin were classified as Hispanic, regardless of their race. High-poverty schools are those in which 75 percent or more 

of students are eligible for the federal free or reduced-price lunch program. Low-poverty schools are those in which less 

than 10 percent of students are eligible. The United States met guidelines for sample participation rates only after 

substitute schools were included. The National Defined Population covered 90 percent to 95 percent of the National 

Target Population. See table E-37 (available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001) for standard 

deviations of the U.S. and other countries’ student populations. See table E-38 (available at http://nces.ed.gov/

pubsearch/pubsinfo.asp?pubid=2009001) for standard deviations of U.S. student subpopulations.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International 

Mathematics and Science Study (TIMSS), 2007.
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55

HIGHLIGHTS FROM TIMSS 2007 References

References

Beaton, A.E., and González, E. (1995). The NAEP Primer. 

Chestnut Hill, MA: Boston College.

Cohen, J. (1988). Statistical Power Analysis for the 

Behavioral Sciences, 2nd ed. Hillsdale, NJ: Erlbaum.

Ferraro, D., and Van de Kerckhove, W. (2006). Trends in 

International Mathematics and Science Study (TIMSS) 

2003: Nonresponse Bias Analysis (NCES 2007-044). 

National Center for Education Statistics, Institute of 

Education Sciences, U.S. Department of Education. 

Washington, DC.

Foy, P., Joncas, M., and Zuhlke, O. (2005).TIMSS 2007 

School Sampling Manual. Unpublished Manuscript, 

Chestnut Hill, MA: Boston College.

IEA Data Processing Center. (2006). TIMSS 2007 Data Entry 

Manager Manual. Hamburg, Germany: Author.

Martin, M.O., Mullis, I.V.S., and Foy, P. (2008). TIMSS 2007 

International Science Report: Findings from IEA’s Trends 

in International Mathematics and Science Study at the 

Fourth and Eighth Grades. Chestnut Hill, MA: Boston 

College.

Matheson, N., Salganik, L., Phelps, R., Perie, M., Alsalam, N., 

and Smith, T. (1996). Education Indicators: An 

International Perspective (NCES 96-003). U.S. 

Department of Education. Washington, DC: National 

Center for Education Statistics.

Mullis, I.V.S., Martin, M.O., and Foy, P. (2005). IEA’s TIMSS 

2003 International Report on Achievement in the 

Mathematics Cognitive Domains: Findings From a 

Developmental Project. Chestnut Hill, MA: Boston College.

Mullis, I.V.S., Martin, M.O., Ruddock, G.J., O’Sullivan, C.Y., 

Arora, A., and Erberber, E. (2005). TIMSS 2007 

Assessment Frameworks. Chestnut Hill, MA: Boston 

College.

Mullis, I.V.S., Martin, M.O., and Foy, P. (2008). TIMSS 2007 

International Mathematics Report: Findings from IEA’s 

Trends in International Mathematics and Science Study 

at the Fourth and Eighth Grades. Chestnut Hill, MA: 

Boston College. 

National Center for Education Statistics. (2002). NCES 

Statistical Standards (NCES 2003-601). Institute of 

Education Sciences, U.S. Department of Education. 

Washington, DC: Author.

Olson, J.F., Martin, M.O., and Mullis, I.V.S. (2008). TIMSS 

2007 Technical Report. Chestnut Hill, MA: Boston College.

Rosnow, R.L., and Rosenthal, R. (1996). Computing 

Contrasts, Effect Sizes, and Counternulls on Other 

People’s Published Data: General Procedures for 

Research Consumers. Psychological Methods, 1:331-340.

United Nations Educational, Scientific and Cultural 

Organization (UNESCO). (1999). Classifying Educational 

Programmes Manual for ISCED-97 Implementation in 

OECD Countries (1999 Edition). Paris: Author. Retrieved 

April 9, 2008 from 

http://www.oecd.org/dataoecd/7/2/1962350.pdf.

Westat. (2007). WesVar 5.0 User’s Guide. Rockville, MD: 

Author.
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A-1

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Introduction

The Trends in International Mathematics and Science Study 

(TIMSS) is a cross-national comparative study of the 

performance and schooling contexts of fourth- and eighthgrade students in mathematics and science. In this fourth 

cycle of TIMSS, mathematics and science assessments 

and associated questionnaires were administered in 43 

jurisdictions at the fourth-grade level and 56 jurisdictions at 

the eighth-grade level during 2007. TIMSS is coordinated by 

the International Association for the Evaluation of Educational 

Achievement (IEA), with national sponsors in each 

participating jurisdiction. In the United States, TIMSS is 

sponsored by the National Center for Education Statistics 

(NCES), in the Institute of Education Sciences at the U.S. 

Department of Education. This appendix provides an 

overview of the technical aspects of TIMSS 2007, including 

the sampling, data collection, test development and 

administration, weighting and variance estimation, scaling, 

and statistical testing procedures used to collect and analyze 

the data. More detailed information can be found in the 

TIMSS 2007 Technical Report (Olson, Martin, and Mullis 2008). 

International requirements 

for sampling, data collection, 

and response rates

In order to ensure comparability of the data across countries, 

the IEA provided detailed international guidelines on the 

various aspects of data collection described here, and 

implemented quality control procedures. Participating 

countries were obliged to follow these guidelines. 

Target populations 

In order to identify comparable populations of students to 

be sampled, the IEA defined the target populations as follows 

(Olson, Martin, and Mullis 2008):

Fourth-grade student population. The international 

desired target population is all students enrolled in the grade 

that represents 4 years of schooling, counting from the first 

year of the International Standard Classification of Education 

(ISCED)1 Level 1, providing that the mean age at the time of 

testing is at least 9.5 years. For most countries, the target 

grade should be the fourth grade, or its national equivalent. 

All students enrolled in the target grade, regardless of their 

age, belong to the international desired target population.

Eighth-grade student population. The international 

desired target population is all students enrolled in the grade 

that represents 8 years of schooling, counting from the first 

year of ISCED Level 1, providing that the mean age at the 

time of testing is at least 13.5 years. For most countries, 

the target grade should be the eighth grade, or its national 

equivalent. All students enrolled in the target grade, 

regardless of their age, belong to the international desired 

target population.

Teacher population. The mathematics and science 

teachers linked to the selected students. Note that these 

teachers are not a representative sample of teachers within 

the country. Rather, they are the mathematics and science 

teachers who teach a representative sample of students in 

two grades within the country (grades four and eight in the 

United States).

School population. All eligible schools2 containing either 

of the following: one or more fourth-grade classrooms; or one 

or more eighth-grade classrooms. 

Sampling

The sample design employed by the TIMSS 2007 assessment 

is generally referred to as a three-stage stratified cluster 

sample. The sampling units at each stage were defined 

as follows.

First-stage sampling units. The first-stage sampling 

units consisted of individual schools selected with probability 

proportionate to size (PPS), size being the estimated number 

of students enrolled in the target grade. Prior to sampling, 

schools in the sampling frame could be assigned to a 

predetermined number of explicit or implicit strata. Schools 

were to be sampled using a PPS systematic sampling 

method. Substitution schools—schools selected to replace 

those that were originally sampled but refused to participate—

were to be identified simultaneously.

Second-stage sampling units. The second-stage 

sampling units were classrooms within sampled schools. 

Countries were required to randomly select a minimum of one 

eligible classroom per target grade per school from a list of 

eligible classrooms prepared for each target grade. However, 

countries also had the option of selecting more than one 

eligible classroom per target grade per school and were 

encouraged to do so.

Appendix A: Technical Notes

1The ISCED was developed by the United Nations Educational, Scientific, and Cultural Organization (UNESCO) to facilitate the comparability of educational levels 

across countries. ISCED Level 1 begins with the first year of formal, academic learning (UNESCO 1999). In the United States, ISCED Level 1 begins at grade one. 2Some sampled schools may be considered ineligible for reasons noted in the section below titled “School exclusions.”
A-2

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Third-stage sampling units. The third-stage sampling 

units were students within sampled classrooms. Generally, 

all students in a sampled classroom were to be selected for 

the assessment though it was possible to sample a subgroup 

of students within a classroom, but only after consultation 

with Statistics Canada, the organization serving as the 

sampling referee.

Sample size for the main survey 

TIMSS guidelines call for a minimum of 150 schools to 

be sampled per grade, with a minimum of 4,000 students 

assessed per grade. The basic sample design of one 

classroom per target grade per school was designed to yield 

a otal sample of approximately 4,500 students per population. 

Countries with small class sizes or less than 30 students per 

school, were directed to consider sampling more schools, 

more classrooms per school, or both, to meet the minimum 

target of 4,000 tested students.

In 2007, countries that had participated in TIMSS 2003 were 

required to increase the size of their student samples to provide 

data for a bridge study. This study was designed to evaluate 

the effect of a small change in the assessment design between 

2003 and 2007. Countries that participated in TIMSS 2003 

were asked to include four additional booklets from 2003 in 

with the 14 booklets for TIMSS 2007 at each grade. As a result, 

student sample sizes needed to be increased to ensure that 

the number of students taking each booklet was sufficient for 

the purposes of scaling. The 2003-07 Bridge Study is described 

below in the section on “Scaling”.

Exclusions

The following discussion draws on the TIMSS 2007 School 

Sampling Manual (Foy, Joncas, and Zuhlke 2005). All schools 

and students excluded from the national defined target 

population are referred to as the excluded population. 

Exclusions could occur at the school level, with entire schools 

being excluded, or within schools, with specific students or 

entire classrooms excluded. TIMSS 2007 did not provide 

accommodations for students with disabilities or students who 

were unable to read or speak the language of the test. The 

IEA requirement with regard to exclusions is that they should 

not exceed more than 5 percent of the national desired target 

population (Foy, Joncas, and Zuhlke 2005). 

School exclusions. Countries could exclude schools that

• are geographically inaccessible;

• are of extremely small size;

• offer a curriculum, or school structure, radically different 

from the mainstream educational system; or

• provide instruction only to students in the excluded 

categories defined under “within-school exclusions,” 

such as schools for the blind.

Within-school exclusions. Countries were asked to adapt 

the following international within-school exclusion rules to 

define excluded students:

• Students with intellectual disabilities—Students who, 

in the professional opinion of the school principal or 

other qualified staff members, are considered to have 

intellectual disabilities or who have been tested 

psychologically as such. This includes students who are 

emotionally or mentally unable to follow even the general 

instructions of the test. Students were not to be excluded 

solely because of poor academic performance or normal 

disciplinary problems.

• Students with functional disabilities—Students who are 

permanently physically disabled in such a way that they 

cannot perform in the TIMSS testing situation. Students 

with functional disabilities who are able to respond were 

to be included in the testing.

• Non-native-language speakers—Students who are 

unable to read or speak the language(s) of the test and 

would be unable to overcome the language barrier of 

the test. Typically, a student who had received less than 

1 year of instruction in the language(s) of the test was 

to be excluded.

Defined participation rates

In order to minimize the potential for response biases, the IEA 

developed participation or response rate standards that apply 

to all countries and govern whether or not a nation’s data are 

included in the TIMSS 2007 international dataset and the way 

in which national statistics are presented in the international 

reports. These standards were set using composites of 

response rates at the school, classroom, and student and 

teacher levels and response rates were calculated with and 

without the inclusion of substitute schools that were selected 

to replace schools refusing to participate. 

The response rate standards determine how a jurisdiction’s 

data will be reported in the international reports. These 

standards take the following two forms, distinguished primarily 

by whether or not meeting the school response rate of 85 

percent requires the counting of substitute schools. 

Category 1: Met requirements. Countries that meet all 

of the following conditions are considered to have fulfilled the 

IEA requirements: (a) a minimum school participation rate of 

85 percent, based on original sampled schools only; and (b) 

a minimum classroom participation rate of 95 percent, from 

both original and substitute schools; and (c) a minimum 

student participation rate of 85 percent, from both original 

and substitute schools. 
A-3

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Category 2: Met requirements after substitutes. In the 

case of countries not meeting the category 1 requirements, 

provided that at least 50 percent of schools in the original 

sample participate, a country’s data are considered 

acceptable if the following requirements are met: a minimum 

combined school, classroom and student participation rate 

of 75 percent, based on the product of the participation rates 

described above. That is, the product of (a), (b) and (c), as 

defined in the Category 1 standard, must be greater than 

or equal to 75 percent. 

Countries satisfying the Category 1 standard are included in the 

international tabular presentations without annotation. Those 

only able to satisfy the Category 2 standard are included as 

well but are annotated to indicate their response rate status. 

The data from countries failing to meet either standard are 

presented separately in the international tabular presentations.

Sampling, data collection, and 

response rates in the United States 

and other countries

The U.S. TIMSS sample design

In the United States and most other countries, the target 

populations of students corresponded to the fourth and eighth 

grades. In sampling these populations TIMSS used a threestage stratified cluster sampling design.3 While the U.S. 

sampling frame was not explicitly stratified it was implicitly 

stratified (that is, sorted for sampling) by four categorical 

stratification variables: type of school (public or private), 

region of the country (Northeast, Central, West, Southeast);4

community type (eight levels);5 and minority status (above 

or below 15 percent of the student population). 

The first stage made use of a systematic PPS technique to 

select schools for the original sample. Using a sampling frame 

based on the 2006 National Assessment of Educational 

Progress (NAEP) school sampling frame,6 schools were 

selected with a probability proportionate to the school’s 

estimated enrollment of fourth- or eighth-grade students. 

Data for public schools were taken from the Common Core 

of Data (CCD), and data for private schools were taken from 

the Private School Universe Survey (PSS). In addition, for 

each original school selected, the two neighboring schools 

in the sampling frame were designated as substitute schools. 

The first school following the original sample school was the 

first substitute and the first school preceding it was the second 

substitute. If an original school refused to participate, the first 

substitute was contacted. If that school also refused to 

participate, the second substitute was contacted. There 

were several constraints on the assignment of substitutes. 

One sampled school was not allowed to substitute for another, 

and a given school could not be assigned to substitute for 

more than one sampled school. Furthermore, substitutes 

were required to be in the same implicit stratum as the 

sampled school. 

The second stage consisted of selecting intact mathematics 

classes within each participating school. Schools provided 

lists of fourth- or eighth-grade classrooms. Within schools, 

classrooms with fewer than 15 students were collapsed into 

pseudo-classrooms, so that each classroom on the school’s 

classroom sampling frame had at least 20 students.7 An equal 

probability sample of two classrooms (pseudo-classrooms) 

was identified from the classroom frame for the school. In 

schools where there was only one classroom, this classroom 

was selected with certainty. At the fourth-grade level, 30 

pseudo-classrooms were created prior to classroom sampling 

with 20 of these being selected in the final fourth-grade 

classroom sample. At the eighth-grade level, 253 pseudoclassrooms were created, of which 58 were included in the 

final classroom sample.

All students in sampled classrooms (pseudo-classrooms) 

were selected for assessment. In this way, the overall sample 

design for the United States was intended to approximate 

a self-weighting sample of students as much as possible, 

with each fourth- or eighth-grade student having an equal 

probability of selection. 

3The primary purpose of stratification is to improve the precision of the survey estimates. If explicit stratification of the population is used, the units of interest 

(schools, for example) are sorted into mutually exclusive subgroups–strata. Units in the same stratum are as homogeneous as possible, and units in different 

strata are as heterogeneous as possible, with respect to the characteristics of interest to the survey. Separate samples are then selected from each stratum. 

In the case of implicit stratification, the units of interest are simply sorted with respect to one or more variables known to have a high correlation with the variable 

of interest. In this way, implicit stratification guarantees that the sample of units selected will be spread across the categories of the stratification variables. 4The Northeast region consists of Connecticut, Delaware, the District of Columbia, Maine, Maryland, Massachusetts, New Hampshire, New Jersey, New York, 

Pennsylvania, Rhode Island, and Vermont. The Central region consists of Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, 

Ohio, Wisconsin, and South Dakota. The West region consists of Alaska, Arizona, California, Colorado, Hawaii, Idaho, Montana, Nevada, New Mexico, Oklahoma, 

Oregon, Texas, Utah, Washington, and Wyoming. The Southeast region consists of Alabama, Arkansas, Florida, Georgia, Kentucky, Louisiana, Mississippi, North 

Carolina, South Carolina, Tennessee, Virginia, and West Virginia.

5Eight community types are distinguished: large city of 250,000+; midsize city of < 250,000; urban fringe of large city; urban fringe of mid-size city; large town 

of 25,000+; small town of 2,500-25,000; rural outside metropolitan statistical area (MSA); rural inside MSA. 6In order to maximize response rates from both districts and schools it was necessary to begin the recruitment of both prior to the end of the 2005-06 school year. 

Since the 2007 NAEP sampling frame was not available until March 2006, it was necessary to base the TIMSS samples on the 2006 NAEP sampling frame. 

7Since classrooms are sampled with equal probability within schools, small classrooms would have the same probability of selection as large classrooms. 

Selecting classrooms under these conditions would likely mean that student sample size would be reduced, and some instability in the sampling weights created. 

To avoid these problems, pseudo-classes are created for the purposes of classroom sampling. Following sampling, the pseudo-class combinations are dissolved 

and the small classes involved retain their own identity. In this way, data on students, teachers, and classroom practices are linked in small classes in the same 

way as with larger classes.
A-4

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

U.S.TIMSS fourth-grade sample 

School sample. The fourth-grade school sample consisted 

of 300 schools. Ten ineligible schools were identified on the 

basis that they served special student populations, or had 

closed or altered their grade makeup since the sampling 

frame was developed. This left 290 schools eligible to 

participate, and 202 agreed to do so. The school response 

rate before substitution then was 70 percent unweighted. 

The analogous weighted school response rate was also 70 

percent (see table A-1) and is given by the following formula:

weighted school response 

rate before replacement

where Y denotes the set of responding original-sample 

schools; N denotes the set of eligible non-responding original 

sample schools; Wi

 denotes the base weight for school i; Wi = 

1/Pi, where Pi denotes the school selection probability for 

school i; and Ei denotes the enrollment size of age-eligible 

students, as indicated on the sampling frame. 

In addition to the 202 participating schools from the original 

sample, 55 substitute schools participated for a total of 257 

participating schools at the fourth grade in the United States 

(see table A-2). This gives a weighted (and unweighted) 

school participation rate after substitution of 89 percent 

(see table A-1).8

Classroom sample. Schools agreeing to participate were 

asked to list their fourth-grade mathematics classes as the 

basis for sampling at the classroom level, resulting in the 

identification of a total of 1,108 mathematics classrooms. 

At this time, schools were given the opportunity to identify 

special classes–classes in which all or most of the students 

had intellectual or functional disabilities or were non-nativelanguage speakers. While these classes were regarded as 

eligible, the students as a group were treated as “excluded” 

since, in the opinion of the school, their disabilities or 

language capabilities would render meaningless their 

performance on the assessment. Some 876 fourth-grade 

students in a total of 99 classrooms in 63 schools were 

excluded in this way. Schools identified 32 classrooms 

containing 222 students with intellectual disabilities (25 

percent), 41 classrooms containing 221 students with 

functional disabilities (25 percent) and 26 classrooms 

containing 433 non-native-language speakers (50 percent). 

The remaining 1,009 classrooms served as the pool from 

which the classroom sample was drawn. 

Classrooms with fewer than 15 students were collapsed into 

pseudo-classrooms prior to sampling so that each eligible 

classroom in a school had at least 20 students. Two 

classrooms (pseudo-classrooms) were selected per school 

where possible. In schools with only one classroom, this 

classroom was selected with certainty. Some 521 classrooms 

were selected as a result of this process. All selected 

classrooms participated in TIMSS yielding a classroom 

response rate of 100 percent (Olson, Martin, and Mullis 2008, 

exhibit A.6). 

Student sample. Schools were asked to list the students 

in each of these 521 classrooms, along with the teachers who 

taught mathematics and science to these students. A total of 

11,454 students were listed as a result. Subsequently, 2,454 

of these students were allocated to the bridge study since 

they completed a TIMSS 2003 assessment booklet rather 

than the TIMSS 2007 assessment (see the description of 

the 2003-07 bridge study in the section on Scaling below). 

Eliminating these students from further consideration leaves 

9,000 fourth-grade students as the pool of students selected 

to take part in TIMSS 2007 proper. These students are 

identified by IEA as “sampled students in participating 

schools” (Olson, Martin, and Mullis 2008, exhibit A.5). 

This pool of students is reduced by within-school exclusions 

and withdrawals. At the time schools listed the students in the 

sampled classrooms, they had the opportunity to identify 

particular students who were not suited to take the test 

because of physical or intellectual disabilities (i.e., students 

with disabilities who had been mainstreamed) or because they 

were non-English-language speakers. Schools identified a 

total of 543 students they wished to have excluded from the 

assessment; 323 students with intellectual disabilities (59 

percent), 92 students with functional disabilities (17 percent), 

and 128 students who were non-English-language speakers 

(24 percent). And, by the time of the assessment a further 

140 of the listed students had withdrawn from the school or 

classroom. In total then, the pool of 9,000 sampled students 

was reduced by 683 students (543 excluded and 140 

withdrawn) to yield 8,317 “eligible” students. The number of 

eligible students is used as the base for calculating student 

response rates (Olson, Martin, and Mullis 2008, exhibit A.5). 

The number of eligible students was further reduced on 

assessment day by 421 student absences, leaving 7,896 

“assessed students” identified as having completed a TIMSS 

2007 assessment booklet (see Table A-2). IEA defines the 

student response rate as the number of students assessed as 

a percentage of the number of eligible students which, in this 

case yields a weighted (and unweighted) student response 

rate of 95 percent (see table A-1).

8Substitute schools are matched pairs and do not have an independent probability of selection. NCES standards (Standard 1-3-8) indicate that, in these 

circumstances, response rates should be calculated without including substitute schools (National Center for Education Statistics 2002). TIMSS response rates 

denoted as “before replacement” conform to this standard. TIMSS response rates denoted as “after replacement” are not consistent with NCES standards since, 

in the calculation of these rates, substitute schools are treated as the equivalent of sampled schools.
A-5

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Table A-1. Coverage of target populations and participation rates, by grade and country: 2007

Grade four

Country

Years 

of formal 

schooling

Percentage of 

international 

desired 

population 

coverage

National 

desired 

population 

overall 

exclusion rate

Weighted 

school 

participation 

rate before 

substitution

Weighted 

school 

participation 

rate after 

substitution

Weighted 

student 

participation 

rate

Combined 

weighted 

school and 

student 

participation 

rate1

Algeria 4 100 2.1 99 99 97 97

Armenia 4 100 3.4 93 100 96 96

Australia 4 100 4.0 99 100 95 95

Austria 4 100 5.0 98 99 98 97

Chinese Taipei 4 100 2.8 100 100 100 100

Colombia 4 100 2.1 93 99 98 97

Czech Republic 4 100 4.9 89 98 94 92

Denmark 4 100 4.1 71 91 94 85

El Salvador 4 100 2.3 99 100 98 98

England 5 100 2.1 83 90 93 84

Georgia 4 85 4.8 92 100 98 98

Germany 4 100 1.3 96 100 97 96

Hong Kong SAR 4 100 5.4 81 84 96 81

Hungary 4 100 4.4 93 99 97 96

Iran, Islamic Rep. of 4 100 3.0 100 100 99 99

Italy 4 100 5.3 91 100 97 97

Japan 4 100 1.1 97 99 97 95

Kazakhstan 4 94 5.3 99 100 100 100

Kuwait 4 100 0.0 100 100 85 85

Latvia 4 72 4.6 93 97 95 92

Lithuania 5 93 5.4 99 100 94 94

Morocco 4 100 1.4 81 81 96 77

Netherlands 4 100 4.8 48 95 97 91

New Zealand 4.5-5.5 100 5.4 97 100 96 96

Norway 4 100 5.1 88 97 95 92

Qatar 4 100 1.8 100 100 97 97

Russian Federation 4 100 3.6 100 100 98 98

Scotland 5 100 4.5 77 94 94 88

Singapore 4 100 1.5 100 100 96 96

Slovak Republic 4 100 3.3 98 100 97 97

Slovenia 4 100 2.1 92 99 95 93

Sweden 4 100 3.1 98 100 97 97

Tunisia 4 100 2.9 100 100 99 99

Ukraine 4 100 0.6 96 96 97 93

United States 4 100 9.2 70 89 95 84

Yemen 4 100 2.0 99 100 98 98

(See notes at end of table)
A-6

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Table A-1. Coverage of target populations and participation rates, by grade and country: 2007

—Continued

Grade eight

Country

Years 

of formal 

schooling

Percentage of 

international 

desired 

population 

coverage

National 

desired 

population 

overall 

exclusion rate

Weighted 

school 

participation 

rate before 

substitution

Weighted 

school 

participation 

rate after 

substitution

Weighted 

student 

participation 

rate

Combined 

weighted 

school and 

student 

participation 

rate1

Algeria 8 100 0.1 99 99 96 95

Armenia 8 100 3.3 94 100 96 96

Australia 8 100 1.9 100 100 93 93

Bahrain 8 100 1.5 100 100 97 97

Bosnia and Herzegovina 8 or 9 100 1.5 100 100 98 98

Botswana 8 100 0.1 100 100 99 99

Bulgaria 8 100 20.3 94 98 96 94

Chinese Taipei 8 100 3.3 100 100 99 99

Colombia 8 100 1.6 96 100 98 98

Cyprus 8 100 2.5 100 100 96 96

Czech Republic 8 100 4.6 92 100 95 95

Egypt 8 100 0.5 99 100 98 98

El Salvador 8 100 2.8 99 100 98 98

England 9 100 2.3 78 86 88 75

Georgia 8 85 3.9 97 100 97 97

Ghana 8 100 0.9 100 100 98 98

Hong Kong SAR 8 100 3.8 73 79 96 75

Hungary 8 100 3.9 92 99 97 96

Indonesia 8 100 3.4 100 100 97 97

Iran, Islamic Rep. of 8 100 0.5 100 100 98 98

Israel 8 100 22.8 94 97 94 91

Italy 8 100 5.0 93 100 96 96

Japan 8 100 3.5 96 97 93 91

Jordan 8 100 2.0 100 100 96 96

Korea, Rep. of 8 100 1.6 100 100 99 99

Kuwait 8 100 0.3 97 97 87 84

Lebanon 8 100 1.4 81 92 93 85

Lithuania 8 92 4.2 98 99 91 90

Malaysia 8 100 3.3 100 100 98 98

Malta 9 100 2.9 100 100 95 94

Norway 8 100 2.6 88 93 93 86

Oman 8 100 1.2 100 100 99 99

Palestinian Nat'l Auth. 8 100 1.0 100 100 98 98

Qatar 9 100 0.8 100 100 97 97

Romania 8 100 1.8 99 99 97 97

Russian Federation 7 or 8 100 2.3 100 100 97 97

Saudi Arabia 8 100 0.5 99 99 95 94

Scotland 9 100 1.7 74 86 90 77

Serbia 8 80 6.8 100 100 98 98

Singapore 8 100 1.8 100 100 95 95

Slovenia 7 or 8 100 1.9 92 99 93 92

Sweden 8 100 3.6 100 100 94 94

Syrian Arab Republic 8 100 0.6 100 100 96 96

Thailand 8 100 3.4 90 100 99 99

Tunisia 8 100 0.0 100 100 98 98

Turkey 8 100 2.6 100 100 98 98

Ukraine 8 100 0.2 98 98 97 95

United States 8 100 7.9 68 83 93 77

1The combined weighted school and student participation rate is derived by multiplying the unrounded weighted school and student participation rates.

NOTE: Only countries that completed the necessary steps for their data to appear in the reports from the International Study Center are listed. In addition to the 

countries listed above, seven separate jurisdictions participated in TIMSS 2007: the provinces of British Columbia, Ontario, and Quebec in Canada; the Basque 

region of Spain; Dubai, UAE; and the states of Massachusetts and Minnesota. Information on these seven jurisdictions can be found in the international TIMSS 

2007 reports (Mullis, Martin, and Foy 2008; Martin, Mullis, and Foy 2008). Countries could participate at either grade level. Countries were required to sample 

students enrolled in the grade that represents 4 years of schooling, counting from the first year of the International Standard Classification of Education (ISCED) 

Level 1, providing that the mean age at the time of testing is at least 9.5 years, or students enrolled in the grade that represents eight years of schooling, 

counting from the first year of ISCED Level 1. In the United States and most countries, this corresponds to grade four and grade eight, respectively. In Bulgaria, 

the science assessment was administered to a diminished number of schools and students. The weighted school participation rate before substitution shown 

above refers to the mathematics assessment. This number should be reduced to 93 percent in describing the science assessment.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
A-7

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Table A-2. Total number of schools and students, by grade and country: 2007

Grade four

Country

Schools 

in original 

sample

Eligible 

schools 

in original 

sample

Schools 

in original 

sample that 

participated

 Substitute 

schools

Total 

schools that 

participated

Sampled 

students in 

participating 

schools

Students 

assessed

Algeria 150 150 149 0 149 4,366 4,223

Armenia 150 148 143 5 148 4,253 4,079

Australia 230 229 226 3 229 4,511 4,108

Austria 199 197 194 2 196 5,158 4,859

Chinese Taipei 150 150 150 0 150 4,260 4,131

Colombia 150 143 132 10 142 5,320 4,801

Czech Republic 150 147 132 12 144 4,583 4,235

Denmark 150 150 105 32 137 3,907 3,519

El Salvador 150 148 146 2 148 4,467 4,166

England 160 159 131 12 143 4,784 4,316

Georgia 152 144 131 13 144 4,384 4,108

Germany 250 247 239 7 246 5,464 5,200

Hong Kong SAR 150 150 122 4 126 3,965 3,791

Hungary 150 145 135 9 144 4,221 4,048

Iran, Islamic Rep. of 240 224 224 0 224 3,939 3,833

Italy 170 170 155 15 170 4,912 4,470

Japan 150 150 145 3 148 4,677 4,487

Kazakhstan 150 141 140 1 141 4,063 3,990

Kuwait 150 150 149 0 149 4,468 3,803

Latvia 150 150 140 6 146 4,188 3,908

Lithuania 163 156 154 2 156 4,345 3,980

Morocco 226 224 184 0 184 4,282 3,894

Netherlands 150 148 72 69 141 3,608 3,349

New Zealand 220 220 213 7 220 5,347 4,940

Norway 150 150 131 14 145 4,462 4,108

Qatar 114 114 114 0 114 7,411 7,019

Russian Federation 206 206 206 0 206 4,659 4,464

Scotland 150 148 114 25 139 4,320 3,929

Singapore 177 177 177 0 177 5,235 5,041

Slovak Republic 184 184 181 3 184 5,269 4,963

Slovenia 150 150 138 10 148 4,664 4,351

Sweden 160 155 151 4 155 4,965 4,676

Tunisia 150 150 150 0 150 4,242 4,134

Ukraine 150 150 144 0 144 4,459 4,292

United States 300 290 202 55 257 9,000 7,896

Yemen 150 144 143 1 144 6,128 5,811

See notes at end of table.

Note that the 876 students excluded because whole classes 

were excluded do not figure in the calculation of student 

response rates. They do, however, figure in the calculation 

of the coverage of the International Target Population. 

Together, these 876 students excluded prior to classroom 

sampling, plus the 543 within-class exclusions resulted in an 

overall student exclusion rate of 9.2 percent (see table A-1 

and Olson, Martin, and Mullis 2008, exhibit A.3). The reported 

coverage of the International Target Population then is 90.8 

percent (see Olson, Martin, and Mullis 2008, Exhibit A.3). 

IEA standards define this degree of coverage as acceptable 

though falling outside the desired range of 95 percent or better.

Combined participation rates. The combined school, 

classroom, and student weighted response rate standard of 

75 percent used by TIMSS in situations in which it is necessary 

to recruit substitute schools was met in this instance. Both the 

weighted and unweighted product of the separate response 

rates (84 percent) exceeded this 75 percent standard (see 

table A-1). The application of international guidelines means, 

however, that U.S. statistics describing fourth-grade students 

are annotated in international reports to indicate that coverage 

of the defined student population was less than the IEA 

standard of 95 percent and that participation rates were met 

only after substitute schools were included. 

Tables A-1 and A-2 are extracts from the international report 

Exhibits noted above and are designed to summarize 

information on school and student responses rates and 

coverage of the fourth- and eighth-grade target populations 

in each nation. 
A-8

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Table A-2. Total number of schools and students, by grade and country: 2007—Continued

Grade eight

Country

Schools 

in original 

sample

Eligible 

schools 

in original 

sample

Schools 

in original 

sample that 

participated

 Substitute 

schools

Total 

schools that 

participated

Sampled 

students in 

participating 

schools

Students 

assessed

Algeria 150 150 149 0 149 5,793 5,447

Armenia 150 148 143 5 148 4,898 4,689

Australia 230 228 228 0 228 4,549 4,069

Bahrain 74 74 74 0 74 4,434 4,230

Bosnia and Herzegovina 150 150 150 0 150 4,373 4,220

Botswana 150 150 150 0 150 4,310 4,208

Bulgaria 170 166 158 5 163 4,312 4,019

Chinese Taipei 150 150 150 0 150 4,164 4,046

Colombia 150 148 142 6 148 5,343 4,873

Cyprus 67 67 67 0 67 4,755 4,399

Czech Republic 150 147 135 12 147 5,182 4,845

Egypt 237 233 231 2 233 6,906 6,582

El Salvador 150 145 143 2 145 4,329 4,063

England 160 160 126 11 137 4,768 4,025

Georgia 152 135 131 4 135 4,533 4,178

Ghana 163 163 163 0 163 5,678 5,294

Hong Kong SAR 152 152 112 8 120 3,657 3,470

Hungary 150 145 133 11 144 4,321 4,111

Indonesia 150 149 149 0 149 4,419 4,203

Iran, Islamic Rep. of 220 208 208 0 208 4,140 3,981

Israel 150 150 140 6 146 3,708 3,294

Italy 170 170 159 11 170 4,873 4,408

Japan 150 150 144 2 146 4,656 4,312

Jordan 200 200 200 0 200 5,733 5,251

Korea, Rep. of 150 150 150 0 150 4,358 4,240

Kuwait 163 163 158 0 158 4,721 4,091

Lebanon 150 148 120 16 136 4,062 3,786

Lithuania 150 144 141 1 142 4,537 3,991

Malaysia 150 150 150 0 150 4,589 4,466

Malta 60 59 59 0 59 5,053 4,670

Norway 150 150 133 6 139 5,085 4,627

Oman 150 146 146 0 146 4,894 4,752

Palestinian Nat'l Auth. 155 148 147 1 148 4,572 4,378

Qatar 67 67 66 0 66 7,558 7,184

Romania 150 150 149 0 149 4,447 4,198

Russian Federation 210 210 210 0 210 4,706 4,472

Saudi Arabia 167 166 165 0 165 4,515 4,243

Scotland 150 150 109 20 129 4,700 4,070

Serbia 150 147 147 0 147 4,246 4,045

Singapore 164 164 164 0 164 4,828 4,599

Slovenia 150 150 138 10 148 4,414 4,043

Sweden 160 159 158 1 159 5,712 5,215

Syrian Arab Republic 150 150 150 0 150 5,025 4,650

Thailand 150 150 134 16 150 5,579 5,412

Tunisia 150 150 150 0 150 4,258 4,080

Turkey 150 146 146 0 146 4,682 4,498

Ukraine 150 150 146 0 146 4,598 4,424

United States 300 287 197 42 239 8,447 7,377

NOTE: Only countries that completed the necessary steps for their data to appear in the reports from the International Study Center are listed. In addition to the 

countries listed above, seven separate jurisdictions participated in TIMSS 2007: the provinces of British Columbia, Ontario, and Quebec in Canada; the Basque 

region of Spain; Dubai, UAE; and the states of Massachusetts and Minnesota. Information on these seven jurisdictions can be found in the international TIMSS 

2007 reports (Mullis, Martin, and Foy 2008; Martin, Mullis, and Foy 2008). Countries could participate at either grade level. Countries were required to sample 

students enrolled in the grade that represents 4 years of schooling, counting from the first year of the International Standard Classification of Education (ISCED) 

Level 1, providing that the mean age at the time of testing is at least 9.5 years, or students enrolled in the grade that represents eight years of schooling, 

counting from the first year of ISCED Level 1. In the United States and most countries, this corresponds to grade four and grade eight, respectively. In Bulgaria, 

the science assessment was administered to a diminished number of schools and students. The numbers shown in the table refer to the mathematics 

assessment. These should be reduced accordingly to describe the science assessment, as follows:eligible schools=142; participating schools in original 

sample=134; total participating schools=134; sampled students in participating schools=3,426; students assessed=3,079.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
A-9

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

U.S.TIMSS eighth-grade sample 

School sample. The eighth-grade school sample consisted 

of 300 schools. Thirteen ineligible schools were identified 

on the basis that they served special student populations, or 

had closed or altered their grade makeup since the sampling 

frame was developed. This left 287 schools eligible to 

participate and 197 agreed to do so. The unweighted school 

response rate before substitution then was 69 percent. The 

analogous weighted school response rate was 68 percent 

(see table A-1). 

In addition to the 197 participating schools from the original 

sample, 42 substitute schools participated for a total of 239 

participating schools at the eighth grade in the United States 

(see table A-2). This gives a weighted (and unweighted) 

school participation rate after substitution of 83 percent 

(see table A-1).9

Classroom sample. Schools agreeing to participate were 

asked to list their eighth-grade mathematics classes as the 

basis for sampling at the classroom level, resulting in the 

identification of a total of 3,125 mathematics classrooms. 

At this time, schools were given the opportunity to identify 

special classes–classes in which all or most of the students 

had intellectual or functional disabilities or were non-Englishlanguage speakers. While these classes were regarded as 

eligible, the students as a group were treated as “excluded” 

since, in the opinion of the school, their disabilities or 

language capabilities would render meaningless their 

performance on the assessment. Some 2,834 eighth-grade 

students in a total of 308 classrooms in 133 schools were 

excluded in this way. Schools identified 106 classrooms 

containing 788 students with intellectual disabilities (28 

percent), 136 classrooms containing 989 students with 

functional disabilities (35 percent) and 66 classrooms 

containing 1,057 non-native-language speakers (37 percent). 

The remaining 2,775 classrooms served as the pool from 

which the sample was drawn.

Classrooms with fewer than 15 students were collapsed into 

pseudo-classrooms prior to sampling so that each eligible 

classroom in a school had at least 20 students. Two 

classrooms (pseudo-classrooms) were selected per school 

where possible. In schools where there was only one 

classroom, this classroom was selected with certainty. 

Some 539 classrooms were selected as a result of this 

process. All selected classrooms participated in TIMSS 

yielding a classroom response rate of 100 percent (Olson, 

Martin, and Mullis 2008, exhibit A6). 

Subsequently, schools were asked to list the students in 

each sampled classroom, along with the teachers who taught 

mathematics and science to these students. At this time, 

schools were given the opportunity to identify particular

students in these classrooms who were not suited to take the 

test because of physical or intellectual disabilities (i.e., students 

with disabilities who had been mainstreamed) or because they 

were non-native- language speakers. 

Student sample. Schools were asked to list the students 

in each of these 539 sampled classrooms, along with the 

teachers who taught mathematics and science to these 

students. A total of 10,793 students were listed as being in the 

selected classrooms. Subsequently, 2,346 of these students 

were allocated to the bridge study since they completed a 

TIMSS 2003 assessment booklet rather than the TIMSS 2007 

assessment (see the description of the 2003-07 bridge study in 

the section on Scaling below). Eliminating these students from 

further consideration leaves 8,447 eighth-grade students as the 

pool of students selected to take part in TIMSS 2007 proper. 

These students are identified by IEA as “sampled students in 

participating schools” (Olson, Martin, and Mullis 2008, exhibit A5).

This pool of students is reduced by within-school exclusions 

and withdrawals. At the time schools listed the students in 

sampled classrooms, they had the opportunity to identify 

particular students who were not suited to take the test 

because of physical or intellectual disabilities (i.e., students 

with disabilities who had been mainstreamed) or because 

they were non-native-language speakers. Schools identified 

a total of 272 students they wished to have excluded from 

the assessment; 154 students with intellectual disabilities 

(57 percent), 48 students with functional disabilities (18 

percent) and 70 students who were non-English-language 

speakers (26 percent). And, by the time of the assessment 

a further 202 of the listed students had withdrawn from the 

school or classroom. In total then, the pool of 8,447 sampled 

students was reduced by 474 students (272 excluded and 202 

withdrawn) to yield 7,973 “eligible” students. The number of 

eligible students is used as the base for calculating student 

response rates (Olson, Martin, and Mullis 2008, exhibit A5). .

The number of eligible students was further reduced on 

assessment day by 596 student absences, leaving 7,377 

“assessed students” identified as having completed a TIMSS 

2007 assessment booklet (see table A-2). The IEA defines the 

student response rate as the number of students assessed as 

a percentage of the number of eligible students which, in this 

case yields a weighted (and unweighted) student response 

rate of 93 percent (see table A-1).

Note that the 2,834 students excluded because whole classes 

were excluded do not figure in the calculation of student 

response rates. They do, however, figure in the calculation of 

the coverage of the International Target Population. Together, 

these 2,834 students excluded prior to classroom sampling, 

plus the 272 within-class exclusions resulted in an overall 

student exclusion rate of 7.9 percent (see table A-1 and Olson, 

9Substitute schools are matched pairs and do not have an independent probability of selection. NCES standards (Standard 1-3-8) indicate that, in these 

circumstances, response rates should be calculated without including substitute schools (National Center for Education Statistics 2002). TIMSS response rates 

denoted as “before replacement” conform to this standard. TIMSS response rates denoted as “after replacement” are not consistent with NCES standards since, 

in the calculation of these rates, substitute schools are treated as the equivalent of sampled schools.
A-10

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Martin, and Mullis 2008, exhibit A.3). The reported coverage 

of the International Target Population then is 92.1 percent 

(see Olson, Martin, and Mullis 2008, exhibit A.3). IEA standards 

define this degree of coverage as acceptable though falling 

outside the desired range of 95 percent or better. 

Combined participation rates. The combined school, 

classroom and student weighted response rate standard of 75 

percent used by TIMSS in situations where substitute schools 

were necessary was met in this instance. Both the weighted 

and unweighted product of the separate response rates (77 

percent) exceeded this 75 percent standard (see table A-1). 

The application of international guidelines means, however, 

that U.S. statistics describing eighth-grade students are 

annotated in international reports to indicate that coverage 

of the defined student population was less than the IEA 

standard of 95 percent and that participation rates were 

met only after substitute schools were included. Table A-2 

summarizes information on the coverage of the eighth-grade 

target populations in each nation. 

Nonresponse bias in the U.S. TIMSS samples

NCES standards require a nonresponse bias analysis if 

the school-level response rate falls below 85 percent of 

the sampled schools (standard 2-2-2; National Center for 

Education Statistics 2002), as they did for both fourth- and 

eighth-grade samples. As a consequence a nonresponse bias 

analysis was initiated and took a form similar to that adopted 

for TIMSS 2003 (Ferraro and Van de Kerckhove 2006). A full 

report of this study will be included in a technical report to be 

released with the U.S. national TIMSS dataset.

Three methods were chosen to perform this analysis. The 

first method focused exclusively on the sampled schools and 

ignored substitute schools. The schools were weighted by their 

school base weights, excluding any nonresponse adjustment 

factor. The second method focused on sampled schools plus 

substitute schools, treating as nonrespondents those schools 

from which a final response was not received. Again, schools 

were weighted by their base weights, with the base weight 

for each substitute school set to the base weight of the 

original school that it replaced. The third method repeated 

the analyses from the second method using nonresponse 

adjusted weights.10

In order to compare TIMSS respondents and nonrespondents, 

it was necessary to match the sample of schools back to the 

sample frame to identify as many characteristics as possible 

that might provide information about the presence of 

nonresponse bias.11 The characteristics available for analysis in 

the sampling frame were taken from the CCD for public 

schools, and from the PSS for private schools. For categorical 

variables, the distribution of the characteristics for respondents 

was compared with the distribution for all schools. The 

hypothesis of independence between a given school 

characteristic and the response status (whether or not the 

school participated) was tested using a Rao-Scott modified 

chi-square statistic. For continuous variables, summary 

means were calculated and the difference between means 

was tested using a t test. Note that this procedure took 

account of the fact that the two samples in question were not 

independent samples, but in fact the responding sample was 

a subsample of the full sample. This effect was accounted for 

in calculating the standard error of the difference. Note also 

that in those cases where both samples were weighted using 

just the base weights, the test is exactly equivalent to testing 

that the mean of the respondents was equal to the mean of 

the nonrespondents.

In addition, multivariate logistic regression models were set 

up to identify whether any of the school characteristics were 

significant in predicting response status when the effects of 

all potential influences were considered simultaneously. 

Public and private schools were modeled together using the 

following variables:12 community type (central city, urban 

fringe/large town, rural/small town); control of school (public 

or private); NAEP region (Northeast, Southeast, Central, 

West); poverty level (percentage of students in school eligible 

for free or reduced-price lunch);13 number of students enrolled 

in fourth or eighth grade; total number of students; and, 

percentage minority students.14

10A detailed treatment of the meaning and calculation of sampling weights, including the nonresponse adjustment factors, is provided in the TIMSS 2007 Technical 

Report (Olson, Martin, and Mullis 2008). 11Comparing characteristics for respondents and nonrespondents is not always a good measure of nonresponse bias if the characteristics are either unrelated 

or weakly related to more substantive items in the survey. Nevertheless, this is often the only approach available. 12NAEP region and community type were dummy coded for the purposes of these analyses. In the case of NAEP region, “West” was used as the omitted group. 

For community type, “urban fringe/large town” was chosen as the omitted group.

13The measure of school poverty is based on the proportion of students in a school eligible for the Free or Reduced-Price Lunch (FRPL) program, a federally 

assisted meal program that provides nutritionally balanced, low-cost or free lunches to eligible children each school day. For the purposes of the nonresponse bias 

analyses, schools were classified as “low poverty” if less than 50 percent of the students were eligible for FRPL, and “high poverty” if 50 percent or more of 

students were eligible. Since the nonresponse bias analyses involve both participating and nonparticipating schools, they are based, out of necessity, on data from 

the sampling frame. TIMSS data are not available for nonparticipating schools. The school frame data are derived from the CCD and PPS. The CCD data provide 

information on the percentage of students in each school who are eligible for free- or reduced-price lunch, but are limited to public schools. The PPS data do not 

provide the same information for private schools. In the interest of retaining all of the schools and students in these analyses, private schools were assumed to be 

low-poverty schools–that is, they were assumed to be schools in which less than 50 percent of students were eligible for FRPL. Separate analyses of the TIMSS 

data for participating private schools suggest the reasonableness of this assumption. Of the 21 grade four private schools, only one reports having 50 percent or 

more of students eligible for FRPL. Among the 21 grade eight private schools, only two report having 50 percent or more of students eligible for FRPL. 

14Two forms of this school attribute were used in the analyses. In the bivariate analyses the percentage of each race/ethnic group was related separately to 

participation status. In the logistic regression analyses a single measure was used to characterize each school, namely, “percentage of minority students.”
A-11

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Results for the original sample of schools. In the 

analyses for the original sample of schools, all substituted 

schools were treated as nonresponding schools. The results 

of these analyses follow. 

• Fourth grade. In the investigation into nonresponse 

bias at the school level for TIMSS fourth-grade schools, 

comparisons between schools in the eligible sample 

and participating schools showed that there was no 

relationship between response status and the majority 

of school characteristics available for analysis. In separate 

variable-by-variable bivariate analyses, three variables 

were found to be related to participation: community type, 

region, and racial/ethnic composition. Central city schools 

were underrepresented among participating schools by 

almost 4 percent and rural small-town schools were 

overrepresented by the same amount. Similarly, schools 

in the Central region were overrepresented by close to 5 

percent, and schools in the West underrepresented by 

about 3.5 percent in the original sample of participating 

schools. And, in regard to racial/ethnic composition, both 

the percentage of White, non-Hispanic and the 

percentage of American Indian or Alaska Native students 

were higher in participating schools than in the eligible 

sample. Although each of these findings indicates some 

potential for nonresponse bias, when all of these factors 

were considered simultaneously in a regression analysis, 

the results indicated that the only independent source of 

bias lay with the fact that, relative to schools in the West, 

schools in the Central region were somewhat 

overrepresented among the participating schools.

• Eighth grade. The bivariate analyses for eighth-grade 

schools showed no relationship between participation and 

any of the school characteristics examined. However, the 

multivariate regression analysis showed that, relative to 

urban fringe/large town schools, central city schools were 

overrepresented among the participating schools. And, 

relative to schools in the West region, schools in the 

Central region were similarly overrepresented. 

Results for the final sample of schools. In the analyses 

for the final sample of schools, all substitute schools were 

included with the original schools as responding schools, 

leaving nonresponding schools as those for which no 

assessment data were available. The results of these 

analyses follow and are somewhat more complicated 

than the analyses for the original sample of schools. 

• Fourth grade. The bivariate results for the final sample 

of fourth-grade schools indicated that two of the three 

variables were still found to be related to participation: 

community type, and racial/ethnic composition. As in the 

earlier analysis, central city schools were underrepresented 

among participating schools (by some 2.5 percent) and 

rural small-town schools were overrepresented (by some 

2 percent). Similarly, both the percentage of White, nonHispanic and the percentage of American Indian or 

Alaska Native students were higher in participating 

schools than in the eligible sample. In each instance the 

differences were substantially reduced over those seen 

in connection with the original sample. These same 

differences could not be demonstrated in the multivariate 

regression analysis which failed to show any variables 

as significant predictors of participation. 

For the final sample of schools with school nonresponse 

adjustments applied to the weights,15 the results were 

identical. These results suggest that there is some 

potential for nonresponse bias in the fourth-grade original 

sample based on the characteristics studied. It also 

suggests that the use of substitute schools reduced the 

potential for bias. The school nonresponse adjustment 

had no effect on the characteristics of the weighted 

responding sample of schools.

• Eighth grade. The bivariate results for the final sample 

indicated that two variables were related to participation: 

community type, and the percentage of American Indian 

or Alaska Native students. Central city schools were 

overrepresented among participating schools by some 

4 percent, and schools in urban fringe/large town were 

underrepresented by nearly 4 percent, And, in regard 

to racial/ethnic composition, the percentage of American 

Indian or Alaska Native students in participating schools 

was higher than in all eligible schools. The multivariate 

regression analysis indicated that, relative to urban

fringe/large town schools, central city schools were 

overrepresented among the participating schools, and 

that the percentage of minority students in participating 

schools was lower than in all eligible schools.

With school nonresponse adjustments applied to the 

weights,16 the results were identical. These results 

suggest that there is some potential for nonresponse bias 

in the original sample based on the characteristics studied. 

It also suggests that, while there is no evidence that the 

use of substitute schools reduced the potential for bias, 

it has not added to it substantially. The school nonresponse 

adjustment had no effect on the characteristics of the 

weighted responding sample of schools.

15The international weighting procedures created a nonresponse adjustment class for each explicit stratum; see the TIMSS 2007 Technical Report (Olson, Martin, 

and Mullis 2008) for details. In the case of the U.S. fourth-grade sample, there was no explicit stratification and thus a single adjustment class. The procedures 

could not be varied for individual countries to account for any specific needs. Therefore, the U.S. nonresponse bias analyses could have no influence on the 

weighting procedures and were undertaken after the weighting process was complete.

16The international weighting procedures created a nonresponse adjustment class for each explicit stratum. For the eighth grade, there was no explicit stratification 

and thus a single adjustment class. Again, the procedures were not varied for individual countries to account for any specific needs. As with the fourth grade, the 

nonresponse bias analyses for the eighth grade could have no influence on the weighting procedures
A-12

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Test development 

TIMSS is a cooperative effort involving representatives from 

every country participating in the study. For TIMSS 2007, 

the test development effort began with a revision of the 

frameworks that are used to guide the construction of the 

assessment (Mullis et al. 2005). The frameworks were 

updated to reflect changes in the curriculum and instruction 

of participating countries. Extensive input from experts in 

mathematics and science education, assessment, and 

curriculum, and representatives from national educational 

centers around the world contributed to the final shape of the 

frameworks. Maintaining the ability to measure change over 

time was an important factor in revising the frameworks. 

As part of the TIMSS dissemination strategy, approximately 

one half of the 2003 assessment items were released for 

public use. To replace assessment items that had been 

released, countries submitted items for review by subjectmatter specialists, and additional items were written by 

the IEA Science and Mathematics Review Committee 

in consultation with item-writing specialists in various 

countries to ensure that the content, as explicated in the 

frameworks, was covered adequately. Items were reviewed 

by an international Science and Mathematics Item Review 

Committee and field-tested in most of the participating 

countries. Results from the field test were used to evaluate 

item difficulty, how well items discriminated between highand low-performing students, the effectiveness of distracters 

in multiple-choice items, scoring suitability and reliability 

for constructed-response items, and evidence of bias toward 

or against individual countries or in favor of boys or girls. 

As a result of this review, 196 new fourth-grade items were 

selected for inclusion in the international assessment. In total, 

353 mathematics and science items were included in the 

fourth-grade TIMSS assessment booklets. At the eighth grade, 

the review of the item statistics from the field test led to the 

inclusion 240 new eighth-grade items in the assessment. In 

total, 429 mathematics and science items were included in the 

eighth-grade TIMSS assessment booklets. More detail on the 

distribution of new and trend items is included in table A-3. 

Table A-3. Number of new and trend mathematics and science items in the 

TIMSS grade four and grade eight assessments, by type: 2007

Grade four

All items New items Trend items

Number Percent Number Percent Number Percent

All items

Total 353 100 196 100 157 100

Multiple choice 189 54 108 55 81 52

Constructed response 164 46 88 45 76 48

Mathematics items

Total 179 100 98 100 81 100

Multiple choice 96 54 55 56 41 51

Constructed response 83 46 43 44 40 49

Science items

Total 174 100 98 100 76 100

Multiple choice 93 53 53 54 40 53

Constructed response 81 47 45 46 36 47

Grade eight

All items New items Trend items

Number Percent Number Percent Number Percent

All items

Total 429 100 240 100 189 100

Multiple choice 224 52 117 49 107 57

Constructed response 205 48 123 51 82 43

Mathematics items

Total 215 100 120 100 95 100

Multiple choice 117 54 61 51 56 59

Constructed response 98 46 59 49 39 41

Science items

Total 214 100 120 100 94 100

Multiple choice 107 50 56 47 51 54

Constructed response 107 50 64 53 43 46

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics 

and Science Study (TIMSS) 2007.
A-13

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Design of instruments

TIMSS 2007 included booklets containing assessment items 

as well as self-administered background questionnaires for 

principals, teachers, and students. 

Assessment booklets

The assessment booklets were constructed such that not all 

of the students responded to all of the items. This is consistent 

with other large-scale assessments, such as the NAEP. To 

keep the testing burden to a minimum, and to ensure broad 

subject-matter coverage, TIMSS used a rotated block design 

that included both mathematics and science items. That is, 

students encountered both mathematics and science items 

during the assessment. 

The 2007 fourth-grade assessment consisted of 14 booklets, 

each requiring approximately 72 minutes of response time. 

To ensure that TIMSS 2007 maintains the trend, and to provide 

for a correction through equating, if necessary, four additional 

“bridge” booklets were required but only for countries that 

participated in TIMSS 2003.17 These bridge study booklets 

were identical to booklets used in 2003. Performance on 

the bridge booklets did not contribute to the overall score for 

TIMSS 2007 but the data were used in the trend scaling that 

placed the 2007 results on the same scale as previous TIMSS 

assessments and so allowed for comparisons across the years. 

For the United States and other countries participating in the 

2003 assessment, this meant a total of 18 booklets. The 18 

booklets were rotated among students, with each participating 

student completing 1 booklet only. The mathematics and 

science items were each assembled separately into 14 

blocks, or clusters, of items. Each block contained either 

mathematics items or science items only. The secure, or 

trend, items used in prior assessments were included in 3 

blocks, with the other 11 blocks containing new items. Each of 

the 14 TIMSS 2007 booklets contained 4 blocks in total. The 4 

additional bridge study booklets from TIMSS 2003 contained 6 

blocks of items each.

The 2007 eighth-grade assessment followed the same pattern 

and consisted of 18 booklets, each requiring approximately 

90 minutes of response time. The 18 booklets were rotated 

among students, with each participating student completing 

1 booklet only. The mathematics and science items were 

assembled into 14 blocks, or clusters, of items. Each block 

contained either mathematics items or science items only. 

The secure, or trend, items used in prior assessments were 

included in 3 blocks, with the other 11 blocks containing new 

items. Each of the 14 TIMSS 2007 booklets contained 4 

blocks in total. The 4 additional bridge study booklets from 

TIMSS 2003 contained 6 blocks of items each. Performance 

on the bridge booklets did not contribute to the overall score 

for TIMSS 2007 but the data were used in the trend scaling 

that placed the 2007 results on the same scale as previous 

TIMSS assessments and so allowed for comparisons across 

the years. 

As part of the design process, it was necessary to ensure that 

the booklets showed a distribution across the mathematics and 

science content domains as specified in the frameworks. The 

number of mathematics and science items in the fourth- and 

eighth-grade TIMSS 2007 assessments is shown in table A-4. 

Grade eight

Response type

Content domain Total

Multiple 

choice

Constructed 

response

Total 429 224 205

Mathematics 215 117 98

Number 63 35 28

Algebra 64 34 30

Geometry 47 31 16

Data and chance 41 17 24

Science 214 107 107

Biology 76 36 40

Chemistry 42 21 21

Physics 55 31 24

Earth science 41 19 22

Grade four

Response type

Content domain Total

Multiple 

choice

Constructed 

response

Total 353 189 164

Mathematics 179 96 83

Number 78 50 28

Geometric shapes and measures 44 32 12

Data display 97 14 83

Science 174 93 81

Life science 74 42 32

Physical science 64 35 29

Earth science 36 16 20

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Table A-4. Number of mathematics and science items in the TIMSS grade four and grade eight 

assessments, by type and content domain: 2007

17A detailed description of the bridge study and the use of the data obtained through the bridge booklets in scaling the 2007 assessment can be found in the 

TIMSS 2007 Technical Report (Olson, Martin, and Mullis 2008).
A-14

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Background questionnaires

As in prior administrations of TIMSS, TIMSS 2007 included 

self-administered questionnaires for principals, teachers, 

and students. To create the questionnaires for 2007, the 2003 

versions were reviewed extensively by the national research 

coordinators from the participating countries as well as a 

Questionnaire Item Review Committee (QIRC). Based on 

this review, the QIRC deleted or revised some questions, 

and added several new ones. Like the assessment items, 

all questionnaire items were field tested, and the results 

reviewed carefully. As a result, some of the questionnaire 

items needed to be revised prior to their inclusion in the final 

questionnaires. The questionnaires requested information to 

help provide a context for the performance scores, focusing 

on such topics as students’ attitudes and beliefs about 

learning, their habits and homework, and their lives both in 

and outside of school; teachers’ attitudes and beliefs about 

teaching and learning, teaching assignments, class size 

and organization, instructional practices, and participation 

in professional development activities; and principals’ 

viewpoints on policy and budget responsibilities, curriculum 

and instruction issues and student behavior, as well as 

descriptions of the organization of schools and courses. 

Detailed results from the student, teacher, and school surveys 

are not discussed in this report but are available in the two 

international reports: the TIMSS 2007 International 

Mathematics Report (Mullis, Martin, and Foy 2008) and 

TIMSS 2007 International Science Report (Martin, Mullis, 

and Foy 2008). 

Calculator usage 

Calculators were not permitted during the TIMSS fourth-grade 

assessment. However, the TIMSS policy on calculator use at 

the eighth grade was to give students the best opportunity to 

operate in settings that mirrored their classroom experiences. 

Calculators were permitted but not required for the eighth-grade 

assessment materials. In the United States, students assigned 

one of the 14 TIMSS 2007 booklets were allowed, but not 

required, to use calculators. However, students assigned one 

of the trend booklets from the 2003 assessment were required 

to follow the 2003 rules in this respect. These students could 

use a calculator only for the second half of the booklet. 

Translation

Source versions of all instruments (assessment booklets, 

questionnaires, and manuals) were prepared in English and 

translated into the primary language or languages of instruction 

in each country. In addition, it was sometimes necessary to 

adapt the instrument for cultural purposes, even in countries 

that use English as the primary language of instruction. All 

adaptations were reviewed and approved by the International 

Study Center to ensure they did not change the substance or 

intent of the question or answer choices. For example, proper 

names were sometimes changed to names that would 

be more familiar to students (e.g., Marja-leena to Maria). 

Each country prepared translations of the instruments 

according to translation guidelines established by the 

International Study Center. Adaptations to the instruments 

were documented by each country and submitted for review. 

The goal of the translation guidelines was to produce 

translated instruments of the highest quality that would 

provide comparable data across countries. 

Translated instruments were verified by an independent, 

professional translation agency prior to final approval and 

printing of the instruments. Countries were required to submit 

copies of the final printed instruments to the International 

Study Center. Further details on the translation process can 

be found in the TIMSS 2007 Technical Report (Olson, Martin, 

and Mullis 2008). 

Recruitment, test administration, 

and quality assurance 

TIMSS 2007 emphasized the use of standardized procedures 

in all countries. Each country collected its own data, based 

on comprehensive manuals and trainings provided by the 

international project team to explain the survey’s 

implementation, including precise instructions for the work 

of school coordinators and scripts for test administrators to 

use in testing sessions. 

Recruitment of schools and students 

With the exception of private schools, the recruitment of 

schools required several steps. Beginning with the sampled 

schools, the first step entailed obtaining permission from 

the school district to approach the sampled school(s) in that 

district. If a district refused permission, then the district of the 

first substitute school was approached and the procedure was 

repeated. With permission from the district, the school(s) was 

contacted in a second step. If a sampled school refused to 

participate, the district of the first substitute was approached 

and the permission procedure repeated. During most of the 

recruitment period sampled schools and substitute schools 

were being recruited concurrently. Each participating school 

was asked to nominate a School Coordinator as the main 

point of contact for the study. The school coordinator worked 

with project staff to arrange logistics and liaise with staff, 

students and parents as necessary. 

On the advice of the school, parental permission for students 

to participate was sought with one of three approaches to 

parents: a simple notification; a notification with a refusal form; 

and a notification with a consent form for parents to sign. 

In each approach, parents were informed that their students 

could opt out of participating. 
A-15

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Gifts to schools, School Coordinators, and students. 

Schools, School Coordinators, and students were provided 

with small gifts as a sign of appreciation for their willingness 

to participate. Schools were provided with an all-in-one 

printer/photocopier/scanner/fax, School Coordinators 

received a TIMSS satchel, and students were given a clockcompass carabiner.

Test administration

Test administration in the United States was carried out 

by professional staff trained according to the international 

guidelines. School personnel were asked only to assist with 

listings of students, identifying space for testing in the school, 

and specifying any parental consent procedures needed for 

sampled students.

Quality assurance 

The International Study Center monitored compliance with 

the standardized procedures. National research coordinators 

were asked to nominate one or more persons unconnected 

with their national center, such as retired school teachers, 

to serve as quality control monitors for their countries. 

The International Study Center developed manuals for 

the monitors and briefed them in 2-day training sessions 

about TIMSS, the responsibilities of the national centers in 

conducting the study, and their own roles and responsibilities. 

Some 30 schools in the U.S. samples were visited by the 

monitors—15 of the 257 schools in the fourth-grade sample, 

and 15 of the 239 schools in the eighth-grade sample. These 

schools were scattered geographically across the nation. 

In addition, each country conducted its own separate quality 

control procedures.

Scoring and scoring reliability 

The TIMSS assessment items included both multiple-choice 

and constructed-response items. A scoring rubric (guide) was 

created for every item included in the TIMSS assessments. 

The rubrics were carefully written and reviewed by national 

research coordinators and other experts as part of the field 

test of items, and revised accordingly. 

The national research coordinator in each country was 

responsible for the scoring and coding of data in that country, 

following established guidelines. The national research 

coordinator and, sometimes, additional staff attended scoring 

training sessions held by the International Study Center. The 

training sessions focused on the scoring rubrics and coding 

system employed in TIMSS. Participants in these training 

sessions were provided extensive practice in scoring example 

items over several days. Information on within-country 

agreement among coders was collected and documented 

by the International Study Center. Information on scoring 

and coding reliability was also used to calculate cross-country 

agreement among coders. Information on scoring reliability 

for constructed-response scoring in TIMSS 2007 is provided 

in table A-5. 

Data entry and cleaning 

The national research coordinator from each country oversaw 

data entry. The data collected for TIMSS 2007 were entered 

into data files with a common international format, as specified 

in the Data Entry Manager Manual (IEA Data Processing 

Center 2006), which accompanied data entry software 

(WinDEM) available to all participating countries. The software 

facilitated the checking and correction of data by providing 

various data consistency checks. The data were then sent to 

the IEA Data Processing Center (DPC) in Hamburg, Germany, 

for cleaning. The DPC checked that the international data 

structure was followed; checked the identification system 

within and between files; corrected single case problems 

manually; and applied standard cleaning procedures to 

questionnaire files. Results of the data cleaning process were 

documented by the DPC. This documentation was shared with 

the national research coordinator with specific questions to be 

addressed. The national research coordinator then provided 

the DPC with revisions to coding or solutions for anomalies. 

The DPC subsequently compiled background univariate 

statistics and preliminary test scores based on classical and 

Rasch item analyses. Detailed information on the entire data 

entry and cleaning process can be found in the TIMSS 2007 

Technical Report (Olson, Martin, and Mullis 2008).

Weighting, scaling, 

and plausible values 

Before the data were analyzed, responses from the groups of 

students assessed were assigned sampling weights to ensure 

that their representation in TIMSS 2007 results matched their 

actual percentage of the school population in the grade 

assessed. With these sampling weights in place, the analyses 

of TIMSS 2007 data proceeded in two phases: scaling and 

estimation. During the scaling phase, item response theory 

(IRT) procedures were used to estimate the measurement 

characteristics of each assessment question. During the 

estimation phase, the results of the scaling were used to 

produce estimates of student achievement. Subsequent 

analyses related these achievement results to the background 

variables collected by TIMSS 2007.

Weighting

Responses from the groups of students were assigned 

sampling weights to adjust for over- or under-representation 

during the sampling of a particular group. The use of sampling 

weights is necessary for the computation of sound, nationally 

representative estimates. The weight assigned to a student’s 

responses is the inverse of the probability that the student 
A-16

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Table A-5. Within-country constructed-response scoring 

reliability for TIMSS grade four and grade eight 

mathematics and science items, by exact percent 

score agreement and country: 2007

Grade four

Mathematics Science

Average 

across items

Range Average 

across items

Range 

Country Min Max Min Max

TIMSS average 98 88 100 96 81 100

Algeria 92 58 99 88 69 98

Armenia 99 94 100 98 93 100

Australia 100 98 100 99 95 100

Austria 99 95 100 98 90 100

Chinese Taipei 98 84 100 97 74 100

Colombia 99 93 100 98 50 100

Czech Republic 98 90 100 94 78 100

Denmark 97 83 100 91 72 100

El Salvador 99 96 100 99 78 100

England 99 91 100 98 88 100

Georgia 97 88 100 92 68 100

Germany 97 75 100 93 73 100

Hong Kong SAR 100 98 100 99 98 100

Hungary 100 97 100 99 96 100

Iran, Islamic Rep. of 99 96 100 97 83 100

Italy 99 94 100 98 85 100

Japan 99 94 100 97 88 100

Kazakhstan 99 96 100 99 97 100

Kuwait 100 98 100 99 94 100

Latvia 95 41 100 85 42 100

Lithuania 98 88 100 95 80 100

Morocco 95 33 100 93 75 100

Netherlands 97 86 100 92 71 100

New Zealand 99 95 100 97 90 100

Norway 99 92 100 97 88 100

Qatar 99 91 100 99 94 100

Russian Federation 100 98 100 100 99 100

Scotland 99 91 100 97 87 100

Singapore 99 93 100 96 90 100

Slovak Republic 99 92 100 99 97 100

Slovenia 100 99 100 99 93 100

Sweden 98 89 100 93 65 100

Tunisia 98 86 100 92 77 100

Ukraine 100 98 100 100 98 100

United States 98 83 100 94 68 100

Yemen 98 83 100 96 85 100

See notes at end of table.
A-17

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Table A-5. Within-country constructed-response scoring 

reliability for TIMSS grade four and grade eight 

mathematics and science items, by exact percent 

score agreement and country: 2007—Continued

Grade eight

Mathematics Science

Average 

across items

Range Average 

across items

Range 

Country Min Max Min Max

TIMSS average 98 89 100 96 82 100

Algeria 95 60 100 94 75 100

Armenia 99 94 100 98 89 100

Australia 99 93 100 97 88 100

Bahrain 100 97 100 94 78 100

Bosnia and Herzegovina 98 90 100 95 74 100

Botswana 98 84 100 95 79 100

Bulgaria 96 70 100 91 69 100

Chinese Taipei 98 47 100 94 66 100

Colombia 99 92 100 98 88 100

Czech Republic 98 86 100 93 75 100

Egypt 99 94 100 97 88 100

El Salvador 100 98 100 100 98 100

England 99 94 100 97 88 100

Georgia 97 76 100 92 67 100

Ghana 100 98 100 99 96 100

Hong Kong SAR 99 95 100 99 96 100

Hungary 98 84 100 95 86 100

Indonesia 98 90 100 97 81 100

Iran, Islamic Rep. of 99 93 100 97 86 100

Israel 96 82 100 92 74 100

Italy 99 85 100 96 63 100

Japan 97 84 100 91 54 100

Jordan 100 97 100 99 93 100

Korea, Rep. of 99 96 100 99 95 100

Kuwait 99 96 100 99 88 100

Lebanon 100 97 100 100 97 100

Lithuania 98 94 100 97 90 100

Malaysia 99 96 100 99 96 100

Malta 97 81 100 93 81 100

Norway 99 94 100 97 88 100

Oman 99 95 100 99 95 100

Palestinian Nat'l Auth. 98 89 100 94 82 100

Qatar 99 91 100 99 95 100

Romania 99 96 100 99 89 100

Russian Federation 100 98 100 99 93 100

Saudi Arabia 100 97 100 99 90 100

Scotland 99 95 100 97 84 100

Serbia 99 94 100 97 74 100

Singapore 98 93 100 96 90 100

Slovenia 100 98 100 100 95 100

Sweden 98 86 100 92 70 100

Syrian Arab Republic 99 95 100 99 92 100

Thailand 98 89 100 90 73 100

Tunisia 97 87 100 91 61 100

Turkey 100 95 100 97 81 100

Ukraine 98 80 100 92 68 100

United States 97 86 100 93 73 100

NOTE: The reliability of constructed-reponse scoring was determined by having two scorers 

independently score a random sample of some 200 student responses to each item. Table A-5 

displays the average and range of the within-country exact percent of inter-rater agreement 

across all items. To gather and document within-country agreement among scorers, systematic 

subsamples of at least 100 students' responses to each constructed-response item were coded 

independently by two readers. The agreement score indicates the degree of agreement. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), 

Trends in International Mathematics and Science Study (TIMSS), 2007.
A-18

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

would be selected for the sample. When responses are 

weighted, none are discarded, and each contributes to the 

results for the total number of students represented by the 

individual student assessed. Weighting also adjusts for various 

situations (such as school and student nonresponse) because 

data cannot be assumed to be randomly missing. The 

internationally defined weighting specifications for TIMSS 

require that each assessed student’s sampling weight should 

be the product of (1) the inverse of the school’s probability 

of selection, (2) an adjustment for school-level nonresponse, 

(3) the inverse of the classroom’s probability of selection, and 

(4) an adjustment for student-level nonresponse.18 All TIMSS 

1995, 1999, 2003, and 2007 analyses are conducted using 

sampling weights. A detailed description of this process is 

provided in the TIMSS Technical 2007 Report (Olson, Martin, 

and Mullis 2008).

Scaling

In TIMSS, scale scores were estimated for each student using 

an item response theory (IRT) model. With IRT the difficulty 

of each item is deduced using information about how likely it 

is for students to get some items correct versus other items. 

Once the difficulty of each item is determined, the ability of 

each student can be estimated even when different students 

have been administered different items. At this point in the 

estimation process achievement scores are expressed in a 

standardized logit scale which ranges from -4 to +4. In order 

to make the scores more meaningful and to facilitate their 

interpretation, the scores are transformed to a new scale 

with a mean of 500 and a standard deviation of 100. 

The procedures TIMSS used for the analyses were developed 

to produce accurate results for groups of students while 

limiting the testing burden on individual students. Furthermore, 

these procedures provided data that could be readily used in 

secondary analyses. IRT scaling provides estimates of item 

parameters (e.g., difficulty, discrimination) that define the 

relationship between the item and the underlying variable 

measured by the test. Parameters of the IRT model are 

estimated for each test question, with an overall scale being 

established as well as scales for each content area and 

cognitive domain specified in the assessment framework. 

For example, the TIMSS 2007 eighth-grade assessment had 

four scales describing four mathematics content areas and 

four science content areas, as well as three cognitive domains 

in each of mathematics and science. 

In order to allow for the calculation of trends in achievement, 

comparisons of scores were necessary across the four TIMSS 

assessments conducted in 1995, 1999, 2003 and 2007. IRT 

estimation procedures were used to place scores from the 

multiple administrations on the same scale (the scale of the 

1995 administration). This is made possible by the inclusion 

of common test items in successive administrations. This 

allows comparison of item parameters (such as the relative 

difficulty of items compared with each other and how well 

individual items predict overall scores) across administrations. 

This comparison of item parameters is used to drop items 

whose item parameters change dramatically across 

administrations and to equate scales across years. It is 

important to note that the item parameters do not depend 

directly on the average ability level of the students tested, 

though they may depend on the range of abilities among 

students tested (for example, to determine which of two 

difficult items is more difficult, it is important to test students 

of sufficient ability to get at least one of the items correct). 

Therefore, even if the average ability levels of students in 

countries participating in TIMSS over time changes, the scales 

still can be equated across administrations.

In TIMSS, scales are equated across administrations by 

linking the data from each administration to the data from 

the administration that preceded it, as follows. Data for 

students in adjacent assessments are pooled together and 

scaled using IRT to determine the difficulty and discrimination 

of each item. This puts the scores from adjacent assessments 

on the same scale. The achievement scores estimated from 

the new item parameters are then put on the original 1995 

TIMSS metric by a linear transformation. 

For example, in order to allow an examination of trends 

in eighth-grade achievement between 1995 and 1999, the 

TIMSS 1999 eighth-grade data were placed on the 1995 

TIMSS scale by first scaling the 1995 and 1999 data for 

countries that participated in both years together to determine 

the item parameters. Ability estimates for all students (those 

assessed in 1995 and those assessed in 1999) based on 

the new item parameters were then estimated. In order to 

put these jointly calibrated 1995 and 1999 scores on the 1995 

metric, a linear transformation is applied. This transformation 

is designed to give the jointly calibrated 1995 scores the 

same mean and standard deviation as the original 1995 

scores that were reported in the 1995 assessment cycle. 

Once this linear transformation is established it is applied 

to the 1999 assessment scores for all countries participating 

in 1999. This puts the 1999 scores on the 1995 (longitudinal) 

metric while preserving any growth that has occurred 

between assessments. 

Following this same procedure, TIMSS 2003 scores were 

jointly calibrated with the 1999 scores to place them on the 

same (1995) metric and, finally, TIMSS 2007 scores were 

jointly calibrated with the 2003 scores to place these on the 

same (1995) metric. By linking scores for each adjacent pair 

of assessments, all four sets of scores are placed on the same 

18These adjustments are for overall response rates and did not include any of the characteristics associated with differential nonresponse as identified in the 

nonresponse bias analyses reported above.
A-19

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

longitudinal scale. As a result, even if the makeup of the 

countries participating in TIMSS changes over time, 

achievement comparisons within and between countries 

are legitimate at a single point in time and across time. 

Information obtained from the bridge study described 

below was incorporated into this scaling to ensure strict 

comparability of scores across the four assessments. 

Details are provided in the TIMSS 2007 Technical Report

(Olson, Martin, and Mullis 2008).

The 2003-07 Bridge Study. As the name suggests, TIMSS 

places a great deal of emphasis on the measurement of 

trends in achievement within and between countries. TIMSS 

provides for the measurement of these trends across the four 

TIMSS assessment years (1995, 1999, 2003, and 2007) by 

placing the scores from each assessment on the same scale. 

However, the TIMSS assessment design changed a little in 

2007, and it was considered prudent to devise a procedure to 

measure the effect of this change, if any, on the comparability 

of the 2007 assessment scores with those from previous 

years. Given an effect, the intent was to incorporate a 

correction into the scaling procedures which establish the 

comparability of the 2007 achievement scores with those 

from 1995, 1999, and 2003. 

In order to evaluate the effect of the change in assessment 

design in TIMSS 2007, a bridge study was incorporated 

into the main survey to allow a comparison of the 2007 

assessment with the 2003 assessment. Countries that 

participated in TIMSS 2003 were asked to include four 

additional booklets from 2003 in with the 14 booklets for 

TIMSS 2007 at each grade. As a result, sample sizes needed 

to be increased to ensure that the number of students taking 

each booklet was sufficient for the purposes of scaling. 

The findings from the bridge study indicated a small effect 

from the change in the assessment design. To accommodate 

this, a correction was introduced into the scaling procedures 

which placed the 2007 assessment scores on the same scale 

as the scores from the 1995, 1999 and 2003 assessments. 

A detailed description of the bridge study is provided in the 

TIMSS 2007 Technical Report (Olson, Martin, and Mullis 2008).

Plausible values 

To keep student burden to a minimum, TIMSS administered a 

limited number of assessment items to each student—too few 

to produce accurate content-related scale scores for each 

student. To accommodate this situation, during the scaling 

process plausible values were estimated to characterize 

students participating in the assessment. Plausible values are 

imputed values and not test scores for individuals in the usual 

sense. In fact, they are biased estimates of the proficiencies 

of individual students. Plausible values do, however, provide 

unbiased estimates of population characteristics.

Plausible values represent what the true performance of an 

individual might have been, had it been observed. They are 

estimated as random draws (usually five) from an empirically 

derived distribution of score values based on the student’s 

observed responses to assessment items and on background 

variables. Each random draw from the distribution is 

considered a representative value from the distribution 

of potential scale scores for all students in the sample who 

have similar characteristics and identical patterns of item 

responses. Differences between the plausible values quantify 

the degree of precision (the width of the spread) in the 

underlying distribution of possible scale scores that could 

have caused the observed performances. 

An accessible treatment of the derivation and use of plausible 

values can be found in Beaton and González (1995). A more 

technical treatment can be found in the TIMSS 2007 Technical 

Report (Olson, Martin, and Mullis 2008).

International benchmarks

International benchmarks for achievement were developed 

in an attempt to provide a concrete interpretation of what the 

scores on the TIMSS mathematics and science achievement 

scales mean (for example, what it means to have a scale 

score of 513 or 426). To describe student performance at 

various points along the TIMSS mathematics and science 

achievement scales, TIMSS used scale anchoring to 

summarize and describe student achievement at four 

points on the mathematics and science scales—Advanced 

International Benchmark (625), High International Benchmark 

(550), Intermediate International Benchmark (475), and Low 

International Benchmark (400). Scale anchoring involves 

selecting benchmarks (scale points) on the TIMSS 

achievement scales to be described in terms of student 

performance and then identifying items that students scoring 

at the anchor points can answer correctly. Subsequently, 

these items are grouped by content area within benchmarks 

and reviewed by mathematics and science experts. These 

experts focus on the content of each item and describe the 

kind of mathematics or science knowledge demonstrated 

by students answering the item correctly. The experts then 

provide a summary description of performance at each anchor 

point leading to a content-referenced interpretation of the 

achievement results. Detailed information on the creation of 

the benchmarks is provided in the international TIMSS reports 

(Mullis, Martin, and Foy 2008; Martin, Mullis, and Foy 2008). 

Data limitations 

As with any study, there are limitations to TIMSS 2007 

that researchers should take into consideration. Estimates 

produced using data from TIMSS 2007 are subject to 

two types of error—nonsampling and sampling errors. 
A-20

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Nonsampling errors can be due to errors made in collecting 

and processing data. Sampling errors can occur because 

the data were collected from a sample rather than a complete 

census of the population. 

Nonsampling errors

Nonsampling error is a term used to describe variations 

in the estimates that may be caused by population coverage 

limitations, nonresponse bias, and measurement error, as 

well as data collection, processing, and reporting procedures. 

The sources of nonsampling errors are typically problems like 

unit and item nonresponse, the difference in respondents’ 

interpretations of the meaning of the survey questions, 

response differences related to the particular time the survey 

was conducted, and mistakes in data preparation. 

Missing data. Five kinds of missing data were identified 

by separate missing data codes: omitted, uninterpretable, 

not administered, not applicable, and not reached. An item 

was considered omitted if the respondent was expected to 

answer the item but no response was given (e.g., no box 

was checked in the item which asked “Are you a girl or a 

boy?”). Items with invalid responses (e.g., multiple responses 

to a question calling for a single response) were coded 

as uninterpretable. The not administered code was used 

to identify items not administered to the student, teacher or 

principal (e.g., those items excluded from the student’s test 

booklet because of the BIB-spiraling of the items). An item 

was coded as not applicable when it is not logical that the 

respondent answer the question (e.g., when the opportunity 

to make the response is dependent on a filter question). 

Finally, items that are not reached were identified by a string 

of consecutive items without responses continuing through 

to the end of the assessment or questionnaire. 

Missing background data on other than key variables19 are not 

included in the analyses for this report and are not imputed. 

Item response rates for variables discussed in this report 

exceeded the NCES standard of 85 percent and so can be 

reported without notation. Of the three key variables identified 

in the TIMSS 2007 data for the United State—sex, race/

ethnicity and the percentage of students eligible for free- or 

reduced-price lunch (FRPL)—as table A-6 indicates, sex has 

no missing responses and race/ethnicity missing responses 

are minimal at some 2 percent. The FRPL variable, however, 

has some 17 percent missing responses among the public 

schools in the sample and these were imputed by substituting 

values taken from the CCD for the schools in question. 

Note, however, that the CCD provides this information only 

for public schools. The comparable database for private 

schools (PPS) does not include data on participation in the 

FRPL program. While most private schools are ineligible 

for this Federal program, a few indicated that some of their 

students were taking part—6 of the 18 fourth-grade schools 

and 3 of the 14 eighth-grade schools. The reported values 

for these schools are included along with the zero values for 

schools who reported that they had no students taking part. 

Missing value codes then are assigned only to the 3 fourthgrade and 7 eighth-grade private schools who did not respond 

to the question. 

19Key variables include survey-specific items for which aggregate estimates are commonly published by NCES. They include, but are not restricted to, variables 

most commonly used in table row stubs. Key variables also include important analytic composites and other policy-relevant variables that are essential elements of 

the data collection. For example, the National Assessment of Educational Progress (NAEP) consistently uses gender, race-ethnicity, urbanicity, region, and school 

type (public/private) as key reporting variables.

Table A-6. Weighted response rates for unimputed variables for TIMSS grade four and grade 

eight: 2007

Grade four Grade eight

Variable Variable ID Source of information

U.S.

response

rate

Range of 

response 

rates in other 

countries

U.S.

response

rate

Range of 

response 

rates in other 

countries

Sex ITSEX Classroom tracking form 100 99.5 - 1001 100 100

Race/ethnicity STRACE Student questionnaire 98 † 98 †

Free or reduced-price lunch FRLUNCH School questionnaire 83 † 83 †

†Not applicable.

1All countries other than Morocco achieved 100 percent response on this variable.

NOTE: FRLUNCH variable available for public schools only.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
A-21

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Sampling errors 

Sampling errors arise when a sample of the population, rather 

than the whole population, is used to estimate some statistic. 

Different samples from the same population would likely 

produce somewhat different estimates of the statistic in 

question. This fact means that there is a degree of uncertainty 

associated with statistics estimated from a sample. This 

uncertainty is referred to as sampling variance and is usually 

expressed as the standard error of a statistic estimated from 

sample data. The approach used for calculating standard 

errors in TIMSS was Jackknife Repeated Replication (JRR). 

Standard errors can be used as a measure for the precision 

expected from a particular sample. Standard errors for all 

of the reported estimates are included in appendix C. 

Confidence intervals provide a way to make inferences 

about population statistics in a manner that reflects the 

sampling error associated with the statistic. Assuming a 

normal distribution, the population value of this statistic can 

be inferred to lie within the confidence interval in 95 out of 100 

replications of the measurement on different samples drawn 

from the same population. 

That is, there is a 95 percent chance that the population value 

of the statistic lies within the range of 1.96 times the standard 

error above or below the estimated score. For example, the 

average mathematics score for the U.S. eighth-grade students 

was 508 in 2007, and this statistic had a standard error of 

2.8. Therefore, it can be stated with 95 percent confidence 

that the actual average of U.S. eighth-grade students in 2007 

was between 503 and 514 (1.96 x 2.8 = 5.5; confidence 

interval = 508 +/- 5.5).

Description of background 

variables 

The international versions of the TIMSS 2007 student, 

teacher, and school questionnaires are available at http://

timss.bc.edu. The U.S. versions of these questionnaires 

are available at http://nces.ed.gov/timss. 

Race/ethnicity 

Students’ race/ethnicity was obtained through student 

responses to a two-part question. Students were asked first 

whether they were Hispanic or Latino, and then whether they 

were members of the following racial groups: American Indian 

or Alaska Native; Asian; Black or African American; Native 

Hawaiian or other Pacific Islander; or White. Multiple 

responses to the race classification question were allowed. 

Results are shown separately for Blacks, Hispanics, Whites, 

Asians and Mixed-Race as distinct groups. The small numbers 

of students indicating that they were American Indian or Alaska 

Native or Native Hawaiian or other Pacific Islander were 

combined into a group labeled “Other.” This category is 

treated as a residual category and is not reported separately 

in the analyses.

Poverty level in public schools 

(percentage of students eligible 

for free or reduced-price lunch) 

The poverty level in public schools was obtained from 

principals’ responses to the school questionnaire. The 

question asked the principal to report, as of approximately 

the first of October 2006, the percentage of students at the 

school eligible to receive free or reduced-price lunch through 

the National School Lunch Program. The answers were 

grouped into five categories: less than 10 percent; 10 to 24.9 

percent; 25 to 49.9 percent; 50 to 74.9 percent; and 75 

percent or more. Analysis was limited to public schools only. 

Missing data on this variable were replaced with measures 

taken from the CCD. The effect of this replacement on the 

confidentiality of the data was examined as part of the 

confidentiality analyses described in the following section.

Confidentiality and disclosure 

limitations 

In accord with NCES standard 4-2-6 (National Center for 

Education Statistics 2002), confidentiality analyses for the 

United States were implemented to provide reasonable 

assurance that public-use data files issued by the IEA would 

not allow identification of individual U.S. schools or students 

when compared against publicly available data collections. 

Disclosure limitations included the identification and masking 

of potential disclosure risks for TIMSS schools and adding 

an additional measure of uncertainty of school, teacher, and 

student identification through random swapping of a small 

number of data elements within the student, teacher, and 

school files. 
A-22

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Statistical procedures 

Tests of significance 

Comparisons made in the text of this report were tested for 

statistical significance. For example, in the commonly made 

comparison of country averages against the average of the 

United States, tests of statistical significance were used to 

establish whether or not the observed differences from the 

U.S. average were statistically significant. The estimation 

of the standard errors that are required in order to undertake 

the tests of significance is complicated by the complex sample 

and assessment designs, both of which generate error 

variance. Together they mandate a set of statistically complex 

procedures in order to estimate the correct standard errors. 

As a consequence, the estimated standard errors contain 

a sampling variance component estimated by the jackknife 

repeated replication (JRR) procedure; and, where the 

assessments are concerned, an additional imputation 

variance component arising from the assessment design. 

Details on the procedures used can be found in the WesVar 

5.0 User’s Guide (Westat 2007). 

In almost all instances, the tests for significance used were 

standard t tests.20 These fell into two categories according 

to the nature of the comparison being made: comparisons 

of independent and nonindependent samples. Before 

describing the t tests used, some background on the 

two types of comparisons is provided below. 

The variance of a difference is equal to the sum of the 

variances of the two initial variables minus two times the 

covariance between the two initial variables. A sampling 

distribution has the same characteristics as any distribution, 

except that units consist of sample estimates and not 

observations. Therefore, 

The sampling variance of a difference is equal to the sum of the 

two initial sampling variances minus two times the covariance 

between the two sampling distributions on the estimates. 

If one wants to determine whether girls’ performance differs 

from boys’ performance, for example, then, as for all statistical 

analyses, a null hypothesis has to be tested. In this particular 

example, it consists of computing the difference between the 

boys’ performance mean and the girls’ performance mean 

(or the inverse). The null hypothesis is 

To test this null hypothesis, the standard error on this 

difference is computed and then compared to the observed 

difference. The respective standard errors on the mean 

estimate for boys and girls ( ) can be 

easily computed. 

The expected value of the covariance will be equal to 0 if the 

two sampled groups are independent. If the two groups are not 

independent, as is the case with girls and boys attending the 

same schools within a country, or comparing a country mean 

with the international mean that includes that particular country, 

the expected value of the covariance might differ from 0. 

In TIMSS, country samples are independent. Therefore, for 

any comparison between two countries, the expected value 

of the covariance will be equal to 0, and thus the standard 

error on the estimate is 

with being any statistic. 

Within a particular country, any subsamples will be considered 

as independent only if the categorical variable used to define 

the subsamples was used as an explicit stratification variable. 

If sampled groups are not independent, the estimation of the 

covariance between, for instance, (boys) and (girls) would 

require the selection of several samples and then the analysis 

of the variation of (boys) in conjunction with (girls). Such a 

procedure is, of course, unrealistic. Therefore, as for any 

computation of a standard error in TIMSS, replication methods 

using the supplied replicate weights are used to estimate the 

standard error on a difference. Use of the replicate weights 

implicitly incorporates the covariance between the two 

estimates into the estimate of the standard error on 

the difference. 

Thus, in simple comparisons of independent averages, such 

as the U.S. average with other country averages, the following 

formula was used to compute the t statistic: 

Est1 and est2 are the estimates being compared (e.g., average 

of country A and the U.S. average), and se1 and se2 are the 

corresponding standard errors of these averages. 

The second type of comparison used in this report occurred 

when comparing differences of nonsubset, nonindependent 

groups (e.g., when comparing the average scores of males 

versus females within the United States). In such comparisons, 

the following formula was used to compute the t statistic: 

Estgrp1 and estgrp2 are the nonindependent group estimates 

being compared. Se(estgrp1 - estgrp2) is the standard error 

of the difference calculated using a JRR procedure, which 

accounts for any covariance between the estimates for the 

two nonindependent groups. 

20Adjustments for multiple comparisons were not applied in any of the t-tests undertaken.
A-23

HIGHLIGHTS FROM TIMSS 2007 APPENDIX A

Effect size

Tests of statistical significance are, in part, influenced by 

sample sizes. To provide the reader with an increased 

understanding of the importance of the significant difference 

between student populations in the United States, effect 

sizes are included in the report. Effect sizes use standard 

deviations, rather than standard errors and, therefore, are 

not influenced by the size of the student population samples. 

Following Cohen (1988) and Rosnow and Rosenthal (1996), 

effect size is calculated by finding the difference between the 

means of two groups and dividing that result by the pooled 

standard deviation of the two groups: 

Estgrp1 and estgrp2 are the student group estimates being 

compared. Sdpooled is the pooled standard deviation of the 

groups being compared. The formula for the pooled standard 

deviation is as follows (Rosnow and Rosenthal 1996): 

where sd1 and sd2 are the standard deviations of the groups 

being compared. 

For example, to calculate the effect size between the 2007 

fourth-grade U.S. average and Hong Kong SAR average in 

mathematics, the difference in the estimated averages (607-

529 = 78) is divided by the pooled standard deviation. The 

pooled standard deviation is calculated by finding the square 

root of the sum of the squared standard deviations for the 

United States (sd = 75) and Hong Kong SAR (sd = 67) divided 

by 2. Using this formula, the pooled standard deviation is 71. 

Dividing the difference in average scores (78) by the pooled 

standard deviation (71) produces an effect size of 1.1. 

Table A-7 shows the differences in average scores, standard 

deviations, pooled standard deviations, and effect sizes for 

the comparisons reported in figures 14 and 27. The standard 

deviations for all countries and U.S. student subpopulations 

discussed in this report are provided in tables E-18 and E-19 

(mathematics) and E-37 and E-38 (science).
A-24

APPENDIX A HIGHLIGHTS FROM TIMSS 2007

Table A-7. Difference between average scores, standard deviations, and pooled standard deviations 

used to calculate effects sizes of mathematics and sciences scores of fourth- and eighthgrade students, by country, sex, race/ethnicity, and school poverty level: 2007

Subject/grade and groups compared

Difference 

in average 

scores

Standard 

deviation of 

group 1

Standard 

deviation of 

group 2

Pooled 

standard 

deviation

Effect 

size

Mathematics grade four

United States v. Hong Kong SAR 78 75 67 71 1.1

U.S. males v. U.S. females 6 77 74 76 0.1

U.S. White students v. U.S. Black students 67 68 70 69 1.0

U.S. White students v. U.S. Hispanic students 46 68 70 69 0.7

U.S. White students v. U.S. Asian students 33 68 74 71 0.5

U.S. White students v. U.S. multiracial students 15 68 84 76 0.2

U.S. public schools with lowest levels of poverty v. U.S. schools with highest levels of poverty 103 64 72 68 1.5

Mathematics grade eight

United States v. Chinese Taipei 90 77 106 93 1.0

U.S. White students v. U.S. Black students 76 69 70 70 1.1

U.S. White students v. U.S. Hispanic students 58 69 73 71 0.8

U.S. White students v. U.S. Asian students 16 69 68 69 0.2

U.S. White students v. U.S. multiracial students 27 69 73 71 0.4

U.S. public schools with lowest levels of poverty v. U.S. schools with highest levels of poverty 92 65 74 70 1.3

Science grade four

United States v. Singapore 48 84 93 89 0.5

U.S. White students v. U.S. Black students 79 73 76 75 1.1

U.S. White students v. U.S. Hispanic students 65 73 81 77 0.8

U.S. White students v. U.S. multiracial students 17 73 85 79 0.2

U.S. public schools with lowest levels of poverty v. U.S. schools with highest levels of poverty 113 67 81 74 1.5

Science grade eight

United States v. Singapore 47 82 104 94 0.5

U.S. males v. U.S. females 12 85 79 82 0.1

U.S. White students v. U.S. Black students 96 70 73 72 1.3

U.S. White students v. U.S. Hispanic students 71 70 77 74 1.0

U.S. White students v. U.S. multiracial students 29 70 77 74 0.4

U.S. public schools with lowest levels of poverty v. U.S. schools with highest levels of poverty 105 68 79 74 1.4

NOTE: Difference calculated by subtracting average score of group 1 from average score of group 2. Standard deviations and pooled standard deviations are 

shown only for statistically significant differences between group means. The pooled standard deviation is calculated by finding the square root of the sum of 

the squared standard deviations for the groups being compared divided by 2, following Rosnow and Rosenthal (1996). Black includes African American. Racial 

categories exclude Hispanic origin. Students who identified themselves as being of Hispanic origin were classified as Hispanic, regardless of their race. Highpoverty schools are those in which 75 percent or more of students are eligible for the federal free or reduced-lunch program. Low-poverty schools are those in 

which less than 10 percent of students are eligible. The United States met guidelines for sample participation rates only after substitutes schools were included. 

The National Defined Population covered 90 to 95 percent of the National Target 

Population. See tables E-18 and E-19 (available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001) for standard deviations of the U.S. and other 

countries' student populations in mathematics. See tables E-37 and E-38 (available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001) for the 

analogous standard deviations in science. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.
B-1

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

Appendix B: Example Items
B-2

APPENDIX B HIGHLIGHTS FROM TIMSS 2007

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 3Nearly satisfied guidelines for sample participation rates only after replacement schools were included 

(see appendix A). 4Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 5National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 6Kuwait tested the same cohort of students as other countries, but late in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Exhibit B1. Example fourth-grade mathematics item: 2007 M031301

Content Domain Number

Cognitive Domain Applying

M031301

Al wanted to nd how much his cat weighed. He weighed himself and noted that 

the scale read 57 kg. He then stepped on the scale holding his cat and found that 

it read 62 kg. 

What was the weight of the cat in kilograms?

Answer: _______________ kilograms

Country

Percent 

full credit

 International average 60

Chinese Taipei 95

Singapore 87

Russian Federation 86

Hong Kong SAR1 86

Kazakhstan2 85

Netherlands3 85

Japan 83

Lithuania2 81

Austria 80

Germany 80

Latvia2 80

Czech Republic 76

Denmark4 75

Hungary 73

Slovenia 69

Italy 68

Ukraine 68

Norway 67

Sweden 66

Armenia 65

Scotland4 64

England 63

Australia 61

Slovak Republic 60

United States4,5 60

Georgia2 59

New Zealand 53

Iran, Islamic Rep. of 43

Tunisia 28

Algeria 23

El Salvador 21

Morocco 19

Colombia 18

Kuwait6 12

Qatar 9

Yemen 5
B-3

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 3Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5Nearly satisfied guidelines for sample participation rates only after replacement schools were included (see 

appendix A).

6Kuwait tested the same cohort of students as other countries, but late in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Exhibit B2. Example fourth-grade mathematics item: 2007

Country

Percent 

full credit

 International average 72

Hong Kong SAR1 91

Slovenia 91

Lithuania2 89

Denmark3 88

Scotland3 88

England 88

Singapore 88

Japan 87

Italy 87

Sweden 86

Australia 85

United States3,4 85

Slovak Republic 84

Norway 84

Czech Republic 83

Austria 82

Chinese Taipei 81

Hungary 81

Latvia2 81

Russian Federation 81

New Zealand 81

Netherlands5 79

Kazakhstan2 77

Germany 76

Armenia 74

Ukraine 67

Colombia 59

Georgia2 59

Iran, Islamic Rep. of 58

El Salvador 50

Algeria 44

Kuwait6 40

Morocco 39

Tunisia 38

Qatar 32

Yemen 13

M031271

M031271

same size and shape.

Content Domain Geometric Shapes and Measures

Cognitive Domain Knowing
B-4

APPENDIX B HIGHLIGHTS FROM TIMSS 2007

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 3Nearly satisfied guidelines for sample participation rates only after replacement schools were included 

(see appendix A). 4Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 5National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 6Kuwait tested the same cohort of students as other countries, but late in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Exhibit B3. Example fourth-grade mathematics item: 2007 M041336

Class A and B each have 40 students.

There are more girls in Class A than in Class B. How many more?

a 14

b 16

c 24

d 30

M041336

Girls

Boys Girls

Boys

Class A Class B

0

4

8

12

16

20

24

Content Domain Data Display

Cognitive Domain Reasoning

Country

Percent 

full credit

 International average 32

Singapore 63

Hong Kong SAR1 63

Kazakhstan2 51

Chinese Taipei 47

Lithuania2 46

Netherlands3 44

Russian Federation 42

Japan 41

England 40

Slovak Republic 39

United States4,5 38

Hungary 37

Sweden 37

Latvia2 37

Australia 36

Slovenia 35

Germany 35

Denmark4 34

Scotland4 34

Austria 34

Armenia 33

Ukraine 32

New Zealand 32

Norway 31

Czech Republic 31

Georgia2 26

Italy 26

Algeria 21

Morocco 15

Iran, Islamic Rep. of 15

Tunisia 14

Qatar 13

Kuwait6 12

Yemen 9

El Salvador 9

Colombia 9
B-5

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 3National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 4National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 5National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Country

Percent 

full credit

 International average 63

Korea, Rep. of 89

Japan 85

Hong Kong SAR1,2 82

Chinese Taipei 81

United States2,3 81

Singapore 81

Sweden 77

England2 77

Hungary 77

Australia 75

Czech Republic 74

Lithuania4 74

Malaysia 74

Scotland2 74

Norway 73

Russian Federation 73

Slovenia 72

Malta 72

Italy 70

Cyprus 70

Thailand 68

Israel5 66

Turkey 64

Ukraine 63

Romania 62

Bahrain 61

Tunisia 61

Serbia3,4 60

Bulgaria 59

Kuwait6 56

Iran, Islamic Rep. of 55

Lebanon 55

Colombia 54

Algeria 54

Bosnia and Herzegovina 53

Indonesia 52

Syrian Arab Republic 51

Georgia4 51

Jordan 48

El Salvador 47

Oman 46

Armenia 46

Qatar 44

Egypt 44

Saudi Arabia 41

Botswana 41

Palestinian Nat'l Auth. 41

Ghana 34

M022043

Exhibit B4. Example eighth-grade mathematics item: 2007

Content Domain Number

Cognitive Domain Knowing

Which circle has approximately the same fraction of its area shaded as the 

rectangle above?

a b 

c d 

e 

M022043
B-6

APPENDIX B HIGHLIGHTS FROM TIMSS 2007

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 3National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 4National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

5National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA).

Trends in International Mathematics and Science Study (TIMSS), 2007.

Exhibit B5. Example eighth-grade mathematics item: 2007 M042263

Country

Percent 

full credit

 International average 18

Chinese Taipei 68

Korea, Rep. of 68

Singapore 59

Hong Kong SAR1,2 53

Japan 42

United States2,3 37

Australia 36

England2 34

Sweden 34

Slovenia 30

Scotland2 29

Czech Republic 25

Hungary 24

Israel4 24

Malta 21

Armenia 21

Italy 19

Russian Federation 19

Norway 18

Turkey 18

Bulgaria 17

Lithuania5 15

Serbia3,5 15

Romania 14

Malaysia 14

Thailand 13

Cyprus 11

Ukraine 11

Colombia 9

Georgia5 8

Indonesia 8

Bosnia and Herzegovina 8

Tunisia 6

Lebanon 5

Jordan 5

Oman 4

Bahrain 4

Iran, Islamic Rep. of 3

Saudi Arabia 3

Syrian Arab Republic 3

El Salvador 2

Algeria 2

Egypt 2

Kuwait6 2

Botswana 2

Qatar 2

Ghana 1

Palestinian Nat'l Auth. 1

Joe knows that a pen costs 1 zed more than a pencil. 

His friend bought 2 pens and 3 pencils for 17 zeds. 

How many zeds will Joe need to buy 1 pen and 2 pencils?

Show your work.

M042263

Content Domain Algebra

Cognitive Domain Reasoning
B-7

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 3National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Exhibit B6. Example eighth-grade mathematics item: 2007 M032294

Country

Percent 

full credit

 International average 57

Chinese Taipei 86

Korea, Rep. of 82

Japan 81

Hong Kong SAR1,2 80

Slovenia 80

Lithuania3 78

Singapore 77

Russian Federation 77

Hungary 74

Malaysia 73

Scotland2 68

Ukraine 68

Serbia3,4 67

Malta 65

Lebanon 65

Israel5 64

England2 63

Czech Republic 63

Kuwait6 63

Romania 62

Italy 61

Bahrain 59

Indonesia 59

Oman 59

Bulgaria 58

Syrian Arab Republic 58

Egypt 58

Norway 56

Bosnia and Herzegovina 55

Thailand 55

Jordan 54

Armenia 53

Australia 51

Cyprus 51

Algeria 50

Iran, Islamic Rep. of 49

Sweden 48

Saudi Arabia 46

United States2,4 45

Georgia3 41

Palestinian Nat'l Auth. 41

Turkey 38

Qatar 38

El Salvador 33

Colombia 30

Botswana 30

Tunisia 26

Ghana 26

M032294

Two points M and N are shown in the gure above. John is looking for a point P

such that MNP is an isosceles triangle. Which of these points could be point P ?

a (3,5)

b (3,2) 

c (1,5)

d (5,1)

x O

2

3

4

5

6

y

1

M N

1 2 3 4 5 6

Content Domain Geometry

Cognitive Domain Applying
B-8

APPENDIX B HIGHLIGHTS FROM TIMSS 2007

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 3National Target Population does not include all of the International Target Population defined by TIMSS (see 

appendix A).

4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Exhibit B7. Example eighth-grade mathematics item: 2007 M04220

Country

Percent 

full credit

 International average 27

Korea, Rep. of 76

Singapore 75

Chinese Taipei 70

Japan 68

Hong Kong SAR1,2 66

Sweden 56

Lithuania3 51

Hungary 48

Czech Republic 45

England2 45

Slovenia 44

Norway 41

United States2,4 40

Malta 40

Australia 38

Scotland2 38

Russian Federation 35

Malaysia 35

Cyprus 33

Israel5 31

Romania 29

Serbia3,4 27

Italy 27

Thailand 26

Ukraine 24

Bulgaria 23

Jordan 22

Turkey 17

Lebanon 15

Georgia3 15

Indonesia 14

Bosnia and Herzegovina 13

Armenia 12

Iran, Islamic Rep. of 11

Colombia 10

Egypt 10

Bahrain 9

Tunisia 8

Palestinian Nat'l Auth. 8

Botswana 7

Syrian Arab Republic 7

Oman 6

El Salvador 4

Qatar 4

Saudi Arabia 3

Algeria 3

Kuwait6 3

Ghana 2

M042220

Make a bar chart showing the number of students in each category in the pie 

chart.

Popularity of Rock Bands

Dreadlocks 30% Red Hot Peppers 25%

Stone Cold 45%

200

150

100

50

0

Red Hot Peppers Stone Cold Dreadlocks

Number of Students

Popularity of Rock Bands

Content Domain Data and Chance

Cognitive Domain Applying
B-9

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

# Rounds to zero. 

1Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 2National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 3National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 4Nearly satisfied guidelines for sample participation rates only after replacement schools were included 

(see appendix A). 5Kuwait tested the same cohort of students as other countries, but late in 2007, at the beginning of the next 

school year.

6Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007. S041018

Exhibit B8. Example fourth-grade science item: 2007

Country

Percent 

full credit

 International average 33

Japan 93

Slovak Republic 66

Singapore 64

Chinese Taipei 61

Hungary 56

Australia 56

Sweden 53

New Zealand 52

United States1,2 48

Denmark1 45

Lithuania3 43

Czech Republic 40

Latvia3 39

Germany 38

Netherlands4 37

Austria 36

England 36

Scotland1 33

Kuwait5 32

Italy 32

Kazakhstan3 26

Slovenia 25

Iran, Islamic Rep. of 23

Russian Federation 23

Hong Kong SAR6 22

Armenia 21

Norway 20

Ukraine 18

Georgia3 16

Qatar 7

El Salvador 5

Colombia 4

Algeria 1

Tunisia 1

Yemen #

Morocco #

The diagram below shows the life cycle of a moth. 

Write the name of each stage in the boxes provided. 

One stage has been completed for you.

adult moth

Content Domain Life Science

Cognitive Domain Knowing
B-10

APPENDIX B HIGHLIGHTS FROM TIMSS 2007

Exhibit B9. Example fourth-grade science item: 2007 S031078

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 3Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5Nearly satisfied guidelines for sample participation rates only after replacement schools were included 

(see appendix A). 6Kuwait tested the same cohort of students as other countries, but late in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Country

Percent 

full credit

 International average 57

Japan 92

Singapore 88

Hong Kong SAR1 75

Russian Federation 70

Slovenia 70

Czech Republic 69

Latvia2 69

Hungary 67

Kazakhstan2 67

England 67

United States3,4 66

Netherlands5 65

Chinese Taipei 65

Italy 65

Ukraine 65

Germany 64

Austria 63

Lithuania2 63

Slovak Republic 63

Denmark3 62

Australia 59

Scotland3 58

New Zealand 58

Armenia 56

Sweden 55

Norway 53

Georgia2 41

Qatar 40

Colombia 39

El Salvador 36

Algeria 35

Kuwait6 35

Tunisia 31

Morocco 24

Iran, Islamic Rep. of 24

Yemen 20

Beans are fixed on a metal ruler with butter as shown in the figure above. The 

ruler is heated at one end. In which order will the beans fall off?

a 1, 2, 3, 4, 5

b 5, 4, 3, 2, 1

c 1, 3, 5, 4, 2

d All at the same time

1 2 3 4 5

Beans

Metal Ruler

Candle

Content Domain Physical Science

Cognitive Domain Reasoning
B-11

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

Exhibit B10. Example fourth-grade science item: 2007 S031081

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 3National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5Nearly satisfied guidelines for sample participation rates only after replacement schools were included 

(see appendix A). 6Kuwait tested the same cohort of students as other countries, but late in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Country

Percent 

full credit

 International average 58

Chinese Taipei 90

Singapore 88

Japan 88

Hong Kong SAR1 82

Australia 80

England 78

Scotland2 76

Latvia3 76

Russian Federation 75

United States2,4 75

Netherlands5 75

Kazakhstan3 74

Sweden 72

Slovak Republic 72

New Zealand 70

Italy 70

Slovenia 68

Hungary 68

Denmark2 68

Lithuania3 67

Czech Republic 64

Austria 63

Germany 57

Norway 53

Ukraine 53

Georgia3 49

Armenia 44

Colombia 37

Tunisia 29

Iran, Islamic Rep. of 29

Kuwait6 24

El Salvador 23

Qatar 20

Algeria 16

Yemen 15

Morocco 12

Content Domain Earth Science

Cognitive Domain Applying

S031081

A ribbon is tied to a pole to measure the wind strength as shown below. 

Write the numbers 1, 2, 3, and 4 in the correct order that shows the wind 

strength from the strongest to weakest.

Answer : _____, _____, _____, _____

1 2 3 4
B-12

APPENDIX B HIGHLIGHTS FROM TIMSS 2007

Exhibit B11. Example eighth-grade science item: 2007 S032385

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 3National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 4Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

5National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

6National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A).

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Country

Percent 

full credit

 International average 63

Chinese Taipei 91

Hong Kong SAR1,2 86

Thailand 84

Turkey 82

Syrian Arab Republic 79

Hungary 78

Lithuania3 76

Slovenia 76

Japan 75

Czech Republic 74

Armenia 73

Cyprus 72

Jordan 72

Saudi Arabia 72

Kuwait4 70

Bulgaria5 70

Korea, Rep. of 70

Georgia3 69

Israel5 68

Serbia3,6 67

Bosnia and Herzegovina 67

Bahrain 66

Romania 66

Italy 65

Russian Federation 63

Iran, Islamic Rep. of 60

Singapore 60

Lebanon 60

Algeria 58

Australia 56

Palestinian Nat'l Auth. 55

Indonesia 55

Malaysia 55

Colombia 54

Ukraine 54

Botswana 53

United States2,6 53

El Salvador 53

Sweden 53

England2 53

Norway 51

Qatar 49

Oman 49

Tunisia 48

Malta 44

Scotland2 41

Egypt 40

Ghana 31

Which characteristic is found ONLY in mammals?

a eyes that detect color

b glands that make milk

c skin that absorbs oxygen

d bodies that are protected by scales 

Content Domain Biology

Cognitive Domain Knowing
B-13

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

Exhibit B12. Example eighth-grade science item: 2007 S042106

1National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 2National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

3Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

4Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 5National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Country

Percent 

full credit

 International average 23

Japan 65

Korea, Rep. of 51

Chinese Taipei 51

Italy 46

Czech Republic 43

Slovenia 39

Hungary 39

Russian Federation 39

Sweden 38

Singapore 37

Lithuania1 37

Israel2 33

Hong Kong SAR3,4 30

Ukraine 29

England4 28

Armenia 28

Malta 27

Australia 25

Norway 25

Thailand 25

United States4,5 24

Cyprus 24

Scotland4 22

Tunisia 22

Romania 22

Serbia1,5 20

Jordan 19

Bulgaria2 19

Bahrain 18

Lebanon 18

Bosnia and Herzegovina 17

Colombia 16

Turkey 16

Malaysia 14

Iran, Islamic Rep. of 13

Syrian Arab Republic 13

Palestinian Nat'l Auth. 11

El Salvador 9

Oman 9

Egypt 8

Algeria 7

Kuwait6 7

Indonesia 6

Saudi Arabia 5

Georgia1 4

Qatar 3

Ghana 3

Botswana 1

The mass of substances A and B are measured on a balance, as shown in 

Figure 1. Substance B is put into the beaker and substance C is formed. The empty 

beaker is put back on the balance, as shown in Figure 2.

The scale in Figure 1 shows a mass of 110 grams. 

What will it show in Figure 2?

(Check one box.)

C More than 110 grams

C 110 grams

C Less than 110 grams

Explain your answer.

Figure 1 Figure 2

110g

A C

B

???g

Content Domain Chemistry

Cognitive Domain Applying
B-14

APPENDIX B HIGHLIGHTS FROM TIMSS 2007

Exhibit B13. Example eighth-grade science item: 2007 S032392

1Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 2National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 3National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

4National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 5Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Country

Percent 

full credit

 International average 78

Singapore 96

United States1,2 91

Bulgaria3 91

Russian Federation 91

Korea, Rep. of 91

Hungary 90

Ukraine 90

Lithuania4 89

Slovenia 88

Turkey 88

Serbia2,4 87

Italy 87

Indonesia 86

Iran, Islamic Rep. of 86

Czech Republic 86

Australia 86

Lebanon 86

Malta 86

England1 85

Malaysia 84

Scotland1 83

Georgia4 82

Sweden 82

Japan 82

Chinese Taipei 81

Armenia 80

Romania 79

Syrian Arab Republic 79

Jordan 79

Bosnia and Herzegovina 78

Norway 76

Hong Kong SAR1,5 75

Thailand 74

Cyprus 72

Algeria 71

Israel3 71

Bahrain 70

Egypt 70

Colombia 70

El Salvador 68

Kuwait6 67

Palestinian Nat'l Auth. 65

Botswana 64

Ghana 63

Saudi Arabia 61

Oman 58

Qatar 55

Tunisia 49

Work is done when an object is moved in the direction of an applied force. A 

person performed different tasks as shown in the diagrams below. In which 

diagram is the person doing work?

a b

c d

Holding a 

heavy object

Pushing 

against a wall

Pushing a 

cart up a ramp

Reading a book

Content Domain Physics

Cognitive Domain Applying
B-15

HIGHLIGHTS FROM TIMSS 2007 APPENDIX B

Exhibit B14. Example eighth-grade science item: 2007 SO22244

Country

Percent 

full credit

 International average 20

Korea, Rep. of 48

Singapore 47

Hong Kong SAR1,2 42

Lithuania3 42

Japan 39

Slovenia 38

England2 38

Chinese Taipei 35

Hungary 34

Australia 32

Jordan 30

Scotland2 28

Italy 27

Russian Federation 25

Czech Republic 25

Sweden 24

United States2,4 23

Bulgaria 23

Malta 22

Bosnia and Herzegovina 21

Norway 20

Armenia 20

Romania 19

Ukraine 18

Thailand 18

Bahrain 17

Israel5 17

Egypt 17

Serbia3,4 16

Malaysia 16

Iran, Islamic Rep. of 15

Syrian Arab Republic 13

Algeria 13

Georgia3 12

Indonesia 11

Palestinian Nat'l Auth. 11

Oman 11

Turkey 10

Lebanon 9

Saudi Arabia 8

Cyprus 7

Colombia 7

Kuwait6 5

Tunisia 5

El Salvador 4

Botswana 3

Ghana 3

Qatar 2

1Hong Kong is a Special Administrative Region (SAR) of the People’s Republic of China.

2Met guidelines for sample participation rates only after replacement schools were included (see appendix A). 3National Target Population does not include all of the International Target Population defined by TIMSS 

(see appendix A). 4National Defined Population covers 90 percent to 95 percent of National Target Population (see appendix A). 5National Defined Population covers less than 90 percent of National Target Population (but at least 77 

percent, see appendix A).

6Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next 

school year.

NOTE: Countries are sorted by 2007 average percent correct. The answer shown illustrates the type of student 

response that was given full credit. 

SOURCE: International Association for the Evaluation of Educational Achievement (IEA). 

Trends in International Mathematics and Science Study (TIMSS), 2007.

Content Domain Earth science

Cognitive Domain Reasoning

S022244

coal burns, sulfur that is present in the coal reacts with oxygen to form sulfur 

How does this process result in acid rain?
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C-1

HIGHLIGHTS FROM TIMSS 2007 APPENDIX C APPENDIX B

How Does the Content of TIMSS 

Compare with That of Other 

Assessments?

It is often asked how TIMSS compares with other assessments 

that measure similar subjects and populations, in particular, the 

National Assessment of Educational Progress (NAEP). The 

various assessments in which the United States participates, 

including NAEP, TIMSS, and the Program for International 

Student Assessment (PISA), vary in some obvious ways, such 

as the goals of the studies (and whether they are focused 

on national objectives or shared international objectives); 

the precise definitions of the populations they are measuring;

the degree of precision required for estimates and resulting 

different sample sizes; their frameworks and specifications;

and, for TIMSS and PISA, the different groups of countries that 

participate. However, there also are differences that are less 

obvious and that can only be found by comparing the content 

of the assessments through examination of the items. 

In a recent comparison study, TIMSS 2007 mathematics 

and science items were classified to the NAEP assessment

frameworks (2005/2007 for mathematics and 2005 for 

science) in terms of content topics and objectives, grade-level 

expectations, and cognitive dimensions in order to allow a 

direct comparison of the two assessments. In other studies 

(one past and one recent), PISA mathematics and science 

items also were placed on the NAEP frameworks, which 

allows content comparison of the TIMSS and PISA via the 

national frameworks. This section highlights some of the main 

findings; additional details on the comparison study will be

included in a technical report to be released with the U.S. 

national TIMSS dataset at a later date.

Although the TIMSS and NAEP fourth- and eighth-grade 

mathematics frameworks are organized similarly and, broadly, 

cover the same range of content (e.g., number, measurement, 

geometry, algebra, and data), there are some differences 

in the relative emphases on the different topic areas between 

the assessments. For example, at the fourth grade, NAEP has 

a greater percentage of items that focus on measurement 

topics than does TIMSS (21 versus 14 percent, respectively), 

whereas TIMSS has a greater percentage of items focusing 

on geometry than NAEP (20 versus 16 percent, respectively). 

There are similar examples at the eighth-grade level among 

TIMSS, NAEP, and PISA, which focuses on an older group 

of students.

As with mathematics, the TIMSS and NAEP science

frameworks cover the same range of major content areas, 

including Earth, physical (including chemistry), and life 

sciences. However, again, there are differences in the 

distribution of items even at the broad content level. 

These differences tend to be larger for science than for 

mathematics, with differences between the two assessments 

in the percentage of items in a given content area reaching 

14 percent or more in Earth science and 8 percent or more in 

physical sciences at both grades. As an example, 37 percent 

of the TIMSS fourth-grade assessment is devoted to physical 

science compared to 29 percent of NAEP’s fourth-grade 

assessment. This pattern continues at eighth grade. NAEP, 

on the other hand, has higher percentages of Earth science 

items than does TIMSS at both grades. PISA’s focus (with 

47 percent of items) tends to be on life science.

There is one other notable finding from the comparison study

of science assessments. Twelve and 20 percent of fourthand eighth-grade TIMSS items, respectively, could not 

be placed within the more detailed objectives of the NAEP 

framework, indicating that there are some differences at 

the item level between the two assessments, not just in 

distribution of items across content areas. 

Appendix C: TIMSS-NAEP Comparison
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D-1

HIGHLIGHTS FROM TIMSS 2007 APPENDIX D

Online Resources

The NCES website (http://nces.ed.gov/timss) provides 

background information on the TIMSS surveys, copies of 

NCES publications that relate to TIMSS, information for 

educators about ways to use TIMSS in the classroom, and 

data files. The international TIMSS website (http://www.

timss.org) includes extensive information on the study, 

including the international reports and databases.

NCES Publications

The following publications are intended to serve as examples 

of some of the numerous reports that have been produced 

in relation to the Trends in International Mathematics and 

Science Study (TIMSS) by NCES. All of the publications 

listed here are available at http://nces.ed.gov/timss.

TIMSS 2003 Achievement Report 

Gonzales, P., Guzmán, J.C., Partelow, L., Pahlke, E., Jocelyn, 

L., Kastberg, D., and Williams, T. (2004). Highlights From 

the Trends in International Mathematics and Science 

Study (TIMSS) 2003 (NCES 2005–005). National Center 

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

Washington, DC.

TIMSS 1999 Achievement Reports

Gonzales, P., Calsyn, C., Jocelyn, L., Mak, K., Kastberg, D., 

Arafeh, S., Williams, T., and Tsen, W. (2000). Pursuing 

Excellence: Comparisons of International Eighth-Grade 

Mathematics and Science Achievement From a U.S. 

Perspective, 1995 and 1999 (NCES 2001–028). National 

Center for Education Statistics, U.S. Department of 

Education. Washington, DC.

Gonzales, P., Calsyn, C., Jocelyn, L., Mak, D., Kastberg, D., 

Arafeh, S., Williams, T., and Tsen, W. (2000). Highlights 

From TIMSS-R (NCES 2001–027). National Center for 

Education Statistics, U.S. Department of Education. 

Washington, DC.

TIMSS 1995 Achievement Reports

National Center for Education Statistics, U.S. Department 

of Education. (1997). Pursuing Excellence: A Study of U.S. 

Fourth-Grade Mathematics and Science Achievement in 

International Context (NCES 97–255). National Center for 

Education Statistics, U.S. Department of Education. 

Washington, DC.

Peak, L. (1996). Pursuing Excellence: A Study of U.S. 

Eighth-Grade Mathematics and Science Teaching, 

Learning, Curriculum, and Achievement in International 

Context (NCES 97–198). National Center for Education 

Statistics, U.S. Department of Education. Washington, DC. 

Takahira, S., Gonzales, P., Frase, M., and Salganik, L.H. 

(1998). Pursuing Excellence: A Study of U.S. TwelfthGrade Mathematics and Science Achievement in 

International Context (NCES 98–049). National Center 

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

Washington, DC.

TIMSS Videotape Classroom 

Study Reports

Hiebert, J., Gallimore, R., Garnier, H., Givvin Bogard, K., 

Hollingsworth, H., Jacobs, J., Miu-Ying Chui, A., Wearne, 

D., Smith, M., Kersting, N., Manaster, A., Tseng, E., 

Etterbeek, W., Manaster, C., Gonzales, P., and Stigler, J. 

(2003). Teaching Mathematics in Seven Countries: 

Results From the TIMSS 1999 Video Study (NCES 2003–

013 Revised). National Center for Education Statistics, 

Institute of Education Sciences, U.S. Department of 

Education. Washington, DC. 

National Center for Education Statistics, U.S. Department 

of Education. (2000). Highlights From the TIMSS 

Videotape Classroom Study (NCES 2000–094). National 

Center for Education Statistics, U.S. Department of 

Education. Washington, DC.

Roth, K.J., Druker, S.L., Garnier, H., Lemmens, M., Chen, C., 

Kawanaka, T., Rasmussen, D., Trubacova, S., Warvi, D., 

Okamoto, Y., Gonzales, P., Stigler, J., and Gallimore, R. 

(2006). Teaching Science in Five Countries: Results From 

the TIMSS 1999 Video Study (NCES 2006-011). National 

Center for Education Statistics, Institute of Education 

Sciences, U.S. Department of Education. Washington, DC.

Stigler, J.W., Gonzales, P., Kawanaka, T., Knoll, S., and 

Serrano, A. (1999). The TIMSS Videotape Classroom 

Study: Methods and Findings From an Exploratory 

Research Project on Eighth-Grade Mathematics 

Instruction in Germany, Japan, and the United States

(NCES 1999–074). National Center for Education 

Statistics, U.S. Department of Education. Washington, DC. 

Appendix D: Online Resources and Publications
D-2

APPENDIX D HIGHLIGHTS FROM TIMSS 2007

IEA Publications

The following publications are intended to serve as examples 

of some of the numerous reports that have been produced 

in relation to TIMSS by the IEA. All of the publications 

listed here are available at http://timss.bc.edu.

TIMSS 2007 Achievement Reports

Martin, M.O., Mullis, I.V.S., and Foy, P. (2008). TIMSS 2007

International Science Report: Findings From IEA’s Trends 

in International Mathematics and Science Study at the 

Eighth and Fourth Grades. Chestnut Hill, MA: Boston 

College. 

Mullis, I.V.S., Martin, M.O., and Foy, P. (2008). TIMSS 2007 

International Mathematics Report: Findings From IEA’s 

Trends in International Mathematics and Science Study at 

the Eighth and Fourth Grades. Chestnut Hill, MA: Boston 

College.

TIMSS 2003 Achievement Reports

Martin, M.O., Mullis, I.V.S., González, E.J., and Chrostowski, 

S.J. (2004). TIMSS 2003 International Science Report: 

Findings From IEA’s Trends in International Mathematics 

and Science Study at the Eighth and Fourth Grades. 

Chestnut Hill, MA: Boston College. 

Mullis, I.V.S., Martin, M.O., González, E.J., and Chrostowski, 

S.J. (2004). TIMSS 2003 International Mathematics 

Report: Findings From IEA’s Trends in International 

Mathematics and Science Study at the Eighth and Fourth 

Grades. Chestnut Hill, MA: Boston College.

TIMSS 1999 Achievement Reports

Martin, M.O., Mullis, I.V.S., González, E.J., Gregory, K.D., 

Smith, T.A., Chrostowski, S.J., Garden, R.A., and 

O’Connor, K.M. (2000). TIMSS 1999 International Science 

Report: Findings From IEA’s Repeat of the Third 

International Mathematics and Science Study at the 

Eighth Grade. Chestnut Hill, MA: Boston College. 

Mullis, I.V.S., Martin, M.O., González, E.J., Gregory, K.D., 

Garden, R.A., O’Connor, K.M., Chrostowski, S.J., and 

Smith, T.A. (2000). TIMSS 1999 International Mathematics 

Report: Findings From IEA’s Repeat of the Third 

International Mathematics and Science Study at the 

Eighth Grade. Chestnut Hill, MA: Boston College.

TIMSS 1995 Achievement Reports

Beaton, A.E., Martin, M.O., Mullis, I.V.S., González, E.J., Smith, 

T.A., and Kelly, D.L. (1996). Science Achievement in the 

Middle School Years: IEA’s Third International Mathematics 

and Science Study. Chestnut Hill, MA: Boston College. 

Beaton, A.E., Mullis, I.V.S., Martin, M.O., González, E.J., Kelly, 

D.L., and Smith, T.A. (1996). Mathematics Achievement in the 

Middle School Years: IEA’s Third International Mathematics 

and Science Study. Chestnut Hill, MA: Boston College.

Martin, M.O., Mullis, I.V.S., Beaton, A.E., González, E.J., 

Smith, T.A., and Kelly, D.L. (1997). Science Achievement in 

the Primary School Years: IEA’s Third International 

Mathematics and Science Study. Chestnut Hill, MA: 

Boston College.

Mullis, I.V.S., Martin, M.O., Beaton, A.E., González, E.J., Kelly, 

D.L., and Smith, T.A. (1997). Mathematics Achievement in 

the Primary School Years: IEA’s Third International 

Mathematics and Science Study. Chestnut Hill, MA: Boston 

College.

Mullis, I.V.S., Martin, M.O., Beaton, A.E., González, E.J., 

Kelly, D.L., and Smith, T.A. (1998). Mathematics and 

Science Achievement in the Final Year of Secondary 

School: IEA’s Third International Mathematics and 

Science Study. Chestnut Hill, MA: Boston College.

TIMSS Technical Reports 

and Frameworks

Martin, M.O., and Kelly, D.L. (Eds.). (1996). Third International 

Mathematics and Science Study Technical Report, 

Volume I: Design and Development. Chestnut Hill, MA: 

Boston College.

Martin, M.O., and Kelly, D.L. (Eds.). (1998). Third International 

Mathematics and Science Study Technical Report, 

Volume II: Implementation and Analysis, Primary and 

Middle School Years. Chestnut Hill, MA: Boston College.

Martin, M.O., and Kelly, D.L. (Eds.). (1999). Third International 

Mathematics and Science Study Technical Report, 

Volume III: Implementation and Analysis, Final Year of 

Secondary School. Chestnut Hill, MA: Boston College

Martin, M.O., Gregory, K.D., and Stemler, S.E. (2000). TIMSS 

1999 Technical Report. Chestnut Hill, MA: Boston College.

Martin, M.O., Mullis, I.V.S. and Chrostowski, S.J. (2004). 

TIMSS 2003 Technical Report: Findings From IEA’s 

Trends in International Mathematics and Science Study at 

the Eighth and Fourth Grades. Chestnut Hill, MA: Boston 

College.

Mullis, I.V.S., Martin, M.O., Smith, T.A., Garden, R.A., Gregory, 

K.D., González, E.J., Chrostowski, S.J., and O’Connor, K.M. 

(2003). TIMSS Assessment Frameworks and Specifications 

2003: 2nd Edition. Chestnut Hill, MA: Boston College.

Mullis, I.V.S., Martin, M.O., Ruddock, G.J., O’Sullivan, C.Y., 

Arora, A., and Erberber, E. (2005). TIMSS 2007 Assessment 

Frameworks. Chestnut Hill, MA: Boston College.

Olson, J.F., Martin, M.O., and Mullis, I.V.S. (2008). TIMSS 

2007 Technical Report. Chestnut Hill, MA: Boston College.

TIMSS Encyclopedia

Mullis, I.V.S., Martin, M.O., Olson, J.F., Berger, D.R., Milne, D., 

and Stanco, G.M. (Eds.). (2008). TIMSS 2007 Encyclopedia: 

A Guide to Mathematics and Science Education Around the 

World. Chestnut Hill, MA: Boston College.