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- Executive Summary
- Introduction
- How Do U.S. Students Compare With Their Peers in Other Countries?
- Focus Points
- Summary
- List of Tables
- List of Figures
- References
- Appendix A: Technical Notes
- A.1 Limitations of sampled data
- A.2 International requirements for sampling, data collection, and response rates
- A.3 Test development
- A.4 Scoring
- A.5 Data entry and cleaning
- A.6 Weighting and scaling
- A.7 Cutpoint scores and achievement levels
- A.8 Comparing results from PISA 2000, 2003, and 2006
- A.9 Comparing results from TIMSS 1995 and 1999
- A.10 Confidentiality and disclosure limitations
- A.11 Nonresponse bias analysis
- A.12 State participation in international assessments

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Mathematics results for 4th- and 8th-graders

The 2007 TIMSS results showed that U.S. students' average mathematics score was 529 for 4th-graders and 508 for 8th-graders (tables 4 and 5). Both scores were above the TIMSS scale average, which is set at 500 for every administration of TIMSS at both grades. The U.S. 4th-grade average score reflects the fact that U.S. 4th-graders performed above the TIMSS scale average in all three mathematics content domains (numbers, geometric shapes and measures, and data display). The U.S. 8th-grade average score reflects the fact that U.S. 8th-graders performed above the TIMSS scale average in two of the four mathematics content domains (numbers and data and chance) in 2007 (Gonzales et al. 2008, table 6). In algebra they did not score measurably different from the TIMSS scale average, and in geometry they scored 20 score points below the TIMSS scale average (Gonzales et al. 2008, table 7).

Comparing the performance of U.S. students with the performance of their peers in other countries, 4th-graders in 8 countries (Hong Kong, Singapore, Chinese Taipei, Japan, Kazakhstan, Russian Federation, England, and Latvia) scored above their U.S. peers, on average (table 4). The top 10 percent of U.S. 4th-graders scored 625 or higher, a cutpoint score below that of the top 10 percent of students in 7 countries (all of which had higher average scores than the United States), while the bottom 10 percent scored 430 or lower, a cutpoint score below that of the bottom 10 percent of students in 6 countries (5 of which had higher average scores than the United States).

Eighth-graders in 5 countries (Chinese Taipei, Korea, Singapore, Hong Kong, and Japan) scored above their U.S. peers, on average (table 5). The top 10 percent of U.S. 8th-graders scored 607 or higher, a cutpoint score below that of the top 10 percent of students in 6 countries, including the 5 countries with average scores higher than the U.S. average scores. The bottom 10 percent of U.S. 8th-graders scored 408 or lower, a cutpoint score below that of the bottom 10 percent of students in 4 countries (all of which had average scores higher than the United States).

TIMSS has developed four international benchmarks to help analyze the range of students' performance in mathematics within each participating country. ^{31} The Advanced benchmark is set at 625 score points for both grades. ^{32}

Fourth-graders reaching the Advanced benchmark demonstrate a developing understanding of fractions and decimals and the relationship between them. They can select appropriate information to solve multi-step word problems involving proportions. They can formulate or select a rule for a relationship. They show understanding of area and can use measurement concepts to solve a variety of problems. They show some understanding of rotation. They can organize, interpret, and represent data to solve problems.

Eighth-graders reaching the Advanced benchmark can organize information, make generalizations, solve non-routine problems, and draw and justify conclusions from data. They can compute percentage change and apply their knowledge of numeric and algebraic concepts and relationships to solve problems. They can solve simultaneous linear equations and model simple situations algebraically. They can apply their knowledge of measurement and geometry in complex problem situations. They can interpret data from a variety of tables and graphs, including interpolation and extrapolation.

In 2007, ten percent of U.S. 4th-graders and 6 percent of U.S. 8th-graders reached the Advanced benchmark (figures 5 and 6). In comparison, 7 participating countries had a higher percentage of 4th-graders who reached this benchmark (ranging from 41 to 16 percent): Singapore, Hong Kong, Chinese Taipei, Japan, Kazakhstan, England, and the Russian Federation (the same 7 countries with higher cutpoints for their top 10 percent of students). A slightly different set of 7 participating countries had a measurably higher percentage of 8th-graders who reached this benchmark (ranging from 45 to 8 percent): Chinese Taipei, Korea, Singapore, Hong Kong, Japan, Hungary, and the Russian Federation (6 of these 7 countries had higher cutpoints for their top 10 percent of students).

*Change over time*

Among the 16 countries that participated in both the first TIMSS in 1995 and the most recent TIMSS in 2007, at grade 4, the average mathematics score increased in 8 countries, including in the United States, and decreased in 4 countries (figure 7). Among the 20 countries that participated in both the 1995 and 2007 TIMSS at grade 8, the average mathematics score increased in 6 countries, including in the United States, and decreased in 10 countries (figure 8).

Between 1995 and 2007 the average score of U.S. 4th-graders increased 11 score points (from 518 to 529). In 4 countries, the average score of 4th-graders increased more than in the United States during this time: England, Hong Kong, Slovenia, and Latvia. Increases in England (57 points) and Latvia (38 points) moved their 4th-graders from scoring below their U.S. peers in 1995 to scoring higher than their U.S. peers in 2007. Increases in Slovenia (40 points) and Hong Kong (50 points) did not change their standing relative to the United States.

Scores decreased during this time for 4th-graders in Hungary (12 points), The Netherlands (14 points), Austria (25 points), and the Czech Republic (54 points). As a result, the performance of U.S. 4th-graders showed improvement relative to their peers in these countries.

At grade 8, the U.S. average score increased 16 score points (from 492 to 508) between 1995 and 2007. In 2 countries, the average score of 8th-graders increased more than in the United States during this time: Colombia (47 points) and Lithuania (34 points). Neither of these countries outperformed the United States in 2007.

Scores decreased during this time for 8th-graders in 10 countries, with the decreases ranging from 10 points in Hungary to 63 points in Bulgaria. The decreases in Australia (13 points), Sweden (48 points), and Bulgaria (63 points) were large enough that their 8th-graders' average scores in 2007 were below those of their U.S. peers, whereas in 1995 their students outperformed their U.S. peers.

The next TIMSS assessment will be administered in 2011. More detailed results for TIMSS 2007 can be found in Gonzales et al. (2008; available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001) and Mullis et al. (2008a; available at http://timss.bc.edu/TIMSS2007/mathreport.html). For more information on TIMSS, see http://nces.ed.gov/timss/.

^{31} See figures 5 and 6 for the cut scores established for all the international benchmarks. For details about the international benchmarks, see Mullis et al. (2008a), chapter 2.

^{32} The IEA set international benchmarks for TIMSS based on an analysis of score points. The score points for each benchmark remain the same across assessments; however, the configuration of items that define what students reaching a benchmark can do may vary slightly from one assessment to the next. For more details, see appendix A.