How Do U.S. Students and Adults Compare With Their Peers in Other Countries?
Three international assessments measure aspects of mathematical skills. The Trends in International Mathematics and Science Study (TIMSS), which assesses 4th- and 8th-grade mathematics knowledge and skills; the Program for International Student Assessment (PISA), which focuses on mathematics literacy, or the ability of 15-year-olds to apply mathematics to a wide variety of materials within a real-life context; and the Adult Literacy and Lifeskills Survey (ALL), which measures the numeracy skills of adults ages 16–65.
TIMSS, which was administered in grades 4 and 8 in 1995 and 2003 and in grade 8 in 1999, is designed to measure the achievement of 4th- and 8th-graders in mathematics and science. The study is closely linked to the curricula of the participating countries, providing an indication of the degree to which students have learned the concepts of mathematics that they have studied in school. Some 46 countries participated in TIMSS in 2003, at either the 4th- or 8th-grade level, or both.
In mathematics, students in some countries (notably several Asian countries, such as Japan and Hong Kong, but also including the Netherlands and Belgium) consistently outperformed U.S. students, on average, regardless of the year of assessment, measure, grade, or age tested (Gonzales et al. 2004). Overall, however, the current picture of U.S. performance, as measured by TIMSS, is mixed at the 4th- and 8th-grade levels.
When comparing the United States with the other 24 countries participating at grade 4 in 2003, U.S. 4th-graders performed better, on average, than their peers in 13 countries but worse than their peers in 11 countries (table 5). TIMSS also provided scores for five mathematics content areas at grade 4: number, patterns and relationships, measurement, geometry, and data. U.S. 4th-graders performed above the international average in four of the five content areas in 2003 (all but measurement); they performed best in data and least well in measurement (Mullis et al. 2004b).
Comparing results from 1995 and 2003 suggests that while the performance of U.S. students was stable during this period, it did not keep pace with improved scores among students in several other countries (Gonzales et al. 2004). That is, of the other 14 countries participating in both 1995 and 2003, 4th-graders in more countries outperformed their U.S. peers in 2003 than in 1995, on average. Students in seven countries (Singapore, Japan, Hong Kong, the Netherlands, Latvia, England, and Hungary) outscored U.S. students in 2003, while students in four countries (Singapore, Japan, Hong Kong, and the Netherlands) outscored U.S. students in 1995.
In grade 8, U.S. students showed gains in their mathematics skills and abilities. As mentioned above, TIMSS assessed 8th-graders in mathematics in 1995, 1999, and 2003. In comparison to the other 44 countries that assessed 8th-graders in 2003, U.S. 8th-graders outperformed their peers in 25 countries, on average, and were outperformed by students in 9 countries (table 5; Gonzales et al. 2004). U.S. 8th-graders had higher average scores in 2003 than in 1995, with the increase occurring primarily between 1995 and 1999. Moreover, the relative standing of U.S. 8th-graders was higher in 2003 than in 1995 in relation to students in the 21 other countries participating in TIMSS in both years. That is, of the 21 other countries participating in both 1995 and 2003, U.S. 8th-graders were outscored by their international peers, on average, in fewer countries in 2003 than in 1995 (12 countries in 1995 vs. 7 countries in 2003). In addition, TIMSS provided achievement results in five mathematics content areas: number, algebra, measurement, geometry, and data. U.S. 8th-graders improved their performance in two of these content areas (algebra and data) between 1999 and 2003.
TIMSS 2003 also examined the mathematics performance of 4th- and 8th-graders by achievement level, sex, and race/ethnicity. At both grades, 7 percent of U.S. students performed at the highest international benchmark (called “advanced”) in 2003, percentages that were not measurably different from the international averages (Mullis et al. 2004b). In the United States, boys outperformed girls in mathematics at both grades 4 and 8. The gap in mathematics achievement scores between White and Black 4th- and 8th-graders narrowed between 1995 and 2003 (Gonzales et al. 2004). More detailed results for TIMSS 2003 can be found in Gonzales et al. (2004; available at http://nces.ed.gov/pubsearch/
pubsinfo.asp?pubid=2005005) and Mullis et al. (2004b; available at http://isc.bc.edu/timss2003i/mathD.html).
While the primary emphasis of PISA in 2000 was on reading literacy, in 2003, the assessment turned its focus to mathematics literacy of 15-year-olds, with 39 countries participating. PISA uses the term mathematics literacy to indicate its broader focus on students’ ability to apply their mathematical knowledge and skills to a range of situations they are likely to encounter in their everyday lives. Thus, unlike TIMSS, PISA does not focus exclusively on outcomes that can be directly linked to curricula, but instead emphasizes larger ideas such as space and shape or uncertainty in mathematics. PISA complements information obtained from studies such as TIMSS because it addresses whether students can apply what they have learned, both in and out of school.
The PISA 2003 results suggest that when applying mathematical skills, U.S. 15-year-olds performed worse, on average, than many of their international peers (table 6). For this age group, the mathematics literacy performance of U.S. students was lower than the average student performance for the majority of the 28 other OECD-member countries, and below the OECD average.4 In addition to overall mathematics literacy scores, PISA reports on performance by four broad content areas connected to overarching ideas in mathematics: space and shape, change and relationships, quantity, and uncertainty. In each content area, U.S. 15-year-olds were outperformed, on average, by students in a majority of OECD countries and performed below the OECD average (Lemke et al. 2004). Fifteen-year-olds in 23 OECD countries outperformed their U.S. counterparts on the quantity measure (which focuses on quantitative reasoning and understanding of numerical patterns and measures and includes number sense, estimating, and computations) than on the other content areas measured. For the other content areas, the number of OECD countries in which students outperformed their U.S. counterparts was 16 countries on the uncertainty measure (which focuses on data and chance), 18 countries on the change and relationships measure (which focuses on the representation of change, including mathematics functions such as linear or exponential), and 20 countries on the space and shape measure (which focuses on recognizing shapes and patterns, describing and decoding visual information, and the relationship between visual representations and real shapes and images).
Further analysis of these data shows that, in 2003, the United States had a greater percentage of students than the OECD average at the lowest levels of performance in mathematics literacy and the four broad content areas (Lemke et al. 2004).
Differences in mathematics literacy performance within the United States were apparent by sex and race/ethnicity. U.S. 15-year-old females scored lower in mathematics literacy than their male counterparts, a pattern evidenced in 25 other countries (20 OECD and 5 non-OECD countries) as well (Lemke et al. 2004). Among U.S. 15-year-olds, Black and Hispanic students scored lower in mathematics literacy, on average, than their White and Asian counterparts, but Hispanic students outperformed their Black peers. More detailed information on the PISA 2003 results can be found in Lemke et al. (2004; available at http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=
2005003) and OECD (2004b; available at http://www.pisa.oecd.org/dataoecd/1/60/
The ALL 2003 study included measures of adult numeracy skills, defined as knowledge and skills required to manage mathematical demands in diverse situations. Unlike mathematics literacy skills, numeracy skills go beyond the ability to apply arithmetic skills to include number sense, estimation, measurement, and statistics. Adults were asked to complete items that required understanding of arithmetic, proportionality, data reading and interpretation, estimation, measurement, recognition of patterns and relationships, and the ability to solve simple and multi-step problems. The goal of ALL was to ascertain the degree to which the adult population could perform tasks that they would likely encounter in everyday life and workplace situations.
Mirroring the ALL 2003 results on literacy skills and knowledge, U.S. adults outperformed Italian adults in numeracy, on average. Adults in Switzerland, Norway, Canada, and Bermuda scored better, on average, than their U.S. peers (table 7).
Besides outperforming U.S. adults on average, adults in the four higher performing countries had higher numeracy scores than U.S. adults at both the high and low ends of the score distribution (Lemke et al. 2005). The highest performers (the top 10 percent of adults) had numeracy scores of 352 or higher in Switzerland, 343 or higher in Norway, 342 or higher in Bermuda, and 341 or higher in Canada, compared with 333 or higher in the United States. The lowest performers (those in the bottom 10 percent) in Bermuda and Canada had average scores of 198 or lower, 224 or lower in Norway, and 230 or lower in Switzerland, compared with 185 or lower in the United States.
Further analysis also revealed that among U.S. adults, males outperformed females in numeracy skills, and White adults outscored Black and Hispanic adults, on average (Lemke et al. 2005).
As additional countries collect ALL data, international comparisons of adults’ numeracy and mathematics literacy skills should reveal more information. Details on the results from the first round of ALL can be found in Statistics Canada and OECD (2005; available at http://www.statcan.ca/english/freepub/89-603-XIE/
4The international average reported for PISA is based on results only from the OECD-member countries. Because PISA is primarily an OECD study, results for non-OECD-member countries are displayed separately from those of OECD countries and are not included in the OECD average. (back to text)
Figures and Tables
Table 5: Average TIMSS mathematics scores of 4th- and 8th-graders, by country: 2003
Table 6: Average PISA mathematics literacy scores of 15-year-olds, by country: 2003
Table 7: Average ALL numeracy scores of adults ages 16–65, by country: 2003
Table SA6: Standard errors for table 5: Average TIMSS mathematics scores of 4th- and 8th-graders, by country: 2003
Table SA7: Standard errors for table 6: Average PISA mathematics literacy scores of 15-year-olds, by country: 2003
Table SA8: Standard errors for table 7: Average ALL numeracy scores of adults ages 16–65, by country: 2003