U.S. 4th- and 8th-graders performed above the international averages in knowing mathematical facts, procedures, and concepts; in applying mathematical knowledge and understanding; and in mathematical reasoning.

The Trends in International Mathematics and Science Study (TIMSS) conducted in 2003 assessed students’ mathematics performance in 25 countries at grade 4 and 46 countries at grade 8. In addition to reporting overall mathematics scores, TIMSS developed scales in three mathematics cognitive domains: knowing facts, procedures, and concepts needed to solve mathematical problems; applying knowledge of facts, skills, and procedures to create representations and solve routine problems; and reasoning to solve more complex, nonroutine problems through logical thinking.¹

At grade 4, U.S. students scored above the international average of all 25 countries in the mathematics cognitive domains of knowing, applying, and reasoning (see table 17-1). U.S. 4th-graders performed relatively better in knowing than in applying and reasoning: U.S. students outperformed students in 17 countries in knowing, 11 countries in applying, and 12 countries in reasoning.

Among the participating countries with a high value on the United Nations Development Program’s Human Development Index (HDI),² U.S. 4th-graders, on average, outperformed their peers in Australia, Italy, New Zealand, Norway, Scotland, and Slovenia across the three domains. Fourth-graders in Belgium (Flemish), Chinese Taipei, Hong Kong SAR, Japan, and Singapore outperformed U.S. students, on average, across all three cognitive domains. Students in England and the Netherlands outperformed U.S. 4th-graders in applying and reasoning, but not in knowing.

Like their 4th-grade counterparts, U.S. 8th-graders scored above the international average of all 46 countries in all three mathematics cognitive domains and relatively better in knowing than in applying and reasoning (see table 17-2). U.S. 8th-graders outperformed students in 31 countries in knowing, 25 countries in applying, and 27 countries in reasoning.

Among the high-HDI-value participating countries, U.S. 8th-graders, on average, outperformed their peers in Italy, Norway, and Slovenia across the three domains (see chart). U.S. students outperformed their peers in an additional five countries in the knowing domain and in one country in the reasoning domain. Eighth-graders in Belgium (Flemish), Chinese Taipei, Hong Kong SAR, Japan, Korea, Netherlands, and Singapore outperformed their U.S. peers, on average, across all three cognitive domains.

¹The cognitive domain scales were created to have the same mean and standard deviation as the overall TIMSS 2003 mathematics achievement scales: a mean of 495 and standard deviation of 100 at grade 4 and a mean of 467 and standard deviation of 100 at grade 8. (back to text)

²The Human Development Index (HDI) ranks countries along three dimensions of human development: life expectancy at birth; the adult literacy rate and gross enrollment for primary, secondary, and tertiary education; and gross domestic product (GDP) per capita (using purchasing power parity [PPP] indices). The index has a minimum value of 0 and a maximum value of 1. Countries with high index values enjoy long life expectancy, high levels of school enrollment and adult literacy, and a good standard of living. For this indicator, a high index value is 0.9 or above. The index is explained in detail in the United Nations Development Program’s (UNDP) Human Development Report 2005, available at http://hdr.undp.org/reports/global/2005/. Though Chinese Taipei is not assigned an HDI value in the UNDP report, it is included here because it is a high-achieving country in mathematics (back to text)