Happily, the United States has improved! The average math scores for both fourth-graders and eighth-graders have risen since 1995, the first year the test was administered. Most of those gains took place among the lowest-performing students. That could be a result, analysts say, of the increased focus on bringing up America's struggling students without as much attention to those at the top. (See US students improve in math.)
I was trying to find a chart that would list the average student achievement by countries, but I couldn't find it directly online; only in the downloadable documents. So I took screenshots from the full report to post the charts here, for your convenience. Note: Not all countries of the world participate in the TIMSS.
8th Grade Student Achievement:
Quoting from the press release:
CHESTNUT HILL, MA (12-9-08) – Students from Asian countries were top performers in math and science at both the fourth and eighth grade levels, according to the most recent reports of the Trends in International Mathematics and Science Study (TIMSS), released today by the study's directors Michael O. Martin and Ina V.S. Mullis of Boston College.
In mathematics, at the fourth grade level, Hong Kong SAR and Singapore were the top performing countries, followed by Chinese Taipei and Japan. Kazakhstan, the Russian Federation, England, Latvia, and the Netherlands also performed very well. In mathematics achievement at the eighth grade, Chinese Taipei, Korea, and Singapore were followed by Hong Kong SAR and Japan. There was a substantial gap in average mathematics achievement between the five Asian countries and the next group of four similarly performing countries, including Hungary, England, the Russian Federation, and the United States.
You can download and read the executive summary here. It explains some more details about the study, including various factors associated with higher achievement in mathematics.
Download the full report from TIMSS website here.