sents a serious challenge to U.S. education. In 1994, NAEP began collecting information on participation in Title I programs, programs designed to help disadvantaged students, and in 1996 on eligibility for free or reduced-priced lunches. At both grades 4 and 8, students who participated in Title I programs and students who were eligible for free or reduced-priced lunches scored lower than their nonparticipating or noneligible classmates.¹⁰⁴ The low mathematics achievement of poor children is embedded in the larger social issues of poverty and poses another serious challenge to U.S. education.

International comparisons of mathematics achievement demonstrate many of the same findings as the NAEP results. On several international mathematics assessments conducted since the 1970s, the overall performance of U.S. students has lagged behind the performance of students in other countries. In TIMSS, U.S. fourth graders performed above the international average of the 26 participating countries at fourth grade but still significantly below the levels of the top-performing countries. U.S. eighth graders performed slightly below the international average in mathematics among the 41 participating countries.

As this volume went to press, the results of TIMSS-R (Third International Mathematics and Science Study-Repeat), the 1999 version of TIMSS, had just been released. Between 1995 and 1999, there was no significant change in the mathematics achievement of U.S. eighth graders. Furthermore, the eighth graders in 1999, who compared quite well internationally in 1995 as fourth graders, were very much like the 1995 eighth graders, performing near the international average.¹⁰⁵

One way to quantify U.S. students’ performance is in terms of the average number of points they scored on the 1995 TIMSS assessment. Each student answered a subset of the TIMSS questions, and an average score was calculated for each question, with some questions worth more than one point. The U.S. fourth graders scored, on average, 71 out of the 113 points available on the TIMSS achievement test, which contained 102 questions.¹⁰⁶ That was about 4 points above the performance across all 26 countries, but it was 11 to 15 points below the performance of students in the top four countries (Singapore, Korea, Japan, and Hong Kong) and was in a band of performance comparable with that found in the Czech Republic, Ireland, and Canada. In the assessment of eighth graders, U.S. students scored, on average, 86 points out of the 162 available on the 151 TIMSS items, which was 3 points below the 41-country average. Students in the four top-scoring countries—Singapore, Japan, Korea, and Hong Kong—scored, on average, between 113 and 128 points.¹⁰⁷