The Trends in International Mathematics and Science Study (TIMSS) 2003 is the most recent in a very ambitious series of international assessments conducted in nearly 50 countries to measure trends in mathematics and science learning. The aim of TIMSS, the Trends in International Mathematics and Science Study, is to improve the teaching and learning of mathematics and science by providing data about students' achievement in relation to different types of curricula, instructional practices, and school environments. The variation across the nearly 50 participating countries provides a unique opportunity to study different approaches to educational practices and how these can improve achievement. TIMSS is a project of the International Association for the Evaluation of International Achievement (IEA), an independent international cooperative of national research institutions and government agencies that has been conducting studies of cross-national achievement since 1959. Conducted first in 1995 and then in 1999, the regular four-year cycle of TIMSS studies provides countries with an unprecedented opportunity to obtain comparative information about their students' achievement in mathematics and science. This report contains the mathematics results for 46 countries and four benchmarking participants at the eighth grade and for 25 countries and three benchmarking participants at the fourth grade. Trend data are provided at the eighth and fourth grades for those countries that also participated in 1995 and 1999. After an executive summary and introduction, this book presents eight chapters: (1) International Student Achievement in Mathematics; (2) Performance at International Benchmarks; (3) Average Achievement in the Mathematics Content Areas; (4) Students' Backgrounds and Attitudes Towards Mathematics; (5) The Mathematics Curriculum; (6) Teachers of Mathematics; (7) Classroom Characteristics and Instruction; and (8) School Contexts for Learning and Instruction. This book concludes with the following Appendices: (1) Overview of TIMSS Procedures for Assessing Mathematics; (2) Multiple Comparisons of Average Achievement in Mathematics Content Areas; (3) The Test-Curriculum Matching Analysis: Mathematics; (4) Percentiles and Standard Deviations of Mathematics Achievement; (5) Descriptions of Mathematics Items at Each Benchmark; (6) Syrian Arab Republic and Yemen--Mathematics Achievement; and (7) Acknowledgements. [This document was also published by the TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.]