The Second International Mathematics Study investigated the status of the curriculum, achievement, and instructional practices at grades 8 and 12 in about 20 countries. The introductory first chapter explores the need for change in mathematics programs. Chapter two describes the achievement of U.S. students compared to others. At grade 8, U.S. students were slightly above the international average in computational arithmetic, well below the average in noncomputational arithmetic, average in algebra, and among the bottom 25% in geometry, while Japanese students obtained the highest scores. For grade 12, Hong Kong achieved highest, with Japan a close second. In the United States, the achievement of calculus classes was at or near the international average; precalculus students were substantially below average. Chapter three discusses the opportunity to learn; the United States was typically at or below average. Attitudes toward mathematics of United States and most other students were positive; attitudes of Japanese students tended to be negative, however. Chapter five discusses five deceptive explanations for the data. The sixth chapter considers the underachieving curriculum in terms of content and goals, while chapter seven discusses it in terms of opportunity to learn. Finally, the "road to renewal" is considered. Appendices include background information and data. (MNS)