The Second International Mathematics Study (SIMS) of the International Association for the Evaluation of Educational Achievement (IEA) was conducted in 20 countries on two sampled populations: Population A of 13-year-olds and Population B of students studying mathematics in their final year of secondary school. Mathematics achievement was measured with a large number of test items (180 or 176 for the 13-year-olds, 136 for the older students) distributed across the curricular content of mathematics found at these grade levels. In addition, a substantial amount of background information was collected from pupils, teachers, and schools, e.g., behavior problems, enrollment (by sex), mathematics anxiety, school days per year, teaching periods per week, textbooks used, beginning-of-year and end-of-year performance, opportunity to learn the specific mathematics of the tests. The Population A surveys described here were conducted on 13-year-olds in eight geographic areas (in seven countries): Belgium Flemish, Canada (British Columbia), Canada (Ontario), France, Japan, New Zealand, Thailand, United States. The standard IEA-type survey design was augmented with two innovations: (1) a pretest (beginning of school year) measure based on the same mathematics item pool, and (2) rich documentation of classroom teaching practices. The resulting Population A machine-readable data file (MRDF) is comprised of 39 subfiles. There are three response files corresponding to the schools, the teachers (or classrooms), and the students, for each of the eight geographic regions (3x8=24). There are 9 documentation subfiles and 6 control, working, and demonstration subfiles. The data include responses from 37,558 13-year-old students. Student backgrounds and attitudes were surveyed, along with their knowledge of algebra, geometry, fractions, measurement, ratio, proportion, and percent. Teacher backgrounds, attitudes, and teaching practices were surveyed. School principals were queried about school operations and organization. The SIMS file provides for the first time international mathematical achievement datasets gathered under common and rigorous survey conditions. The survey results for the United States are contained in "Second International Mathematics Study: Summary Report for the United States" (ED 259 896). TYPE OF SURVEY: National Survey; International Survey; Longitudinal Survey. RESPONDENTS: 13-year-old students (37,558) (including their school principals and mathematics teachers). YEAR OF DATA: 1981-1982. (WTB)