In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment which, for the first time in the NAEP's history, made voluntary state-by-state assessments. This 1992 mathematics report marks the first attempt of the National Center for Education Statistics to shift to standards-based reporting of National Assessment statistics. NAEP results are reported by achievement levels which are descriptions of how students should perform relative to a body of content reflected in the NAEP frameworks; in other words, how much students should know. The 1992 assessment covered six mathematics content areas: (1) numbers and operations; (2) measurement; (3) geometry; (4) data analysis, statistics, and probability; (5) algebra and functions; and (6) estimation. In North Carolina, 2,884 fourth-grade students in 116 public schools and 2,769 eighth-grade students in 103 public schools were assessed. This report describes the mathematics performance of North Carolina fourth- and eighth-grade students in public schools and compares their overall performance to students in the Southeast region of the United States and the nation. The distribution of the results are provided for subpopulations of students including race/ethnicity; type of community--advantaged/disadvantaged urban, extreme rural, and other; parents' education level; gender; and content area performance. To provide a context for understanding students' mathematics proficiency, students, their mathematics teachers, and principals completed questionnaires which focused on: what are students taught? (curriculum coverage, homework, and instructional emphasis); how is mathematics instruction delivered? (resources, collaborating in small groups, using mathematical objects, and materials); how are calculators and computers used? (access and use of calculators, availability of computers, and when to use a calculator); who is teaching mathematics? (educational background); and conditions beyond school that facilitate mathematics learning and teaching (amount of reading materials in the home, hours of television watched per day, student absenteeism, and students' perceptions of mathematics). The average proficiency of fourth-grade students in North Carolina on the NAEP mathematics scale was 211 compared to 217 nationwide; for North Carolina eighth-grade students the average proficiency was 258 compared to 266 nationwide. (ASK)