The National Assessment of Educational Progress (NAEP), also known as "The Nation's Report Card," is a congressionally mandated survey of educational achievement of American students in a variety of curriculum areas and of changes in that achievement across time. Part 1 of this report consists of the results of NAEP's 1990 national mathematics assessment of nationally representative samples of more than 26,000 students in grades 4, 8, and 12 in more than 1,300 schools. Part 2 consists of the results of NAEP's 1990 "Trial State Assessment Program," a voluntary eighth-grade mathematics assessment administered to representative samples of 2,500 public school students at grade 8 in about a 100 schools in each of the 40 participating states and jurisdictions. This is the first time NAEP has provided results by state. The report is organized as follows: (1) executive summary; (2) NAEP history; (3) scope of the assessment; (4) results for grade 4, 8, 12, respectively; (5) results of the Trial State Assessment Program. Appendices include: contextual and background factors; participation rates; procedures; anchoring processes; and tabular data. Overall mathematics performance in the nation at each of the three grade levels tested was characterized as follows: FOURTH GRADE: 72 percent demonstrated the ability to consistently solve third grade level problems (e.g., addition and subtraction with whole numbers); 11 percent demonstrated a grasp of fifth grade level problems (e.g., multiplication). No fourth graders indicated an understanding of fractions, decimals, percents, or simple algebra. EIGHTH GRADE: 98 percent demonstrated a grasp of third grade level problems; 67 percent consistently understood fifth grade content; only 14 percent showed successful performance with seventh grade material (fractions, decimals, percents, simple algebra); no eighth graders showed the breadth of understanding necessary to begin the study of relatively advanced mathematics. TWELFTH GRADE: All high school seniors demonstrated success with third-grade materials; 91 percent showed mastery of fifth-grade material; 46 percent demonstrated a consistent grasp of seventh grade material (decimals, percents, fractions, simple algebra); 5 percent showed an understanding of geometry and algebra. Many students appear to be graduating from high school with little of the mathematics understanding required by the fastest growing occupations or for college work. Approximately half of graduating twelfth graders appear to have an understanding of mathematics that does not extend much beyond simple problem solving with whole numbers. The Trial State Assessment Program showed great variation in student achievement within each state, to the extent that the variation within states tended to exceed the variation in average performance across states. The higher performing states (e.g., North Dakota, Montana, Iowa, Nebraska, Minnesota, Wisconsin) appear to have fewer urban areas, fewer disadvantaged students, and fewer minority students. (JJK/WTB)