This report presents the national and state results of the National Assessment of Educational Progress (NAEP) assessment in mathematics and compares them to results from assessments in 2003 and in the first year data were available, usually 1990. In 2005, nationally representative samples of about 172,000 fourth-grade and 162,000 eighth-grade students nationwide participated in that assessment. Results are presented in two ways: in terms of scale scores and as the percentage of students scoring at or above three benchmarks called achievement levels. NAEP mathematics scores are reported for grades 4 and 8 on a 0-500 scale. Scale score results also are presented for students at various percentiles. Item maps provide interpretative information about a scale score in terms of the skills and knowledge students with a certain score are likely to have. Items placed along the scale in an item map demonstrate how skills correspond to levels of performance. NAEP results are reported at three achievement levels: Basic, Proficient, and Advanced. Achievement levels are performance standards showing what students should know and be able to do. They are set by the National Assessment Governing Board (NAGB), based on recommendations from panels of educators and members of the public, to provide a context for interpreting student performance on NAEP. In this report, the achievement-level results are reported as percentages of students performing at or above Basic and at or above Proficient. (Contains 16 figures and 20 tables.)