About the NAEP Mathematics Assessment

The National Assessment of Educational Progress (NAEP) is a congressionally mandated project administered by the National Center for Education Statistics (NCES) within the U.S. Department of Education and is the largest continuing and nationally representative assessment of what our nation's students know and can do in select subjects. NCES first administered NAEP in 1969 to measure student achievement nationally. The National Assessment of Educational Progress (NAEP) mathematics assessment at grades 4 and 8 is a digitally based assessment administered on tablets. The NAEP mathematics assessment measures students' knowledge and skills in mathematics and their ability to solve problems in mathematical and real-world contexts. Results are reported for the nation overall, for states and jurisdictions, and for districts participating in the Trial Urban District Assessment (TUDA).

Samples, Inclusion, and Participation

NAEP Samples

The schools and students participating in NAEP assessments are selected to be representative of all schools nationally and of public schools at the state/jurisdiction and Trial Urban District Assessment (TUDA) district levels. The results from the 2019 mathematics assessment at grades 4 and 8 are based on a representative sample of 149,500 fourth-graders from 8,280 schools and 147,400 eighth-graders from 6,960 schools who took the assessment on tablets. Samples of schools and students are drawn from each state and from the District of Columbia and Department of Defense schools. The sample of students participating in the TUDA school districts is an extension of the sample of students who would usually be selected by NCES as part of the national and state samples for the NAEP assessment. Representative samples of 34,400 fourth-grade and 33,400 eighth-grade public school students from 27 urban districts participated in the 2019 mathematics assessment. These 27 TUDA districts are listed below.


Albuquerque Dallas Houston
Atlanta Denver Jefferson County (KY)
Austin Detroit Los Angeles
Baltimore City District of Columbia (DCPS) Miami-Dade
Boston Duval County (FL) Milwaukee
Charlotte-Mecklenburg Fort Worth New York City
Chicago Fresno Philadelphia
Clark County (NV) Guilford County (NC) San Diego
Cleveland Hillsborough County (FL) Shelby County (TN)

The results from the assessed students are combined to provide accurate estimates of the overall performance of students in the nation and in individual states and other jurisdictions. Results for the nation reflect the performance of students attending public schools, private schools, Bureau of Indian Education schools, and Department of Defense schools. While Puerto Rico participated in the 2019 NAEP assessment, their results did not contribute to the national overall results. Results for states/jurisdictions and for districts reflect the performance of students in public schools only and are reported along with the results for public school students in the nation. Charter schools are included in the public school samples at the state level. For TUDA districts, beginning in 2009, results for charter schools are included in district results only if they contribute to the district's Adequate Yearly Progress (AYP) report to the U.S. Department of Education. Download the summary data tables via the link at the bottom of the page to see the national, state/jurisdiction, and district sample sizes for the 2019 mathematics assessment.

Each school that participated in the assessment, and each student assessed, represents only a portion of the larger population of interest. The results are weighted to account for the disproportionate representation of some groups in the selected sample, including the oversampling of schools with high concentrations of students from certain racial/ethnic groups and the lower sampling rates of students who attend small schools. Read more about sampling and weighting.

NAEP Inclusion

Assessing representative samples of students, including students with disabilities (SD) and English language learners (ELL), helps to ensure that NAEP results accurately reflect the educational performance of all students in the target population and are a meaningful measure of U.S. students' academic achievement over time.

To ensure that all selected students from the population can be assessed, many of the same accommodations that SD and ELL students use on other tests are provided for those students participating in NAEP. Read more about accommodations available in NAEP. Accommodations were first made available for the mathematics assessment in 1996. The 1996 mathematics assessments at grades 4 and 8 used a split-sample design to make it possible to continue reporting trends in students' mathematics achievement and, at the same time, to examine how including students assessed with accommodations affect overall assessment results. Separate samples of students were assessed with each of the administration procedures (accommodations permitted and not permitted samples). In the report, the first year with a split sample—1996—shows results for the accommodations permitted sample and for the sample assessed without accommodations. For subsequent assessment years, only results from the accommodated sample are shown. In the 2017 NAEP mathematics assessment, accommodations were provided for both DBA and PBA. In DBA, some accommodations were provided by the test delivery system (e.g., extended time) while others were available outside of the test delivery system (e.g., breaks during the test). DBA also included a set of accessibility features, referred to as universal design elements that were available to all students.

Even with the availability of accommodations, some students may still be excluded. Differences in student populations and in state/jurisdiction and district policies and practices for identifying and including SD and ELL students should be considered when comparing variations in exclusion and accommodation rates. States/jurisdictions and districts also vary in their proportions of special-needs students. Download the summary data tables via the link at the bottom of the page to see the percentages of SD and/or ELL students identified, excluded, and assessed in mathematics in 2019.

Because providing accommodations represented a change in testing conditions that could potentially affect the measurement of changes over time, split national samples of students were assessed in 1996—one sample permitted accommodations and the other did not. Although the results for both samples are presented in the tables and figures, any comparisons to 1996 in the text are based only on the sample eligible for accommodations.

The National Assessment Governing Board, which sets policy for NAEP, has been exploring ways to ensure that NAEP continues to appropriately include as many students as possible and to do so in a consistent manner for all jurisdictions and districts assessed and reported. In March 2010, the Governing Board adopted a new policy outlining specific inclusion goals for NAEP samples. At the national, state, and district levels, the goal is to include 95 percent of all students selected for the NAEP samples, and 85 percent of those in the NAEP sample who are identified as SD or ELL. Read more about the inclusion policy and how the percentages of students are calculated.

All of the states/jurisdictions and almost all of the urban districts participating in the 2019 NAEP mathematics assessment met or exceeded the 95 percent inclusion goal for grades 4 and 8. The goal was not met in one district in the 2019 mathematics assessment: Detroit at grade 8 (where approximately 94% of students were assessed).

Download the summary data tables to see the inclusion rates in mathematics for states/jurisdictions and the 27 participating TUDA districts in 2019.

School and Student Participation

National participation

To ensure unbiased samples, NAEP requires that participation rates for original school samples be 70 percent or higher to report national results separately for public and private schools. In instances where participation rates meet the 70 percent criteria but fall below 85 percent, a nonresponse bias analysis is conducted to determine if the responding school sample is not representative of the population, thereby introducing the potential for nonresponse bias.

Before replacing originally sampled schools that declined to participate with substitute schools, the weighted national school participation rates for the 2019 mathematics assessment were 96 percent for grade 4 (100 percent for public schools, 53 percent for private schools, and 77 percent for Catholic schools), and 96 percent for grade 8 (99 percent for public schools, 50 percent for private schools, and 73 percent for Catholic schools). In 2019, the school participation rates for private schools at both grades 4 and 8 did not meet the criteria so their results are not reportable.

Weighted student participation rates were 94 percent at grade 4 (93 percent for public school students, 95 percent for private school students, and 95 percent for Catholic school students) and 92 percent at grade 8 (92 percent for public school students, 94 percent for private school students, and 94 percent for Catholic school students).

State and TUDA participation

Standards established by the National Assessment Governing Board require that school participation rates for the original state/jurisdiction and TUDA district samples need to be at least 85 percent for results to be reported. In 2019, all 52 states and jurisdictions and all 27 TUDA districts met this participation rate requirement with school participation rates of 89 to 100 percent.

Download the summary data tables via the link at the bottom of the page to see the participation rates in mathematics for the nation, states, and the 27 participating districts.