NAEP Report Card: Mathematics

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 2022 mathematics assessment at grades 4 and 8 are based on a representative sample of 116,200 fourth-graders from 5,780 schools and 111,000 eighth-graders from 5,190 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 26,100 fourth-grade and 24,700 eighth-grade public school students from 26 urban districts participated in the 2022 mathematics assessment. These 26 TUDA districts are listed below.

2022 TUDA DISTRICTS

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 2022 NAEP assessment, its 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 report to the U.S. Department of Education. For the District of Columbia, beginning in 2009, TUDA results for DCPS do not include charter school results due to a change in the education governance structure for the District of Columbia. In 2019, results for Los Angeles at grades 4 and 8 and Fresno at grade 4 did not include affiliated charter schools. 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 2022 mathematics assessment.

The results from the 2019 mathematics assessment at grade 12 are based on approximately 25,400 twelfth-graders from 1,770 schools who took the assessment on paper or tablets. Results for the nation reflect the performance of students attending public schools, private schools, Bureau of Indian Education schools, and Department of Defense schools. Download the summary data tables via the link at the bottom of the page to see the national sample sizes for the 2019 grade 12 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 NAEP sampling and weighting in the NAEP Technical Documentation.

NAEP Inclusion

Assessing representative samples of students, including students with disabilities (SD) and English learners (EL), 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 EL 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 (samples for whom accommodations were permitted and samples for whom they were not permitted). In the report, the first year with a split sample—1996—shows results for the sample with accommodations permitted and for the sample assessed without accommodations. For subsequent assessment years, only results from the accommodated sample are shown. In the NAEP mathematics digitally based assessments (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 EL students should be considered when comparing variations in exclusion and accommodation rates. States/jurisdictions and districts also vary in their proportions of SD and EL students. Download the summary data tables via the link at the bottom of the page to see the percentages of SD and/or EL students identified, excluded, and assessed in mathematics in 2022.

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 at grades 4 and 8, 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 EL. Read more about the inclusion policy and how the percentages of students are calculated.

All of the states/jurisdictions and all of the urban districts participating in the 2022 NAEP mathematics assessment met or exceeded the 95 percent inclusion goal for grades 4 and 8.

Download the summary data tables to see the inclusion rates in grades 4 and 8 mathematics for states/jurisdictions and the 26 participating TUDA districts in 2022.

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 whether 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 2022 mathematics assessment were 94 percent for grade 4 (100 percent for public schools, 37 percent for private schools, and 67 percent for Catholic schools), and 95 percent for grade 8 (100 percent for public schools, 35 percent for private schools, and 61 percent for Catholic schools). In 2019, these school participation rates were 84 percent for grade 12 (88 percent for public schools, 35 percent for private schools, and 55 percent for Catholic schools). In 2022, the school participation rates for private schools at grades 4 and 8 did not meet the criteria so their results are not reportable. This is also the case for the grade 12 mathematics assessment in 2019.

In 2022, the school participation rates for the original Catholic school samples at grades 4 and 8 fell below the NAEP reporting standard of 70 percent or more. At grade 4, the results from the Catholic school nonresponse bias analysis showed no evidence of nonresponse bias for school characteristics evaluated in the analysis after school substitution and adjusting for school nonresponse. At grade 8, there was bias among the school characteristics evaluated in the nonresponse bias analysis after school substitution and adjusting for school nonresponse, which gives rise to potential bias in performance results. It was determined that the potential bias was not enough to prohibit the reporting of performance results. Furthermore, it was determined that the sample sizes for participating Catholic schools at grades 4 and 8 are sufficient to support reporting reliable estimates for Catholic schools in 2022.

Weighted student participation rates for the 2022 mathematics assessment were 92 percent at grade 4 (92 percent for public school students, 94 percent for private school students, and 94 percent for Catholic school students) and 89 percent at grade 8 (89 percent for public school students, 94 percent for private school students, and 94 percent for Catholic school students). In 2019, these student participation rates were 72 percent at grade 12 (72 percent for public school students, 75 percent for private school students, and 72 percent for Catholic school students).

State and TUDA participation at grades 4 and 8

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 2022, all 52 states and jurisdictions and all 26 TUDA districts met this participation rate requirement with school participation rates of 91 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, the states, and the 26 participating districts.