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More About NAEP Mathematics

The NAEP mathematics assessment results present a broad view of what our nation’s students know and can do in mathematics.

On this page, learn more about:

The NAEP mathematics framework

The National Assessment Governing Board oversees the development of NAEP frameworks that describe the specific knowledge and skills to be assessed in each subject. Frameworks incorporate ideas and input from subject area experts, school administrators, policymakers, teachers, parents, as well as the NAEP Mathematics Standing Committee. The NAEP Mathematics Framework describes the assessment content, how students' responses are evaluated, what kinds of exercises it ought to feature, and the goals of the mathematics assessment. Although the mathematics framework has undergone changes over the years, the content objectives for grades 4 and 8 have not changed, allowing students' performance in 2015 to be compared with previous assessment years going back to 1990. Changes to the framework for grade 12, however, necessitated starting a new trend line in 2005.

The framework directs that questions at be based on the following five content areas:

  • number properties and operations,
  • measurement,
  • geometry,
  • data analysis, statistics, and probability, and 
  • algebra.

The framework also specifies that each of the above content areas should occupy a certain proportion of the assessment; see the target and actual distribution of questions by content area for the 2015 assessment.

Assessment question formats

The assessment consisted of both multiple-choice and constructed-response questions. Short constructed-response questions required students to provide answers to computation problems or to describe solutions in one or two sentences. Extended constructed-response questions required students to give longer responses when answering the questions. To learn more, see questions from previous NAEP mathematics assessments in the NAEP Questions Tool.

NAEP also gives questionnaires to teachers, students, and schools that are part of the NAEP sample. Responses to these questionnaires provide information about school policies affecting mathematics instruction, as well as information about schools' resources.


Number of students who took the assessment

The NAEP 2015 mathematics assessment was conducted throughout the nation at grades 4, 8, and 12. Approximately 139,900 grade 4 students, 136,900 grade 8 students, and 13,200 grade 12 students took the assessment. State results are available for all 50 states, the District of Columbia, and Department of Defense schools at grades 4 and 8. Only national results are available at grade 12. See details about participation rates and about sample size and target population by state at grades 4 and 8PDF File(1.03 MB), and nationally at grade 12.

Results of the 2015 NAEP Trial Urban District Assessment (TUDA) in mathematics are based on representative samples of 1,000 to 1,800 public school students at grade 4 and 900 to 1,600 public school students at grade 8 in each of the 21 participating urban districts. See details about participation rates and about sample size and target population by districtPDF File(1.04 MB).

The NAEP program does not, and is not designed to, report on the performance of individual students. Instead, groups of the student population that from representative national samples are assessed. For example, NAEP reports results for male and female students, Black students and White students, and students attending schools in different types of school locations. Samples are selected using a complex sampling design.

Permitted Accommodations

Accommodations for students with disabilities (SD) and English language learners (ELL) have been permitted beginning with the 1996 mathematics assessment. See the types of accommodations permitted.

For grades 4 and 8:

For grade 12:

Assessment sample

NAEP assesses representative samples of students rather than the entire population of students. The sample selection process utilizes a probability sample design in which each school and each student has a known probability of being selected (the probabilities are proportionate to the estimated number of students in the grade assessed). Samples are selected according to a multistage design, with students drawn from within sampled public and private schools nationwide. Read details of assessment sample design in the technical documentation and see a diagram of sample selection for NAEP state assessments.

The Common Core of Data (CCD) file, a comprehensive list of operating public schools in each jurisdiction that is compiled each school year by NCES, served as the sampling frame for the selection of public schools in each state/jurisdiction. The sample of students in districts participating in the Trial Urban District Assessment (TUDA) represents an augmentation of the sample of students selected as part of the state samples. All students at more local geographic sampling levels also make up part of the broader samples. For example, the TUDA samples are included as part of the corresponding state samples, and the state samples are included as part of the national sample.

The Private School Survey (PSS), a survey of all U.S. private schools carried out biennially by the Census Bureau under contract to NCES, served as the sampling frame for private schools. While state and district results are based on samples of public schools only, the national results are based on the combined samples of public and private schools.

Because 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 make appropriate inferences between the student samples and the respective populations from which they are drawn. Sampling weights are adjusted for the disproportionate representation of some groups in the selected sample. This includes oversampling of schools with high concentrations of students from certain racial/ethnic groups and the lower sampling rates of students who attend very small schools. Read more about the technical aspects of the NAEP sample design.

View the sample sizes and target populations for the NAEP 2015 mathematics assessment at grades 4 and 8PDF File(1.03 MB), .
View the sample sizes and target populations for the NAEP 2015 mathematics assessment at grade 12.
View the school and student participation rates at grades 4 and 8PDF File(1.03 MB), and at grade 12.

Additional resources

Learn more about NAEP, the nation's largest continuing and nationally representative assessment of what students know and can do in core subjects.

View the results of the 2015 mathematics assessment at grades 4 and 8.

View the results of the 2015 mathematics assessment at grade 12.

View the results of the 2015 Trial Urban District Assessment (TUDA).

Explore the most recent NAEP results in any subject on the website of The Nation’s Report Card.


Last updated 20 April 2016 (FW)