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 NAEP mathematics assessment measures students' knowledge and skills in mathematics and their ability to solve problems in mathematical and real-world contexts. Results for grades 4 and 8 are reported for the nation overall, for states and jurisdictions, and for districts participating in the Trial Urban District Assessment (TUDA); results for grade 12 are reported for the nation only.

The NAEP mathematics assessments at grades 4 and 8 were administered as digitally based assessments. In 2019, for grade 12, both a digitally based assessment and paper-based assessment were administered. Twelfth-grade students were randomly assigned to take either the digitally based or paper-based assessment. Read more about the NAEP Digitally Based Mathematics Assessment.

Digitally Based Assessment

NAEP Digitally Based Mathematics Assessment

The NAEP mathematics digitally based assessments at grades 4, 8, and 12 were administered on tablets supplied by NCES using a secure, local NAEP network. This allowed the NAEP administrators to create a stable administration environment by bringing in their own equipment that would not be influenced by school-based equipment or school internet connectivity, thereby maintaining consistency across the assessed schools. Students were able to interact with the tablets via touchscreen, with an attached keyboard, or using a stylus provided by NCES. The digitally based mathematics assessment provided students with a variety of onscreen tools, including an equation editor for entering numbers and expressions using the correct mathematical symbols; a scratchwork tool for annotating figures, performing computations, drawing diagrams, and highlighting portions of a question; and a calculator. The use of an onscreen calculator was available to students on approximately 30 percent of the test questions at both grades 4 and 8 and on approximately 40 percent of test questions at grade 12. At the beginning of the assessment session, students viewed an interactive tutorial that provided the information needed to take the assessment on tablets; for example, the tutorial explains how to progress through questions, how to indicate answers for multiple-choice questions, and how to use onscreen tools effectively when answering questions. The interactive nature of the tutorial allowed students to familiarize themselves with the digital delivery system before beginning the actual assessment. See how the mathematics digitally based assessment was presented to students.

The digitally based mathematics assessment was designed to continue reporting trends in student performance while keeping pace with the new generation of classroom environments in which digital technology has increasingly become a part of students' learning. At grades 4 and 8, trend performance dates to 1990; at grade 12, changes to the grade 12 NAEP mathematics framework in 2005 necessitated the start of a new trend line beginning with the 2005 mathematics assessment.

The 2019 assessment content at grades 4 and 8, and the 2019 assessment content at grade 12 was composed of questions that were transadapted from previous paper-based assessment questions as well as new, digitally based questions that were developed to take advantage of the new digital delivery system. Assessment content at grades 4, 8, and 12 were developed with the same mathematics frameworks used to develop the 2015 paper-based assessments.

Grades 4 and 8

The NAEP mathematics assessment at grades 4 and 8 transitioned from paper-based assessment (PBA) to digitally based assessment (DBA) in 2017. See a description of the 2017 NAEP transition. Technical details about the DBA transition are available in The 2017 NAEP Transition to Digitally Based Assessments in Mathematics and Reading at Grades 4 and 8: Mode Evaluation Study. Because the transition that placed the DBA results onto the trend line took place in 2017, the usual NAEP procedure of common item linking was used to calculate the trend line from 2017 to 2019. The 2019 results at grades 4 and 8 presented in this report are based on the performance of students who took the assessment on tablets. Approximately two-thirds of the questions from the 2019 DBA were also administered in the 2017 DBA.

Grade 12

The NAEP mathematics assessment at grade 12 was administered for the first time as a DBA in 2019; prior to 2019, PBAs were administered. Just as was done for the grades 4 and 8 assessments in 2017, a multistep process was used for the transition from PBA to DBA in order to preserve trend lines that show student performance over time. The transition process involved administering the assessment in both the DBA and PBA formats to randomly equivalent groups of twelfth-grade students in 2019. The results from DBA can therefore be compared to those from previous years, showing how students' performance in mathematics has changed over time. Read more about the grade 12 transition and mode evaluation.

At grade 12, approximately 60 percent of the questions from the 2015 PBA were adapted to the 2019 DBA. The previously used PBA questions were adapted to fit a tablet screen, but the mathematical content was not changed. The goal of adapting questions was to retain the same measurement targets as the original version of the question. Seven of the eleven assessment blocks administered in 2019 used only questions that had been adapted from PBA, and six of those seven blocks were assembled to be as similar as possible to their corresponding paper versions. Four of the eleven blocks at grade 12 consisted of questions newly developed for the 2019 digital administration.

In addition to the DBA, random subsamples of students were administered the complete 2015 paper-based version of the grade 12 assessment in 2019. NCES administered the assessment in both modes—paper-based and digitally based—in all the sampled schools to investigate potential differences in performance between students taking the assessment on a tablet and students taking the PBA. However, in schools with fewer than 21 students, all students were assigned to either DBA or PBA. Each participating student took the assessment in only one mode.

After the administration of the assessment at grade 12, NCES conducted rigorous analyses of the data and aligned the 2019 results to previous assessment years using a two-step process.

  • First, common item linking was used to calculate the trend line from 2015 to 2019 based on the PBA results. This kind of linking was possible because the majority of 2019 assessment questions were also administered in 2015 and showed the same statistical properties.
  • Second, common population linking was used to align the 2019 PBA results with the 2019 DBA results. This kind of linking was possible because the samples of students for each assessment mode were randomly equivalent; that is, each random sample included students from the same school, ensuring that the students' educational experiences and characteristics were equivalent.

Once the common population linking aligned the digital results to the paper results on the national level, the analyses evaluated whether the linking allowed for fair and meaningful comparisons for national student groups. These evaluations supported making trend comparisons between DBA and previous PBAs for student groups.

These analyses—common item linking based on paper results and common population linking of paper results to digital results—enabled NCES to successfully maintain the mathematics trend line while transitioning to the digital assessment in 2019. The 2019 grade 12 mathematics assessment results in this report are based on the combined performance of students who took the assessment on paper and students who took the assessment on tablets.