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.
Survey Questionnaire Indices
As part of the NAEP mathematics assessment, survey questionnaires are given to students, teachers, and school administrators at grades 4 and 8 and to students and school administrators only at grade 12. These questionnaires collect contextual information to provide a better understanding of educational experiences and factors that are related to students' learning, both inside and outside of the classroom, and to allow for meaningful student group comparisons. Learn more about NAEP survey questionnaires.
The highlighted findings in this report demonstrate the range of information available from the NAEP mathematics survey questionnaires. They do not provide a complete picture of students' learning experiences inside and outside of school. The NAEP mathematics student, teacher, and school questionnaire data can be explored further using the NAEP Data Explorer. Explore the 2019 NAEP mathematics student (grade 4, grade 8, and grade 12), teacher (grade 4 and grade 8), and school (grade 4, grade 8, and grade 12) questionnaires.
NAEP survey questionnaire responses provide additional information for understanding NAEP performance results. Although comparisons in students' performance are made based on student, teacher, and school characteristics and educational experiences, these results cannot be used to establish a cause-and-effect relationship between the characteristics or experiences and student achievement. NAEP is not designed to identify the causes of performance differences. Therefore, results must be interpreted with caution. There are many factors that may influence average student achievement, including local educational policies and practices, the quality of teachers, available resources, and the demographic characteristics of the student body. Such factors may change over time and vary among student groups.
While some survey questions are analyzed and reported individually (for example, the numbers of books in students' homes), several questions on the same topic are combined into an index measuring a single underlying construct or concept. More information about the 2019 NAEP mathematics indices and their corresponding questions can be found in the 2019 NAEP mathematics student (grade 4, grade 8, and grade 12) questionnaires.
The creation of 2019 indices involved the following four main steps:
- Selection of constructs of interest. The selection of constructs of interest to be measured through the survey questionnaires was guided in part by the National Assessment Governing Board framework for collection and reporting of contextual information. In addition, NCES reviewed relevant literature on key contextual factors linked to student achievement in mathematics to identify the types of survey questions and constructs needed to examine these factors in the NAEP assessment.
- Question development. Survey questions were drafted, reviewed, and revised. Throughout the development process, the survey questions were reviewed by external advisory groups that included survey experts, subject-area experts, teachers, educational researchers, and statisticians. As noted above, some questions were drafted and revised with the intent of analyzing and reporting them individually; others were drafted and revised with the intent of combining them into indices measuring constructs of interest.
- Evaluation of questions. New and revised survey questions underwent pretesting, whereby a small sample of participants (students, teachers, and school administrators) are interviewed to identify potential issues with their understanding of the questions and their ability to provide reliable and valid responses. Some questions were dropped or further revised based on the pretesting results. The questions were then further pretested among a larger group of participants and responses were analyzed. The overall distribution of responses was examined to evaluate whether participants were answering the questions as expected. Relationships between survey responses and student performance were also examined. A method known as factor analysis was used to examine the empirical relationships among questions to be included in the indices measuring constructs of interest. Factor analysis can show, based on relationships among responses to the questions, how strongly the questions "group together" as a measure of the same construct. Convergent and discriminant validity of the construct with respect to other constructs of interest were also examined. If the construct of interest had the expected pattern of relationships and non-relationships, the construct validity of the factor as representing the intended index was supported.
- Index scoring. Using the item response theory (IRT) partial credit scaling model, index scores were estimated from students' responses and transformed onto a scale that ranged from 0 to 20. As a reporting aid, each index scale was divided into low, moderate, and high index score categories. The cut points for the index score categories were determined based on the average response to the set of survey questions in each index. In general, high-average responses to individual questions correspond to high index score values, and low-average responses to individual questions correspond to low index score values. As an example, for a set of index survey questions with five response categories (such as not at all, a little bit, somewhat, quite a bit, and very much), students with an average response of less than 3 (somewhat) would be classified as low on the index. Students with an average response greater than or equal to 3 (somewhat) to less than 4 (quite a bit) would be classified as moderate on the index. Finally, students with an average response of greater than or equal to 4 (quite a bit) would be classified as high on the index.