About the NAEP Mathematics Assessment
The NAEP Mathematics Assessment 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 and how the assessment questions should be designed and scored. The NAEP mathematics assessment framework specifies five broad content areas and three levels of mathematical complexity. Because most measurement topics suitable for twelfth-grade students are geometric in nature, geometry and measurement are combined into one for reporting.
The NAEP mathematics framework for grade 12 was updated in 2005. Changes were made to reflect adjustments in curricular emphasis and to ensure an appropriate balance of content. Due to these changes, the twelfth-grade mathematics results in 2005 and subsequent years cannot be compared to previous assessments necessitating the start of a new trend line beginning with the 2005 mathematics assessment.
Mathematics Content Areas
To ensure a balance of content and allow for a variety of ways of knowing and doing mathematics, the framework specifies assessing students in five broad areas of mathematical content. This division into content areas is not intended to separate mathematics into discrete elements, but to provide a helpful classification scheme that describes the full spectrum of mathematical content assessed by NAEP. At grade 12, the five content areas are collapsed into four, with geometry and measurement combined into one. This reflects the fact that the majority of measurement topics suitable for twelfth-grade students are geometric in nature.
Number properties and operations measures students' understanding of ways to represent, calculate, and estimate with numbers.
Measurement assesses students' knowledge of measurement for such attributes as capacity, length, area, volume, time, angles, and rates; this includes the use of instruments for measuring and the application of processes to solve problems.
Geometry measures students' knowledge and understanding of shapes in two and three dimensions and relationships between shapes, such as symmetry and transformations.
Data analysis, statistics, and probability measures students' understanding of data representation, characteristics of data sets, experiments and samples, and probability.
Algebra measures students' understanding of patterns, using variables, algebraic representation, relationships, and functions.
The table below shows the percentage distribution of NAEP mathematics questions by content area for the full 2024 assessment and for the subset of mathematics questions publicly released in 2024.
Table Percentage distribution of questions in NAEP mathematics assessment by mathematics content area: 2024
| NAEP Mathematics content areas | Grade 4 | Grade 8 | ||
|---|---|---|---|---|
| Percentage of questions released | Percentage of questions in full assessment | Percentage of questions released | Percentage of questions in full assessment | |
| Number properties and operations | 41 | 40 | 19 | 23 |
| Measurement | 22 | 17 | 16 | 16 |
| Geometry | 16 | 15 | 19 | 17 |
| Data analysis, statistics, and probability | 9 | 12 | 16 | 16 |
| Algebra | 13 | 16 | 31 | 28 |
Table Percentage distribution of questions in the NAEP grade 12 mathematics assessment by mathematics content area: 2024
| NAEP Mathematics content areas | Percentage of questions released | Percentage of questions in full assessment |
|---|---|---|
| Number properties and operations | 14 | 13 |
| Measurement and geometry | 31 | 30 |
| Data analysis, statistics, and probability | 20 | 24 |
| Algebra | 34 | 33 |
Levels of Mathematical Complexity
Each NAEP question assesses an objective that can be associated with one of the mathematics content areas. Each question also makes certain demands on students' thinking. These demands determine the mathematical complexity of an item. Mathematical complexity deals with what the students are asked to do in a question. Incorporating levels of complexity in assessment design allows for a balanced testing of mathematical thinking. The framework describes three levels of mathematical complexity.
Low-complexity questions typically specify what a student is to do, which usually involves carrying out a routine mathematical procedure.
Moderate-complexity questions involve more flexibility of thinking and often require a response with multiple steps.
High-complexity questions make heavier demands on students' thinking and often require abstract reasoning or analysis in a novel situation.
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. 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.