## 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.

### 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 fourth- and eighth-grade 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.

**Number properties and operations** measures studentsâ€™ understanding of ways to represent, calculate, and estimate with numbers.

**Measurement** assesses studentsâ€™ knowledge, including the use of instruments and the application of processes for attributes such as capacity, length, area, volume, time, angles, and rates.

**Geometry** measures studentsâ€™ 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 studentsâ€™ understanding of data representation, characteristics of data sets, experiments and samples, and probability.

**Algebra** measures studentsâ€™ understanding of patterns, using variables, algebraic representation, and functions.

### 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 studentsâ€™ 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 studentsâ€™ thinking and often require abstract reasoning or analysis in a novel situation.

## About the NAEP Mathematics Assessment

The National Assessment of Educational Progress (NAEP) mathematics assessment at grades 4 and 8 measures studentsâ€™ knowledge and skills in mathematics and their ability to solve problems in mathematical and real-world contexts. Results are reported for the nation overall, for states and jurisdictions, and for districts participating in the Trial Urban District Assessment (TUDA). In 2017, the NAEP mathematics assessment was administered for the first time as a digitally based assessment (DBA) at grades 4 and 8; prior to 2017, paper-based assessments (PBA) were administered. A multi-step process was used for the transition from PBA to DBA in order to preserve trend lines that show student performance over time. The process involved administering the assessment in both the DBA and PBA formats to randomly equivalent groups of students in 2017. The results from the 2017 assessment can therefore be compared to those from previous years, showing how studentsâ€™ performance in mathematics has changed over time.