## Framework and Design

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. The grade 12 assessment measures four content areas; because most measurement topics suitable for twelfth-grade students are geometric in nature, geometry and measurement are combined into one content area.

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. The 2009 mathematics framework for grades 4 and 8 is similar to earlier frameworks that guided previous mathematics assessments, while the grade 12 framework underwent some changes to help NAEP report how well prepared twelfth-grade students are for postsecondary education and training. The results of a special analysis (2009 Mathematics Trend Study at Grade 12) determined that the trend line could be continued after the changes introduced in the 2009 framework.

### 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.

**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.

### 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.

## 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.