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- What the Assessment Measures

The National Assessment of Educational Progress (NAEP) mathematics assessment measures students' knowledge and skills in mathematics and students' ability to apply their knowledge in problem-solving situations. The NAEP frameworks provide the theoretical basis for the assessments and describe the types of questions that should be included and how they should be designed and scored. As with all NAEP frameworks, the mathematics framework was developed under the guidance of the National Assessment Governing Board. View a copy of the NAEP Mathematics Framework.

Although the frameworks are updated periodically, the mathematics content objectives for grades 4 and 8 have not changed, allowing students' performance in 2019 to be compared with previous years.

For 2005, the Governing Board adopted a new mathematics framework for grade 12 to reflect changes in high school standards and coursework. Additional changes were made for the 2009 assessment to facilitate reporting on twelfth-graders' preparedness for post-secondary education and training. Results from special analyses determined the 2009 grade 12 mathematics assessment results could be compared with those from 2005. Find out about changes to the 2009 assessment and how the 2005 mathematics framework compares with the 1990–2003 mathematics framework. To read more about the mathematics objectives used for previous assessments, explore the 1990–2003 mathematics framework.

The mathematics framework classifies assessment questions in two dimensions, content area and mathematical complexity, that are used to guide the assessment. Each question is designed to measure one of the five mathematics content areas.

- number properties and operations,
- measurement,
- geometry,
- data analysis, statistics, and probability, and
- algebra.

Certain aspects of mathematics, such as computation, occur in all content areas. Although the names of the content areas (as well as some topics in those areas) have changed from one framework to the next, a consistent focus has remained on measuring student performance in all five content areas. The distribution of questions among each content area differs by grade to reflect the knowledge and skills appropriate for each grade level. At grade 12, the measurement and geometry content areas are combined into one for reporting purposes to reflect the fact that the majority of measurement topics suitable for grade 12 students are geometric in nature. Students at grade 12 are provided with a reference sheet (919K PDF) containing selected formulas related to geometry, trigonometry, conic sections, interest rates, series, and combinations and permutations.

These divisions are not intended to separate mathematics into discrete elements. Rather, they are intended to provide a helpful classification scheme that describes the full spectrum of mathematical content assessed by NAEP.

Items are also classified by mathematical complexity.

- low complexity,
- moderate complexity, and
- high complexity

Mathematical complexity attempts to focus on the cognitive demands of the assessment question. Each level of complexity includes aspects of knowing and doing mathematics, such as reasoning, performing procedures, understanding concepts, or solving problems. The levels of complexity form an ordered description of the demands an item may make on a student. Items at the low level of complexity, for example, may ask a student to recall a property. At the moderate level, an item may ask the student to make a connection between two properties; at the high level, an item may ask a student to analyze the assumptions made in a mathematical model. This is an example of the distinctions made in item complexity to provide balance in the assessment. The ordering is not intended to imply that mathematics is learned or should be taught in such an ordered way.

The complexity dimension builds on the dimensions of mathematical ability (conceptual understanding, procedural knowledge, and problem solving) and mathematical power (reasoning, connections, and communication) that were used in the mathematics framework for the 1996-2003 NAEP assessments.

The mathematics framework specifies the percentage of questions devoted to each content area by grade.

Sample Questions booklets for the mathematics assessment are available for download.

The mathematics assessment contains some sections for which calculators are not allowed, and other sections that contain some questions that would be difficult to solve without a calculator. At each grade level, approximately two-thirds of the assessment measures students’ mathematical knowledge and skills without access to a calculator; the other third allow a calculator’s use. The type of calculator students may use varies by grade level, as follows:

- At grade 4, a four-function calculator is supplied to students, with training at the time of administration.
- At grades 8 and 12, students are allowed to bring whatever calculator, graphing or otherwise, they are accustomed to using in the classroom with some restrictions for test security purposes. For students who do not bring a calculator to use on the assessment, NAEP will provide a scientific calculator.

No questions in the test are designed to provide an advantage to students with a graphing calculator. Questions are categorized according to the degree to which a calculator is useful in responding to the item:

- A calculator inactive question is one whose solution neither requires nor suggests the use of a calculator.
- A calculator is not necessary for solving a calculator neutral question; however, given the option, some students might choose to use one.
- A calculator is necessary or very helpful in solving a calculator active question; a student would find it very difficult to solve the problem without the aid of a calculator.

Last updated 22 October 2019 (FW)