For every subject assessed, the NAEP program reports how well students of various demographic groups performed. (Note that NAEP does not report individual student scores.) For example, results are reported for male students and female students, for students of various racial or ethnic categories, and for students in schools in different regions.
How does NAEP summarize what students in these groups know and can do, in order to be able to compare how the groups performed?
In mathematics, NAEP has created a scale ranging from 0–500 at grades 4 and 8 and a scale from 0–300 at grade 12, based on statistical procedures called Item Response Theory (IRT). IRT is a set of statistical procedures useful in summarizing student performance across a collection of test exercises requiring similar knowledge and skills. All NAEP subject-area scales are produced using these procedures. In 2005, the scale for grade 12 was changed to 0–300. The new mathematics framework for 2005 initiated minor changes at grades 4 and 8 and more substantial changes at grade 12. This means that trend may be maintained at the lower grades but a new trend line must be established at grade 12. To maintain consistency with past reporting of grade 4 and 8 results, the results since 2005 are reported on the 0–500 scale.
The mathematics data are scaled separately by the content areas. The composite scale is a weighted combination of these subscales. IRT information functions are only strictly comparable when the item parameters are estimated together. Because the composite scale is based on separate estimation runs, there is no direct way to compare the information provided by the questions on the composite scale.
To give meaning to the levels of the scale, it is useful to create an "item map." An item map is a representation of the skills and abilities demonstrated by students at various levels of the NAEP mathematics scale. The map indicates which kinds of questions students are likely to answer correctly at each level on the scale. View the NAEP mathematics item maps.