NAEP is an ongoing, congressionally mandated survey designed to measure what students know and can do. The goal of NAEP is to estimate educational achievement and changes in that achievement over time for American students of specified grades as well as for subpopulations defined by demographic characteristics and by specific background characteristics and experiences. In 1996, NAEP collected mathematics and science data from nationally representative samples of students in public and private schools in grades 4, 8, and 12. Additionally, directly comparable state assessments were conducted in public and private schools in participating states and jurisdictions at grade 4 for mathematics and at grade 8 for mathematics and science. For many of the states and jurisdictions the sample of private school students was not adequate to support reporting of private school results. Accordingly, state-level results were reported by NAEP for the public schools samples only. State-level NAEP mathematics and science results are available for grade 8 public school students in 44 states and jurisdictions.

TIMSS is the largest and most ambitious study ever conducted by the International Association for the Evaluation of Educational Achievement (IEA). TIMSS is an international comparative study designed to provide information about educational achievement and learning contexts for the participating countries. Each participating country assessed mathematics and science in the two grades with the largest proportion of 13-year-olds (grades 7 and 8 in most countries, including the United States). Mathematics and science results are available for 41 countries for the higher of these grade levels—which, for convenience, will be referred to as the grade 8 level in this report.

The U.S. results are based on a sample of students from public and private schools. In addition, three states opted to collect grade 8 TIMSS data from representative samples of their students. Minnesota participated in a state-level administration of grade 8 TIMSS mathematics and science in 1995, while Missouri and Oregon participated in state-level administrations of grade 8 TIMSS in 1997. All three states also participated in the 1996 State NAEP. Thus, released public school NAEP results are available for all three states, as well as released TIMSS results for Minnesota. However, the TIMSS results for Missouri and Oregon cannot be explicitly included in this report since those results have not yet been publicly released.

A number of key characteristics of the NAEP and TIMSS results have a bearing on the adequacy of any link between the two assessments. These include the following:

• Both NAEP and TIMSS are based on complex probability samples of the student population. Both U.S. samples include public and private students in grade 8. The sample sizes for the two assessments in the United States are similar, being 7,146 and 7,087 for NAEP and TIMSS grade 8 mathematics, and 7,774 and 7,087 for NAEP and TIMSS grade 8 science.
• TIMSS was conducted in the United States (and in most Northern Hemisphere countries) in April and May 1995. NAEP was conducted January through March 1996. Thus, the TIMSS results are applicable to the achievement of the 1995 student population at the end of the school year, while the NAEP results are applicable to the achievement of the 1996 student population some months before the end of the school year.
• The frameworks that defined the NAEP and TIMSS assessments are not identical but appear similar. Both assessments include multiple-choice and short- and extended-constructed response questions, but NAEP has a higher proportion of constructed response items than does TIMSS. The two assessments have no items in common. (Appendix A contains the results of a content analysis of the NAEP and TIMSS assessments.)
• In TIMSS, the same students participated in both the mathematics and science testing, with 90 minutes total testing time across the two subjects or 45 minutes for each. Both mathematics and science were mixed within each booklet. In NAEP, each sampled student received either a mathematics or a science instrument. Total testing time for the mathematics instrument was 45 minutes, comparable to TIMSS mathematics. Total testing time for NAEP science was 90 minutes at grade 8, including 30 minutes of hands-on tasks.
• Both NAEP and TIMSS scaled their data using Item Response Theory (IRT) techniques. TIMSS used a Rasch partial credit model to create a single scale for each subject, while NAEP used a variety of scaling models (two and three parameter logistic and generalized partial credit) to develop subscales for mathematics and science. NAEP mathematics and science composites were then created as weighted averages of the mathematics and science subscales. Both NAEP and TIMSS used methodology to account for the imprecision of measurement of individual students' abilities (plausible values). These allow for appropriate estimates for any subgroups contained in the conditioning model. However, grade 8 TIMSS only conditioned for grade within country, while NAEP conditioned on several hundred variables.

Clearly, while similar, the NAEP and TIMSS assessments do differ in ways that will impact the link between the two. The next section reviews the types of linking available and indicates what the NAEP-TIMSS link will be.