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NAEP 1996 Mathematics Cross-State Data Compendium for Grade 4 and Grade 8 Assessment

December 1997


Authors: Catherine A. Shaughnessy, Jennifer E. Nelson, and Norma A. Norris

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Introduction

The National Assessment of Educational Progress (NAEP) is a congressionally mandated project of the National Center for Education Statistics (NCES) that has, for more than a quarter of a century, continually collected and reported information on what American students know and can do. It is the nation’s only ongoing, comparable, and representative assessment of student achievement. Its assessments are based on a national probability sample of public and nonpublic school students enrolled in grades 4, 8, or 12. Results are provided only for group performance. NAEP is forbidden by law to report results at an individual or school level. The assessment questions are written around a framework prepared for each content area -- reading, writing, mathematics, science and others -- that represents the consensus of groups of curriculum experts, educators, and members of the general public on what should be covered in such a test. In addition, students, their teachers, and their schools are asked to fill out questionnaires, to gather information on student demographics, teacher preparation, instructional practices, school policies, and out-of-school activities related to educational achievement.

In response to legislation passed by Congress in 1988, the NAEP program includes voluntary state-by-state assessments. The state assessment program was initiated in 1990 on a trial basis with the assessment of mathematics achievement of eighth-grade students in public schools. The 1992 Trial State Assessment (TSA) assessed public school students in fourth-and eighth-grade mathematics and fourth-grade reading. In 1994, 44 jurisdictions participated in a fourth-grade reading assessment. Because of the positive evaluations of the 1990, 1992, and 1994 TSAs, the 'trial' designation has been removed from the 1996 state-level NAEP assessment. The NAEP 1996 Mathematics State Assessment Program was comprised of a state-by-state mathematics assessment of fourth- and eighth-grade students enrolled in both public and nonpublic schools, with 48 jurisdictions participating in this assessment program, for at least one of the grade levels.

Because the NAEP State Assessments are voluntary, the participating jurisdictions have the final authority to release or withhold their results. All jurisdictions gave permission to have their results released. To help ensure valid state-by-state results, the 1996 State Assessment Program continued the use of minimum school and student participation rate standards (see Appendix A for details) for its reporting activities. Results are not reported for jurisdictions that failed to meet these standards. Three states -- Nevada, New Hampshire, and New Jersey -- did not meet the minimum school participation standards for public schools; therefore, their grade 8 public school results are not presented in this report. Several other states failed to meet more stringent participation rate standards; results for these jurisdictions are included in the report and are noted in the relevant tables in Appendix A.

Figure 1: Participating Jurisdictions in the NAEP 1996 State Assessment Program in Mathematics

This is the first of two data compendia from the 1996 NAEP State Assessment. Science data will be presented in a separate report. This compendium presents fourth- and eighth-grade cross-state results of the NAEP 1996 State Assessment in mathematics; no interpretations of the data are made in this document. It contains tables of cross-state information for the variables discussed in the NAEP 1996 Mathematics Report Card for the Nation and States and the NAEP 1996 Mathematics State Report and is intended to be used as a companion document to these reports. The results for the nation and the regions of the country are based on the nationally and regionally representative samples of public and nonpublic school students who were assessed as part of the national NAEP program. Using the regional and national results from the 1996 national NAEP program is necessary because of the voluntary nature of the State Assessment Program. Since not every state participated in the program, the aggregated data across states did not necessarily provide representative national and regional results. General information about the instrumentation, sampling, data collection, and analysis procedures for the State Assessment Program can be found in the NAEP 1996 individual state reports (Appendices A and C), in Appendix A of this report, and in the Technical Report of the NAEP 1996 State Assessment Program in Mathematics. [1]

Another significant purpose of this compendium is to make available revised results from comparable assessments conducted in 1990 (grade 8 only) and 1992 (both grades 4 and 8) for the nation and states and territories that participated in the 1996 state assessment and met established participation guidelines. The revisions were required because of two technical problems that were discovered in the procedures that were originally used to develop the NAEP mathematics scale and achievement levels determined for the 1990 and 1992 mathematics assessments. These problems were discovered after the NAEP 1994 assessment had been conducted and subsequent to the publication of the 1990 and 1992 mathematics reports. The first technical problem resulted from an error in the computer program used to compute NAEP scale score results. The second technical problem involved the development of the NAEP mathematics achievement level cut scores. The technical errors are described in further detail in Appendix A and in the Technical Report of the NAEP 1996 State Assessment Program in Mathematics. [2] Although the impact on results of those technical errors was small, both have been corrected and the revised national and state scale score results for 1992 and achievement level results for 1990 and 1992 are presented in this data compendium, as well as all other 1996 NAEP mathematics reports. Note that the corrected 1990 and 1992 data in this compendia supercedes previously released NAEP State Mathematics data for these assessment years.

Chapter 1 presents the results for the nation, the four regions, and the participating jurisdictions in the context of the overall average mathematics scale scores and scale scores for content strands and type of school. Chapter 2 presents scale score information for selected population subgroups: gender, race/ethnicity, parents’ highest education level, Title I participation, free/reduced-price lunch program eligibility, and type of location.

Chapter 3 presents achievement levels for the nation and the states. Chapter 4 presents achievement levels by the same population subgroups given in Chapter 2. Chapters 5 through 8 contain results by background information collected from the student, teacher, and school characteristics and policies questionnaires. In particular, school characteristics related to mathematics instruction are examined in Chapter 5, and Chapter 6 reports on classroom practices related to mathematics instruction. Chapter 7 covers potential influences beyond school that facilitate learning mathematics, and Chapter 8 pertains to teacher preparation.

Each chapter contains a section presenting the grade 4 results, followed by a section presenting the grade 8 results. It is important to note that for a few student, teacher, and school background questions, results from previous assessments cannot be reported due to substantial changes in item format or wording. For example, results cannot be reported separately for the racial/ethnic categories of Asian and Pacific Islander because in 1992, they were combined into a single response option.


How to Read the Tables in This Report

The title for each table indicates: (1) assessment year, grade, and school-type sample for which results are being presented; (2) the reported statistics (e.g. average scale scores, achievement level percentages, or percentiles); and (3) when appropriate, the variables by which results are broken out. The abbreviation SS found in the column heading of the tables denotes average overall composite mathematics scale score with the exception of Table 1.1, where it denotes the average overall scale score, as well as the scale scores for the indicated percentiles, and Table 1.2, where it denotes the average scale score for the Mathematics content strands. The standard error of the percentages and scale scores appears in parentheses and is abbreviated SE. The participating jurisdictions appear in the left margin, as follows: the nation and four regions of the United States; the participating states listed in alphabetical order; and other jurisdictions, including Department of Defense Domestic Dependent Elementary and Secondary Schools (DDESS), Department of Defense Dependents Schools (DoDDS), and Guam.

The national and regional results presented in this report are based on nationally representative probability samples of fourth- and eighth-grade students. The sample was selected using a complex multistage sampling design involving the sampling of students from selected schools within selected geographic areas across the country. The results of the 1996 State Assessment Program provided in the report are based on state-level samples of fourth-and eighth-grade, public school students. The samples were selected based on a two-stage sample design selection of schools within participating states and selection of students within schools. The first-stage samples of schools were selected with probability proportional to the fourth- and eighth-grade enrollments in the schools. Special procedures were used for states with many small schools, and for jurisdictions having a small number of schools.


Cautions in Interpretations

The reader is cautioned against making simple or causal inferences related to population subgroup membership, background variables, effectiveness of public and nonpublic schools, and state educational systems. For example, differences observed among racial/ethnic subgroups can almost certainly be associated with a broad range of socioeconomic and educational factors not discussed in this report and possibly not addressed by the NAEP assessment program. Similarly, differences between public and nonpublic schools may be better understood after accounting for factors such as composition of the student body, parents’ education levels, and parental interest. Finally, differences in mathematics performance among states most likely reflect an interaction between the effectiveness of the educational programs within the state and the challenges posed by economic constraints and student demographic demands.


  1. Allen, N.L., Jenkins, F., Kulick, E. & Zelenak, C.A. (1997). Technical report of the NAEP 1996 state assessment program in mathematics. Washington, DC: National Center for Education Statistics

  2. Ibid.


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NCES 98-481 Ordering information

Last updated 22 March 2001 (RH)

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