• Introduction
• Major Findings for the Nation
• Major Findings for the States and Other Jurisdictions
• National Results for Student Subgroups
• Home and School Contexts for Mathematics Performance
• Sample Mathematics Questions and Student Responses

The National Assessment of Educational Progress (NAEP) is the nation's only ongoing representative sample survey of student achievement in core subject areas. Authorized by Congress and administered by the National Center for Education Statistics (NCES) in the U.S. Department of Education, NAEP regularly reports to the public on the educational progress of students in grades 4, 8, and 12.

In 2000, NAEP conducted a national mathematics assessment of fourth-, eighth-, and twelfth-grade students. State-level results were also collected at the fourth and eighth grades within participating states and jurisdictions. This article presents highlights from the NAEP 2000 Mathematics Assessment for the nation and the states. Results in 2000 are compared to results in 1990, 1992, and 1996. Following the performance results are several sample questions and student responses typical of those from recent NAEP mathematics assessments.

Students' performance on the assessment is described in terms of average scores on a 0-500 scale and in terms of the percentages of students attaining three achievement levels: Basic, Proficient, and Advanced. The achievement levels are performance standards adopted by the National Assessment Governing Board (NAGB) as part of its statutory responsibilities. The achievement levels are collective judgments of what students should know and be able to do:

• Basic denotes partial mastery of prerequisite knowledge and skills that are fundamental for proficient work at each grade.
• Proficient represents solid academic performance for each grade assessed. Students reaching this level have demonstrated competency over challenging subject matter, including subject-matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to the subject matter.
• Advanced signifies superior performance.

In addition to providing average scores and achievement level performance at the national and state levels, this article includes national results for selected subgroups of students as well as a discussion of home and school contexts for mathematics performance. However, this article does not include results for a second sample of students assessed at both the national and state levels—one in which testing accommodations were provided to students with special needs (i.e., students with disabilities or students with limited English proficiency). For results that include the performance of special-needs students who were assessed with accommodations, see the complete report, The Nation's Report Card: Mathematics 2000. Such results were omitted from the highlights presented in this article in order to allow comparisons with past assessment results, which did not include accommodated students.

National results are for students attending both public and nonpublic schools.

Results for the NAEP 2000 Mathematics Assessment show overall gains in fourth-, eighth-, and twelfth-graders' national average scores since 1990, the first year in which the current mathematics assessment was administered (figure A). Fourth- and eighth-graders made steady progress, with higher average scores in 2000 than in 1996, 1992, or 1990. However, this was not the case for twelfth-graders. Although twelfth-graders' average score was higher in 2000 than in 1990, it was lower in 2000 than in 1996.

Figure A.—Average mathematics scores, grades 4, 8, and 12: 1990-2000

The percentages of fourth- and eighth-graders at or above Basic and at or above Proficient increased across the decade, reaching their highest levels in both grades in 2000 (figure B). At grade 12, the results are mixed. From 1996 to 2000, there was a decrease in the percentage at or above Basic. However, the percentage of twelfth-graders at or above both Basic and Proficient was higher in 2000 than in 1990.

Figure B.—Percentage of students within and at or above the mathematics achievement levels, grades 4, 8, and 12: 1990-2000

• The italicized percentages to the right of the shaded bars represent the percentages of students at or above Basic and Proficient.
• The percentages in the shaded bars represent the percentages of students within each achievement level.

The gains in average mathematics scores at all three grades since 1990 are reflected in students' performance across the score distribution. Lower-, middle-, and higher-performing students had higher scores in 2000 than in 1990 (figure C). This finding is the result of analyzing scores at percentiles—or points across the score distribution—on the NAEP mathematics scale.

Figure C.—Average mathematics scores by percentile, grades 4, 8, and 12: 1990-2000

The score increases seen since 1990 for fourth-, eighth-, and twelfth-graders were evident across the score distribution (at the 10th, 25th, 50th, 75th, and 90th percentiles). However, the decline at grade 12 since 1996 occurred at the lower and middle points of the distribution (at the 10th, 25th, and 50th percentiles).

In addition to national results on students' mathematics performance, the 2000 assessment collected performance data for fourth- and eighth-graders who attended public schools in states and other jurisdictions that volunteered to participate. State-level data have been collected since 1992 at grade 4 and since 1990 at grade 8. In 2000, 40 states and 6 other jurisdictions participated at grade 4, and 39 states and 5 other jurisdictions participated at grade 8. The results of the state assessment are only for students attending public schools.

Of the 36 states and jurisdictions that participated in both 2000 and the first state assessment at grade 4 in 1992, 26 had higher average scores in 2000 than in 1992. Of the 31 states and jurisdictions that participated in both 2000 and the first state assessment at grade 8 in 1990, 27 had higher average scores in 2000 than in 1990.

In 2000, no state scored higher at grade 4 than these nine: Connecticut, Indiana, Iowa, Kansas, Massachusetts, Minnesota, North Carolina, Texas, and Vermont. Figure D shows states' and other jurisdictions' 2000 average score performance in comparison to the national average score for public schools. Of the 46 states and jurisdictions that participated in the 2000 assessment at grade 4, 14 had scores that were higher than the national average score, 14 had scores that were not different from the national average, and 18 had scores that were lower than the national average.

Figure D.—State versus national average mathematics scores, grade 4 public schools: 2000

In 2000, no state scored higher at grade 8 than these three: Kansas, Minnesota, and Montana. Figure E shows that of the 44 states and other jurisdictions that participated in the 2000 assessment at grade 8, 16 had scores that were higher than the national average score, 13 had scores that were not different from the national average, and 15 had scores that were lower than the national average.

Figure E.—State versus national average mathematics scores, grade 8 public schools: 2000

At grade 4, 4 states and other jurisdictions had higher percentages of students at or above Proficient than did the nation, 23 had percentages that were not different from the percentage for the nation, and 19 had percentages that were lower than that for the nation. At grade 8, 13 states and other jurisdictions had higher percentages of students at or above Proficient than did the nation, 12 had percentages that were not different from the percentage for the nation, and 19 had percentages that were lower than that for the nation.

In addition to presenting information about all students' performance, NAEP also looks at the achievement of various subgroups of students. The performance of various racial/ethnic subgroups and of males and females reveals how these students did in comparison to each other in the year 2000 and whether they progressed over the past decade. While the complete report describes the performance of student subgroups at both the state and national levels, the highlights in this article are for the nation only.

When reading these results, it is important to keep in mind that there is no simple, causal relationship between membership in a subgroup and mathematics achievement. A complex mix of educational and socioeconomic factors may interact to affect student performance.

Of the five racial/ethnic subgroups of students identified in the 2000 mathematics assessment, three—White, Black, and Hispanic—had average scores that showed overall gains since 1990. While White students were the only subgroup whose average scores were higher in 2000 than in 1990 at all three grades, Black and Hispanic students' average scores were higher than in 1990 at grades 4 and 8.

Comparing performance across the subgroups of students in 2000 shows that White and Asian/Pacific Islander students scored higher, on average, than Black, Hispanic, and American Indian students at grades 8 and 12. Asian/Pacific Islander students scored higher than White students at grade 12.

Across the assessments from 1990 to 2000, the score gaps between White and Black students and between White and Hispanic students were large at every grade. There was no evidence in the 2000 assessment of any narrowing of the racial/ethnic group score gaps since 1990.

The mathematics achievement of students in the racial/ethnic subgroups was similar to their average score performance—while there were improvements over the past 10 years, not all groups improved at all grades. At grade 4, higher percentages of White, Black, Hispanic, and American Indian students performed at or above the Proficient level in 2000 than in 1990. There were also higher percentages of White, Black, and Hispanic students at or above the Basic level in 2000 than in 1990 or 1992.

At grade 8, more White and Hispanic students were at or above Proficient in 2000 than in 1990, and more White, Black, and Hispanic students were at or above Proficient in 2000 than in 1992. At or above the Basic level, there were higher percentages of White, Black, and Hispanic eighth-graders in 2000 than in 1990 or 1992.

There were few changes over the decade for twelfth-graders; only White students had higher percentages at or above the Proficient level in 2000 than in 1990. There were also higher percentages of White students at or above the Basic level in 2000 than in 1990.

Comparing the subgroups' 2000 performance shows that, in general, the percentages at or above the Basic achievement level were higher for White and Asian/Pacific Islander students than for the other subgroups of students.

At all three grades, both males and females had higher scores in 2000 than they did in 1990 and, at grade 4, they both showed relatively steady improvement across the four assessments from 1990 to 2000.

In 2000, males outperformed females in mathematics at grades 8 and 12. There was no significant difference between males' and females' average scores at grade 4.

The gap between the average scores of males and females was quite small at all three grades and fluctuated only slightly across the assessments from 1990 to 2000.

At grade 4, there were higher percentages of both males and females at or above Proficient and at or above Basic in 2000 than in 1990, 1992, or 1996.

At grade 8, there were higher percentages of both males and females at or above Proficient in 2000 than in 1990 and 1992, and a higher percentage of males at or above Proficient than in 1996. There were also more male and female eighth-graders at or above Basic in 2000 than in 1990 or 1992, and more male eighth-graders at or above Basic than in 1996.

At grade 12, there were higher percentages of males and females at or above Proficient in 2000 than in 1990. There was a decline in the percentage of both male and female twelfth-graders at or above Basic in 2000 compared to 1996, although both groups' percentages were up in 2000 over 1990.

A comparison of males' and females' results in 2000 shows that there were higher percentages of males at or above Proficient at grades 4, 8, and 12.

Many factors influence students' learning. Activities that take place while students are either at school or at home as well as the attitudes they develop about learning mathematics may enhance or detract from their ability to do math. The NAEP 2000 Mathematics Assessment focused on students' performance in light of responses to questions about mathematics activities at school and at home and attitudes toward mathematics. While these findings may suggest a positive or negative relationship between performance on the mathematics assessment and certain activities or attitudes, it is important to remember that the relationships are not necessarily causal—there are many factors that play a role in mathematics performance.

Results from the 2000 mathematics assessment suggest a relationship between student-reported calculator use for classwork and mathematics performance that is markedly different at grade 4 than at grades 8 and 12. At grade 4, more frequent calculator use was associated with lower scores, while at grades 8 and 12 the opposite was generally true: students who said they use calculators more often tended to score higher than their peers who reported using them less frequently (figure F).

In mathematics, as in other subjects assessed by NAEP, most students who spent time doing homework every day scored higher than those who did not do homework. Only at grade 4, where homework demands are light in comparison to higher grades, did students who reported spending an hour or more on homework score lower than their peers who did not do homework. How much time in general is associated with higher mathematics performance on NAEP? Results from the 2000 mathematics assessment suggest that at grades 4 and 8, a moderate amount of time—between 15 and 45 minutes depending on grade level—is associated with a higher average score on NAEP than a longer time of 1 hour or more. This was not the case at grade 12, where there was no statistically significant difference in the performance of students spending any time between 15 minutes and 1 hour or more on mathematics homework.

The attitudes of students who took the NAEP mathematics assessment were strongly related to their performance. Students who participated in the 2000 assessment were asked to consider several statements about mathematics designed to gauge their attitudes toward the subject. The results for two of those statements are presented here: At all three grade levels, students who agreed that they like math and that math is useful for solving problems scored higher than students who disagreed with these statements.

Figure F.—Average mathematics scores by frequency of calculator use for classwork, grades 4, 8, and 12: 2000