Dr. Gary W. Phillips
Acting Commissioner of the National Center for Education Statistics
The Release of the National Assessment of Educational Progress (NAEP)
The Nation's Report Card Mathematics 2000
August 2, 2001
In 2000, NCES conducted the National Assessment of Educational Progress (NAEP) in mathematics at the national level among fourth-, eighth-, and twelfth-grade students, and at the State level among fourth and eighth grade students within participating states and jurisdictions.
The NAEP mathematics assessment was based upon a framework developed by the National Assessment Governing Board. This framework was originally developed for the 1990 assessment, and used as a basis for the 1992, 1996, and 2000 assessments. The 2000 data are comparable with three previous assessments.
Results for the 2000 assessment are available for the nation and participating states. National results are based on nationally representative samples of students at grades 4, 8, and 12. Results for individual states and other jurisdictions are available for grades 4 and 8. In addition to data for 2000, grade 4 data for individual jurisdictions are shown for 1992 and 1996, while grade 8 data are given for 1990, 1992, and 1996
The Math Report Card also provides results for subgroups of students defined by various background and contextual characteristics. Furthermore, the report contains results for a second sample in which testing accommodations were provided to students with special needs (students with disabilities or limited English proficient students).
The number of students assessed in 2000 totaled about 250,000 students. These included about 50,000 in the national samples at grades 4, 8, and 12, while the state samples total about 200,000 for grades 4 and 8 combined.
In the national sample, approximately 14,000 fourth-graders from 742 schools, 16,000 eighth-graders from 744 schools, and 13,000 twelfth-graders from 558 schools were assessed. In the state assessment, approximately 100,000 students at each of grades 4 and 8 were assessed. Approximately 2,500 students from about 100 schools in each jurisdiction participated at each grade.
A Cautionary Note on Interpreting the Results
Please note that because NAEP scores are based on samples, there is a margin of error associated with each score. When we make comparisons between scores, or compare the percentages of students at the various achievement levels, we must test the differences to see if they are larger than the margin of error involved-differences that we call statistically significant. NCES only discusses statistically significant differences.
Content of the 2000 Mathematics Assessment
The NAEP mathematics framework identified five content strands for mathematics. These are:
Results Reported from the 2000 Mathematics Assessment
Mathematics performance of students is reported in two ways: 1) as average scale scores, and 2) as percents of students performing at or above various achievement levels. An average scale score reflects the overall mathematics performance of a particular group or subgroup of students. Results are also reported according to three mathematics achievement levels established by the National Assessment Governing Board, which establishes policy for NAEP. These achievement levels are intended to describe standards for what students should know and be able to do. The three achievement levels are defined as Basic, Proficient, and Advanced. NAGB believes that all students should be performing at or above the Proficient level.
National Scale Score Results Across Years
The NAEP mathematics scale runs from 0 to 500. The scale covers all three grades. The average scores at all three grades assessed were higher in 2000 than it was in 1990 (grade 4: 228 vs. 213; grade 8: 275 vs. 263; grade 12: 301 vs. 294). At both the 4th and 8th grades, scores in 2000 were also higher than in the last assessment, in 1996 (grade 4: 228 vs. 224; grade 8: 275 vs. 272). For 12th graders, results were somewhat mixed. Twelfth-graders have made progress over the decade as a whole, but their scores have come down a bit since 1996 (from 304 to 301).
National Scale Score Percentiles Across Years
In addition to presenting average scores, the results are presented for students at various levels of performance, or percentiles. The report indicates performance trends for students scoring at the 10th, 25th, 50th, 75th, and 90th percentiles in each grade. At grade 4, students at all five different percentile levels show increased scores in 2000 as compared to 1990, 1992, and 1996. At grade 8, there are similar increases over both 1990 and 1992, but only students in the 50th percentile show an increase over 1996.
At the 12th grade the pattern is different. All five percentile levels show an increase over 1990, but none show an increase over 1992, and the three lowest levels show a decline since 1996.
National Achievement Level Results Across Years
In terms of the percent of students attaining the Basic, Proficient, and Advanced achievement levels, there is a similar pattern of improvement at grade 4. A declining percentage of students were "below Basic," falling from 50 percent in 1990 to 31 percent in 2000. Most students were at or above Basic (69 percent in 2000). The percentage at or above Proficient doubled from 1990 to 2000, increasing from 13 percent to 26 percent. And the percentage at Advanced increased from 1 percent to 3 percent over the same time period.
Results were similar for grade 8-an increase in the percentages at or above Basic from 52 percent in 1990 to 66 percent in 2000; an increase in the percentage at or above Proficient from 15 percent in 1990 to 27 percent in 2000; and an increase in the percentage at Advanced from 2 percent in 1990 to 5 percent in 2000.
For 12th grade, we see mixed results once more-student performance was better than in 1990, but not as good as in 1996. Fifty-eight percent of 12th graders were at or above Basic in 1990. This percentage rose to 69 percent in 1996 but then fell to 65 percent in 2000. At the same time, the percentage at or above Proficient was higher in 2000 than in 1990 (17 percent as compared to 12 percent) and did not show a decline compared to 1996.
Average Scale Scores Across Years by Gender
Average performance patterns for male and female students are quite similar to those for students overall. Scores for 4th-grade males and females increased steadily over time (males: 229 in 2000 vs. 214 in 1990; females: 226 in 2000 vs. 213 in 1990). At grade 8, however, males showed an increase over 1996 (from 272 to 277) while females did not, and at grade 12, females showed a decline from 1996 (from 303 to 299) while males did not.
Gender Gaps in Average Scale Scores Across Years
Gaps in scores for males and females were quite small for all three grades, only 3 or 4 points in 2000, and there has been little change since 1990 in these gaps.
Average Scale Scores Across Years by Race/Ethnicity
Average scores of race and ethnic groups followed patterns similar to those for overall scores, with some differences. For example, white students at all three grades showed a long-term gain from 1990 to 2000 (grade 4: 220 vs.236; grade 8: 270 vs.286; grade 12: 301 vs. 308).
For black students, we see a long-term increase at the 4th and 8th grades (grade 4: 189 vs. 205; grade 8: 238 vs. 247 in 1990 and 2000 respectively), but none for 12th graders (268 vs. 274. We see a similar pattern of increase for Hispanic students at grades 4 and 8 (grade 4: 198 to 212; grade 8: 244 to 253), but no significant increase at grade 12 (276 to 283-the apparent change was not significant).
Asians and Pacific Islanders are a very small percentage of the student population, and their scores show no statistically significant change over time (grade 8: 279 vs. 288; grade 12: 311 vs. 319 in 1990 and 2000 respectively). The 4th-grade score for 2000 and the 8th grade score for 1996 for Asians and Pacific Islanders are omitted from the report because of concerns about the accuracy of the data.
American Indians, like Asians and Pacific Islanders, are a small percentage of the student population, and once again the data show no significant changes (grade 4: 208 vs. 216; grade 8: 246 vs. 255 in 1990 and 2000 respectively). The sample sizes for American Indian 12th graders in 1990 and 1992 were so small that we have omitted scores for those years.
Racial/Ethnic Gaps in Average Scale Scores Across Years
The Report Card contains charts showing the gaps in scores between whites and blacks, and between whites and Hispanics across the decade. The gaps are substantial. The white-black gap ranges from 31 to 39 points in 2000 across the three grades. The white-Hispanic gap ranges from 24 to 33 points. These gaps have not changed significantly across the past four assessments for any of the grades.
State Results: Grade 4
The NAEP 2000 Mathematics Assessment assessed the performance of 4th graders in 46 states and other jurisdictions. The report presents a state map that shows changes in performance by state for 4th graders in the 36 states and jurisdictions that participated in both the 1992 and 2000 assessments. The 1992 mathematics assessment was the first to obtain state-level data for 4th graders. In 26 of these jurisdictions, scores were higher in 2000 than in 1992. One jurisdiction, the Pacific island of Guam, recorded a decrease from 1992 to 2000. Between 1996 and 2000, eleven states and jurisdictions out of 39 that participated in the assessment in both years showed an increase, while most states others showed no change. No state or jurisdiction declined.
State Results: Grade 8
For 8th graders, of the 31 states and jurisdictions that participated in both the 1990 and 2000 assessments, 27 showed significant gains, four showed no change and none declined. Of the 37 states and jurisdictions that participated at grade 8 in the 1996 and 2000 assessments, 13 showed an increase in performance. The other 24 did not change.
Background Factors
In addition to assessing performance in mathematics, data are collected in NAEP on student, teacher, and school characteristics that may be related to performance. Some of those factors that showed an association with performance are discussed below.
Current Mathematics Course: Grade 8
The NAEP data indicate a clear relation between eighth-grade students' scores and their current mathematics course. Students taking pre-algebra performed better in 2000 than students taking what is called "8th-grade math" (270 vs. 264) and students taking first-year algebra do better than those taking pre-algebra (301 vs. 270).
There were few differences in course-taking patterns between males and females. The percentages of males and females taking 8th-grade math, pre-algebra, and algebra were similar.
There was more variation in course-taking patterns between race and ethnic groups, and these patterns correspond to variations in performance. Blacks and Hispanics are less likely to take first-year algebra than whites and Asians and Pacific Islanders, and they are more likely to take 8th-grade math. (These data, though not in the Math Report Card, can be found on the NAEP website)
Teachers' Report of Total Years Taught: Grades 4 and 8
At the 4th-grade level, the number of years taught had no effect on student performance. Students whose teachers had two years of experience or less had scores that were no different than students whose teachers had been teaching for decades. At the 8th-grade level, students whose teachers had taught 11 to 24 years, or 25 years or more, outperformed students whose teachers had no more than two years of experience (278 and 282 vs. 270). However, it should be pointed out that many school systems allow teachers with seniority to choose which school and which classes they will teach. It may be that experienced teachers are, in effect, choosing to teach higher-performing students. As has been mentioned, NAEP data can indicate relationships, but do not indicate causality.
Teachers' Report of Calculator Use: Grades 4 and 8
Scores for 8th graders whose teachers reported calculator use at least weekly outperformed less frequent calculator users. However, scores for 4th graders remained constant whether students used calculators every day or they never used them.
Students' Report of Frequency of Calculator Use For Classwork
In contrast to the relationship between student scores in 2000 and calculator use as reported by teachers, at the 4th grade, students who reported using a calculator every day had lower scores than their peers who reported less frequent use of calculators. At the 8th and 12th grade, however, students who used a calculator every day had higher scores than other students.
Students' Report of Time Spent Daily On Homework
There is no direct relationship between the amount of time spent on daily homework and student scores. In general, students who spent about 15 minutes a day on mathematics homework had scores as high or higher than any other group of students, at all three grades. Students who did not do homework at all had lower scores. Students who reported spending more than an hour a day had relatively low scores at both the 4th and 8th grades. These may have been students who were having problems with mathematics.
Student-Reported Attitudes Toward Mathematics
Students were asked several questions about their attitudes toward mathematics. Students who reported they like mathematics performed better than those who disagreed with this statement, at all three grades. Students who agreed that math is useful for solving problems outperformed those who disagreed. Further, students who disagreed that math is mostly memorizing facts or that there is only one way to solve a problem attained higher scores than students who agreed with these statements.
Accommodations Permitted in the 2000 Mathematics Assessment
The NAEP 2000 results, for the first time in mathematics, include data from students who received accommodations. Beginning in 2000, NCES has allowed accommodations for the NAEP mathematics assessment for students with disabilities and limited English proficient students who could not otherwise participate in the assessment. For the NAEP 2000 mathematics assessment, NCES allowed most accommodations that students used in their usual classroom testing. The following types of accommodations were used most frequently: one-on-one testing; small-group testing; extended time; bilingual English-Spanish test booklet; read-aloud; large-print book; and use of an aide for transcribing responses.
NCES does not allow accommodations that affect what is being assessed. The 2000 reading assessment, for example, did not allow bilingual dictionaries, because that accommodation would have affected assessing students' proficiency in reading English. But bilingual dictionaries were allowed in the mathematics assessment, because NAEP does not regard English reading skills as a part of mathematics proficiency.
To allow comparisons with previous NAEP assessments, which did not allow accommodations, NCES assessed two separate samples in 2000, one that allowed accommodations and one that did not. For the nation, the average scale scores for the non-accommodated samples and for the accommodated samples were similar (grade 4: 228 vs. 226; grade 8: 275 vs. 274; grade 12: 301 vs. 300). The slight differences between the two averages were not statistically significant at any grade. There were some differences between these two samples in individual states at grade 8. At grade 8, the "with accommodations" sample in 7 states had the lower score, differing by 5 points or less from the nonaccommodated sample. These states were Maryland, Massachusetts, Missouri, Nevada, New York, North Carolina, and West Virginia. No differences were found between samples at grade 4.
Students with Disabilities
In 1992, 7 percent of 4th- and 8th -graders in the national sample were identified as disabled. In 2000, 11 percent were identified as disabled. The schools identify which students selected into the sample are disabled at each of these grades. The corresponding percentages at 12th grade were 4 percent and 7 percent. The increase in the number of disabled students in the sample may in part reflect the requirements of the Individuals with Disabilities Education Act, or IDEA, which requires that states test all students, regardless of disability, in their own state tests.
The percentage of students excluded from the NAEP mathematics assessment for reasons related to a disability, as a percent of all students in the accommodated sample, were 2 to 3 percent in 2000. About 4 to 5 percent of all students were disabled and were assessed without accommodations. The percentage of all students who were disabled and were assessed with accommodations was four percent at grade 4, 2 percent at grade 8, and 1 percent at grade 12.
Limited English Proficieny (LEP) Students
For the 4th grade, the percent of students identified as LEP in the national sample was 3 percent in 1992 and 5 percent in 2000. The percentage of students who are LEP and were excluded from the NAEP mathematics assessment has always been small, no more than 2 percent, at all three grade levels. About 1 percent of all students were accommodated LEP students in 2000.
Comparison of Overall National Results in the Two NAEP Samples
In 1996, at the national level only, NAEP permitted accommodations in part of the sample to assess the effects of offering accommodations. The data for this subsample was not released at that time, but those results can now be compared to those for 2000. At the 4th and 8th grades, the average score in 2000 was higher than in 1996 for the "no accommodations" samples, and for the accommodated samples as well. For the 12th-grade "no accommodations" sample, scores were lower in 2000 than in 1996. However, for the 12th-grade "with accommodations" sample, there was no difference in scores for the two assessments.
When comparing scores for the two different samples in the same year, no difference in scores was found for the 4th and 8th grade in either the 1996 or the 2000 assessment. The only significant score difference occurred at the 12th grade, in 1996 only, where the average score for the "with accommodations" sample was lower than the score for the "no accommodations" sample, 302 as compared to 304.
Mathematics 2000, the full report, is available on the web at http://nces.ed.gov/nationsreportcard.
