The Nation's Report Card: Mathematics 2000

The National Assessment of Educational Progress (NAEP) is the nation's only ongoing representative sample survey of student achievement in core subject areas. 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.

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. This report presents the results of the NAEP 2000 mathematics assessment for the nation and the states. Results in 2000 are compared to results of previous 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 as part of its statutory responsibilities. The achievement levels are collective judgments of what students should know and be able to do. The Governing Board is an independent, bipartisan group created by Congress in 1988 to set policy for the National Assessment of Educational Progress.

As provided by law, the Acting Commissioner of Education Statistics, upon review of a congressionally mandated evaluation of NAEP, determined that the achievement levels are to be considered developmental and should be interpreted and used with caution. However, both the Acting Commissioner and the Board believe these performance standards are useful for understanding trends in student achievement. They have been widely used by national and state officials, including the National Education Goals Panel, as a common yardstick of academic performance.

In addition to providing average scores and achievement level performance at the national level and state level, this report provides results for subgroups of students defined by various background and contextual characteristics. This report also contains results for a second sample at both the national and state levels -- one in which testing accommodations were provided to students with special needs (students with disabilities or students with limited English proficiency).

The results presented in this report are based on representative samples of students for the nation and for participating states. 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 assessments, approximately 100,000 students at each of grades 4 and 8 were assessed.

A summary of major findings from the 2000 NAEP mathematics assessment is presented on the following pages. Differences between results across years or between groups of students are discussed only if they have been determined to be statistically significant.

Major Findings for the Nation, Regions, and States

For the Nation:

• Fourth-, eighth-, and twelfth-grade students had higher average scores in 2000 than in 1990, the first assessment year in which the current mathematics framework was used. Fourth- and eighth-graders showed steady progress across the decade. Twelfth-graders made gains from 1990 to 1996, but their average score declined between 1996 and 2000.
  
  
• In 2000, the percentage of students performing at or above Proficient -- identified by the Governing Board as the level that all students should reach -- was 26 percent at grade 4, 27 percent at grade 8, and 17 percent at grade 12. At each grade, the percentage of students performing at or above this level was higher in 2000 than in 1990. There were gains over the decade at the Basic and Advanced levels as well. However, from 1996 to 2000, the percentage of twelfth-graders reaching the Basic level declined.
  
  
• Score increases are evident across the performance distribution -- higher-, middle-, and lower-performing students have made gains since 1990 at each grade. At grade 12, however, the decline in the average score between 1996 and 2000 was reflected mostly in the scores of students in the middle- and lower- performance ranges: scores declined only at the 50th, 25th, and 10th percentiles.

For the Regions:

• Average scores in the Southeast, Central, and West were higher in 2000 than in 1990 for students in all three grades. Average scores in the Northeast were higher in 2000 than in 1990 for fourth- and eighth-graders, but the apparent difference for twelfth-graders was not statistically significant.
  
  
• In 2000, average scores for fourth-graders were higher in the Northeast and Central regions than in the Southeast. For eighth- and twelfth-graders, scores in the Northeast, Central, and West were higher than in the Southeast.

For the States and Other Jurisdictions:

• In the NAEP 2000 state-by-state assessment, 40 states and 6 other jurisdictions at grade 4, and 39 states and 5 other jurisdictions at grade 8 met the participation guidelines for reporting results. Only public schools participated in the state-by-state assessment.

At grade 4:

• In 2000, no state scored higher than these nine: Connecticut, Indiana, Iowa, Kansas, Massachusetts, Minnesota, North Carolina, Texas, and Vermont. The states with the highest percentages of students at or above Proficient were Connecticut, Indiana, Kansas, Massachusetts, Michigan, Minnesota, and Vermont. Their percentages at or above Proficient ranged from 29 percent to 34 percent.
  
  
• 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.

At grade 8:

• In 2000, no state scored higher than these three: Kansas, Minnesota, and Montana. The two states with the highest percentages of students at or above Proficient were Minnesota (40 percent) and Montana (37 percent).
  
  
• 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.

National Results for Student Subgroups

In addition to overall results for the nation and jurisdictions, NAEP reports on the performance of various subgroups of students. Observed differences between student subgroups in NAEP mathematics performance most likely reflect a range of socioeconomic and educational factors not addressed in this report or by NAEP.

Gender

• In 2000, there was no significant difference between the average scores of male and female fourth-graders, but the average score of males was higher than that of females for both eighth- and twelfth-graders.
  
  
• At all three grades, both male and female students had higher average scores in 2000 than in 1990.
  
  
• The difference, or "gap," between the average scores of male and female students at every grade was relatively small and has shown little change in its size over the four assessments beginning in 1990.

Race/Ethnicity

• In 2000, at all three grades, the average scores of white students were higher than those of black, Hispanic, and American Indian students.
  
  
• In 2000, at grade 12, the average score of Asian/Pacific Islander students was higher than the scores of white, black, and Hispanic students.
  
  
• White, black, and Hispanic students at grades 4 and 8 had higher average scores in 2000 than in 1990. At grade 12, only white students had a higher average score in 2000 than in 1990. 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.

Parents' Level of Education

• Generally, students in grades 8 and 12 with higher scores reported higher levels of parental education in 2000. This result is consistent with past NAEP assessments.
  
  
• At grade 8, students at each level of parental education had higher scores in 2000 than in 1990. At grade 12, however, only students who reported their parents' highest level of education as "graduated from college" had higher scores in 2000 than in 1990.

Type of School

• At all three grades in 2000, students attending nonpublic schools outperformed their peers attending public schools.
  
  
• Over the period from 1990 to 2000, public, nonpublic, and Catholic schools had increased average scores for fourth-graders. For eighth-graders, the scores of public, nonpublic, Catholic, and other nonpublic school students also increased over the 10 year period. Similarly, for twelfth-graders, average scores for all the school types were higher in 2000 than in 1990.

Type of Location

• In 2000, fourth-, eighth-, and twelfth-graders in central city schools had lower average scores than their counterparts in urban fringe/large town schools. Fourth- and eighth-graders in central city schools had lower average scores than their counterparts in rural/small town schools. Fourth-graders in urban fringe/large town schools had higher scores than their counterparts in rural/small town schools.

Free/Reduced-Price Lunch Program

• At all three grades in 2000, students eligible for the free/reduced-price National School Lunch Program administered by the U.S. Department of Agriculture (USDA) had lower average scores than those who were not eligible. Free/reduced-price lunches are intended for children at or near the poverty line: eligibility is determined by the USDA's income eligibility guidelines (309K PDF).

Becoming a More Inclusive NAEP

A second set of results from the NAEP 2000 mathematics assessment includes the performance of special-needs students who were provided with testing accommodations. A similar set of results is available from 1996 at the national level only, allowing for comparisons between 1996 and 2000 national results based on administration procedures that permitted accommodations.

For the Nation:

• At grades 4 and 8, the small differences between the "accommodations-permitted" and "accommodations-not-permitted" national average scores were not statistically significant in either 1996 or 2000. At grade 12, there was no significant difference between the two sets of results in the 2000 assessment, but in the 1996 assessment the average score was higher when accommodations were not permitted.
  
  
• Between 1996 and 2000, average scores increased at grades 4 and 8 in both sets of results. At grade 12, the average score declined in both sets of results during the same time period; however, the apparent decline in "accommodations-permitted" results was not statistically significant.

For the States and Other Jurisdictions:

• At grade 4, there were no statistically significant differences observed between the "accommodations-not-permitted" results and the "accommodations-permitted" results for any participating state or jurisdiction in 2000.
  
  
• At grade 8, the seven states that had average scores that were higher in the "accommodations-not-permitted" results than in the "accommodations-permitted" results were Maryland, Massachusetts, Missouri, Nevada, New York, North Carolina, and West Virginia.

School Contexts for Learning

NAEP collects information about the contexts for student learning by administering questionnaires to assessed students, their teachers, and their school administrators. Using the student as the unit of analysis, NAEP examines the relationship between selected contextual variables drawn from these questionnaires and students' average scores on the mathematics assessment. Readers are cautioned that the relationship between a contextual variable (for example, teacher self-reported preparation levels, or classroom instructional activities) and student mathematics performance is not necessarily causal (see page 130 for more on this topic).

Teacher Preparation (grades 4 and 8 only)

• In 2000, eighth-graders whose teachers majored in either mathematics or mathematics education had higher average scores than did students whose teachers did not major in these subjects.
  
  
• Most fourth- and eighth-grade students in 2000 were taught by teachers who considered themselves to be well prepared to teach the mathematics content areas assessed by NAEP. There were no significant differences in the average scores of fourth-graders based on teachers' self-reported level of preparation in NAEP content areas. However, eighth-graders whose teachers reported being very well prepared in these content areas had higher average scores than did students whose teachers reported they were less well prepared.
  
  
• Eighth-graders in 2000 who were taught by mathematics teachers with 11 or more years of experience had higher average scores than those taught by teachers with 2 years or less of experience.

Technology

• Eighth-graders whose teachers reported that they permitted unrestricted use of calculators had higher average scores in 2000 than did the students whose teachers restricted calculator use.
  
  
• In 2000, eighth-graders whose teachers reported that they permitted calculator use on class tests had higher average NAEP scores than students whose teachers did not permit calculator use on tests. (NAEP permits calculators on certain sections of the assessment.)
  
  
• In grades 4, 8, and 12, there was an increase between 1996 and 2000 in the percentage of students in schools that reported computers were available at all times in classrooms.

Instructional Time and Homework

• In 2000, the average scores of eighth-graders, but not fourth-graders, generally increased as the amount of homework that teachers reported assigning increased.
  
  
• In 2000, 82 percent of eighth-grade students attended schools that reported offering algebra to eighth-graders for high school course placement or credit.

Classroom Practices and Home Contexts for Learning

Teachers' Classroom Practices

• In 2000, the majority of students at all three grade levels reported that they did mathematics textbook problems in school every day. Eighth- and twelfth-graders who reported doing textbook problems in school every day had higher average scores than did students who reported doing textbook problems less frequently.

Calculator Usage

• At both grades 4 and 8, the percentage of students who reported using calculators every day for classwork and for homework declined between 1996 and 2000. For twelfth-graders, however, there was no change over the same time span in the frequency of use of calculators for classwork or homework.
  
  
• While frequent usage of calculators reported by fourth-graders in 2000 was associated with lower average mathematics scores than less frequent usage, for eighth- and twelfth-graders just the opposite was true -- more frequent calculator usage was associated with higher scores.
  
  
• In 2000, more frequent usage of calculators on both homework and quizzes as reported by students was again associated with lower average scores for fourth-graders, but with higher scores for eighth- and twelfth-graders.
  
  
• There was an increase between 1996 and 2000 in the percentage of twelfth-graders who reported using graphing calculators for schoolwork. In 2000, eighth- and twelfth-graders who used graphing calculators in class had higher average NAEP scores than did nonusers.

Courses Taken by Twelfth-Grade Students

• Twelfth-graders' responses to the NAEP questionnaire in 2000 indicated that 94 percent had taken first-year algebra, 88 percent had taken geometry, 18 percent had taken statistics, and 18 percent had taken calculus.
  
  
• Analysis of course-taking patterns revealed a positive association between higher levels of mathematics courses taken and progressively higher NAEP mathematics scores.

Time Spent on Homework

• In 2000, eighth-graders who reported spending a moderate amount of time on mathematics homework had higher average scores than did those who spent either no time on homework or more than 1 hour. Twelfth-graders who spent some time doing mathematics homework had higher average scores than either the 29 percent who were not taking math or the 12 percent who spent no time on homework.

Hours Worked at a Part-Time Job

• More than two-thirds of twelfth-graders reported spending time working at a part-time job in 2000. Those who worked 15 or fewer hours had higher average scores than did those who worked 21 or more hours.

Television Viewing Habits

• Fourth-graders reported watching less television in 2000 than in earlier assessment years. In 2000, the scores of fourth-, eighth-, and twelfth-graders who reported heavy television watching were lower than for students who watched little or a moderate amount of television.

Attitudes Toward Mathematics

• Fourth-, eighth-, and twelfth-graders in 2000 who reportedly agreed that they liked math and that math was useful for solving problems had higher average scores than those who disagreed.
  
  
• Students at all three grades in 2000 who disagreed with the statements that math was mostly memorizing facts and that there was only one way to solve a mathematics problem scored higher, on average, than those who agreed.
  
  
• Fewer eighth- and twelfth-graders reported liking mathematics in 2000 than in the early 1990s.