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This article was excerpted from The Nation's Report Card: Mathematics Highlights 2003, a tabloidstyle publication. The sample survey data are from the National Assessment of Educational Progress (NAEP) 1990, 1992, 1996, 2000, and 2003 Mathematics Assessments.  
 
Introduction
Since 1969, the National Assessment of Educational Progress (NAEP) has been an ongoing nationally representative indicator of what American students know and can do in major academic subjects. Over the years, NAEP has measured students' achievement in many subjects, including reading, mathematics, science, writing, U.S. history, geography, civics, and the arts. In 2003, NAEP conducted a national and state assessment in mathematics at grades 4 and 8. NAEP is a project of the National Center for Education Statistics (NCES) within the Institute of Education Sciences of the U.S. Department of Education, and is overseen by the National Assessment Governing Board (NAGB). Beginning in 2002, the NAEP national sample was obtained by aggregating the samples from each state, rather than by obtaining an independently selected national sample. As a consequence, the size of the national sample increased, and smaller differences between years or between types of students were found to be statistically significant than would have been detected in previous assessments. In keeping with past practice, all statistically significant differences are indicated in the current report. The results presented in this report distinguish between two different reporting samples that reflect a change in administration procedures beginning in 1996. This change involved permitting students with disabilities or limitedEnglishproficient students to use certain accommodations (e.g., extended time, small group testing). Comparisons between results from 2003 and those from assessment years in which both types of administration procedures were used (1996 and 2000) are discussed based on the results when accommodations were permitted, although significant differences in results when accommodations were not permitted may be noted in the figures and tables. Achievement Levels Provide Standards for Student Performance
Achievement levels are performance standards set by NAGB to provide a context for interpreting student performance on NAEP. These performance standards, based on recommendations from broadly representative panels of educators and members of the public, are used to report what students should know and be able to do at the Basic, Proficient, and Advanced levels of performance in each subject area and at each grade assessed.* The minimum scale scores for achievement levels are as follows:
As provided by law, NCES, upon review of a congressionally mandated evaluation of NAEP, has determined that achievement levels are to be used on a trial basis and should be interpreted and used with caution. However, both NCES and NAGB believe that these performance standards are useful for understanding trends in student achievement. NAEP achievement levels have been widely used by national and state officials. NAEP 2003 Mathematics Assessment Design
Assessment framework
The NAEP mathematics framework, which defines the content for the 1990–2003 assessments, was developed through a comprehensive national consultative process and adopted by NAGB. The mathematics framework calls for the assessment to include questions based on five mathematics content areas: (1) number sense, properties, and operations; (2) measurement; (3) geometry and spatial sense; (4) data analysis, statistics, and probability; and (5) algebra and functions. In addition, the framework specifies that each question measure one of three mathematical abilities. The three mathematical abilities specified by the framework are (1) conceptual understanding, (2) procedural knowledge, and (3) problem solving. The complete framework is available on the NAGB web site (http://www.nagb.org/pubs/pubs.html). Student samples
Results from the 2003 mathematics assessment are reported for the nation and states at grades 4 and 8. The national results are based on a representative sample of students in both public schools and nonpublic schools, while the state results are based only on public school students. Accommodations
It is NAEP's intent to assess all selected students from the target population. Before 1996, no testing accommodations were provided to students with disabilities and limitedEnglishproficient students who participated in the NAEP mathematics assessments. In 1996 (national only) and 2000 (national and state), NAEP was administered to two reporting samples—"accommodations not permitted" and "accommodations permitted." Beginning in 2003, the NAEP mathematics assessment has adopted the new "accommodationspermitted" procedure as its only administration procedure, and thus again had only one reporting sample as in mathematics assessment years prior to 1996. Because the representativeness of samples is ultimately a validity issue, NCES has commissioned studies of the impact of assessment accommodations on overall scores. One paper that explores the impact of two possible scenarios on NAEP is available on the NAEP web site (http://nces.ed.gov/nationsreportcard/pdf/main2002/statmeth.pdf) (PDF 283 kb). Fourth and EighthGraders' Average Mathematics Scores Increase
Average scores were higher in 2003 than in all the previous assessment years at both grades 4 and 8 (figure A). (Differences are discussed in the report only if they were found to be statistically significant.) Figure A. Average mathematics scores, grades 4 and 8: 1990–2003
How Well Did Students Perform in 2003?
Thirtytwo percent of fourthgraders and 29 percent of eighthgraders performed at or above the Proficient level in 2003. The percentages of students performing at or above Basic in 2003 were 77 percent at grade 4 and 68 percent at grade 8. Gain Overall Since 1990 in AchievementLevel Performance
The percentages of fourth and eighthgraders at or above Basic, at or above Proficient, and at Advanced were all higher in 2003 than in 1990. There were also recent increases from 2000 to 2003 in the percentages of fourthgraders at or above Basic and Proficient and at Advanced, and in the percentages of eighthgraders at or above Basic and Proficient. Improvement Seen Among Lower, Middle, and HigherPerforming Students
Looking at changes in scores for students at lower, middle, and higher performance levels gives a more complete picture of student progress. An examination of scores at different percentiles on the 0–500 mathematics scale at each grade indicates whether or not the changes seen in the national average score results are reflected in the performance of lower, middle, and higherperforming students. The percentile indicates the percentage of students whose scores fell below a particular score. For example, 25 percent of assessed students' scores fell below the 25th percentile score and 75 percent fell below the 75th percentile score. At both grades 4 and 8, scores at the 10th, 25th, 50th, 75th, and 90th percentiles were higher in 2003 than in any of the previous assessment years. At grade 4, gains detected between 2000 and 2003 ranged from approximately 5 scale score points for students performing at the 90th percentile to 13 points for students at the 10th percentile. At grade 8, increases since 2000 ranged from approximately 3 scale score points at the 90th percentile to 7 points at the 10th percentile. Most Participating States and Jurisdictions Show Gains at Grades 4 and 8
In addition to national results, the 2003 mathematics assessment collected performance data for fourth and eighthgraders who attended public schools in 50 states and 3 other jurisdictions that participated. State average score results
Among the 43 states and jurisdictions that participated in both the 2000 and 2003 fourthgrade assessments, all showed increases in average scores. Similarly, all 42 of the states and jurisdictions that participated in the 1992 and 2003 assessments showed increases in average scores. At grade 8, of the 42 states and jurisdictions that participated in both the 2000 and 2003 assessments, 28 had higher average scores in 2003 and none showed a decline. All 38 states and jurisdictions that participated in both 1990 and 2003 had higher average scores in 2003. State versus national comparisons
In 2003, 26 of the 53 states and other jurisdictions that participated at grade 4 had average scores that were higher than the national average, 11 had scores that were not found to differ significantly from the national average, and 16 had scores that were lower than the national average. Of the 53 states and other jurisdictions that participated at grade 8, 30 had average scores higher than the national average, 7 had average scores that were not found to differ significantly from the national average, and 16 had average scores that were lower than the national average. State achievementlevel results
At grade 4, 18 states and other jurisdictions had higher percentages of students at or above Proficient than the nation, 19 had percentages that were not found to be statistically different from the nation, and 16 had percentages that were lower than the nation. At grade 8, 24 states and other jurisdictions had higher percentages of students at or above Proficient than the nation, 12 had percentages that were not found to be significantly different from the nation, and 17 had percentages that were lower than the nation. Percentage of students at or above Proficient across years by state
The percentage of fourthgraders at or above Proficient was higher in 2003 than in 2000 for all 43 states and jurisdictions that participated in both years. The percentages also increased from 1992 to 2003 for all 42 states and jurisdictions that participated in both those assessment years. Among the 42 states and jurisdictions that participated in both the 2000 and 2003 eighthgrade assessments, 18 showed an increase in the percentage of students at or above Proficient and none showed a decline. The percentage of eighthgraders at or above Proficient was higher in 2003 than in 1990 for all 38 states and jurisdictions that participated in both years. Subgroup Results Reveal How Various Groups of Students Performed on NAEP
In addition to reporting on overall students' performance on its assessments, NAEP also reports on the performance of various subgroups of students. The mathematics performance of subgroups of students in 2003 indicates whether they have progressed since earlier assessments and allows for comparisons with the performance of other subgroups in 2003. When reading these subgroup results, it is important to keep in mind that there is no simple, causeandeffect relationship between membership in a subgroup and achievement in NAEP. A complex mix of educational and socioeconomic factors may interact to affect student performance. Gender
Average mathematics scores by gender. At both grades 4 and 8, the average scores for male and female students were higher in 2003 than in any of the previous assessment years. In 2003, male students scored higher on average than female students at both grades. Achievementlevel results by gender. At grade 4, the percentages of male and female students at or above Basic and Proficient were higher in 2003 than in any of the previous assessment years. At grade 8, the percentages of male and female students at or above Basic and Proficient were also higher in 2003 than in all previous assessment years. Race/ethnicity
Average mathematics scores by race/ethnicity. At grades 4 and 8, White, Black, and Hispanic students all had higher average scores in 2003 than in any of the previous assessment years (figure B). The average score of Asian/Pacific Islander students was higher in 2003 than in 1990 at both grades 4 and 8. There was no significant change detected in the average score for Asian/Pacific Islander students between 2000 and 2003 at grade 8. American Indian/Alaska Native students had higher average scores in 2003 than in 2000 at grade 4, but the apparent increase at grade 8 was not found to be statistically significant. At both grades 4 and 8, Asian/Pacific Islander students scored higher on average in 2003 than White students. Both White and Asian/Pacific Islander students had higher average scores than Black, Hispanic, and American Indian/Alaska Native students. Hispanic and American Indian/Alaska Native students scored higher on average than Black students at both grades. Average mathematics score gaps between selected racial/ethnic subgroups. At grade 4, the score gap between White and Black students decreased between 2000 and 2003, and was smaller in 2003 than in 1990. The gap between White and Hispanic fourthgraders also narrowed between 2000 and 2003, but the gap in 2003 was not found to be significantly different from that in 1990. At grade 8, the score gap between White and Black students was narrower in 2003 than in 2000, but the gap in 2003 was not found to differ significantly from 1990. The score gap between White and Hispanic eighthgraders in 2003 was not found to differ significantly from the gap in any of the previous assessment years. Achievementlevel results by race/ethnicity. At grade 4, the percentages of White, Black, and Hispanic students at or above the Basic and Proficient levels were higher in 2003 than in any of the previous assessment years. The percentages of Asian/Pacific Islander students at or above Basic and Proficient were higher in 2003 than in 1990. The percentage of American Indian/Alaska Native students at or above Basic was higher in 2003 than in 2000, but the apparent increase in the percentage at or above Proficient was not found to be statistically significant. At grade 8, the percentages of White, Black, and Hispanic students at or above Basic and Proficient were higher in 2003 than in any of the previous assessment years. The percentages of Asian/Pacific Islander students at or above Basic and Proficient were higher in 2003 than in 1990. Figure B. Average mathematics scale scores, by selected race/ethnicity, grades 4 and 8: 1990–2003
Eligibility for free/reducedprice school lunch
Average mathematics scores by students' eligibility for free/reducedprice school lunch. NAEP collects data on students' eligibility for free/reducedprice lunch as an indicator of family economic status. Eligibility for free and reducedprice lunches is determined by students' family income in relation to the federally established poverty level. Free lunch qualification is set at 130 percent of the poverty level, and reducedprice lunch qualification is set at between 130 and 185 percent of the poverty level. Information regarding students' eligibility in 2003 was not available for 10 percent of fourthgraders and 11 percent of eighthgraders, either because their schools did not participate in the National School Lunch Program or for other reasons. At both grades 4 and 8, average mathematics scores in 2003 were higher than the scores in 1996 and 2000 both for students who were eligible and for students who were not eligible for free/reducedprice lunch. The average mathematics score for students who were eligible for free/reducedprice lunch was lower than the average score for students who were not eligible at both grades. Results broken down by students' eligibility for free lunch and eligibility for reducedprice lunch are available on the NAEP web site (http://nces.ed.gov/nationsreportcard/nde). Achievementlevel results by students' eligibility for free/reducedprice lunch. At both grades 4 and 8, the percentages of students at or above Basic and Proficient were higher in 2003 than in 1996 and 2000 for both students who were eligible and students who were not eligible for free/reducedprice lunch. Average mathematics score gaps between students who were eligible and those who were not eligible for free/reducedprice lunch. At grade 4, the average score gap between students who were eligible and students who were not eligible for free/reducedprice lunch decreased from 2000 to 2003, but the gap in 2003 was not found to be significantly different from the gap in 1996. No significant change was detected in the gap in 2003 compared to the gap in any of the previous assessment years at grade 8.
Footnotes
*The NAEP achievement levels are as follows: 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 subjectmatter knowledge, application of such knowledge to realworld situations, and analytical skills appropriate to the subject matter. Advanced signifies superior performance. Detailed descriptions of the NAEP mathematics achievement levels can be found on the NAGB web site (http://www.nagb.org/pubs/pubs.html).
