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 For grade 4:

·                       The average mathematics scale score for students in Maine was 238. This was higher than that of 1992 (232) and was higher than that in 2000 (230).

·                       Maine 's average score (238) was higher than that of the nation's public schools (234).

·                       Students' average scores in Maine were higher than those in 23 jurisdictions, not significantly different from those in 21 jurisdictions, and lower than those in 8 jurisdictions.

·                       The percentage of students in Maine who performed at or above the Proficient level was 34 percent. This was greater than that in 1992 (27 percent) and was greater than that in 2000 (23 percent).

·                       In Maine , the percentage of students who performed at or above Proficient was not found to differ significantly from that for the nation's public schools (31 percent).

This report provides selected results from the National Assessment of Educational Progress (NAEP) for Maine 's public-school students at grade 4. Since 1990, mathematics has been assessed in five different years at the state level (at grade 8 in 1990, and at both grades 4 and 8 in 1992, 1996, 2000, and 2003). In 2003, 53 jurisdictions participated: the 50 states, District of Columbia , Department of Defense Domestic Dependent Elementary and Secondary Schools, and Department of Defense Dependents Schools (Overseas). Maine participated and met the criteria for reporting public-school results at both grades 4 and 8 in 1992, 1996, 2000, and 2003.

NAEP is a project of the National Center for Education Statistics (NCES). For more information about the assessment, see The Nation's Report Card, Mathematics Highlights 2003 or The Nation's Report Card: Mathematics 2003, which will be available in 2004. The full set of results is available in an interactive database on the NAEP web site (http://nces.ed.gov/nationsreportcard/). Released test questions, scoring guides, and question-level performance data are also available on the web site.

Introduction

Who Was Assessed?

In 2003, 53 jurisdictions participated in NAEP: the 50 states, District of Columbia , Department of Defense Domestic Elementary and Secondary Schools, and Department of Defense Dependents Schools (Overseas). The target sample for each state or other jurisdiction was approximately 100 schools at a grade and approximately 3,000 students for each subject at a grade, except in small or sparsely populated jurisdictions. The sample of schools and students was chosen in a two-stage sampling process. First, the sample of schools was selected by probability sampling methods. Then, within the participating schools, random samples of students were chosen. Beginning in 2002, the national sample was obtained by aggregating the samples from each state. The national results include the results from the states, weighted appropriately to represent the U.S. student population. Only public schools, however, are included in the state reports. The overall participation rates for schools and students must meet guidelines established by the National Center for Education Statistics (NCES) and the National Assessment Governing Board (NAGB) in order for assessment results to be reported publicly. Data are not reported to the public for a state or jurisdiction that participates but does not meet minimum participation guidelines (see http://nces.ed.gov/nationsreportcard/about/participrates.asp). Participation rates for the 2003 mathematics assessment are available at the NAEP web site (http://nces.ed.gov/nationsreportcard/mathematics/sampledesign.asp).

Cautions in Interpreting Results

The averages and percentages in this report have a standard error—a range of up to a few points above or below the score—which takes into account potential score fluctuation due to sampling error and measurement error. Statistical tests that factor in these standard errors are used to determine whether the differences between average scores or percentages are significant. All differences were tested for statistical significance at the 0.05 level. NAEP sample sizes have increased since 2002 compared to previous years, resulting in smaller standard errors. As a consequence, smaller differences are detected as statistically significant than in previous assessments.

In this report, statistically significant differences are referred to as "significant differences" or "significantly different." Significant differences between 2003 and prior assessments are marked with a notation (*) in the tables. Any differences in scores within a year or across years that are mentioned in the text as "higher," "lower," "greater," or "smaller" are statistically significant.

Estimates based on small subgroups are likely to have large standard errors. Consequently some seemingly large differences may not be statistically significant. The reader is cautioned to rely on reported differences in the tables and/or text, which are statistically significant, rather than on the apparent magnitude of any difference. Readers are also cautioned against interpreting NAEP results causally. Inferences related to subgroup performance, for example, should take into account the many socioeconomic and educational factors that may affect student performance.


NAEP Mathematics 2003 Overall Scale Score and Achievement-Level Results for Public School Students

Overall Scale Score Results

In this section student performance is reported as an average score based on the NAEP mathematics scale, which ranges from 0 to 500. Scores on this scale are comparable from 1990 through 2003.

Prior to 2000, testing accommodations were not provided for students with special needs in state mathematics assessments. In 2000 only, results were reported for two samples of students: one in which accommodations were permitted and one in which accommodations were not pemitted. Subsequent assessment results were based on the more inclusive samples.

Table 1 shows the overall performance results of grade 4 public school students in Maine and the nation. The first column of results presents the average score on the NAEP mathematics scale. The subsequent columns show the score at selected percentiles. The percentile indicates the percentage of students who performed below the score for that percentile. For example, 10 percent of the students had scores that were lower than the score shown for the 10th percentile.

1

 

 

The Nation's Report Card 2003 State Assessment

Average mathematics scale scores and selected percentiles, grade 4 public schools: 1992–2003

 

 

Average
Scale Score

Scale score distribution

10th Percentile

25th Percentile

50th Percentile

75th Percentile

90th Percentile

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Accommodations not permitted

 

 

1992

Maine

232

(1.0)*

196

(1.9)*

214

(1.7)*

233

(1.4)*

251

(0.8)*

265

(1.3)

 

Nation (Public)

219

(0.8)*

176

(1.1)*

197

(0.8)*

220

(0.9)*

241

(1.3)*

259

(0.8)*

1996

Maine

232

(1.0)*

197

(1.5)*

214

(1.2)*

233

(1.1)*

251

(1.5)*

267

(2.0)

 

Nation (Public)

222

(1.0)*

180

(1.7)*

201

(1.3)*

224

(1.1)*

244

(1.3)*

261

(0.8)*

2000

Maine

231

(0.9)*

196

(1.8)*

213

(1.8)*

231

(1.1)*

249

(1.0)*

264

(1.5)

 

Nation (Public)

226

(1.0)*

185

(1.1)*

206

(1.4)*

228

(0.9)*

249

(1.2)*

265

(0.9)*

Accommodations permitted

 

 

2000

Maine

230

(1.0)*

195

(3.1)*

213

(0.9)*

230

(1.1)*

247

(1.1)*

263

(1.8)*

 

Nation (Public)

224

(1.0)*

183

(1.4)*

203

(1.4)*

225

(1.3)*

247

(1.2)*

264

(1.0)*

2003

Maine

238

(0.7)

204

(2.0)

221

(1.1)

239

(0.7)

255

(1.2)

269

(1.8)

 

Nation (Public)

234

(0.2)

196

(0.3)

215

(0.3)

235

(0.2)

254

(0.3)

270

(0.2)

 

 

 

* Value is significantly different from the value for the same jurisdiction in 2003.
NOTE: The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics in the table appear in parentheses. All differences were tested for statistical significance at the 0.05 level using unrounded numbers. Performance comparisons may be affected by differences in exclusion rates for students with disabilities and limited-English-proficient students in the NAEP samples and changes in sample sizes. NAEP sample sizes have increased since 2002 compared to previous years, resulting in smaller detectable differences than in previous assessments. In addition to allowing for accommodations, the accommodations-permitted results for national public schools (2000 and 2003) differ slightly from previous years' results, and from previously reported results for 2000, due to changes in sample weighting procedures.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992–2003 Mathematics Assessments.


Overall Achievement-Level Results

In this section student performance is reported as the percentage of students performing relative to standards set by the National Assessment Governing Board (NAGB). These performance standards for what students should know and be able to do were based on the recommendations of broadly representative panels of educators and members of the public. In 2000 only, results were obtained for student samples for which accommodations were permitted and were not permitted.

Table 2 presents the percentage of students at grade 4 who performed below Basic, at or above Basic, at or above Proficient, and at the Advanced level. Because the percentages are cumulative from Basic to Proficient to Advanced, they sum to more than 100 percent. Only the percentage of students performing at or above Basic (which includes the students at Proficient and Advanced) plus the students below Basic will sum to 100 percent (except for rounding).

 

 

 



T
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B
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E

2

 

 

The Nation's Report Card 2003 State Assessment

Percentage of students at or above each mathematics achievement level, grade 4 public schools: 1992–2003

 

 

 

 

 

Below Basic

At or above Basic

At or above

 

Proficient

Advanced

 

 

 

 

 

 

 

 

 

 

 

 

Accommodations not permitted

 

1992

Maine

25

(1.5)*

75

(1.5)*

27

(1.5)*

2

(0.5)

 

Nation (Public)

43

(1.2)*

57

(1.2)*

17

(1.1)*

2

(0.3)*

1996

Maine

25

(1.4)*

75

(1.4)*

27

(1.4)*

3

(0.6)

 

Nation (Public)

38

(1.4)*

62

(1.4)*

20

(1.0)*

2

(0.3)*

2000

Maine

26

(1.8)*

74

(1.8)*

25

(1.3)*

2

(0.4)

 

Nation (Public)

33

(1.2)*

67

(1.2)*

25

(1.2)*

2

(0.3)*

Accommodations permitted

 

2000

Maine

27

(1.4)*

73

(1.4)*

23

(1.5)*

2

(0.3)*

 

Nation (Public)

36

(1.4)*

64

(1.4)*

22

(1.1)*

2

(0.3)*

2003

Maine

17

(1.3)

83

(1.3)

34

(1.3)

3

(0.5)

 

Nation (Public)

24

(0.3)

76

(0.3)

31

(0.3)

4

(0.1)

 

 

* Value is significantly different from the value for the same jurisdiction in 2003.
NOTE: The standard errors of the statistics in the table appear in parentheses. Achievement levels correspond to the following points on the NAEP mathematics scale: below Basic, 213 or lower; Basic, 214-248; Proficient, 249-281; and Advanced, 282 and above. All differences were tested for statistical significance at the 0.05 level using unrounded numbers. Details may not sum to totals due to rounding. Performance comparisons may be affected by differences in exclusion rates for students with disabilities and limited-English-proficient students in the NAEP samples and changes in sample sizes. NAEP sample sizes have increased since 2002 compared to previous years, resulting in smaller detectable differences than in previous assessments. In addition to allowing for accommodations, the accommodations-permitted results for national public schools (2000 and 2003) differ slightly from previous years' results, and from previously reported results for 2000, due to changes in sample weighting procedures.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992–2003 Mathematics Assessments.

Comparisons Between Maine and Other Participating States and Jurisdictions

In 2003, 53 jurisdictions participated in the mathematics assessment. These include the 50 states, the District of Columbia and the two groups of Department of Defense Education Activity (DoDEA) schools: Domestic Dependent Elementary and Secondary Schools (DDESS) and Department of Defense Dependents Schools (DoDDS).

 

Comparisons by Average Scale Scores

Figure 1 compares Maine 's 2003 overall mathematics scale scores at grade 4 with those of all other participating states and jurisdictions. The different shadings indicate whether a state's or jurisdiction's average scale score was found to be higher than, lower than, or not significantly different from that of Maine in the NAEP 2003 mathematics assessment.

 

 

F
I
G
U
R
E

1

 

 

The Nation's Report Card 2003 State Assessment

Maine's average mathematics scale score compared with scores for other participating jurisdictions, grade 4 public schools: 2003

Comparisons by Achievement Levels


Figure 2 permits comparisons of all jurisdictions participating in the NAEP 2003 mathematics assessment in terms of percentages of grade 4 students performing at or above the Proficient level. The participating states and jurisdictions are grouped into categories reflecting student performance compared to that in Maine . The jurisdictions are grouped by whether the percentage of their students with scores at or above the Proficient level (including Advanced) was found to be higher than, not significantly different from, or lower than the percentage in Maine . Note that the arrangement of the states and the other jurisdictions within each category is alphabetical; statistical comparisons among jurisdictions in each of the three categories are not included in this report.

 

 

F
I
G
U
R
E

2

 

 

The Nation's Report Card 2003 State Assessment

Percentage of students within each mathematics achievement-level range, and Maine 's percentage at or above Proficient compared with other participating jurisdictions, grade 4 public schools: By state, 2003


Mathematics Performance by Demographic Characteristics

 

This section of the report presents trend results for students in Maine and the nation by demographic characteristics. Student performance data are reported for:

 

  • Gender

 

Definitions of NAEP reporting groups are available on the NAEP web site (http://nces.ed.gov/nationsreportcard/mathematics/
results2003/interpret-results.asp#RepGroups).

Each of the variables is reported in tables that present the percentage of students belonging to each subgroup in the first column and the average scale score in the second column. The columns to the right show the percentage of students at or above each achievement-level.

 

The reader is cautioned against making causal inferences about the performance of groups of students relative to demographic variables. Many factors other than those discussed here, including home and school factors, may affect student performance.

NAEP collects information on many additional variables, including school and home factors related to achievement. All of this information is in an interactive database available on the NAEP web site (http://nces.ed.gov/nationsreportcard/naepdata/).

 

Gender

Information on student gender is reported by schools on rosters of students eligible to be assessed.

Table 3 shows scale scores and achievement-level data for public-school students at grade 4 in Maine and the nation by gender. In 2000 only, results were obtained for student samples for which accommodations were permitted and were not permitted.

 

 

 

 



T
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3

 

 

The Nation's Report Card 2003 State Assessment

Average mathematics scale scores and percentage of students at or above each achievement level, by gender, grade 4 public schools: 1992–2003

 

 

Percentage
of Students

Average
Scale Score

Below Basic

 

 

At or above
Basic

At or above

 

Proficient

At Advanced

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Male

 

 

 

Accommodations not permitted

 

 

 

1992

Maine

49

(1.1)

232

(1.2)*

25

(1.8)*

75

(1.8)*

28

(1.8)*

3

(0.7)

 

Nation (Public)

50

(0.7)

220

(0.9)*

41

(1.3)*

59

(1.3)*

19

(1.2)*

2

(0.4)*

1996

Maine

50

(1.1)

234

(1.3)*

24

(1.5)*

76

(1.5)*

29

(2.0)*

4

(1.0)

 

Nation (Public)

51

(0.7)

224

(1.2)*

37

(1.8)*

63

(1.8)*

22

(1.2)*

3

(0.5)*

2000

Maine

50

(1.0)

232

(1.3)*

23

(2.0)*

77

(2.0)*

27

(1.8)*

3

(0.7)

 

Nation (Public)

51

(0.7)

227

(1.1)*

32

(1.2)*

68

(1.2)*

27

(1.3)*

3

(0.4)*

Accommodations permitted

 

 

 

2000

Maine

51

(1.0)

232

(1.2)*

24

(1.7)*

76

(1.7)*

25

(2.1)*

2

(0.6)

 

Nation (Public)

51

(0.6)

225

(1.1)*

35

(1.5)*

65

(1.5)*

25

(1.3)*

3

(0.4)*

2003

Maine

51

(0.8)

239

(0.9)

16

(1.6)

84

(1.6)

37

(1.7)

4

(0.8)

 

Nation (Public)

51

(0.2)

235

(0.3)

23

(0.4)

77

(0.4)

34

(0.4)

5

(0.2)

Female

 

 

 

Accommodations not permitted

 

 

 

1992

Maine

51

(1.1)

231

(1.3)*

25

(2.2)*

75

(2.2)*

27

(1.9)

2

(0.6)

 

Nation (Public)

50

(0.7)

218

(1.1)*

44

(1.8)*

56

(1.8)*

16

(1.4)*

1

(0.3)*

1996

Maine

50

(1.1)

231

(1.2)*

25

(2.0)*

75

(2.0)*

26

(1.5)*

2

(0.5)

 

Nation (Public)

49

(0.7)

221

(1.1)*

39

(1.7)*

61

(1.7)*

17

(1.2)*

1

(0.4)*

2000

Maine

50

(1.0)

229

(1.0)*

28

(2.0)*

72

(2.0)*

22

(1.5)*

2

(0.5)

 

Nation (Public)

49

(0.7)

225

(1.0)*

34

(1.4)*

66

(1.4)*

22

(1.3)*

2

(0.4)*

Accommodations permitted

 

 

 

2000

Maine

49

(1.0)

227

(1.3)*

29

(2.2)*

71

(2.2)*

20

(1.4)*

1

(0.4)

 

Nation (Public)

49

(0.6)

223

(1.1)*

38

(1.7)*

62

(1.7)*

20

(1.3)*

1

(0.4)*

2003

Maine

49

(0.8)

236

(0.9)

19

(1.5)

81

(1.5)

31

(1.6)

3

(0.6)

 

Nation (Public)

49

(0.2)

233

(0.2)

25

(0.4)

75

(0.4)

29

(0.3)

3

(0.1)

 

 

 

 

* Value is significantly different from the value for the same jurisdiction in 2003.
NOTE: The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics in the table appear in parentheses. Achievement levels correspond to the following points on the NAEP mathematics scale: below Basic, 213 or lower; Basic, 214-248; Proficient, 249-281; and Advanced, 282 and above. All differences were tested for statistical significance at the 0.05 level using unrounded numbers. Details may not sum to totals due to rounding. Performance comparisons may be affected by differences in exclusion rates for students with disabilities and limited-English-proficient students in the NAEP samples and changes in sample sizes. NAEP sample sizes have increased since 2002 compared to previous years, resulting in smaller detectable differences than in previous assessments. In addition to allowing for accommodations, the accommodations-permitted results for national public schools (2000 and 2003) differ slightly from previous years' results, and from previously reported results for 2000, due to changes in sample weighting procedures.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992–2003 Mathematics Assessments.

Toward a More Inclusive NAEP

NAEP endeavors to assess all students selected in the randomized sampling process, including students with disabilities (SD) as well as students who are classified by their schools as limited-English-proficient (LEP). Some students sampled for participation in NAEP can be excluded from the sample according to carefully defined criteria. School personnel, guided by the student's Individualized Education Program (IEP), as well as eligibility for Section 504 services, make decisions regarding inclusion in the assessment of students with disabilities. They also make decisions regarding inclusion of LEP students, based on NAEP's guidelines. This includes evaluating the student's capability of participating in the assessment in English, as well as taking into consideration the number of years the student has been receiving instruction in English.

Percentages of students excluded from NAEP may vary considerably across states, and within a state, across years. Comparisons of results across states and within a state across years should be interpreted with caution if the exclusion rates vary widely. The percentages of students classified as SD or LEP in all participating states and jurisdictions are available in an interactive database at the NAEP web site (http://nces.ed.gov/nationsreportcard/naepdata/).

The results displayed in this report and in other publications of the NAEP 2003 mathematics results are based on representative samples that include SD and LEP students who were assessed either with or without accommodations, based on NAEP's guidelines. Prior to 2000, however, in state NAEP mathematics assessments no testing accommodations or adaptations were made available to the special-needs students in the samples that served as the basis for reported results.

In the 1996 national and 2000 national and state mathematics assessments, NAEP drew a second representative sample of schools. Accommodations were made available for students in this sample who required them, provided the accommodation did not change the nature of what was tested. For example, students could be assessed one-on-one or in small groups, receive extended time, or use a large-print test book. In mathematics, students had the option of using a bilingual English–Spanish test book. However, for mathematics students were not allowed to use calculators for any questions on which calculators were not permitted. NAEP has used these comparable samples to study the effects of allowing accommodations for special-needs students in the assessments. A series of technical research papers covering various NAEP subject areas has been published with the results of these comparisons (see http://nces.ed.gov/nationsreportcard/about/inclusion.asp #research).

Table 4 presents the total number of students assessed, the percentage of students sampled that were excluded, and average scale scores for all participating states and other jurisdictions at grade 4.

 

 

 



T
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4

 

 

The Nation's Report Card 2003 State Assessment

Total number of students assessed, percentage of students sampled that were excluded, and average mathematics scale scores, grade 4 public schools: By state, 2003.

 

 

Grade 4

 

Number
assessed

Percentage
excluded

Average
scale score

Alabama

3,559

2

( 0.3)

223

( 1.2)

Alaska

2,825

1

( 0.3)

233

( 0.8)

Arizona

3,952

5

( 0.5)

229

( 1.1)

Arkansas

3,273

2

( 0.4)

229

( 0.9)

California

8,544

3

( 0.5)

227

( 0.9)

Colorado

3,460

2

( 0.3)

235

( 1.0)

Connecticut

3,221

4

( 0.6)

241

( 0.8)

Delaware

3,124

7

( 0.4)

236

( 0.5)

Florida

3,615

3

( 0.5)

234

( 1.1)

Georgia

5,372

2

( 0.3)

230

( 1.0)

Hawaii

3,629

3

( 0.6)

227

( 1.0)

Idaho

3,394

2

( 0.3)

235

( 0.7)

Illinois

5,000

4

( 0.6)

233

( 1.1)

Indiana

3,666

2

( 0.4)

238

( 0.9)

Iowa

3,238

3

( 0.5)

238

( 0.7)

Kansas

3,041

2

( 0.3)

242

( 1.0)

Kentucky

3,451

3

( 0.5)

229

( 1.1)

Louisiana

2,917

3

( 0.9)

226

( 1.0)

Maine

2,879

3

( 0.5)

238

( 0.7)

Maryland

3,470

4

( 0.7)

233

( 1.3)

Massachusetts

4,499

3

( 0.4)

242

( 0.8)

Michigan

3,784

4

( 0.4)

236

( 0.9)

Minnesota

3,551

3

( 0.3)

242

( 0.9)

Mississippi

3,241

5

( 0.5)

223

( 1.0)

Missouri

3,495

4

( 0.4)

235

( 0.9)

Montana

2,912

2

( 0.3)

236

( 0.8)

Nebraska

2,748

3

( 0.4)

236

( 0.8)

Nevada

3,315

4

( 0.6)

228

( 0.8)

New Hampshire

3,218

3

( 0.4)

243

( 0.9)

New Jersey

3,422

2

( 0.6)

239

( 1.1)

New Mexico

2,930

4

( 0.9)

223

( 1.1)

New York

4,308

5

( 0.6)

236

( 0.9)

North Carolina

4,912

4

( 0.4)

242

( 0.8)

North Dakota

3,066

2

( 0.3)

238

( 0.7)

Ohio

4,767

4

( 0.5)

238

( 1.0)

Oklahoma

3,199

4

( 0.5)

229

( 1.0)

Oregon

3,306

4

( 0.5)

236

( 0.9)

Pennsylvania

3,459

3

( 0.6)

236

( 1.1)

Rhode Island

3,201

3

( 0.6)

230

( 1.0)

South Carolina

3,438

6

( 0.6)

236

( 0.9)

South Dakota

3,342

1

( 0.3)

237

( 0.7)

Tennessee

3,615

3

( 0.5)

228

( 1.0)

Texas

5,653

7

( 0.6)

237

( 0.9)

Utah

3,733

3

( 0.4)

235

( 0.8)

Vermont

2,840

4

( 0.4)

242

( 0.8)

Virginia

3,497

6

( 0.8)

239

( 1.1)

Washington

3,769

3

( 0.5)

238

( 1.0)

West Virginia

2,810

3

( 0.4)

231

( 0.8)

Wisconsin

3,136

4

( 0.5)

237

( 0.9)

Wyoming

2,781

1

( 0.1)

241

( 0.6)

DC

2,748

4

( 0.3)

205

( 0.7)

DoDEA/DDESS

1,313

2

( 0.4)

237

( 0.7)

DoDEA/DoDDS

2,777

1

( 0.2)

237

( 0.5)

 

NOTE: The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics in the table appear in parentheses.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 Mathematics Assessment.

 

Appendix
Overview of Procedures Used for the NAEP 2003 Mathematics Assessment

 

Drawing Inferences from the Results

The reported statistics are estimates and are therefore subject to a measure of uncertainty. There are two sources of such uncertainty. First, NAEP uses a sample of students rather than testing all students. Second, all assessments have some amount of uncertainty related to the fact that they cannot ask all questions that might be asked in a content area. The magnitude of this uncertainty is reflected in the standard error of each of the estimates. When the percentages or average scale scores of certain groups are compared, the estimated standard error should be taken into account. Therefore, the comparisons are based on statistical tests that consider the estimated standard errors of those statistics and the magnitude of the difference among the averages or percentages.

For the data in this report, all the estimates have corresponding estimated standard errors of the estimates. For example, the following tables show the average national public-school scale score for the NAEP 1990–2003 national assessments and the percentage of students within each achievement-level range and at or above achievement levels. In both tables, estimated standard errors appear in parentheses next to each estimated scale score or percentage. For the estimated standard errors corresponding to other data from this report, the reader can go to the Data Tool on the NCES web site at http://nces.ed.gov/nationsreportcard/naepdata/.

Average mathematics scale scores and standard errors, grades 4 and 8: 1990–2003

 

Accommodations not permitted

Accommodations permitted

 

1990

1992

1996

2000

1996

2000

2003

Grade 4

213

(0.9)*

220

(0.7)*

224

(0.9)*

228

(0.9)*

224

(1.0)*

226

(0.9)*

235

(0.2)

Grade 8

263

(1.3)*

268

(0.9)*

272

(1.1)*

275

(0.8)*

270

(0.9)*

273

(0.8)*

278

(0.3)

* Significantly different from 2003.
NOTE: Standard errors of the estimated scale scores appear in parentheses.
In addition to allowing for accommodations, the accommodations-permitted results (1996–2003) differ slightly from previous years' results, and from previous reported results for 1996 and 2000 due to changes in sample weighting procedures.
Significance tests were performed using unrounded numbers.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992, 1996, 2000, and 2003 Mathematics Assessments.

Percentage of students and standard errors, by mathematics achievement level, grades 4 and 8: 1990–2003

 

Below Basic

At Basic

At or above
Basic

At or above
Proficient

Grade 4

Accommodations not permitted

1990

50

(1.4)*

1

(0.4)*

50

(1.4)*

13

(1.2)*

 

1992

41

(1.0)*

2

(0.3)*

59

(1.0)*

18

(1.0)*

 

1996

36

(1.2)*

2

(0.3)*

64

(1.2)*

21

(0.9)*

 

2000

31

(1.1)*

3

(0.3)*

69

(1.1)*

26

(1.1)*

Accommodations permitted

1996

37

(1.3)*

2

(0.3)*

63

(1.3)*

21

(1.1)*

 

2000

35

(1.3)*

3

(0.3)*

65

(1.3)*

24

(1.0)*

 

2003

23

(0.3)

4

(0.1)

77

(0.3)

32

(0.3)


Grade 8

Accommodations not permitted

1990

48

(1.4)*

2

(0.3)*

52

(1.4)*

15

(1.1)*

 

1992

42

(1.1)*

3

(0.4)*

58

(1.1)*

21

(1.0)*

 

1996

38

(1.1)*

4

(0.5)*

62

(1.1)*

24

(1.1)*

 

2000

34

(0.8)*

5

(0.5)

66

(0.8)*

27

(0.9)

Accommodations permitted

1996

39

(1.0)*

4

(0.4)*

61

(1.0)*

23

(1.0)*

 

2000

37

(0.9)*

5

(0.4)

63

(0.9)*

26

(0.8)*

 

2003

32

(0.3)

5

(0.1)

68

(0.3)

29

(0.3)

* Significantly different from 2003.
NOTE: Standard errors of the estimated percentages appear in parentheses.
Detail may not sum to totals because of rounding.
In addition to allowing for accommodations, the accommodations-permitted results (1996–2003) differ slightly from previous years' results, and from previously reported results for 1996 and 2000 due to changes in sample weighting procedures.
Significance tests were performed using unrounded numbers.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992, 1996, 2000, and 2003 Mathematics Assessments.

 

 

Using confidence intervals based on the standard errors provides a way to take into account the uncertainty associated with sample estimates and to make inferences about the population averages and percentages in a manner that reflects that uncertainty. An estimated sample average scale score plus or minus 1.96 standard errors approximates a 95 percent confidence interval for the corresponding population quantity. This statement means that one can conclude with an approximately 95 percent level of confidence that the average performance of the entire population of interest (e.g., all fourth-grade students in public schools) is within plus or minus 1.96 standard errors of the sample average.

For example, suppose that the average mathematics scale score of the students in a particular group was 256 with an estimated standard error of 1.2. An approximately 95 percent confidence interval for the population quantity would be as follows:

Average ± 1.96 standard errors
256 ± 1.96 x 1.2
256 ± 2.4
(253.6, 258.4)

Thus, one can conclude with a 95 percent level of confidence that the average scale score for the entire population of students in that group is between 253.6 and 258.4. It should be noted that this example and the examples in the following sections are illustrative. More precise estimates carried out to one or more decimal places are used in the actual analyses.

Similar confidence intervals can be constructed for percentages, if the percentages are not extremely large or extremely small. Extreme percentages should be interpreted with caution. Adding or subtracting the standard errors associated with extreme percentages could cause the confidence interval to exceed 100 percent or fall below 0 percent, resulting in numbers that are not meaningful.


Where to Find More Information

The NAEP Mathematics Assessment

The latest news about the NAEP 2003 Mathematics assessment and the national results can be found on the NAEP web site at http://nces.ed.gov/nationsreportcard/mathematics/results/. The individual snapshot reports for each participating state and other jurisdictions are also available in the state results section of the web site at http://nces.ed.gov/nationsreportcard/states/. The Nation's Report Card Mathematics Highlights 2003 may be ordered or downloaded at the NAEP web site. The Nation's Report Card: Mathematics 2003 will be available at the NAEP web site in 2004. The Mathematics Framework for the 2003 National Assessment of Educational Progress, on which this assessment is based, is available at the Internet address http://www.nagb.org/pubs/math_fw_03.pdf.

Additional Results from the Mathematics Assessment

For more findings from the 2003 Mathematics assessments, refer to the NAEP 2003 results at http://nces.ed.gov/nationsreportcard/naepdata/. The interactive database at this site includes student, teacher, and school variables for all participating states and other jurisdictions, the nation, and the four regions. Data tables are also available for each jurisdiction, with all background questions cross-tabulated with the major demographic variables.

Technical Documentation

For explanations of NAEP survey procedures see Allen, N. L., Donoghue, J. R., and Schoeps, T. L. (2001). The NAEP 1998 Technical Report. (NCES 2001–509). Washington , DC : U.S. Department of Education, Office of Educational Research and Improvement, National Center for Education Statistics. Technical information may also be found on the NAEP web site (http://nces.ed.gov/nationsreportcard/mathematics/results2003/interpret-results.asp).

Publications on the inclusion of students with disabilities and limited English proficient students

Olson, J. F., and Goldstein, A. A. (1997). The Inclusion of Students with Disabilities and Limited-English-Proficient Students in Large-Scale Assessments: A Summary of Recent Progress (NCES 97–482). Washington , DC : U.S. Department of Education, Office of Educational Research and Improvement, National Center for Education Statistics.

Mazzeo, J., Carlson, J. E., Voelkl, K. E., and Lutkus, A. D. (2000). Increasing the Participation of Special-Needs Students in NAEP: A Report on 1998 Research Activities (NCES 2000–473). Washington , DC : U.S. Department of Education, Office of Educational Research and Improvement, National Center for Education Statistics.

Lutkus, A. D., and Mazzeo, J. (2003). Including Special-Needs Students in the NAEP 1998 Mathematics Assessment, Part I: Comparison of Overall Results With and Without Accommodations (NCES 2003–467). Washington , DC : U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics.

Lutkus, A. D. (forthcoming). Including Special-Needs Students in the NAEP 1998 Mathematics Assessment, Part II: Results for Students with Disabilities and Limited English Proficient Students (NCES 2003–468). Washington , DC : U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics.

To Order Publications

Recent NAEP publications related to mathematics are listed on the mathematics page of the NAEP web site and are available electronically. Publications can also be ordered from:

Education Publications Center (ED Pubs)
U.S. Department of Education
 P.O. Box 1398
Jessup , MD 20794–1398

Call toll free: 1-877-4ED PUBS (1-877-433-7827)
TTY/TDD: 1-877-576-7734
FAX: 1-301-470-1244