National Assessment of Educational Progress

The Nation’s Report CardTM

U.S. Department of Education

Institute of Education Sciences

NCES 2006–453

CONTENTS

Mathematics

2005

Executive Summary 1

National Results 2

Student Group Results 3

Percentiles 12

State Results 13

Student Demographics 22

Framework and

Sample Questions 24

Technical and Data Appendix 32
The Nation’s Report CardTM, the National 

Assessment of Educational Progress (NAEP), 

is a nationally representative and continuing 

assessment of what America’s students know 

and can do in various subject areas. For over 

three decades, assessments have been conducted 

periodically in reading, mathematics, science, 

writing, history, geography, and other subjects.

 By making objective information on student performance available to policymakers at the national, state, 

and local levels, NAEP is an integral part of our nation’s 

evaluation of the condition and progress of education. 

Only information related to academic achievement and 

relevant variables is collected under this program. The 

privacy of individual students and their families is protected, and the identities of participating schools are not 

released. 

 NAEP is a congressionally mandated project of the 

National Center for Education Statistics within the 

Institute of Education Sciences of the U.S. Department 

of Education. The Commissioner of Education Statistics 

is responsible, by law, for carrying out the NAEP project 

through competitive awards to qualified organizations.

 In 1988, Congress established the National 

Assessment Governing Board (NAGB) to oversee and 

set policy for NAEP. The Board is responsible for selecting the subject areas to be assessed; setting appropriate 

student achievement levels; developing assessment objectives and test specifications; developing a process for 

the review of the assessment; designing the assessment 

methodology; developing guidelines for reporting and 

disseminating NAEP results; developing standards and 

procedures for interstate, regional, and national comparisons; determining the appropriateness of all assessment 

items and ensuring the assessment items are free from 

bias and are secular, neutral, and nonideological; taking 

actions to improve the form, content, use, and reporting 

of results of the National Assessment; and planning and 

executing the initial public release of NAEP reports. 

What is The Nation's

Report CardTM?

Darvin M. Winick, Chair 

President

Winick & Associates

Dickinson, Texas 

Sheila M. Ford, Vice Chair

Former Principal

Horace Mann Elementary

 School

Washington, D.C. 

Francie Alexander 

Chief Academic Officer, 

 Scholastic, Inc.

Senior Vice President, 

 Scholastic Education

New York, New York 

David J. Alukonis 

Chairman

Hudson School Board

Hudson, New Hampshire 

Amanda P. Avallone 

Assistant Principal &

 Eighth-Grade Teacher

Summit Middle School 

Boulder, Colorado 

Honorable Jeb Bush 

Governor of Florida

Tallahassee, Florida 

Barbara Byrd-Bennett 

Chief Executive Officer

Cleveland Municipal

 School District

Cleveland, Ohio

Carl A. Cohn 

Superintendent

San Diego City Schools

San Diego, California

Shirley V. Dickson 

Educational Consultant 

Laguna Niguel, California 

John Q. Easton 

Executive Director

Consortium on Chicago

 School Research

Chicago, Illinois

Honorable Dwight Evans 

Member

Pennsylvania House of 

 Representatives

Philadelphia, Pennsylvania

David W. Gordon 

Sacramento County 

 Superintendent of Schools 

Sacramento County Office 

 of Education 

Sacramento, California 

Kathi M. King 

Twelfth-Grade Teacher

Messalonskee High School

Oakland, Maine

Honorable Keith King 

Member

Colorado House of

 Representatives

Colorado Springs, Colorado

Kim Kozbial-Hess 

Fourth-Grade Teacher

Fall-Meyer Elementary School

Toledo, Ohio

Andrew C. Porter 

Professor

Leadership Policy and 

 Organizations

Vanderbilt University

Nashville, Tennessee 

Luis A. Ramos 

Community Relations Manager

PPL Susquehanna

Berwick, Pennsylvania

Mark D. Reckase 

Professor

Measurement and 

 Quantitative Methods

Michigan State University

East Lansing, Michigan

John H. Stevens 

Executive Director

Texas Business and 

 Education Coalition

Austin, Texas

Mary Frances Taymans, SND 

Executive Director

National Catholic

 Educational Association

Washington, D.C.

Oscar A. Troncoso

Principal

Socorro High School

Socorro Independent School 

 District

El Paso, Texas

Honorable Thomas J. Vilsack

Governor of Iowa 

Des Moines, Iowa

Michael E. Ward 

Former State Superintendent 

 of Public Instruction

North Carolina Public Schools

Jackson, Mississippi 

Eileen L. Weiser 

Member, State Board of

 Education 

Michigan Department of

 Education

Lansing, Michigan

Grover J. Whitehurst (Ex officio) 

Director 

Institute of Education Sciences

U.S. Department of Education

Washington, D.C.

Charles E. Smith 

Executive Director

NAGB

Washington, D.C.

U.S. DEPARTMENT OF EDUCATION

Margaret Spellings

Secretary 

INSTITUTE OF EDUCATION SCIENCES

Grover J. Whitehurst

Director

NATIONAL CENTER FOR 

EDUCATION STATISTICS

Grover J. Whitehurst

Acting Commissioner 

OCTOBER 2005

The National Assessment Governing Board

The Nation’s Report CardTM
Mathematics 2005 1

Executive Summary

EXECUTIVE SUMMARY

This report presents the national and state results of the 

NAEP assessment in mathematics and compares them 

to results from assessments in 2003 and in the first year 

data were available, usually 1990. In 2005, nationally 

representative samples of about 172,000 fourth-grade 

and 162,000 eighth-grade students nationwide participated in that assessment.

National Mathematics Results 

Fourth-graders’ average score was 3 points higher, and 

eighth-graders’ average score was 1 point higher in 2005 

than in 2003 on a 0 to 500 point scale. The average 

scores increased since the first assessment year, 1990, by 

25 points at grade 4 and by 16 points at grade 8. 

 Between 1990 and 2005, the percentage of fourthgraders performing at or above Basic increased by 30 

percentage points, 

from 50 to 80 

percent, and the percentage performing 

at or above Proficient

increased from 13 

to 36 percent. The 

percentage of eighthgraders performing at 

or above Basic was 17 percentage points higher in 2005 

(69 percent) than in 1990 (52 percent), and the percentage performing at or above Proficient increased from 

15 to 30 percent. 

Mathematics Results for Student Groups at 

Grade 4

White fourth-graders scored higher on average in mathematics than their Black and Hispanic peers in 2005. 

The average scores for all three racial/ethnic groups were 

higher in 2005 than in any previous assessment year. 

 In 2005, students who were eligible for free or 

reduced-price school lunch and those who were not eligible had higher average scores in 2005 than in 1996. 

 In 2005, male students scored higher on average than 

their female counterparts. Both male and female fourthgraders’ average scores were higher in 2005 than in any 

previous assessment year.

Mathematics Results for Student Groups at 

Grade 8

The average scores for White, Black, and Hispanic 

eighth-graders were higher in 2005 than in any previous 

assessment year. 

 Students who were eligible for free or reduced-price 

lunch and those who were not eligible scored higher on 

average in 2005 than in any previous assessment year 

from 1996 through 

2003. 

 Average scores for 

male and female 

eighth-graders were 

both higher in 2005 

than in 1990 or in 

2003.

Mathematics 

Results for the States

Examining the short-term trends between 2003 and 

2005, when all 50 states and the District of Columbia 

and Department of Defense Schools were assessed, 

shows average scores for students at grade 4 increased in 

31 states and both jurisdictions. The percentage of students performing at or above Basic increased in 23 states 

and the District of Columbia.

 At grade 8, there were 7 states with higher average 

scores in 2005 than in 2003. The percentage of students 

performing at or above Basic increased in 5 states.

 Turning to the longer trend, the first state assessment 

at grade 4 was given in 1992 in 42 states and jurisdictions. Each of them had a higher average score and 

showed a greater percentage of students performing at 

or above Basic in 2005 compared to 1992.

 At grade 8, there were 38 states and jurisdictions that 

participated in both 1990 and 2005. Each of them had 

a higher average score and showed a greater percentage 

of students performing at or above Basic in 2005 than 

in 1990.

For More Information...

The NAEP initial release website (www.nationsreportcard.gov) provides additional information on the NAEP 

assessments, including an interactive view of state results and links to PDF versions of all NAEP reports, a data 

tool for exploring results and calculating the statistical signifi cance of differences, and a tool for examining released questions. 

Average scores for White, 

Black, and Hispanic 

students were higher in 

2005 than in any previous assessment year at 

both grades 4 and 8.

Average mathematics 

scores increased between 2003 and 2005 

at both grades 4 and 8.
2 The Nation’s Report CardTM

Results are presented in two ways: in terms of scale scores 

and as the percentage of students scoring at or above 

three benchmarks called achievement levels. For results to 

be presented in this report, each reporting group must 

meet minimum reporting standards. Reporting standards 

were met for public schools in the nation and the states. 

However, too few private schools participated for their 

results to be reported separately. See the Technical Notes 

on page 32 for more information.

Scale Scores

NAEP mathematics scores are reported for grades 4 and 

8 on a 0–500 scale. Scale score results also are presented 

for students at various percentiles. An examination of 

scores at different percentiles on the 0–500 scale indicates 

whether or not the trends seen in the overall national 

average score results are reflected in the performance of 

lower-, middle-, and higher-performing students.

 Item maps, presented on pages 26 and 30, provide 

interpretive information about a scale score in terms of 

the skills and knowledge students with a certain score 

are likely to have. Items placed along the scale in an item 

map demonstrate how skills correspond to levels of performance.

 Scales are created for other subjects independently, so 

even when another subject’s scale has the same numerical 

range (0–500), average scores should not be compared 

across subjects.

Achievement Levels

NAEP results are reported at three achievement levels: 

Basic, Proficient, and Advanced. Achievement levels are 

performance standards showing what students should 

know and be able to do. They are set by the National 

Assessment Governing Board (NAGB), based on recommendations from panels of educators and members of 

the public, to provide a context for interpreting student 

performance on NAEP. In this report, the achievement-level results are reported as percentages of students 

performing at or above Basic and at or above Proficient.

 As provided by law, the National Center for Education 

Statistics (NCES), upon review of congressionally mandated evaluations of NAEP, has determined that achievement 

levels are to be used on a trial basis and should be interpreted with caution. However, NCES and NAGB have 

affirmed the usefulness of these performance standards for 

understanding trends in achievement. NAEP achievement 

levels have been widely used by national and state officials.

Interpreting Results

NAEP uses widely accepted statistical standards in analyzing data. For instance, this report discusses only findings 

that are statistically significant at the .05 level. However, 

some differences that are statistically significant appear 

small, particularly in recent assessment years, when the 

sample sizes have been larger. See the Technical Notes on 

page 33 for more information on interpreting the size of 

score differences.

 Differences between scale scores or percentages are 

calculated using unrounded numbers. In some instances, 

the result of the subtraction differs from what would be 

obtained by subtracting the rounded values shown in the 

accompanying figure or table. The first part of the report 

presents the national results of all schools. However, when 

state results are compared to the nation, only public 

school results are shown. The national public numbers 

may differ slightly from overall national numbers.

 Finally, most figures show data for two samples. One 

sample includes students who received accommodations 

when they needed them, and the other includes students 

for whom no accommodations were permitted. In 1996, 

administration procedures were first introduced that 

allowed the use of accommodations for students who 

needed them. Therefore, the results from more recent 

years are more inclusive than results from earlier years. 

See tables A-1–A-3 for exclusion rates. Any comparisons 

between 2005 and 1998 will be made with the accommodated sample.

Understanding NAEP Results

NATIONAL RESULTS

NAEP Achievement-Level Descriptions

The three NAEP achievement levels, from lowest to highest, are

Basic—denotes partial mastery of the knowledge and skills that are fundamental for profi cient work at a given grade.

Profi cient—represents solid academic performance. Students reaching this level have demonstrated competency over 

challenging subject matter.

Advanced—signifi es superior performance.

Detailed descriptions of the NAEP achievement levels for each subject and grade can be found on the NAGB website 

(http://www.nagb.org/pubs/pubs.html). 
✓ KEY FINDINGS

Mathematics 2005 3

NATIONAL RESULTS

Figure 1. Average scale scores and achievement-level results in mathematics, grades 4 and 8: 

Various years, 1990–2005

* Signifi cantly different from 2005.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, 

National Assessment of Educational Progress (NAEP), various years, 1990–2005 Mathematics Assessments.

! Average scores were higher 

in 2005 than in any previous 

assessment year for students 

in both grades 4 and 8.

! The national average 

mathematics scale score 

increased by 3 points from 

2003 to 2005 and by 25 

points from 1990 to 2005.

! In 2005, the percentages of 

students performing at or 

above Basic (80 percent) and 

at or above Profi cient (36 

percent) were higher than in 

any previous assessment year.

! The national average 

mathematics score was 16 

points higher in 2005 than in 

1990 and showed a 1-point 

increase between 2003 and 

2005.

! Higher percentages of 

students performed at or 

above Basic (69 percent) 

and at or above Proficient

(30 percent) in 2005 than 

in any previous assessment 

year.

GRADE 8

GRADE 4

224*

226*

220*

224*

213*

235* 238

270*

273*

268*

272*

263*

278* 279

YEAR

13*

50*

18*

59*

21*

63*

24*

65*

32*

77*

36

80

21*

64*

0

’90 ’92 ’96 ’00 ’03 ’05

100

0

PERCENT

’90 ’92 ’96 ’00 ’03 ’05 YEAR

’90 ’92 ’96 ’00 ’03 ’05 YEAR

15*

52*

21*

58*

23*

61*

24*

62*

100

0

PERCENT

’90 ’92 ’96

26*

63*

’00

29*

68*

’03

30

69

’05 YEAR

Grade 8

SCALE SCORE

280

270

260

250

500

0

Grade 4

SCALE SCORE

240

230

220

210

500

0

Accommodations

permitted

Accommodations

not permitted

At or above 

Proficient

At or above 

Basic

Accommodations not permitted

Accommodations permitted

Reporting Student Groups

In addition to national results, NAEP reports results for specifi ed groups of students. 

Because performance of a particular student group can be signifi cantly different from 

the performance of the overall student population, it is important to examine separately the performance of each major student group. 

 Results are provided on the following pages for student groups defi ned by race/ethnicity, eligibility for free/reduced-price school lunch, and gender. These results show 

how these groups of students performed in comparison with one another, and over 

time. More information, including interactive charts of performance for various student 

groups, can be found at www.nationsreportcard.gov.

 Typically, NAEP reports also show results separately for public and private schools. 

However, overall, an insuffi cient proportion of private schools participated in NAEP 

in 2005, so the results are shown in the Technical Notes for Catholic and Lutheran 

schools only.
4 The Nation’s Report CardTM

* Signifi cantly different from 2005. 1 Sample size was insuffi cient to 

permit reliable estimates for Asian/

Pacifi c Islander students in 1990. 

Special analyses raised concerns 

about the accuracy and precision 

of national grade 4 Asian/Pacifi c 

Islander results in 2000. As a result, 

they are omitted from this report.

2 Sample sizes were insuffi cient to 

permit reliable estimates for American Indian/Alaska Native students in 

1990, 1992, 1996, and 2000. 

SOURCE: U.S. Department of 

Education, Institute of Education Sciences, National Center for Education 

Statistics, National Assessment of 

Educational Progress (NAEP), various 

years, 1990–2005 Mathematics 

Assessments.

Figure 2. Average scale scores and achievement-level results in mathematics, by race/ethnicity, 

grade 4: Various years, 1990–2005

Results for Groups of Students

Results by Race/Ethnicity

NAEP reports data on student race/ethnicity based on 

information obtained from school rosters. Figures 2 and 3 

show results for five mutually exclusive categories: White, 

Black, Hispanic, Asian/Pacific Islander, and American 

Indian/Alaska Native. Black includes African American, 

Hispanic includes Latino, and Pacific Islander includes 

Native Hawaiian. Race categories exclude Hispanic origin 

unless specified. For information about the performance 

of students not classified in one of these categories, visit 

www.nationsreportcard.gov.

220

234*

232*

220* 227*

243*

226

203*

198*

193* 188*

216*

226

207* 208*

202* 200*

222*

251

229*

231* 231*

205*

199*

226*

246*

246

223*

Black

Hispanic

American Indian/Alaska Native2

White

Asian/Pacific Islander1

500

Grade 4

0

SCALE SCORE

YEAR

270

260

250

240

230

220

210

200

190

180

170

’90 ’92 ’96 ’00 ’03 ’05

YEAR

0

100

17*

64

21

68

American Indian/Alaska Native2

’90 ’92 ’96 ’00 ’03 ’05

48*

87*

55

90

27*

67*

21*

65*

28*

73*

Asian/Pacific Islander1

16*

62*

19

68

7*

42*

7*

40*

7*

39*

6*

33* 34*

Hispanic

10*

54*

13

60

5*

36*

3*

27*

4*

30*

2*

17* 22*

Black

PERCENT

43*

87*

47

90

31*

78*

27*

76*

27*

74*

22*

69*

16*

59*

White 100

0

100

0

100

0

100

0

100

0

1*

5*

Accommodations

permitted

Accommodations

not permitted

At or above 

Proficient

At or above 

Basic

Accommodations not permitted

Accommodations permitted

STUDENT GROUP RESULTS
✓ KEY FINDINGS

! Students from all fi ve racial/

ethnic groups scored higher, 

on average, in 2005 than in 

2003.

! White, Black, and Hispanic 

students scored higher, on 

average, in 2005 than in the 

fi rst assessment year, 1990.

! Higher percentages of White, 

Black, Hispanic, and Asian/

Pacifi c Islander students 

scored at or above Basic in 

2005 than in any previous 

assessment year.

! Higher percentages of students 

from all fi ve NAEP racial/ethnic 

groups scored at or above 

Proficient in 2005 than in 

2003. 

! White, Black, and Hispanic 

students all showed higher 

average scores in 2005 than in 

any previous assessment year.

! Higher percentages of Black 

and Hispanic students scored 

at or above Basic than in any 

previous assessment year.

! Higher percentages of White, 

Black, and Hispanic students 

performed at or above 

Proficient in 2005 than in any 

previous assessment year. 

Mathematics 2005 5

STUDENT GROUP 

RESULTS

* Signifi cantly different from 2005. 1 Sample size was insuffi cient to permit reliable estimates for Asian/Pacifi c Islander students in 1990. Special analyses 

raised concerns about the accuracy and precision of national grade 8 Asian/Pacifi c Islander results in 1996. As a 

result, they are omitted from this report.

2 Sample sizes were insuffi cient to permit reliable estimates for American Indian/Alaska Native students in 1990, 

1992, 1996, and 2000. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, 

National Assessment of Educational Progress (NAEP), various years, 1990–2005 Mathematics Assessments.

Figure 3. Average scale scores and achievement-level results in mathematics, by race/ethnicity, 

grade 8: Various years, 1990–2005

GRADE 4

GRADE 8

262

251* 253*

249* 246* 255

244*

240* 237* 237*

252*

259* 264 263

295 290 288 291*

289

284* 281*

277*

251*

242*

281*

287*

270*

288*

Asian/Pacific Islander1

Black

Hispanic

American Indian/Alaska Native2

White

500

Grade 8

0

SCALE SCORE

YEAR

300

290

280

270

260

250

240

230

220

210

200

’90 ’92 ’96 ’00 ’03 ’05

YEAR

15

52

14

53

American Indian/Alaska Native2

’90 ’92 ’96 ’00 ’03 ’05

43*

78

47

81

41

75*

43

76

41

74*

Asian/Pacific Islander1

12*

48*

13

52

8*

41*

8*

39*

9*

39*

7*

35*

7*

34*

Hispanic

7*

39*

9

42

5*

31*

4*

25*

5*

27*

2*

20*

5*

22*

Black

PERCENT

37*

80

39

80

34*

76*

30*

73*

30*

73*

26*

68*

18*

60*

White 100

0

100

0

100

0

100

0

100

0

Accommodations

permitted

Accommodations

not permitted

At or above 

Proficient

At or above 

Basic

Accommodations not permitted

Accommodations permitted
White –Black and White –Hispanic Score Gaps

Another way to view trends in student performance is 

to determine whether the score “gap” between student 

groups has narrowed or widened since earlier years. 

Figures 4 and 5 show the score gaps between White and 

Black students and between White and Hispanic students 

across assessment years. Score gaps are calculated by subtracting the unrounded average scale score of one student 

group from that of another. Here, the average score for 

Black or Hispanic students is subtracted from the average 

score for White students. 

Figure 4. Average mathematics scale scores and score gaps for White –Black and 

White –Hispanic students, grade 4: Various years, 1990–2005

6 The Nation’s Report CardTM

220

234* 232* 227*

220*

243*

203*

198*

193*

188*

216*

231*

199*

246

Black

White

500

Grade 4

0

SCALE SCORE

YEAR

270

260

250

240

230

220

210

200

190

180

170

’90 ’92 ’96 ’00 ’03 ’05

Score gap

32* 35* 32* 34* 31*

27* 26

White – Black

234* 232*

227*

220*

243*

226

208* 207* 202* 200*

222*

231*

205*

246

Hispanic

White

500

Grade 4

0

SCALE SCORE

YEAR

270

260

250

240

230

220

210

200

190

180

170

’90 ’92 ’96 ’00 ’03 ’05

Score gap

25 27*

22 20

27 25* 20

White – Hispanic

* Signifi cantly different from 2005.

NOTE: Score gaps, displayed in the shaded area, are calculated based on differences 

between unrounded average scale scores.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1990–2005 Mathematics Assessments.

Accommodations not permitted

Accommodations permitted

STUDENT GROUP RESULTS
✓ KEY FINDINGS

! In 2005, at both grades 4 

and 8, White students scored 

higher, on average, than Black 

and Hispanic students.

! The White – Black score gap 

was narrower in 2005 than in 

any previous assessment year.

! The apparent change between 2005 and 2003 in 

the White – Hispanic score 

gap was not statistically 

signifi cant.

! There was no signifi cant 

change in the White – Black 

gap between 1990 and 2005, 

but the gap narrowed from 

35 to 34 between 2003 and 

2005.

! The White – Hispanic score 

gap narrowed from 29 to 27 

between 2003 and 2005, but 

was not statistically different 

between 1990 and 2005.

Figure 5. Average mathematics scale scores and score gaps for White –Black and 

White –Hispanic students, grade 8: Various years, 1990–2005

GRADE 4

GRADE 8

Mathematics 2005 7

STUDENT GROUP 

RESULTS

255

244*

240* 237* 237*

252*

289 284* 281*

277*

242*

281*

270*

288*

Black

White

500

Grade 8

0

SCALE SCORE

YEAR

300

290

280

270

260

250

240

230

220

210

200

’90 ’92 ’96 ’00 ’03 ’05

Score gap

33 40* 39* 40* 35* 34

41*

White – Black

262

253* 251* 249* 246*

259*

284* 289 281* 277*

251*

281*

270*

288*

Hispanic

White

500

Grade 8

0

SCALE SCORE

YEAR

300

290

280

270

260

250

240

230

220

210

200

’90 ’92 ’96 ’00 ’03 ’05

Score gap

24 28 30 30 31* 29* 27

White – Hispanic

* Signifi cantly different from 2005.

NOTE: Score gaps, displayed in the shaded area, are calculated based on differences 

between unrounded average scale scores.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1990–2005 Mathematics Assessments.

Accommodations not permitted

Accommodations permitted
8 The Nation’s Report CardTM

Results by Eligibility for Free/Reduced-Price School Lunch

An indicator of a student’s socioeconomic status is 

whether or not that student is eligible for free or 

reduced-price lunch under the National School Lunch 

Program (NSLP). Children from families with incomes 

at or below 130 percent of the poverty level are eligible 

for free meals. Those with incomes between 130 percent and 185 percent of the poverty level are eligible 

for reduced-price meals. (For the period July 1, 2004, 

through June 30, 2005, for a family of four, 130 percent of the poverty level was $24,505, and 185 percent 

was $34,873. See http://www.fns.usda.gov/cnd/lunch/ 

for more information.)

 Average mathematics scores and achievement-level 

results by students’ eligibility for free/reduced-price school 

lunch are shown in figure 6 for grade 4 and figure 7 for 

grade 8. NAEP first began collecting information on student eligibility for the program in 1996; therefore, results 

for these student groups are not available for 1990 and 

1992. 

 The percentage of students with available information has changed over time. In addition, the regulations 

on classifying students as eligible have changed over the 

years. See Changing Demographics of Students at Grades 

4 and 8 on page 22 for more information.

* Signifi cantly different from 2005.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1996–2005 Mathematics Assessments.

Figure 6. Average scale scores and achievement-level results in mathematics, by students’

eligibility for free/reduced-price lunch, grade 4: Various years, 1996–2005

232*

208* 207*

235*

Not eligible

Eligible

244*

222*

248

225

500

Grade 4

0

SCALE SCORE

YEAR

270

260

250

240

230

220

210

200

190

180

170

’96 ’00 ’03 ’05

237*

231*

Information

241* not available

244

YEAR

0

41*

84*

45

87

36*

80*

28*

72*

Information

not available

’96 ’00 ’03 ’05

0

45*

88*

49

90

32*

78*

27*

76*

Not eligible

0

PERCENT

15*

62*

19

67

8*

43*

8*

40*

Eligible 100

0

100

0

100

0

At or above 

Proficient

At or above 

Basic

STUDENT GROUP RESULTS
✓ KEY FINDINGS

! In 2005, students who 

were not eligible for free 

or reduced-price school 

lunch had higher average 

mathematics scores than 

students who were eligible at 

both grades 4 and 8.

! Average scores were higher 

in 2005 than in any previous 

assessment year both for 

students who were eligible for 

free or reduced-price lunch 

and for those who were not 

eligible.

! The percentages of students 

who were eligible and of 

those who were not eligible 

performing at or above Basic

and at or above Proficient

were higher in 2005 than in 

any previous assessment year.

! Average scores were higher 

in 2005 than in any previous 

assessment year both for 

students who were eligible for 

free or reduced-price lunch 

and for those who were not 

eligible.

! The percentages of students 

performing at or above Basic

and at or above Proficient

were higher in 2005 than in 

any previous assessment year 

both for students who were 

eligible and for those who 

were not 

eligible.

Mathematics 2005 9

STUDENT GROUP 

RESULTS

GRADE 4

GRADE 8

* Signifi cantly different from 2005.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1996–2005 Mathematics Assessments.

Figure 7. Average scale scores and achievement-level results in mathematics, by students’

eligibility for free/reduced-price lunch, grade 8: Various years, 1996–2005

276*

285*

289

277*

253* 250*

283*

Not eligible

Eligible

287*

259*

288

262

500

Grade 8

0

SCALE SCORE

YEAR

300

290

280

270

260

250

240

230

220

210

200

’96 ’00 ’03 ’05

279*

Information

not available

36

75*

40

79

29*

67*

30*

70*

Information

not available

37*

79*

39

79

34*

74*

28*

69*

Not eligible

PERCENT

12*

48*

13

51

9*

41*

8*

38*

Eligible

YEAR ’96 ’00 ’03 ’05

100

0

100

0

100

0

At or above 

Proficient

At or above 

Basic
10 The Nation’s Report CardTM

* Signifi cantly different from 2005.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National 

Assessment of Educational Progress (NAEP), various years, 1990–2005 Mathematics Assessments.

Figure 8. Average scale scores and achievement-level results in mathematics, by gender, 

grade 4: Various years, 1990–2005

Results by Gender

The average mathematics scores and percentages of 

students at or above Basic and at or above Proficient are 

shown by gender at grade 4 in figure 8 and at grade 8 in 

figure 9.

223*

227*

219*

221*

222*

226*

213*

224*

214* 224*

Female

Male

233*

236* 239

237

500

Grade 4

0

SCALE SCORE

YEAR

270

260

250

240

230

220

210

200

190

180

170

’90 ’92 ’96 ’00 ’03 ’05

YEAR

30*

76*

34

80

22*

64*

20*

63*

19*

63*

16*

57*

12*

49*

Female

’90 ’92 ’96 ’00 ’03 ’05

PERCENT

35*

78*

38

81

26*

67*

22*

63*

24*

65*

19*

60*

13*

51*

Male 100

0

100

0 Accommodations

permitted

Accommodations

not permitted

At or above 

Proficient

At or above 

Basic

Accommodations not permitted

Accommodations permitted

STUDENT GROUP RESULTS
✓ KEY FINDINGS

! In 2005, male students scored 

higher on average than female 

students at both grades 4 

and 8. 

! The average scores in 2005 

were 239 and 237 for 

male and female students, 

respectively—the highest 

average scores of any 

assessment year.

! Greater percentages of both 

male and female students 

scored at or above Basic

and at or above Proficient in 

2005 than in any previous 

assessment year.

! The average score was higher 

in 2005 than in 1990 or 

in 2003 for both male and 

female students.

! The percentages of both 

male and female students 

performing at or above Basic

were higher in 2005 than in 

1990 or in 2003.

! The percentages of both 

male and female students 

performing at or above 

Proficient were higher in 

2005 than in 1990, and 

the percentage for female 

students increased from 27 

percent in 2003 to 28 percent 

in 2005.

Mathematics 2005 11

STUDENT GROUP 

RESULTS

Figure 9. Average scale scores and achievement-level results in mathematics, by gender, 

grade 8: Various years, 1990–2005

* Signifi cantly different from 2005.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1990–2005 Mathematics Assessments.

269*

269*

268*

272* 272*

262*

271* 272* 263*

274*

Female

Male

277*

278*

278

280

500

Grade 8

0

SCALE SCORE

YEAR

300

290

280

270

260

250

240

230

220

210

200

’90 ’92 ’96 ’00 ’03 ’05

YEAR

27*

67*

28

69

24*

63*

22*

60*

23*

63*

21*

58*

14*

52*

Female

’90 ’92 ’96 ’00 ’03 ’05

PERCENT

30

69*

31

70

27*

64*

25*

62*

25*

62*

21*

57*

17*

52*

Male 100

0

100

0

Accommodations

permitted

Accommodations

not permitted

At or above 

Proficient

At or above 

Basic

Accommodations not permitted

Accommodations permitted

GRADE 4

GRADE 8
12 The Nation’s Report CardTM PERCENTILES

Figure 10. Mathematics scale score percentiles, grades 4 and 8: Various years, 1990–2005

* Signifi cantly different from 2005. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment 

of Educational Progress (NAEP), various years, 1990–2005 Mathematics Assessments.

Comparing Scores Among Lower-, Middle-, and Higher-Performing 

Students

Examining trends in the performance of students at 

selected percentiles can indicate whether trends for 

lower-, middle-, or higher-scoring students diverge 

from the picture for students overall. The 10th and 

25th percentiles represent lower-scoring students; the 

50th represents middle-scoring, and the 75th and 

90th percentiles represent higher-scoring students. A 

percentile indicates the percentage of students whose 

scores fell at or below a particular score. For example, 

figure 10 shows that 25 percent of students assessed at 

grade 4 scored at or below 220 in 2005, higher than the 

25th percentile score of any previous assessment year. 

At both grades 4 and 8, the score at each of the selected 

percentiles was higher in 2005 than in any previous 

assessment year.

297* 294*

288*

300* 303* 304 316* 315*

307*

320* 323* 324

273*

269*

264*

275*

279* 280

245* 243* 239*

249*

254* 255

221* 221*

298*

317*

273*

248*

224*

215*

223*

230* 231

90th

75th

50th

25th

10th

182*

184*

177*

171*

197* 200

203*

205*

199*

193*

216* 220

225*

227*

221*

214*

236* 239

245*

248*

242*

235*

255* 258 262*

265*

259*

182*

204*

226*

246*

262*

253*

270* 273 90th

75th

50th

25th

10th

500

Grade 4

0

SCALE SCORE

YEAR

270

260

250

240

230

220

210

200

190

180

170

500

Grade 8

0

SCALE SCORE

YEAR

320

310

300

290

280

270

260

250

240

230

220

’90 ’92 ’96 ’00 ’03 ’05

’90 ’92 ’96 ’00 ’03 ’05

PERCENTILE

PERCENTILE

Accommodations not permitted

Accommodations permitted
✓ KEY FINDINGS

! Between 2003 and 2005, 

33 states showed increases 

ranging from 2 to 7 scale 

score points.

! Between 2003 and 2005, the 

percentage performing at or 

above Basic increased for 24 

states.

! Each of the 42 states 

participating in both 1992 

and 2005 showed an increase 

in average scale scores.

! Between 1992 and 2005, 

the percentage of students 

performing at or above Basic

increased in all participating 

states.

! Seven states showed average 

score increases between 2003 

and 2005.

! The percentage performing 

at or above Basic increased 

between 2003 and 2005 for 5 

states. 

! Each of the 38 states that 

participated in both the 1990 

and 2005 assessments had 

higher average scores in 

2005. 

! Between 1990 and 2005, 

the percentage at or above 

Basic increased in all 38 

participating states.

Mathematics 2005 13

STATE RESULTS

Student Samples

The national results are based on a representative sample of students in public 

schools, private schools, Bureau of Indian Affairs schools, and Department of Defense schools. Private schools include Catholic, Conservative Christian, Lutheran, 

and other private schools. The state results are based on public school students 

only.

 Before 2002, the national sample was separate from the state sample. Beginning 

in 2002, the NAEP national sample was obtained by aggregating the samples from 

each state, rather than by obtaining an independent national sample. As a result, 

the size of the national sample increased, and smaller differences between years or 

between types of students were found to be statistically signifi cant than would have 

been detected in assessments before 2002.

Fourth- and Eighth-Grade Mathematics Results 

for States and Jurisdictions

The following pages show the results of 

the 2005 mathematics assessment for 

students at grades 4 and 8 who attended 

public schools in the 50 states and 2 other 

jurisdictions (which are all referred to as 

“states” in the key findings).

 Beginning in 2003, states were required 

to participate biennially in NAEP reading 

and mathematics assessments at grades 4 

and 8 in order to receive Title I funding. 

Results do not appear for some states in 

the early years because they either did not 

participate or did not meet the minimum 

participation guidelines for reporting. In 

2005, all states met the minimum participation guidelines at both grades 4 and 

8. The percentage of students scoring at 

or above Basic is shown in every year for 

which state data are available, beginning 

in 1992 at grade 4 (see table 1) and in 

1990 at grade 8 (see table 2).

 In comparing states to one another, 

it is important to consider that overall 

averages do not take into account the 

different demographics of the states’ student populations. Further information 

on student groups is provided in tables 

5 and 6 as well as in the appendix tables. 

For instance, the performance of Black 

students from different states can be 

compared for the same grade level. More 

information on these types of comparisons, including interactive state maps and 

state ranking tools, can be found at www.

nationsreportcard.gov. 

 When making comparisons across 

states and within states over time, it is 

important to consider the different exclusion rates across the states and over time. 

Although every effort is made to include 

as many students as possible, different 

states have different policies, and those 

policies have changed over time. States 

that are more inclusive—that is, they 

assess greater percentages of their students 

with disabilities and English language 

learners—may have lower average scores 

than states that exclude greater percentages of these students. Table A-3 shows 

the exclusion rates for each state.

 Finally, sample sizes and rounding 

can result in apparent inconsistencies. 

Small increases between 2003 and 2005 

may be marked as significant, while 

increases of the same size between 1990 

and 2005 may not be. See the Technical 

Notes beginning on page 32 for more 

information.

 More information on performance for a 

particular state is available at http://nces.

ed.gov/nationsreportcard/states.

GRADE 4 (pages 14–15, 18)

GRADE 8 (pages 16–17, 19)
14 The Nation’s Report CardTM

Figure 11. Average mathematics scale scores and percentage of students within each achievement level, grade 4 public 

schools: By state, 2005

Percentage below Basic Percentage at Basic, Proficient, and Advanced

Nation (public) ation (public)

Alabama

Alaska

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Georgia

Hawaii

Idaho

Illinois

Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montana

Nebraska

Nevada

New Hampshire

New Jersey

New Mexico

New York

North Carolina

North Dakota

Ohio

Oklahoma

Oregon

Pennsylvania

Rhode Island

South Carolina

South Dakota

Tennessee

Texas

Utah

Vermont

Virginia

Washington

West Virginia

Wisconsin

Wyoming

Other jurisdictions Other jurisdictions

District of Columbia

DoDEA1

Nation (public) Nation (public)

Alabama

Alaska

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Georgia

Hawaii

Idaho

Illinois

Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montana

Nebraska

Nevada

New Hampshire

New Jersey

New Mexico

New York

North Carolina

North Dakota

Ohio

Oklahoma

Oregon

Pennsylvania

Rhode Island

South Carolina

South Dakota

Tennessee

Texas

Utah

Vermont

Virginia

Washington

West Virginia

Wisconsin

Wyoming

Other jurisdictions Other jurisdictions

District of Columbia

DoDEA1

Average

State/jurisdiction score State/jurisdiction

below Basic Basic Proficient Advanced

100 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100

21 44 30 5

34 46 19 2

23 43 29 5

30 42 25 3

22 44 30 4

29 43 24 4

19 42 33 6

16 42 36 7

16 48 32 4

18 46 31 5

24 47 26 4

27 46 24 3

14 46 36 5

26 42 27 5

16 46 33 5

15 47 33 4

12 41 39 8

25 49 24 3

26 50 22 2

16 46 34 5

21 41 31 7

9 42 41 8

21 41 32 5

12 40 39 8

31 50 18 1

21 48 28 3

15 47 35 4

20 44 32 4

28 46 23 3

11 42 41 6

14 40 38 8

35 46 17 2

19 45 32 4

17 43 33 7

11 48 37 4

16 41 36 7

21 50 26 2

20 43 31 6

18 41 35 6

24 46 27 4

19 46 31 5

14 46 36 4

26 46 25 3

13 47 35 5

17 46 33 4

13 43 37 6

17 43 34 6

16 42 36 6

25 50 24 2

16 43 35 5

13 45 37 5

55 35 8 1

15 50 32 3

237

225

236

230

236

230

239

242

240

239

234

230

242

233

240

240

246

231

230

241

238

247

238

246

227

235

241

238

230

246

244

224

238

241

243

242

234

238

241

233

238

242

232

242

239

244

240

242

231

241

243

211

239

1 Department of Defense Education Activity.

NOTE: The NAEP mathematics scale ranges from 0 to 500. Detail may not sum to totals because of rounding. The shaded bars are graphed using unrounded numbers.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

STATE RESULTS
Mathematics 2005 15

STATE RESULTS

— Not available. The jurisdiction did not participate or did not meet the minimum participation guidelines for reporting.

* Signifi cantly different from 2005 when only one jurisdiction or the nation is being examined. 1 National results for assessments prior to 2003 are based on the national sample, not on aggregated state samples.

2 Department of Defense Education Activity (overseas and domestic schools). Before 2005, DoDEA overseas and domestic schools were separate jurisdictions in NAEP. 

Pre-2005 data presented here were recalculated for comparability.

NOTE: State-level data were not collected in 1990.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 

various years, 1992–2005 Mathematics Assessments. 

Table 1. Percentage of students at or above Basic in mathematics, grade 4 public schools: By state, 

various years, 1992–2005

Accommodations not permitted Accommodations permitted

State/jurisdiction 1992 1996 2000 2000 2003 2005

Nation (public)1 57* 62* 67* 64* 76* 79

Alabama 43* 48* 57* 55* 65 66

Alaska — 65* — — 75 77

Arizona 53* 57* 58* 57* 70 70

Arkansas 47* 54* 56* 55* 71* 78

California 46* 46* 52* 50* 67* 71

Colorado 61* 67* — — 77 81

Connecticut 67* 75* 77* 76* 82 84

Delaware 55* 54* — — 81* 84

Florida 52* 55* — — 76* 82

Georgia 53* 53* 58* 57* 72* 76

Hawaii 52* 53* 55* 55* 68* 73

Idaho 63* — 71* 68* 80* 86

Illinois — — 66* 63* 73 74

Indiana 60* 72* 78* 77* 82 84

Iowa 72* 74* 78* 75* 83 85

Kansas — — 75* 76* 85* 88

Kentucky 51* 60* 60* 59* 72 75

Louisiana 39* 44* 57* 57* 67* 74

Maine 75* 75* 74* 73* 83 84

Maryland 55* 59* 61* 60* 73* 79

Massachusetts 68* 71* 79* 77* 84* 91

Michigan 61* 68* 72* 71* 77 79

Minnesota 71* 76* 78* 76* 84* 88

Mississippi 36* 42* 45* 45* 62* 69

Missouri 62* 66* 72* 71* 79 79

Montana — 71* 73* 72* 81* 85

Nebraska 67* 70* 67* 65* 80 80

Nevada — 57* 61* 60* 69 72

New Hampshire 72* ——— 87 89

New Jersey 68* 68* — — 80* 86

New Mexico 50* 51* 51* 50* 63 65

New York 57* 64* 67* 66* 79 81

North Carolina 50* 64* 76* 73* 85 83

North Dakota 72* 75* 75* 73* 83* 89

Ohio 57* — 73* 73* 81 84

Oklahoma 60* — 69* 67* 74* 79

Oregon — 65* 67* 65* 79 80

Pennsylvania 65* 68* — — 78* 82

Rhode Island 54* 61* 67* 65* 72* 76

South Carolina 48* 48* 60* 59* 79 81

South Dakota ———— 82* 86

Tennessee 47* 58* 60* 59* 70 74

Texas 56* 69* 77* 76* 82* 87

Utah 66* 69* 70* 69* 79* 83

Vermont — 67* 73* 73* 85 87

Virginia 59* 62* 73* 71* 83 83

Washington — 67* — — 81 84

West Virginia 52* 63* 68* 65* 75 75

Wisconsin 71* 74* — — 79* 84

Wyoming 69* 64* 73* 71* 87 87

Other jurisdictions

District of Columbia 23* 20* 24* 24* 36* 45

DoDEA2 — 64* 70* 69* 84 85
16 The Nation’s Report CardTM

Figure 12. Average mathematics scale scores and percentage of students within each achievement level, grade 8 public 

schools: By state, 2005

Percentage below Basic Percentage at Basic, Proficient, and Advanced

Nation (public) ation (public)

Alabama

Alaska

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Georgia

Hawaii

Idaho

Illinois

Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montana

Nebraska

Nevada

New Hampshire

New Jersey

New Mexico

New York

North Carolina

North Dakota

Ohio

Oklahoma

Oregon

Pennsylvania

Rhode Island

South Carolina

South Dakota

Tennessee

Texas

Utah

Vermont

Virginia

Washington

West Virginia

Wisconsin

Wyoming

Other jurisdictions Other jurisdictions

District of Columbia

DoDEA1

Nation (public) Nation (public)

Alabama

Alaska

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Georgia

Hawaii

Idaho

Illinois

Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montana

Nebraska

Nevada

New Hampshire

New Jersey

New Mexico

New York

North Carolina

North Dakota

Ohio

Oklahoma

Oregon

Pennsylvania

Rhode Island

South Carolina

South Dakota

Tennessee

Texas

Utah

Vermont

Virginia

Washington

West Virginia

Wisconsin

Wyoming

Other jurisdictions Other jurisdictions

District of Columbia

DoDEA 1

Average

State/jurisdiction score State/jurisdiction

below Basic Basic Proficient Advanced

100 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100

32 39 23 6

47 38 13 2

31 40 23 6

36 38 21 5

36 42 19 3

43 35 17 5

30 38 26 6

30 35 27 8

28 43 25 5

35 39 21 5

38 39 19 4

44 37 16 2

27 43 25 5

32 40 23 5

26 44 25 5

25 42 28 6

23 42 29 5

36 42 19 3

41 43 14 2

26 44 25 5

34 37 23 7

20 37 32 11

32 38 24 6

21 36 32 11

48 38 12 1

32 42 22 4

20 44 30 6

25 40 29 6

40 39 18 3

23 43 28 7

26 38 27 9

47 39 13 1

30 39 25 6

28 40 25 7

19 46 30 5

26 41 27 7

37 43 18 2

28 39 26 7

28 41 25 6

37 40 20 3

29 42 23 7

20 44 30 6

39 40 18 3

28 41 25 6

29 42 25 5

22 40 29 9

25 41 25 8

25 39 27 9

40 42 16 1

24 40 29 7

24 47 26 3

69 24 5 2

24 44 27 5

278

262

279

274

272

269

281

281

281

274

272

266

281

278

282

284

284

274

268

281

278

292

277

290

262

276

286

284

270

285

284

263

280

282

287

283

271

282

281

272

281

287

271

281

279

287

284

285

269

285

282

245

284

1 Department of Defense Education Activity.

NOTE: The NAEP mathematics scale ranges from 0 to 500. Detail may not sum to totals because of rounding. The shaded bars are graphed using unrounded numbers.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

STATE RESULTS
Mathematics 2005 17

STATE RESULTS

— Not available. The jurisdiction did not participate or did not meet the minimum participation guidelines for reporting.

* Signifi cantly different from 2005 when only one jurisdiction or the nation is being examined. 1 National results for assessments prior to 2003 are based on the national sample, not on aggregated state samples.

2 Department of Defense Education Activity (overseas and domestic schools). Before 2005, DoDEA overseas and domestic schools were separate jurisdictions in NAEP. Pre-2005 data 

presented here were recalculated for comparability.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1990–2005 Mathematics Assessments. 

Table 2. Percentage of students at or above Basic in mathematics, grade 8 public schools: By state, various years, 

1990–2005

Accommodations not permitted Accommodations permitted

State/jurisdiction 1990 1992 1996 2000 2000 2003 2005

Nation (public)1 51* 56* 61* 65* 62* 67* 68

Alabama 40* 39* 45* 52 53 53 53

Alaska — — 68 — — 70 69

Arizona 48* 55* 57* 62 60 61 64

Arkansas 44* 44* 52* 52* 49* 58* 64

California 45* 50* 51* 52* 50* 56 57

Colorado 57* 64* 67 — — 74 70

Connecticut 60* 64* 70 72 70 73 70

Delaware 48* 52* 55* — — 68* 72

Florida 43* 49* 54* — — 62 65

Georgia 47* 48* 51* 55* 54* 59 62

Hawaii 40* 46* 51* 52* 51* 56 56

Idaho 63* 68* — 71 70 73 73

Illinois 50* — — 68 67 66 68

Indiana 56* 60* 68* 76 74 74 74

Iowa 70* 76 78 — — 76 75

Kansas ——— 77 76 76 77

Kentucky 43* 51* 56* 63 60 65 64

Louisiana 32* 37* 38* 48* 47* 57 59

Maine — 72 77 76 73 75 74

Maryland 50* 54* 57* 65 62 67 66

Massachusetts — 63* 68* 76* 70* 76* 80

Michigan 53* 58* 67 70 68 68 68

Minnesota 67* 74* 75* 80 80 82 79

Mississippi — 33* 36* 41* 42* 47* 52

Missouri — 62* 64 67 64 71 68

Montana 74* — 75* 80 79 79 80

Nebraska 68* 70* 76 74 73 74 75

Nevada ——— 58 55* 59 60

New Hampshire 65* 71* ——— 79 77

New Jersey 58* 62* ——— 72 74

New Mexico 43* 48* 51 50 48* 52 53

New York 50* 57* 61* 68 63* 70 70

North Carolina 38* 47* 56* 70 67* 72 72

North Dakota 75* 78 77* 77 76* 81 81

Ohio 53* 59* — 75 73 74 74

Oklahoma 52* 59* — 64 62 65 63

Oregon 62* — 67* 71 71 70 72

Pennsylvania 56* 62* ——— 69 72

Rhode Island 49* 56* 60 64 59 63 63

South Carolina — 48* 48* 55* 53* 68 71

South Dakota ————— 78 80

Tennessee — 47* 53* 53* 52* 59 61

Texas 45* 53* 59* 68* 67* 69* 72

Utah — 67* 70 68 66* 72 71

Vermont — — 72* 75 73* 77 78

Virginia 52* 57* 58* 67* 65* 72 75

Washington — — 67* — — 72 75

West Virginia 42* 47* 54* 62 58 63 60

Wisconsin 66* 71* 75 — — 75 76

Wyoming 64* 67* 68* 70* 69* 77 76

Other jurisdictions

District of Columbia 17* 22* 20* 23* 23* 29 31

DoDEA2 — — 64* 70* 68* 79 76
18 The Nation’s Report CardTM

Table 3. Average mathematics scale scores, grade 4 public schools: By state, various years, 1992-2005

Accommodations not permitted Accommodations permitted

State/jurisdiction 1992 1996 2000 2000 2003 2005

Nation (public)1 219* 222* 226* 224* 234* 237

Alabama 208* 212* 218* 217* 223 225

Alaska — 224* — — 233 236

Arizona 215* 218* 219* 219* 229 230

Arkansas 210* 216* 217* 216* 229* 236

California 208* 209* 214* 213* 227* 230

Colorado 221* 226* — — 235* 239

Connecticut 227* 232* 234* 234* 241 242

Delaware 218* 215* — — 236* 240

Florida 214* 216* — — 234* 239

Georgia 216* 215* 220* 219* 230* 234

Hawaii 214* 215* 216* 216* 227* 230

Idaho 222* — 227* 224* 235* 242

Illinois — — 225* 223* 233 233

Indiana 221* 229* 234* 233* 238 240

Iowa 230* 229* 233* 231* 238 240

Kansas — — 232* 232* 242* 246

Kentucky 215* 220* 221* 219* 229 231

Louisiana 204* 209* 218* 218* 226* 230

Maine 232* 232* 231* 230* 238* 241

Maryland 217* 221* 222* 222* 233* 238

Massachusetts 227* 229* 235* 233* 242* 247

Michigan 220* 226* 231* 229* 236 238

Minnesota 228* 232* 235* 234* 242* 246

Mississippi 202* 208* 211* 211* 223* 227

Missouri 222* 225* 229* 228* 235 235

Montana — 228* 230* 228* 236* 241

Nebraska 225* 228* 226* 225* 236 238

Nevada — 218* 220* 220* 228* 230

New Hampshire 230* ——— 243* 246

New Jersey 227* 227* — — 239* 244

New Mexico 213* 214* 214* 213* 223 224

New York 218* 223* 227* 225* 236 238

North Carolina 213* 224* 232* 230* 242 241

North Dakota 229* 231* 231* 230* 238* 243

Ohio 219* — 231* 230* 238* 242

Oklahoma 220* — 225* 224* 229* 234

Oregon — 223* 227* 224* 236 238

Pennsylvania 224* 226* — — 236* 241

Rhode Island 215* 220* 225* 224* 230* 233

South Carolina 212* 213* 220* 220* 236 238

South Dakota ———— 237* 242

Tennessee 211* 219* 220* 220* 228* 232

Texas 218* 229* 233* 231* 237* 242

Utah 224* 227* 227* 227* 235* 239

Vermont — 225* 232* 232* 242 244

Virginia 221* 223* 230* 230* 239 240

Washington — 225* — — 238* 242

West Virginia 215* 223* 225* 223* 231 231

Wisconsin 229* 231* — — 237* 241

Wyoming 225* 223* 229* 229* 241* 243

Other jurisdictions

District of Columbia 193* 187* 193* 192* 205* 211

DoDEA2 — 224* 228* 227* 237* 239

— Not available. The jurisdiction did not participate or did not meet the minimum participation guidelines for reporting.

* Signifi cantly different from 2005 when only one jurisdiction or the nation is being examined. 1 National results for assessments prior to 2003 are based on the national sample, not on aggregated state samples.

2 Department of Defense Education Activity (overseas and domestic schools). Before 2005, DoDEA overseas and domestic schools were separate jurisdictions in NAEP. Pre2005 data presented here were recalculated for comparability.

NOTE: State-level data were not collected in 1990. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various 

years, 1992–2005 Mathematics Assessments.

STATE RESULTS
Mathematics 2005 19

STATE RESULTS

— Not available. The jurisdiction did not participate or did not meet the minimum participation guidelines for reporting.

* Signifi cantly different from 2005 when only one jurisdiction or the nation is being examined. 1 National results for assessments prior to 2003 are based on the national sample, not on aggregated state samples.

2 Department of Defense Education Activity (overseas and domestic schools). Before 2005, DoDEA overseas and domestic schools were separate jurisdictions in NAEP. Pre-2005 data presented here 

were recalculated for comparability.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 1990–2005 

Mathematics Assessments.

Table 4. Average mathematics scale scores, grade 8 public schools: By state, various years, 1990–2005

Accommodations not permitted Accommodations permitted

State/jurisdiction 1990 1992 1996 2000 2000 2003 2005

Nation (public)1 262* 267* 271* 274* 272* 276* 278

Alabama 253* 252* 257* 262 264 262 262

Alaska — — 278 — — 279 279

Arizona 260* 265* 268* 271 269* 271 274

Arkansas 256* 256* 262* 261* 257* 266* 272

California 256* 261* 263* 262* 260* 267 269

Colorado 267* 272* 276* — — 283 281

Connecticut 270* 274* 280 282 281 284 281

Delaware 261* 263* 267* — — 277* 281

Florida 255* 260* 264* — — 271 274

Georgia 259* 259* 262* 266* 265* 270 272

Hawaii 251* 257* 262* 263 262* 266 266

Idaho 271* 275* — 278 277* 280 281

Illinois 261* — — 277 275 277 278

Indiana 267* 270* 276* 283 281 281 282

Iowa 278* 283 284 — — 284 284

Kansas ——— 284 283 284 284

Kentucky 257* 262* 267* 272 270* 274 274

Louisiana 246* 250* 252* 259* 259* 266 268

Maine — 279 284 284 281 282 281

Maryland 261* 265* 270* 276 272* 278 278

Massachusetts — 273* 278* 283* 279* 287* 292

Michigan 264* 267* 277 278 277 276 277

Minnesota 275* 282* 284* 288 287 291 290

Mississippi — 246* 250* 254* 254* 261 262

Missouri — 271* 273 274 271* 279 276

Montana 280* — 283* 287 285 286 286

Nebraska 276* 278* 283 281* 280* 282 284

Nevada ——— 268 265* 268 270

New Hampshire 273* 278* —— — 286 285

New Jersey 270* 272* —— — 281 284

New Mexico 256* 260* 262 260 259* 263 263

New York 261* 266* 270* 276 271* 280 280

North Carolina 250* 258* 268* 280 276* 281 282

North Dakota 281* 283* 284* 283* 282* 287 287

Ohio 264* 268* — 283 281 282 283

Oklahoma 263* 268* — 272 270 272 271

Oregon 271* — 276* 281 280 281 282

Pennsylvania 266* 271* —— — 279 281

Rhode Island 260* 266* 269* 273 269* 272 272

South Carolina — 261* 261* 266* 265* 277* 281

South Dakota — — —— — 285* 287

Tennessee — 259* 263* 263* 262* 268 271

Texas 258* 265* 270* 275* 273* 277* 281

Utah — 274* 277 275* 274* 281 279

Vermont — — 279* 283* 281* 286 287

Virginia 264* 268* 270* 277* 275* 282 284

Washington — — 276* — — 281* 285

West Virginia 256* 259* 265* 271 266 271 269

Wisconsin 274* 278* 283 — — 284 285

Wyoming 272* 275* 275* 277* 276* 284 282

Other jurisdictions

District of Columbia 231* 235* 233* 234* 235* 243 245

DoDEA2 — — 274* 278* 277* 285 284
20 The Nation’s Report CardTM STATE RESULTS

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: Results are not shown for students whose race/ethnicity was “unclassifi ed” and for students whose eligibility status for free/reduced-price lunch was not available.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

Table 5. Average mathematics scale scores, grade 4 public schools: By state and student group, 2005

Race/ethnicity

Eligibility for free/reducedprice school lunch Gender

State/jurisdiction White Black Hispanic

Asian/Pacifi c 

Islander

American 

Indian/Alaska 

Native Eligible Not eligible Male Female

Nation (public) 246 220 225 251 227 225 248 238 236

Alabama 235 211 ‡‡‡ 214 238 225 225

Alaska 244 226 227 238 220 223 243 236 235

Arizona 243 217 218 241 ‡ 220 242 233 227

Arkansas 242 214 229 ‡ ‡ 226 247 236 235

California 245 215 219 249 228 219 244 231 229

Colorado 247 222 223 242 ‡ 224 248 241 238

Connecticut 250 219 223 253 ‡ 223 249 244 241

Delaware 249 226 229 260 ‡ 229 247 241 238

Florida 247 224 233 259 ‡ 229 250 240 238

Georgia 243 221 229 255 ‡ 224 245 234 233

Hawaii 241 221 219 229 ‡ 220 239 229 231

Idaho 245 ‡ 226 ‡ ‡ 234 248 242 241

Illinois 245 212 219 258 ‡ 218 245 234 232

Indiana 245 221 230 ‡ ‡ 231 247 240 240

Iowa 242 224 222 ‡ ‡ 231 244 242 238

Kansas 249 228 234 262 ‡ 235 254 247 245

Kentucky 234 217 ‡‡‡ 224 240 233 230

Louisiana 241 219 ‡‡‡ 224 244 231 229

Maine 241 ‡‡ ‡ ‡ 230 245 243 239

Maryland 250 220 232 256 ‡ 221 247 240 237

Massachusetts 252 228 225 258 ‡ 231 254 248 247

Michigan 245 211 ‡‡‡ 223 246 240 236

Minnesota 251 219 223 242 ‡ 231 252 247 245

Mississippi 238 216 ‡‡‡ 221 241 227 226

Missouri 240 215 221 ‡ ‡ 225 243 237 233

Montana 243 ‡ 234 ‡ 223 231 247 243 239

Nebraska 244 211 219 ‡ ‡ 225 246 239 236

Nevada 240 214 219 243 ‡ 219 239 231 229

New Hampshire 246 ‡ 226 ‡ ‡ 232 249 247 244

New Jersey 251 224 230 264 ‡ 227 252 246 242

New Mexico 238 213 218 ‡ 217 217 238 225 223

New York 247 222 226 254 ‡ 228 248 240 237

North Carolina 250 225 234 256 ‡ 229 251 242 241

North Dakota 245 ‡‡ ‡ 223 234 247 244 241

Ohio 248 221 231 ‡ ‡ 227 252 243 241

Oklahoma 240 217 226 ‡ 229 227 243 235 233

Oregon 243 222 218 248 ‡ 230 244 239 238

Pennsylvania 247 219 220 ‡ ‡ 225 250 241 240

Rhode Island 241 211 211 240 ‡ 218 243 234 233

South Carolina 250 223 236 ‡ ‡ 227 250 238 238

South Dakota 245 ‡‡ ‡ 221 232 249 243 240

Tennessee 238 214 229 ‡ ‡ 220 242 233 231

Texas 254 228 235 264 ‡ 233 253 244 240

Utah 242 ‡ 220 235 ‡ 229 244 240 237

Vermont 244 ‡‡ ‡ ‡ 230 250 246 241

Virginia 247 224 230 256 ‡ 225 249 242 239

Washington 246 231 224 245 ‡ 231 250 242 241

West Virginia 231 226 ‡‡‡ 225 238 232 229

Wisconsin 247 210 224 236 ‡ 225 249 242 239

Wyoming 245 ‡ 234 ‡ ‡ 236 247 244 242

Other jurisdictions

District of Columbia 266 207 215 ‡ ‡ 206 229 212 211

DoDEA1 245 227 235 239 ‡‡‡ 241 237
Mathematics 2005 21

STATE RESULTS

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: Results are not shown for students whose race/ethnicity was “unclassifi ed” and for students whose eligibility status for free/reduced-price lunch was not available.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

Table 6. Average mathematics scale scores, grade 8 public schools: By state and student group, 2005

Race/ethnicity

Eligibility for free/reducedprice school lunch Gender

State/jurisdiction White Black Hispanic

Asian/Pacifi c 

Islander

American 

Indian/Alaska 

Native Eligible Not eligible Male Female

Nation (public) 288 254 261 294 266 261 288 278 277

Alabama 276 240 ‡‡‡ 248 276 261 264

Alaska 288 266 272 270 264 264 287 280 278

Arizona 288 261 260 ‡ 259 260 285 274 274

Arkansas 281 243 266 ‡ ‡ 260 282 270 273

California 284 248 254 293 ‡ 254 282 269 268

Colorado 292 256 260 ‡ ‡ 261 290 281 281

Connecticut 293 249 254 292 ‡ 255 292 281 281

Delaware 291 264 268 306 ‡ 265 288 283 279

Florida 286 251 265 299 ‡ 260 285 276 272

Georgia 284 255 258 301 ‡ 257 285 273 272

Hawaii 277 ‡ 257 264 ‡ 251 276 265 266

Idaho 284 ‡ 261 ‡ ‡ 272 286 280 282

Illinois 289 249 265 300 ‡ 258 290 279 276

Indiana 286 257 261 ‡ ‡ 268 290 283 280

Iowa 286 256 264 ‡ ‡ 269 290 283 284

Kansas 289 256 266 ‡ ‡ 270 293 285 283

Kentucky 276 255 ‡‡‡ 264 283 275 273

Louisiana 281 252 ‡‡‡ 258 280 267 268

Maine 281 ‡‡ ‡ ‡ 269 286 282 280

Maryland 292 258 262 304 ‡ 258 287 278 278

Massachusetts 297 263 265 314 ‡ 273 299 291 292

Michigan 285 247 265 ‡ ‡ 258 285 279 275

Minnesota 296 251 263 285 ‡ 270 297 291 289

Mississippi 279 247 ‡‡‡ 253 279 263 262

Missouri 284 247 ‡‡‡ 262 286 278 275

Montana 290 ‡‡ ‡ 259 272 293 286 287

Nebraska 289 243 261 ‡ ‡ 268 291 285 283

Nevada 280 247 256 281 ‡ 256 277 270 269

New Hampshire 286 ‡‡ ‡ ‡ 271 288 286 285

New Jersey 295 260 264 309 ‡ 262 292 286 282

New Mexico 279 257 255 ‡ 253 254 278 264 262

New York 290 259 262 298 ‡ 267 291 280 280

North Carolina 292 263 265 303 ‡ 266 293 281 282

North Dakota 290 ‡‡ ‡ 261 274 292 287 287

Ohio 289 255 259 ‡ ‡ 265 290 284 282

Oklahoma 278 249 257 ‡ 267 260 283 272 271

Oregon 287 258 257 299 274 270 289 284 281

Pennsylvania 287 250 267 297 ‡ 262 289 283 279

Rhode Island 281 249 244 278 ‡ 252 282 272 273

South Carolina 294 263 269 ‡ ‡ 267 294 282 281

South Dakota 291 ‡‡ ‡ 260 276 294 287 287

Tennessee 278 246 ‡‡‡ 256 282 270 271

Texas 295 264 271 308 ‡ 268 293 283 279

Utah 283 ‡ 255 273 ‡ 268 284 280 278

Vermont 288 ‡‡ ‡ ‡ 272 293 287 287

Virginia 293 263 270 300 ‡ 263 292 285 283

Washington 289 265 262 294 273 269 294 285 285

West Virginia 270 251 ‡‡‡ 259 278 268 270

Wisconsin 291 246 265 286 ‡ 263 292 285 284

Wyoming 284 ‡ 265 ‡ 262 272 287 283 281

Other jurisdictions

District of Columbia 317 241 252 ‡ ‡ 241 261 246 245

DoDEA1 292 267 280 290 ‡‡‡ 285 283
22 The Nation’s Report CardTM STUDENT DEMOGRAPHICS

NAEP collects information on student demographics. 

Two variables—race/ethnicity and eligibility for free/

reduced-price lunch—have shown changes over time, 

potentially affecting overall results. Figures 13 and 14 

display the distribution over time of students nationwide 

taking the mathematics assessment by these two demographic variables. Table 7 provides similar information for 

national and state-level public schools. Figure 13 shows 

that, for example, at grade 4, White students made up a 

smaller proportion of the population in 2005 than they 

did in 1990, decreasing 17 percentage points over those 

15 years. At the same time, the percentage of Hispanic 

students increased by 13 percentage points.

Changing Demographics of Students at Grades 4 and 8

 Figure 14 shows the distribution of students by eligibility for free or reduced-price school lunch. Here, 

differences could reflect a change in reporting practices 

associated with changing regulations and definitions of 

free lunch eligibility. Alternatively, the differences could 

be associated with changing demographics. For instance, 

at grade 4 the mathematics data show that the percentage of students for whom information on school lunch 

eligibility was not available decreased from 15 percent in 

1996 to 8 percent in 2005. At the same time, the percentage of fourth-graders categorized as eligible for free 

or reduced-price lunch increased from 34 to 42 percent. 

The percentage of students not eligible remained around 

50 percent. 

* Signifi cantly different from 2005.

NOTE: The “unclassifi ed” race/ethnicity category is not shown in this fi gure. Special analyses raised concerns about the accuracy and precision of national grade 4 Asian/Pacifi c Islander results in 

2000 and grade 8 Asian/Pacifi c Islander results in 1996, so their performance results are omitted from this report.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 1990–2005 

Mathematics Assessments. 

Figure 13. Percentage distribution of students by race/ethnicity, grades 4 and 8: Various years, 1990–2005

White Black Hispanic

Asian/Pacific

Islander

American Indian/

Alaska Native

Grade 8

1

1990

1

1992

Percent

2*

2*

7*

8*

16

16

73*

73*

Year

1

1996

2

2000

3*

4

10*

13*

17

16

69*

65*

1

2003

63* 16 15* 4

1

2005

61 16 16 5

Grade 4

1*

1990

1*

1992

Percent

1*

2*

6*

6*

18*

17

75*

73*

Year

1

1996

1

2000

5

4

11*

15*

16

16

66*

64*

1

2003

60* 17 18* 4

1

2005

58 16 19 4

Figure 14. Percentage distribution of students by eligibility for free/reduced-price school lunch, grades 4 and 8: 

Various years, 1996–2005

* Signifi cantly different from 2005.

NOTE: Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 1996–2005 

Mathematics Assessments.

Percent

Year

1996

34* 51

36* 47 16*

2003

2000

2005

50

50

40*

42

15*

10*

8

Grade 4

Percent

Year

1996

27* 54

29* 51* 20*

2003

2000

2005

55

56

33*

36

19*

11*

8

Grade 8

Eligible

Information

Not eligible not available
Mathematics 2005 23

STUDENT 

DEMOGRAPHICS

— Not available. The jurisdiction did not participate or did not meet the minimum participation guidelines for reporting.

# The estimate rounds to zero.

* Signifi cantly different from 2005 when only one jurisdiction or the nation is being examined. 1 Department of Defense Education Activity.

NOTE: State-level data were not collected at grade 4 in 1990.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 1990–2005 Mathematics Assessments.

Table 7. Percentage distribution of students by race/ethnicity, grades 4 and 8: By state, various years, 1990–2005

Grade 4 Grade 8 

White Black Hispanic White Black Hispanic

State/jurisdiction 1992 2005 1992 2005 1992 2005 1990 2005 1990 2005 1990 2005

Nation (public) 72* 57 18 17 7* 20 73* 60 16 17 7* 17

Alabama 65* 57 34 38 #* 2 68* 59 32 37 #* 2

Alaska — 56 — 4 — 4 — 57 — 5 — 4

Arizona 62* 45 4 5 23* 41 62* 50 3* 5 26* 38

Arkansas 75 71 24 22 #* 5 75 71 24 23 1* 4

California 50* 31 7 7 30* 49 49* 33 7 8 30* 45

Colorado 73* 64 6 5 17* 27 77* 64 5 7 15* 25

Connecticut 77* 69 11 14 10 13 79* 66 11* 15 8* 14

Delaware 70* 54 25* 33 2* 9 70* 56 26* 33 2* 7

Florida 63* 48 24 23 12* 24 65* 52 22 22 12* 22

Georgia 60* 48 38 39 1* 8 62* 51 36 37 1* 6

Hawaii 23* 17 3 3 2 3 20* 15 2 2 2 3

Idaho 92* 82 #* 1 6* 13 93* 85 # 1 4* 12

Illinois — 54 — 19 — 22 70* 61 19 21 8* 14

Indiana 87* 73 11* 16 2* 6 87* 81 9 12 2* 4

Iowa 95* 85 2* 5 1* 6 95* 88 2 4 1* 5

Kansas — 74 — 9 — 11 — 77 — 8 — 9

Kentucky 90* 84 9 12 #* 2 90* 86 9 10 #* 1

Louisiana 53 48 45 49 1 1 57 53 40 44 1 2

Maine 98* 97 #* 1 ## — 96 — 2 — 1

Maryland 62* 51 32 35 2* 8 62* 50 31* 40 2 4

Massachusetts 83* 75 8 9 4* 11 — 76 — 8 — 10

Michigan 79* 72 16 20 3 4 82* 73 14* 20 2* 4

Minnesota 91* 79 3* 9 2* 6 93* 81 2* 8 #* 4

Mississippi 42 47 58* 51 # 1 — 46 — 51 — 1

Missouri 83* 76 15 17 1* 4 — 77 — 19 — 2

Montana — 85 — 1 — 2 91* 86 # # 1* 2

Nebraska 90* 75 6* 8 3* 13 92* 83 5 5 2* 9

Nevada — 46 — 12 — 33 — 55 — 10 — 29

New Hampshire 96 94 1* 2 1* 2 98* 94 #* 1 1* 2

New Jersey 69* 57 16 18 11 15 69* 57 17 20 9* 15

New Mexico 45* 30 4* 2 45* 56 42* 34 2 2 42* 51

New York 63* 53 15 21 17 19 61 55 19 19 13 18

North Carolina 65* 59 31* 27 1* 8 63 60 32 29 1* 6

North Dakota 95* 88 #* 1 1 1 93 88 # 1 1 1

Ohio 86* 72 12* 21 1* 2 84 80 12 15 1 1

Oklahoma 77* 59 9 11 3* 9 77* 62 11 11 2* 7

Oregon — 71 — 3 — 17 91* 76 2 3 3* 13

Pennsylvania 81* 74 14 17 3* 7 82 78 14 15 2* 5

Rhode Island 82* 73 7 8 7* 16 86* 73 5* 8 5* 15

South Carolina 58 55 41 41 #* 3 — 57 — 39 — 3

South Dakota — 84 — 2 — 2 — 86 — 1 — 2

Tennessee 73 69 25 26 #* 3 — 75 — 22 — 2

Texas 49* 38 14 13 34* 46 50* 43 14 15 33 39

Utah 93* 81 1 1 4* 13 — 84 — 1 — 10

Vermont — 96 — 1 — 1 — 96 — 2 — 1

Virginia 71* 61 25 24 2* 8 70* 61 25 26 2* 6

Washington — 69 — 6 — 15 — 74 — 4 — 10

West Virginia 96 95 2 4 # 1 96 95 3 4 # 1

Wisconsin 87* 77 6* 11 2* 7 88* 79 9 11 1* 6

Wyoming 90* 85 1 1 6* 9 86 87 1 1 6 7

Other jurisdictions

District of Columbia 5 4 91* 86 3* 8 3 4 93* 88 3* 7

DoDEA1 — 47 — 20 — 14 — 45 — 20 — 13
24 The Nation’s Report CardTM

Item Maps

The item maps presented on pages 26 and 30 illustrate the knowledge and skills demonstrated by 

students performing at different score points on the 2005 NAEP mathematics assessment. In order to 

provide additional context, the cut scores for the three NAEP achievement levels are marked on the item 

maps. The map location for each question represents the probability that, for a given score point, 65 

percent of the students for a constructed-response question, 74 percent of the students for a four-option 

multiple-choice question, or 72 percent of the students for a fi ve-option multiple-choice question answered that question successfully. For constructed-response questions, only responses considered to be 

completely correct are shown on the item maps.

Grade 4 Mathematics Framework 

The content of the NAEP mathematics assessment is 

based on a framework, which describes in detail how 

mathematics should be assessed by NAEP. The current 

NAEP mathematics framework was first used for the 

1990 assessment and has continued to be used through 

2005. It was developed through a comprehensive national 

consultative process and adopted by NAGB. The framework calls for the assessment of mathematics within five 

content areas and at different levels of complexity.

Mathematics content areas. In order to ensure that 

NAEP assesses an appropriate balance of content, the 

framework defines five broad areas of mathematical content. The content areas assessed at grade 4 are number 

properties and operations, measurement, geometry, data 

analysis and probability, and algebra. The framework calls 

for the test questions at grade 4 to be distributed across 

the five content areas in the following proportions:

Mathematical complexity. The framework also calls 

for an assessment that measures different levels of mathematical complexity to make sure that NAEP assesses a 

variety of ways of knowing and doing mathematics. The 

level of complexity of a test question is determined by 

the demands that it places on students. For example, test 

questions with a high level of complexity at grade 4 might 

ask students to solve a problem in more than one way. 

According to the framework, the ideal balance for the 

assessment is that half the score is based on items of moderate complexity, with the remainder of the score based 

equally on items of low and high complexity.

 Revisions were made to the framework for the 1996 

assessment and again for the 2005 assessment. The 

names of some of the content areas changed in 2005, 

but there remains a consistent focus on the five key areas. 

The framework reflects current curricular emphases and 

objectives, while continuing a connection to previous 

frameworks. This connection allows the trend line at grade 

4 that started with the 1990 assessment to be maintained. 

 The grade 4 mathematics assessment consists of ten 

25-minute sections of mathematics questions. Each section contains 14 to 20 questions. The questions are both 

multiple choice and constructed response. Multiple-choice 

questions require students to select an answer from four 

options, while constructed-response questions require 

students to write either short or extended answers. Each 

student receives only a portion of the entire assessment, 

consisting of a booklet containing two 25-minute sections 

of mathematics questions.

FRAMEWORK AND SAMPLE QUESTIONS

Number properties 

and operations Measurement Geometry

40% 20% 15%

Data analysis and 

probability Algebra

10% 15%
Mathematics 2005 25

Achievement-Level Descriptions for Grade 4 

Mathematics achievement-level descriptions are based 

on NAGB achievement-level policy descriptions with 

subject- and grade-specific information added. The 

following descriptions are abbreviated versions of the full 

Basic: Fourth-grade students performing at the Basic level should be able to estimate and use 

basic facts to perform simple computations with whole numbers; show some understanding of 

fractions and decimals; and solve some simple real-world problems in all NAEP content areas. 

Students at this level should be able to use—though not always accurately—four-function 

calculators, rulers, and geometric shapes. Their written responses will often be minimal and 

presented without supporting information.

Profi cient: Fourth-grade students performing at the Profi cient level should be able to use 

whole numbers to estimate, compute, and determine whether results are reasonable. They 

should have a conceptual understanding of fractions and decimals; be able to solve real-world 

problems in all NAEP content areas; and use four-function calculators, rulers, and geometric 

shapes appropriately. Students performing at the Profi cient level should employ problem-solving 

strategies such as identifying and using appropriate information. Their written solutions should 

be organized and presented both with supporting information and explanations of how they 

were achieved.

Advanced: Fourth-grade students performing at the Advanced level should be able to solve 

complex and nonroutine real-world problems in all NAEP content areas. They should display 

mastery in the use of four-function calculators, rulers, and geometric shapes. The students 

are expected to draw logical conclusions and justify answers and solution processes by 

explaining why, as well as how, they were achieved. They should go beyond the obvious in their 

interpretations and be able to communicate their thoughts clearly and concisely.

achievement-level descriptions for grade 4 mathematics. 

The full descriptions can be found at http://www.nagb.org/

pubs/mathbook.pdf.

Cut Scores

Cut scores represent the minimum score required for performance at each NAEP achievement level. NAEP cut 

scores were determined through a standard-setting process that convened a cross-section of educators and 

interested citizens from across the nation. The group was asked to determine what students should know and be 

able to do relative to a body of content refl ected in the mathematics framework. NAGB then adopted a set of cut 

scores on the 0–500 scale that defi ne the lower boundaries of the Basic, Profi cient, and Advanced achievement 

levels. The mathematics cut scores, which appear on the item maps, are as follows:

 Grade 4 Grade 8

Basic 214 262

Profi cient 249 299

Advanced 282 333

FRAMEWORK AND 

SAMPLE QUESTIONS
26 The Nation’s Report CardTM

Grade 4 

Item Map

This map describes the knowledge 

or skill associated with answering 

individual mathematics questions. 

The map identifi es the score point at 

which students had a high probability 

of successfully answering the 

question.1

1 Each grade 4 mathematics question in the 2005 mathematics assessment was mapped onto the NAEP 0–500 mathematics scale. The position of a question on the scale represents the average 

scale score attained by students who had a 65 percent probability of successfully answering a constructed-response question, or a 74 percent probability of correctly answering a four-option multiplechoice question. Only selected questions are presented. Scale score ranges for mathematics achievement levels are referenced on the map. For constructed-response questions, the question description represents students’ performance rated as completely correct.

NOTE: Regular type denotes a constructed-response question. Italic type denotes a multiple-choice question.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

294 Identify equation to describe pattern given in table

286 Identify given measurements on a ruler

284 Subtract fractions with common denominators

276 Approximate fraction of an hour given minutes

273 Solve a story problem involving large numbers (calculator available)

272 Determine missing numbers in number sentence

272 Solve a story problem involving multiplication (calculator available)

260 Determine the width of a rectangle after it is folded

258 Represent a situation with an algebraic expression—Sample Question 1

254 Identify which fi gure on grid has greatest area 

253 Complete a bar graph from a description of data

245 Determine the value of a point on a number line—Sample Question 2

232 Determine next number in given pattern

228 Classify numbers as even or odd

223 Determine which attribute could be measured with a meter stick

219 Subtract two-digit numbers to solve a story problem

211 Identify which shapes are cylinders

211 Subtract two-digit number from three-digit number

203 Identify a number given in expanded notation

197 Determine the most likely outcome in a story problem

Advanced

282

Profi cient

249

Basic

214

500

300

290

280

270

260

250

240

230

220

210

200

190

 O

NAEP Mathematics Scale

FRAMEWORK AND SAMPLE QUESTIONS
Mathematics 2005 27

FRAMEWORK AND 

SAMPLE QUESTIONS

61 percent of fourth-graders answered this question correctly.

Sample Grade 4 Multiple-Choice Question

Sample Question 1 is a multiple-choice question in the algebra content area. This question asked students to represent 

a given situation with an algebraic expression.

1. N stands for the number of hours of sleep Ken gets each night. Which of the 

following represents the number of hours of sleep Ken gets in 1 week?

A N  7

B N 7

N  7

D N  7

56 percent of fourth-graders wrote correct responses.

Sample Grade 4 Short Constructed-Response Question

Sample Question 2 is a short constructed-response question in the number properties and operations content area. 

This question asked students to identify the point indicated on a number line. The response shown here would have 

been rated correct.

5.6 6.2 6.4

P

2. On the number line above, what number would be located at point P?

 Answer: 6.0
28 The Nation’s Report CardTM

Grade 8 Mathematics Framework 

As at grade 4, the content of the mathematics assessment 

at grade 8 is based on a framework that describes in detail 

how mathematics should be assessed by NAEP. The current NAEP mathematics framework was first used for 

the 1990 assessment and has continued to date to be 

the basis for the assessment content. It was developed 

through a comprehensive national consultative process 

and adopted by NAGB. The framework calls for the 

assessment of mathematics within five content areas and 

at different levels of complexity.

Mathematics content areas. In order to ensure that 

NAEP assesses an appropriate balance of content, the 

framework defines five broad areas of mathematical 

content. The content areas assessed at grade 8 are the 

same as those assessed at grade 4: number properties and 

operations, measurement, geometry, data analysis and 

probability, and algebra. At grade 8, however, the emphasis placed on each content area is different from that at 

grade 4, to reflect differences in curricular emphasis at the 

two grades. The framework calls for the eighth-grade test 

questions to be distributed across the five content areas in 

the following proportions:

Mathematical complexity. As at grade 4, the framework 

calls for an assessment at grade 8 that measures different levels of mathematical complexity, to make sure that 

NAEP assesses a variety of ways of knowing and doing 

mathematics. The level of complexity of a test question 

is determined by the demands that it places on students. 

For example, test questions at grade 8 with a high level of 

complexity might ask students to provide a mathematical 

justification. According to the framework, the ideal balance for the assessment is that half the score is based on 

items of moderate complexity, with the remainder of the 

score based equally on items of low and high complexity.

 Revisions were made to the framework for the 1996 

assessment and again for the 2005 assessment. For example, the names of some of the content areas changed in 

2005, but there remains a consistent focus on the five key 

areas. The framework reflects current curricular emphases 

and objectives, while continuing a connection to previous frameworks. This connection allows the trend line at 

grade 8 that started with the 1990 assessment to be maintained. 

 The grade 8 mathematics assessment consists of ten 

25-minute sections of mathematics questions. Each section contains 16 to 21 questions. The questions are either 

multiple choice or constructed response. Multiple-choice 

questions require students to select an answer from four 

or five options, while constructed-response questions 

require students to write either short or extended answers. 

Each student receives only a portion of the entire assessment, consisting of a booklet containing two 25-minute 

sections of mathematics questions.

For More Information...

The complete mathematics framework is available on the NAGB website (http://www.nagb.org/pubs/pubs.html). 

To view more questions, including sample responses and statistics, visit the NAEP questions tool at 

http://nces.ed.gov/nationsreportcard/itmrls/.

Number properties 

and operations Measurement Geometry

20% 15% 20%

Data analysis and 

probability Algebra

15% 30%

FRAMEWORK AND SAMPLE QUESTIONS
Mathematics 2005 29

FRAMEWORK AND 

SAMPLE QUESTIONS

Basic: Eighth-grade students performing at the Basic level should complete problems correctly 

with the help of structural prompts such as diagrams, charts, and graphs. They should be 

able to solve problems in all NAEP content areas through the appropriate selection and use of 

strategies and technological tools—including calculators, computers, and geometric shapes. 

Students at this level also should be able to use fundamental algebraic and informal geometric 

concepts in problem solving.

Profi cient: Eighth-grade students performing at the Profi cient level should be able to conjecture, 

defend their ideas, and give supporting examples. They should understand the connections 

between fractions, percents, decimals, and other mathematical topics such as algebra and 

functions. Students at this level are expected to have a thorough understanding of Basic-level 

arithmetic operations—an understanding suffi cient for problem solving in practical situations.

Advanced: Eighth-grade students performing at the Advanced level should be able to probe 

examples and counterexamples in order to shape generalizations from which they can develop 

models. Eighth-graders performing at the Advanced level should use number sense and geometric awareness to consider the reasonableness of an answer. They are expected to use abstract 

thinking to create unique problem-solving techniques and explain the reasoning processes 

underlying their conclusions.

Mathematics achievement-level descriptions are based on 

NAGB achievement-level policy descriptions with subject- and grade-specific information added. The following 

descriptions are abbreviated versions of the full achievement-level descriptions for grade 8 mathematics. The full 

descriptions can be found at http://www.nagb.org/pubs/

mathbook.pdf.

Achievement-Level Descriptions for Grade 8
30 The Nation’s Report CardTM

Grade 8 

Item Map

This map describes the knowledge 

or skill associated with answering 

individual mathematics questions. 

The map identifi es the score point at 

which students had a high probability 

of successfully answering the 

question.1

1 Each grade 8 mathematics question in the 2005 mathematics assessment was mapped onto the NAEP 0–500 mathematics scale. The position of a question on the scale represents the average 

scale score attained by students who had a 65 percent probability of successfully answering a constructed-response question, a 74 percent probability of correctly answering a four-option 

multiple-choice question, or a 72 percent probability of correctly answering a fi ve-option multiple-choice question. Only selected questions are presented. Scale score ranges for mathematics 

achievement levels are referenced on the map. For constructed-response questions, the question description represents students’ performance rated as completely correct.

NOTE: Regular type denotes a constructed-response question. Italic type denotes a multiple-choice question.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

Advanced

333

Profi cient

299

Basic

262

500

370

360

350

340

330

320

310

300

290

280

270

260

250

240

 O

365 Reason about pattern on a grid using concept of slope

353 Determine a probability (calculator available) 

343 Determine effect of increasing the value of one variable

335 Reason about properties of a parallelogram

330 Determine median price for a gallon of gasoline

319 Estimate the x-coordinate from the graph of a curve

317 Solve a story problem involving percent increase

315 Determine the 6th term in a pattern—Sample Question 3

311 Predict results of experiment using probability

306 Determine an equation given a table of x and y values

302 Solve a story problem with multiple operations

301 Extend a pattern on grid

294 Determine coordinates to complete a rectangle

294 Identify piece of information not needed

291 Solve problem involving square root (calculator available) 

283 Shade a grid to form symmetric pattern—Sample Question 4

282 Determine how many angles are less than 90 degrees

282 Convert a written number to decimal form

274 List angle measures from smallest to largest (protractor available) 

253 Draw the refl ection of a fi gure

252 Determine area of shaded region on grid

247 Solve a multi-step story problem

FRAMEWORK AND SAMPLE QUESTIONS

NAEP Mathematics Scale
Mathematics 2005 31

FRAMEWORK AND 

SAMPLE QUESTIONS

60 percent of eighth-graders answered this question correctly.

Sample Grade 8 Multiple-Choice Question

1, 9, 25, 49, 81,...

3. The same rule is applied to each number in the pattern above. 

What is the 6th number in the pattern?

A 40

B 100

121

D 144

E 169

Sample Question 3 is a multiple-choice question in the algebra content area. This question asked students to infer a rule 

and find the next term in a sequence. The terms in this sequence are the squares of consecutive odd numbers.

58 percent of eighth-graders gave correct responses.

Sample Grade 8 Short Constructed-Response Question

Sample Question 4 is a short constructed-response 

question in the geometry content area. This question 

asked students to shade 5 additional squares in a 

grid that has 3 shaded squares to create a symmetric 

pattern. Students were given paper squares for this 

question. The response shown here would have been 

rated correct.

Fold Line

4. Shade fi ve more squares on the grid below 

so that if your completed fi gure were folded 

along the fold line both sides would match.
32 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

Technical Notes

NAEP Sampling Procedures

The schools and students participating in NAEP assessments are chosen to be nationally representative. Samples 

of schools and students are selected from each state 

and from the District of Columbia and Department of 

Defense schools. The results from the assessed students 

are combined to provide accurate estimates of overall 

national performance and of the performance of individual states and other jurisdictions (hereafter referred to as 

states). Results are weighted to take into account the fact 

that states, and schools within states, represent different 

proportions of the overall national population. For example, since the number of students assessed in most states 

is roughly the same (to allow for stable state estimates 

and administrative efficiencies), the results for students in 

less populous states are assigned smaller weights than the 

results for students in more populous states. The definition of the national sample has changed in 2005; it now 

includes all of the international Department of Defense 

schools.

Accommodations

It is important to assess all selected students from the 

target population. Before 1996, however, no testing 

accommodations were provided in the mathematics 

assessment to students with disabilities and English language learners. In 1996, administration procedures were 

introduced that allowed the use of accommodations for 

students who required them to participate, such as extra 

testing time or individual rather than group administration. The 1996 and 2000 mathematics assessments 

used a split-sample design to make it possible to report 

trends in students’ mathematics achievement across all 

the assessment years and, at the same time, examine 

how including students assessed with accommodations 

affected overall assessment results. Separate samples 

of students were assessed with each of the administration procedures. Based on analysis of the results, it was 

decided that, beginning with the 2003 mathematics 

assessment, NAEP would permit the use of accommodations. In this report, the first year with a split sample, 

1996, shows results from both samples. For subsequent 

years, only results from the accommodated sample are 

shown.

School and Student Participation Rates

In order to ensure unbiased samples, NCES and NAGB 

established participation rate standards that states and 

jurisdictions were required to meet in order for their 

results to be reported. Participation rates for the original 

sample needed to be at least 85 percent for schools in 

order to meet reporting requirements. In the 2005 mathematics assessment, all states and jurisdictions met NAEP 

participation rate standards at both grades 4 and 8.

Private School Results

Results for private school students overall are not presented in this report because the participation rates for 

this group were too low to produce valid and reliable 

estimates. Results are, however, available for students who 

attended certain types of private schools. For example, the 

table below shows average scale scores and achievementlevel results for students in Catholic and Lutheran schools 

in 2005. 

 These data and other private school data are 

available in the NAEP data tool (http://nces.ed.gov/

nationsreportcard/naepdata).

Interpreting Statistical Significance

Comparisons over time or between groups are based on 

statistical tests that consider both the size of the differences and the standard errors of the two statistics being 

compared. Standard errors are margins of error, and estimates based on smaller groups are likely to have larger 

margins of error. The size of the standard errors may also 

be influenced by other factors such as how representative 

Percentage of students

Type of school

Average scale 

score

At or above 

Basic

At or above 

Profi cient

Grade 4

Catholic 244 88 43

Lutheran 245 89 47

Grade 8

Catholic 290 81 40

Lutheran 293 84 44

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics 

Assessment.
Mathematics 2005 33

TECHNICAL AND DATA 

APPENDIX DATA 

TECHNICAL AND

APPENDIX

the students assessed are of the population as a whole. 

When an estimate—such as an average score—has a large 

standard error, a numerical difference that seems large 

may not be statistically significant. Differences of the 

same magnitude may or may not be statistically significant depending upon the size of the standard errors of the 

statistics. For example, a 3-point difference between male 

and female students may be statistically significant, while 

a 3-point difference between White and Hispanic students may not be. Standard errors for the NAEP scores 

and percentages presented in this report are available on 

the NAEP website (http://nces.ed.gov/nationsreportcard/

naepdata/).

 In the tables and charts of this report, the symbol (*) is 

used to indicate that a score or percentage in a previous 

assessment year is significantly different from the comparable measure in 2005. Statistically significant differences 

between groups of students—for example, between 

White students and Black students—are not identified 

in the table and charts, but they were tested in the same 

way. Any difference between scores or percentages that is 

identified as higher, lower, larger, or smaller in this report 

meets the requirements for statistical significance. The 

differences described in this report have been determined 

to be statistically significant at the .05 level with appropriate adjustments for multiple comparisons.

Interpreting Score Differences

Although this report discusses only changes that have 

been calculated to be statistically significant, it is important to provide some context about what constitutes a 

small or large difference in average scale scores. Beginning 

in 2002, the national samples have been derived from the 

sum of all of the state samples, instead of from a separate 

and smaller nationally representative sample. Therefore, 

national sample sizes have increased dramatically. 

Standard errors are an estimate of the uncertainty in the 

data, and larger sample sizes reduce this uncertainty. So 

while a small—1- or 2-point—difference may not have 

met the standard for significance before 2002, that same 

difference may meet that standard in later years because 

of the smaller standard errors. 

 To get a sense of the magnitude of score differences, 

figures A-1 and A-2 provide examples of score gaps of 

different sizes. For instance, in figure A-1, the score gaps 

range in size from 3 points (between male and female 

grade 4 students in 2005) to 34 points (between White 

and Black grade 4 students in 1996). In figure A-2, the 

range at grade 8 is even larger—from 2 points in 2005 

between male and female students to 47 points in 2000 

between students with disabilities and those without 

disabilities.

Figure A-2. Selected average mathematics scale score 

differences, grade 8: Various years, 1996–2005

 50

 45

 40

 35

 30

 25

 20

 15

 10

 5

 0

NOTE: All differences are signifi cant at the .05 level. SD = students with disabilities. ELL = English 

language learners. FRPL = free or reduced-price lunch.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1996–2005 Mathematics Assessments.

Average score difference Year Description of comparison

 50

 45

 40

 35

 30

 25

 20

 15

 10

 5

 0

NOTE: All differences are signifi cant at the .05 level. SD = students with disabilities. ELL = English 

language learners. FRPL = free or reduced-price lunch.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for 

Education Statistics, National Assessment of Educational Progress (NAEP), various years, 

1996–2005 Mathematics Assessments.

Figure A-1. Selected average mathematics scale score 

differences, grade 4: Various years, 1996–2005

Average score difference Year Description of comparison

 34 1996 White – Black

 30 2000 Not SD – SD

 26 2005 White – Black

 24 2005 Non ELL – ELL

 22 2005 Not eligible – Eligible for FRPL

 20 2005 White – Hispanic

 5 2005 Asian/Pacifi c Islander – White

 3 2005 Male – Female

47 2000 Not SD – SD

41 1996 White – Black

37 2005 Non ELL – ELL

34 2005 White – Black

30 2000 Not eligible – Eligible for FRPL

27 2005 White – Hispanic

7 2005 Asian/Pacifi c Islander – White

2 2005 Male – Female
34 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

Table A-1. Total number of students assessed and percentage of sampled students identified, excluded, and assessed with 

and without accommodations, by students with disabilities and English language learners, grades 4 and 8 public and 

nonpublic schools: Various years, 1990–2005

Accommodations not permitted Accommodations permitted

Student characteristics 1990 1992 1996 1996 2000 2003 2005

Grade 4

 Total number of students assessed 3,400 7,200 6,600 6,900 13,900 190,100 172,000

SD and/or ELL

 Identifi ed — 9 14 15 18 21 21

 Excluded —664443

 Assessed — 3 8 11 14 17 18

 Without accommodations —387999

 With accommodations —††5589

SD only

 Identifi ed — 7 11 10 12 13 13

 Excluded —453332

 Assessed — 3 6 7 9 10 10

 Without accommodations —364543

 With accommodations —††4467

ELL only —

 Identifi ed — 3 3 6 7 10 10

 Excluded —211111

 Assessed —125688

 Without accommodations —123466

 With accommodations —††2122

Grade 8

 Total number of students assessed 3,400 7,700 7,100 7,100 15,900 153,200 161,600

SD and/or ELL 

 Identifi ed — 9 11 12 13 17 17

 Excluded —643433

 Assessed — 4 6 8 10 14 14

 Without accommodations —466776

 With accommodations —††3368

SD only

 Identifi ed — 7 9 9 10 13 12

 Excluded —443333

 Assessed — 3 5 6 7 10 10

 Without accommodations —354543

 With accommodations —††2267

ELL only

 Identifi ed —233466

 Excluded —211111

 Assessed —122355

 Without accommodations —122244

 With accommodations —††#111

— Not available. Data on participation of SD/ELL are not available for 1990. 

† Not applicable. Accommodations were not permitted in this sample.

# The estimate rounds to zero.

NOTE: SD = students with disabilities. ELL = English language learners. Students identifi ed as both SD and ELL were counted only once under the combined SD and/or ELL category, but were counted 

separately under the SD and ELL categories. The numbers of students are rounded to the nearest hundred. The percentages presented in the table are based on the number of students selected to be 

assessed, which is different from the number of students actually assessed shown in the table. Detail may not sum to totals because of rounding.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), various years, 1990–2005 

Mathematics Assessments.
Mathematics 2005 35

TECHNICAL AND DATA 

APPENDIX

Table A-2. Percentages of sampled students of each race/ethnicity identified as students with 

disabilities and English language learners, excluded, and assessed, grades 4 and 8 public 

and nonpublic schools: 2005 

Student characteristics White Black Hispanic

Grade 4

SD and/or ELL

 Identifi ed 14 17 46

 Excluded 2 4 6

 Assessed 12 13 40

 Without accommodations 4 3 27

 With accommodations 8 9 14

SD only

 Identifi ed 13 16 12

 Excluded 2 4 3

 Assessed 11 12 9

 Without accommodations 4 3 3

 With accommodations 7 9 6

ELL only

 Identifi ed 1 1 39

 Excluded # # 4

 Assessed 1 1 35

 Without accommodations 1 1 25

 With accommodations # 1 10

Grade 8

SD and/or ELL

 Identifi ed 13 17 33

 Excluded 3 4 5

 Assessed 10 12 28

 Without accommodations 3 4 19

 With accommodations 7 8 9

SD only

 Identifi ed 12 16 12

 Excluded 3 4 3

 Assessed 10 11 9

 Without accommodations 3 3 3

 With accommodations 7 8 5

ELL only

 Identifi ed 1 1 26

 Excluded # # 3

 Assessed 1 1 22

 Without accommodations # 1 17

 With accommodations # # 6

# The estimate rounds to zero.

NOTE: SD = students with disabilities. ELL = English language learners. Students identifi ed as both SD and ELL were counted only once under the combined 

SD and/or ELL category, but were counted separately under the SD and ELL categories. Detail may not sum to totals because of rounding.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress 

(NAEP), 2005 Mathematics Assessment. 
36 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

Table A-3. Percentages of sampled students identified as students with disabilities and English 

language learners and excluded, grades 4 and 8 public schools: By state, 2005

State/jurisdiction

Grade 4 Grade 8

Overall 

excluded

SD ELL Overall 

excluded

SD ELL

Identifi ed Excluded Identifi ed Excluded Identifi ed Excluded Identifi ed Excluded

Nation (public) 3 14 3 10 1 4 13 3 6 1

Alabama 1 11 1 2 # 1 13 1 1 #

Alaska 2 15 1 19 1 2 14 2 15 #

Arizona 4 11 3 20 2 5 10 3 14 2

Arkansas 3 13 2 4 2 3 14 3 1 1

California 4 10 2 33 3 2 9 2 21 1

Colorado 3 12 2 11 1 3 10 2 7 1

Connecticut 2 13 2 5 1 3 13 2 3 #

Delaware 8 16 7 5 1 11 15 10 4 1

Florida 3 18 2 8 1 3 16 2 6 1

Georgia 2 14 2 3 1 2 12 2 2 #

Hawaii 3 11 2 8 1 3 14 2 7 1

Idaho 1 11 1 8 1 2 12 2 6 1

Illinois 3 14 2 9 1 3 15 3 3 1

Indiana 2 15 1 4 1 4 15 4 2 #

Iowa 2 14 2 4 # 3 15 2 2 #

Kansas 3 14 2 6 1 4 14 3 4 1

Kentucky 3 14 2 1 # 3 11 3 1 #

Louisiana 4 24 4 1 # 4 14 4 1 #

Maine 4 19 3 1 # 5 18 4 1 #

Maryland 4 13 3 4 1 4 11 4 2 #

Massachusetts 4 18 3 7 1 6 17 6 3 1

Michigan 4 14 4 3 1 4 14 4 3 #

Minnesota 2 13 2 7 1 2 12 2 7 1

Mississippi 2 11 2 1 # 3931#

Missouri 2 16 2 3 # 4 14 4 1 #

Montana 2 12 2 3 # 2 13 2 5 #

Nebraska 2 18 2 7 1 1 13 1 3 #

Nevada 3 12 3 17 1 2 11 2 9 1

New Hampshire 2 20 2 3 # 2 18 2 1 #

New Jersey 3 15 2 3 1 4 16 3 2 1

New Mexico 3 14 2 25 1 3 16 2 17 2

New York 4 15 3 6 1 4 15 3 5 1

North Carolina 2 15 2 6 1 3 14 2 4 1

North Dakota 3 16 2 2 # 4 16 4 1 #

Ohio 3 12 3 1 # 6 14 5 1 #

Oklahoma 4 16 4 6 1 4 16 4 4 1

Oregon 4 15 3 14 1 3 13 2 8 1

Pennsylvania 3 16 2 2 # 3 15 3 1 #

Rhode Island 3 20 2 7 1 3 17 3 5 1

South Carolina 4 14 4 2 # 6 14 6 1 #

South Dakota 2 16 1 4 # 2 12 2 2 #

Tennessee 3 11 3 2 1 5 14 5 1 #

Texas 6 14 5 15 2 6 13 5 8 2

Utah 2 12 2 12 1 2 11 2 7 1

Vermont 3 16 3 2 # 4 18 4 1 #

Virginia 5 16 4 8 1 5 15 4 4 1

Washington 3 13 2 9 1 2 11 2 5 1

West Virginia 2 19 2 # # 3 17 3 # #

Wisconsin 2 14 2 6 1 4 14 3 4 1

Wyoming 2 15 1 5 # 2 14 2 4 #

Other jurisdictions

District of Columbia 6 16 5 5 1 6 17 5 4 1

DoDEA1 2 10 1 8 1 2 9 1 4 1

# The estimate rounds to zero.

1 Department of Defense Education Activity.

NOTE: SD = students with disabilities. ELL = English language learners. Detail may not sum to totals because of rounding.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational 

Progress (NAEP), 2005 Mathematics Assessment.
Mathematics 2005 37

TECHNICAL AND DATA 

APPENDIX

Table A-4. Average mathematics scale scores and achievement-level results, by race/ethnicity, grade 4 public schools: By state, 2005

White Black Hispanic

Percentage of students Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or

above 

Basic

At or 

above 

Profi cient

Nation (public) 57 246 11 89 47 17 220 40 60 13 20 225 33 67 19

Alabama 57 235 20 80 30 38 211 53 47 7 2 ‡‡‡‡

Alaska 56 244 13 87 44 4 226 33 67 20 4 227 35 65 23

Arizona 45 243 14 86 43 5 217 46 54 13 41 218 43 57 14

Arkansas 71 242 14 86 42 22 214 50 50 10 5 229 28 72 25

California 31 245 12 88 46 7 215 47 53 12 49 219 41 59 14

Colorado 64 247 10 90 49 5 222 39 61 18 27 223 37 63 18

Connecticut 69 250 7 93 53 14 219 42 58 11 13 223 35 65 15

Delaware 54 249 7 93 50 33 226 29 71 15 9 229 26 74 18

Florida 48 247 9 91 49 23 224 33 67 16 24 233 22 78 28

Georgia 48 243 13 87 43 39 221 39 61 12 8 229 27 73 22

Hawaii 17 241 14 86 42 3 221 39 61 16 3 219 37 63 21

Idaho 82 245 10 90 44 1 ‡‡‡‡ 13 226 32 68 17

Illinois 54 245 11 89 44 19 212 54 46 9 22 219 41 59 14

Indiana 73 245 11 89 45 16 221 38 62 13 6 230 25 75 21

Iowa 85 242 13 87 40 5 224 32 68 15 6 222 37 63 17

Kansas 74 249 8 92 52 9 228 30 70 24 11 234 21 79 30

Kentucky 84 234 22 78 29 12 217 44 56 9 2 ‡‡‡‡

Louisiana 48 241 12 88 38 49 219 40 60 9 1 ‡‡‡‡

Maine 97 241 15 85 39 1 ‡‡‡‡ # ‡‡‡‡

Maryland 51 250 9 91 53 35 220 40 60 14 8 232 28 72 26

Massachusetts 75 252 5 95 57 9 228 27 73 18 11 225 27 73 14

Michigan 72 245 11 89 46 20 211 55 45 8 4 ‡‡‡‡

Minnesota 79 251 7 93 54 9 219 43 57 15 6 223 37 63 15

Mississippi 47 238 14 86 32 51 216 46 54 7 1 ‡‡‡‡

Missouri 76 240 15 85 37 17 215 47 53 9 4 221 37 63 10

Montana 85 243 11 89 41 1 ‡‡‡‡ 2 234 20 80 30

Nebraska 75 244 12 88 44 8 211 55 45 7 13 219 41 59 10

Nevada 46 240 15 85 38 12 214 48 52 10 33 219 42 58 13

New Hampshire 94 246 10 90 48 2 ‡‡‡‡ 2 226 36 64 17

New Jersey 57 251 7 93 55 18 224 33 67 17 15 230 26 74 25

New Mexico 30 238 17 83 34 2 213 55 45 6 56 218 43 57 13

New York 53 247 9 91 49 21 222 36 64 13 19 226 30 70 17

North Carolina 59 250 8 92 52 27 225 34 66 17 8 234 20 80 26

North Dakota 88 245 9 91 43 1 ‡‡‡‡ 1 ‡‡‡‡

Ohio 72 248 9 91 51 21 221 41 59 16 2 231 24 76 21

Oklahoma 59 240 15 85 36 11 217 46 54 11 9 226 28 72 16

Oregon 71 243 13 87 42 3 222 34 66 12 17 218 45 55 14

Pennsylvania 74 247 11 89 50 17 219 40 60 13 7 220 40 60 16

Rhode Island 73 241 14 86 37 8 211 54 46 9 16 211 52 48 9

South Carolina 55 250 8 92 53 41 223 34 66 13 3 236 17 83 30

South Dakota 84 245 10 90 45 2 ‡‡‡‡ 2 ‡‡‡‡

Tennessee 69 238 17 83 35 26 214 50 50 9 3 229 31 69 26

Texas 38 254 4 96 60 13 228 25 75 18 46 235 18 82 28

Utah 81 242 13 87 41 1 ‡‡‡‡ 13 220 40 60 13

Vermont 96 244 13 87 44 1 ‡‡‡‡ 1 ‡‡‡‡

Virginia 61 247 11 89 50 24 224 34 66 14 8 230 25 75 22

Washington 69 246 11 89 48 6 231 26 74 26 15 224 34 66 17

West Virginia 95 231 24 76 25 4 226 31 69 17 1 ‡‡‡‡

Wisconsin 77 247 9 91 48 11 210 54 46 7 7 224 34 66 16

Wyoming 85 245 11 89 45 1 ‡‡‡‡ 9 234 22 78 31

Other jurisdictions

District of Columbia 4 266 1 99 78 86 207 59 41 5 8 215 49 51 11

DoDEA1 47 245 9 91 46 20 227 27 73 15 14 235 18 82 28

See notes at end of table.
38 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

Table A-4. Average mathematics scale scores and achievement-level results, by race/ethnicity, 

grade 4 public schools: By state, 2005—Continued

Asian/Pacifi c Islander American Indian/Alaska Native

Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 4 251 11 89 54 1 227 31 69 22

Alabama 1 ‡‡‡‡ 1 ‡‡‡‡

Alaska 8 238 20 80 36 26 220 43 57 15

Arizona 3 241 15 85 43 6 ‡‡‡‡

Arkansas 1 ‡‡‡‡ 1 ‡‡‡‡

California 10 249 11 89 51 1 228 31 69 27

Colorado 3 242 19 81 42 1 ‡‡‡‡

Connecticut 3 253 7 93 57 # ‡‡‡‡

Delaware 3 260 6 94 70 # ‡‡‡‡

Florida 2 259 4 96 66 # ‡‡‡‡

Georgia 3 255 5 95 57 # ‡‡‡‡

Hawaii 66 229 29 71 25 1 ‡‡‡‡

Idaho 2 ‡‡‡‡ 2 ‡‡‡‡

Illinois 4 258 8 92 66 # ‡‡‡‡

Indiana 1 ‡‡‡‡ # ‡‡‡‡

Iowa 2 ‡‡‡‡ 1 ‡‡‡‡

Kansas 3 262 8 92 71 2 ‡‡‡‡

Kentucky 1 ‡‡‡‡ # ‡‡‡‡

Louisiana 1 ‡‡‡‡ # ‡‡‡‡

Maine 1 ‡‡‡‡ # ‡‡‡‡

Maryland 6 256 5 95 59 # ‡‡‡‡

Massachusetts 5 258 5 95 64 # ‡‡‡‡

Michigan 3 ‡‡‡‡ # ‡‡‡‡

Minnesota 5 242 18 82 40 2 ‡‡‡‡

Mississippi 1 ‡‡‡‡ # ‡‡‡‡

Missouri 2 ‡‡‡‡ # ‡‡‡‡

Montana 1 ‡‡‡‡ 11 223 38 62 17

Nebraska 2 ‡‡‡‡ 2 ‡‡‡‡

Nevada 8 243 12 88 42 1 ‡‡‡‡

New Hampshire 2 ‡‡‡‡ # ‡‡‡‡

New Jersey 9 264 3 97 74 # ‡‡‡‡

New Mexico 1 ‡‡‡‡ 10 217 44 56 9

New York 7 254 7 93 61 1 ‡‡‡‡

North Carolina 2 256 6 94 63 2 ‡‡‡‡

North Dakota 1 ‡‡‡‡ 8 223 34 66 13

Ohio 1 ‡‡‡‡ # ‡‡‡‡

Oklahoma 1 ‡‡‡‡ 19 229 24 76 21

Oregon 5 248 16 84 54 2 ‡‡‡‡

Pennsylvania 2 ‡‡‡‡ # ‡‡‡‡

Rhode Island 2 240 17 83 39 1 ‡‡‡‡

South Carolina 1 ‡‡‡‡ # ‡‡‡‡

South Dakota 1 ‡‡‡‡ 11 221 38 62 13

Tennessee 1 ‡‡‡‡ # ‡‡‡‡

Texas 3 264 4 96 72 # ‡‡‡‡

Utah 3 235 24 76 33 1 ‡‡‡‡

Vermont 1 ‡‡‡‡ # ‡‡‡‡

Virginia 5 256 5 95 64 # ‡‡‡‡

Washington 8 245 16 84 46 2 ‡‡‡‡

West Virginia 1 ‡‡‡‡ # ‡‡‡‡

Wisconsin 3 236 20 80 29 1 ‡‡‡‡

Wyoming 1 ‡‡‡‡ 3 ‡‡‡‡

Other jurisdictions

District of Columbia 1 ‡‡‡‡ # ‡‡‡‡

DoDEA1 7 239 15 85 32 1 ‡‡‡‡

# The estimate rounds to zero. 

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: Results are not shown for students whose race/ethnicity was “unclassifi ed.” Detail may not sum to totals because of rounding.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational 

Progress (NAEP), 2005 Mathematics Assessment. 
Mathematics 2005 39

TECHNICAL AND DATA 

APPENDIX

Table A-5. Average mathematics scale scores and achievement-level results, by gender, grade 4 

public schools: By state, 2005

Male Female

Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 51 238 20 80 37 49 236 21 79 33

Alabama 51 225 34 66 22 49 225 33 67 20

Alaska 50 236 24 76 35 50 235 22 78 32

Arizona 52 233 26 74 32 48 227 33 67 24

Arkansas 53 236 22 78 36 47 235 22 78 32

California 51 231 28 72 30 49 229 30 70 26

Colorado 52 241 18 82 41 48 238 21 79 36

Connecticut 51 244 14 86 45 49 241 17 83 40

Delaware 51 241 15 85 38 49 238 16 84 34

Florida 50 240 17 83 38 50 238 19 81 35

Georgia 51 234 24 76 30 49 233 24 76 29

Hawaii 51 229 29 71 26 49 231 26 74 28

Idaho 51 242 14 86 42 49 241 14 86 39

Illinois 51 234 25 75 33 49 232 28 72 30

Indiana 50 240 16 84 38 50 240 16 84 38

Iowa 53 242 14 86 40 47 238 17 83 34

Kansas 52 247 11 89 48 48 245 12 88 45

Kentucky 51 233 24 76 29 49 230 26 74 24

Louisiana 52 231 25 75 26 48 229 27 73 21

Maine 51 243 14 86 41 49 239 17 83 36

Maryland 51 240 21 79 40 49 237 22 78 36

Massachusetts 49 248 9 91 50 51 247 10 90 48

Michigan 51 240 19 81 41 49 236 23 77 34

Minnesota 50 247 12 88 50 50 245 13 87 45

Mississippi 51 227 30 70 20 49 226 32 68 18

Missouri 51 237 21 79 34 49 233 22 78 28

Montana 50 243 13 87 42 50 239 16 84 34

Nebraska 50 239 19 81 39 50 236 21 79 33

Nevada 51 231 28 72 28 49 229 29 71 24

New Hampshire 51 247 10 90 50 49 244 12 88 44

New Jersey 52 246 13 87 47 48 242 16 84 43

New Mexico 51 225 35 65 21 49 223 36 64 17

New York 50 240 18 82 39 50 237 19 81 33

North Carolina 51 242 17 83 41 49 241 16 84 38

North Dakota 50 244 10 90 43 50 241 12 88 38

Ohio 51 243 16 84 45 49 241 16 84 40

Oklahoma 51 235 20 80 31 49 233 22 78 26

Oregon 51 239 20 80 37 49 238 19 81 37

Pennsylvania 51 241 18 82 44 49 240 18 82 39

Rhode Island 51 234 24 76 32 49 233 23 77 29

South Carolina 50 238 20 80 37 50 238 18 82 35

South Dakota 51 243 13 87 43 49 240 14 86 38

Tennessee 50 233 26 74 30 50 231 26 74 25

Texas 50 244 12 88 43 50 240 15 85 37

Utah 51 240 16 84 39 49 237 18 82 34

Vermont 53 246 11 89 47 47 241 15 85 39

Virginia 51 242 17 83 42 49 239 18 82 37

Washington 50 242 15 85 43 50 241 17 83 41

West Virginia 52 232 23 77 28 48 229 27 73 22

Wisconsin 51 242 15 85 42 49 239 18 82 39

Wyoming 51 244 12 88 45 49 242 13 87 40

Other jurisdictions

District of Columbia 49 212 56 44 11 51 211 55 45 9

DoDEA1 49 241 14 86 38 51 237 17 83 31 1 Department of Defense Education Activity.

NOTE: Detail may not sum to totals because of rounding.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational 

Progress (NAEP), 2005 Mathematics Assessment. 
40 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

# The estimate rounds to zero. 

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment. 

Table A-6. Average mathematics scale scores and achievement-level results, by eligibility for free/reduced-price school lunch, grade 4 

public schools: By state, 2005 

Eligible Not eligible Information not available

Percentage of students Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 46 225 33 67 19 52 248 10 90 50 2 237 21 79 36

Alabama 55 214 47 53 10 42 238 17 83 34 3 ‡‡‡‡

Alaska 39 223 38 62 18 60 243 14 86 44 1 ‡‡‡‡

Arizona 47 220 42 58 16 38 242 15 85 42 15 ‡‡‡‡

Arkansas 54 226 31 69 22 45 247 11 89 49 # ‡‡‡‡

California 55 219 41 59 15 41 244 14 86 45 4 ‡‡‡‡

Colorado 37 224 35 65 20 63 248 10 90 50 # ‡‡‡‡

Connecticut 27 223 37 63 16 73 249 8 92 52 # ‡‡‡‡

Delaware 38 229 26 74 19 57 247 9 91 48 5 237 19 81 32

Florida 52 229 26 74 22 47 250 9 91 53 1 ‡‡‡‡

Georgia 53 224 35 65 16 46 245 11 89 45 # ‡‡‡‡

Hawaii 46 220 40 60 17 53 239 17 83 35 # ‡‡‡‡

Idaho 43 234 21 79 28 56 248 8 92 50 1 ‡‡‡‡

Illinois 45 218 44 56 15 55 245 12 88 45 # ‡‡‡‡

Indiana 43 231 25 75 24 56 247 10 90 49 2 ‡‡‡‡

Iowa 33 231 25 75 24 67 244 11 89 44 # ‡‡‡‡

Kansas 42 235 20 80 30 58 254 6 94 59 # ‡‡‡‡

Kentucky 52 224 35 65 16 47 240 14 86 37 1 ‡‡‡‡

Louisiana 65 224 34 66 15 34 244 11 89 41 1 ‡‡‡‡

Maine 32 230 26 74 25 65 245 11 89 45 2 ‡‡‡‡

Maryland 32 221 38 62 16 65 247 12 88 49 2 ‡‡‡‡

Massachusetts 29 231 22 78 22 71 254 4 96 60 # ‡‡‡‡

Michigan 34 223 36 64 19 65 246 12 88 48 1 ‡‡‡‡

Minnesota 29 231 26 74 27 71 252 7 93 56 # ‡‡‡‡

Mississippi 69 221 39 61 12 30 241 12 88 36 1 ‡‡‡‡

Missouri 43 225 33 67 17 55 243 12 88 42 2 ‡‡‡‡

Montana 37 231 26 74 25 61 247 8 92 47 3 ‡‡‡‡

Nebraska 40 225 33 67 18 60 246 11 89 48 # ‡‡‡‡

Nevada 45 219 43 57 14 54 239 17 83 36 1 ‡‡‡‡

New Hampshire 21 232 24 76 25 77 249 7 93 53 2 ‡‡‡‡

New Jersey 29 227 31 69 23 65 252 7 93 56 6 ‡‡‡‡

New Mexico 69 217 43 57 12 27 238 18 82 35 4 ‡‡‡‡

New York 48 228 30 70 21 49 248 8 92 50 3 ‡‡‡‡

North Carolina 44 229 27 73 22 54 251 8 92 54 1 ‡‡‡‡

North Dakota 32 234 20 80 28 68 247 7 93 46 # ‡‡‡‡

Ohio 38 227 31 69 21 59 252 7 93 56 3 ‡‡‡‡

Oklahoma 56 227 28 72 19 44 243 12 88 41 # ‡‡‡‡

Oregon 39 230 28 72 25 57 244 14 86 45 4 ‡‡‡‡

Pennsylvania 37 225 34 66 21 62 250 8 92 54 1 ‡‡‡‡

Rhode Island 38 218 43 57 13 62 243 12 88 41 # ‡‡‡‡

South Carolina 53 227 29 71 19 47 250 7 93 54 # ‡‡‡‡

South Dakota 41 232 23 77 26 59 249 7 93 51 # ‡‡‡‡

Tennessee 46 220 40 60 14 53 242 14 86 40 # ‡‡‡‡

Texas 57 233 20 80 26 43 253 5 95 59 1 ‡‡‡‡

Utah 37 229 28 72 23 59 244 11 89 45 4 ‡‡‡‡

Vermont 31 230 25 75 23 68 250 8 92 53 1 ‡‡‡‡

Virginia 34 225 33 67 16 66 249 9 91 52 # ‡‡‡‡

Washington 39 231 26 74 26 56 250 8 92 53 5 ‡‡‡‡

West Virginia 56 225 31 69 18 44 238 16 84 34 # ‡‡‡‡

Wisconsin 34 225 32 68 19 65 249 8 92 51 # ‡‡‡‡

Wyoming 36 236 19 81 32 60 247 9 91 49 3 244 18 82 51

Other jurisdictions

District of Columbia 76 206 62 38 5 22 229 32 68 27 2 ‡‡‡‡

DoDEA1 # ‡‡‡‡ # ‡‡‡‡ 100 239 15 85 35
Mathematics 2005 41

TECHNICAL AND DATA 

APPENDIX

1 Department of Defense Education Activity.

NOTE: SD = students with disabilities. The results for students with disabilities are based on students who were assessed and cannot be generalized to the total population of such students. Detail may 

not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment. 

Table A-7. Average mathematics scale scores and achievement-level results, by students with disabilities (SD), grade 4 public 

schools: By state, 2005

SD Not SD

Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 12 218 44 56 16 88 240 17 83 38

Alabama 10 195 73 27 7 90 229 29 71 22

Alaska 14 218 46 54 15 86 238 19 81 37

Arizona 9 207 58 42 9 91 232 27 73 30

Arkansas 11 208 56 44 8 89 239 18 82 37

California 8 209 56 44 12 92 232 27 73 29

Colorado 10 217 46 54 15 90 242 16 84 42

Connecticut 11 220 39 61 14 89 245 13 87 46

Delaware 10 222 41 59 19 90 242 13 87 38

Florida 16 227 33 67 24 84 241 15 85 39

Georgia 12 218 46 54 15 88 236 21 79 32

Hawaii 10 198 69 31 5 90 234 23 77 29

Idaho 10 215 47 53 10 90 245 10 90 44

Illinois 12 218 43 57 16 88 235 24 76 34

Indiana 14 220 42 58 14 86 243 12 88 42

Iowa 13 216 45 55 9 87 243 11 89 42

Kansas 12 226 32 68 20 88 248 9 91 50

Kentucky 12 215 48 52 12 88 234 22 78 28

Louisiana 21 213 52 48 8 79 235 19 81 28

Maine 16 222 41 59 18 84 244 11 89 43

Maryland 11 219 44 56 17 89 241 18 82 41

Massachusetts 15 230 26 74 22 85 251 6 94 54

Michigan 11 222 39 61 21 89 240 19 81 40

Minnesota 11 228 32 68 26 89 248 10 90 50

Mississippi 9 210 56 44 8 91 228 28 72 21

Missouri 14 222 38 62 18 86 237 19 81 33

Montana 10 220 42 58 14 90 243 12 88 41

Nebraska 16 221 40 60 15 84 241 16 84 40

Nevada 10 212 52 48 13 90 232 26 74 28

New Hampshire 18 227 30 70 18 82 250 7 93 53

New Jersey 13 218 43 57 17 87 248 10 90 50

New Mexico 13 205 62 38 5 87 227 31 69 21

New York 13 215 48 52 11 87 242 14 86 40

North Carolina 13 226 34 66 20 87 244 14 86 43

North Dakota 14 227 30 70 19 86 245 8 92 44

Ohio 9 223 38 62 20 91 244 14 86 45

Oklahoma 13 212 53 47 8 87 237 16 84 32

Oregon 12 222 38 62 16 88 241 17 83 40

Pennsylvania 14 216 48 52 16 86 245 13 87 45

Rhode Island 18 215 48 52 11 82 238 18 82 35

South Carolina 11 220 41 59 16 89 240 16 84 38

South Dakota 15 225 34 66 19 85 244 10 90 44

Tennessee 9 207 59 41 6 91 234 23 77 30

Texas 9 227 32 68 22 91 243 11 89 42

Utah 11 219 41 59 15 89 241 14 86 39

Vermont 13 224 33 67 18 87 246 10 90 47

Virginia 12 224 39 61 21 88 243 14 86 42

Washington 11 219 45 55 15 89 245 12 88 45

West Virginia 18 215 48 52 13 82 234 20 80 28

Wisconsin 12 221 39 61 17 88 243 13 87 44

Wyoming 14 219 44 56 13 86 247 8 92 47

Other jurisdictions

District of Columbia 11 188 83 17 4 89 214 52 48 10

DoDEA1 9 215 50 50 12 91 241 12 88 37
42 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

# The estimate rounds to zero. 

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: ELL = English language learners. Formerly ELL = students who passed their state’s English-language profi ciency examination within the past 2 years. The results for English language learners are 

based on students who were assessed and cannot be generalized to the total population of such students. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment. 

Table A-8. Average mathematics scale scores and achievement-level results, by English language learners (ELL), grade 4 public 

schools: By state, 2005

ELL Non-ELL Formerly ELL

Percentage of students Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 10 216 46 54 11 89 239 18 82 38 1 240 15 85 35

Alabama 2 ‡ ‡ ‡ ‡ 98 225 33 67 21 # ‡ ‡ ‡ ‡

Alaska 19 218 47 53 15 81 240 17 83 38 # ‡ ‡ ‡ ‡

Arizona 19 208 60 40 7 81 235 23 77 33 # ‡ ‡ ‡ ‡

Arkansas 3 229 28 72 24 97 236 22 78 34 # ‡ ‡ ‡ ‡

California 31 214 50 50 10 66 238 20 80 36 2 246 8 92 45

Colorado 11 208 58 42 6 88 243 15 85 43 1 ‡ ‡ ‡ ‡

Connecticut 4 215 50 50 10 96 243 14 86 44 # ‡ ‡ ‡ ‡

Delaware 4 229 30 70 22 96 240 15 85 37 # ‡ ‡ ‡ ‡

Florida 7 219 43 57 15 90 241 16 84 39 4 230 25 75 21

Georgia 2 208 58 42 4 98 234 23 77 30 # ‡ ‡ ‡ ‡

Hawaii 7 204 64 36 4 93 232 25 75 28 # ‡ ‡ ‡ ‡

Idaho 8 221 37 63 10 92 244 12 88 43 1 ‡ ‡ ‡ ‡

Illinois 9 204 64 36 5 91 236 22 78 34 # ‡ ‡ ‡ ‡

Indiana 3 ‡ ‡ ‡ ‡ 97 240 16 84 39 # ‡ ‡ ‡ ‡

Iowa 4 ‡ ‡ ‡ ‡ 96 241 14 86 38 # ‡ ‡ ‡ ‡

Kansas 5 ‡ ‡ ‡ ‡ 94 247 11 89 48 # ‡ ‡ ‡ ‡

Kentucky 1 ‡ ‡ ‡ ‡ 99 232 25 75 26 # ‡ ‡ ‡ ‡

Louisiana 1 ‡ ‡ ‡ ‡ 99 230 26 74 24 # ‡ ‡ ‡ ‡

Maine 1 ‡ ‡ ‡ ‡ 99 241 16 84 39 # ‡ ‡ ‡ ‡

Maryland 3 226 34 66 20 96 239 21 79 39 # ‡ ‡ ‡ ‡

Massachusetts 6 226 32 68 19 93 249 8 92 51 2 ‡ ‡ ‡ ‡

Michigan 3 ‡ ‡ ‡ ‡ 97 238 20 80 38 # ‡ ‡ ‡ ‡

Minnesota 7 222 38 62 14 93 248 10 90 50 # ‡ ‡ ‡ ‡

Mississippi 1 ‡ ‡ ‡ ‡ 99 227 31 69 19 # ‡ ‡ ‡ ‡

Missouri 2 ‡ ‡ ‡ ‡ 98 235 21 79 31 # ‡ ‡ ‡ ‡

Montana 3 ‡ ‡ ‡ ‡ 97 242 13 87 39 # ‡ ‡ ‡ ‡

Nebraska 7 211 56 44 5 92 240 17 83 39 1 ‡ ‡ ‡ ‡

Nevada 16 209 59 41 7 84 234 23 77 30 # ‡ ‡ ‡ ‡

New Hampshire 2 ‡ ‡ ‡ ‡ 98 246 10 90 47 # ‡ ‡ ‡ ‡

New Jersey 3 ‡ ‡ ‡ ‡ 97 245 14 86 46 # ‡ ‡ ‡ ‡

New Mexico 25 208 58 42 5 75 229 28 72 24 # ‡ ‡ ‡ ‡

New York 5 213 50 50 6 89 240 17 83 38 6 240 15 85 36

North Carolina 6 228 26 74 18 93 242 16 84 41 1 249 10 90 55

North Dakota 1 ‡ ‡ ‡ ‡ 99 243 11 89 41 # ‡ ‡ ‡ ‡

Ohio 1 ‡ ‡ ‡ ‡ 99 242 16 84 43 # ‡ ‡ ‡ ‡

Oklahoma 5 222 35 65 11 94 235 20 80 30 # ‡ ‡ ‡ ‡

Oregon 13 215 50 50 12 87 242 15 85 41 # ‡ ‡ ‡ ‡

Pennsylvania 2 218 46 54 17 98 241 17 83 42 # ‡ ‡ ‡ ‡

Rhode Island 6 199 71 29 5 93 236 20 80 32 # ‡ ‡ ‡ ‡

South Carolina 2 ‡ ‡ ‡ ‡ 98 238 19 81 36 # ‡ ‡ ‡ ‡

South Dakota 4 204 63 37 2 96 243 12 88 42 # ‡ ‡ ‡ ‡

Tennessee 2 ‡ ‡ ‡ ‡ 98 232 26 74 28 # ‡ ‡ ‡ ‡

Texas 14 226 31 69 15 84 245 10 90 44 2 244 8 92 39

Utah 11 219 42 58 13 89 241 14 86 40 1 ‡ ‡ ‡ ‡

Vermont 2 ‡ ‡ ‡ ‡ 98 243 13 87 43 # ‡ ‡ ‡ ‡

Virginia 7 232 28 72 25 92 241 16 84 40 # ‡ ‡ ‡ ‡

Washington 8 215 46 54 8 92 244 13 87 45 # ‡ ‡ ‡ ‡

West Virginia # ‡ ‡ ‡ ‡ 100 231 25 75 25 # ‡ ‡ ‡ ‡

Wisconsin 6 225 33 67 19 94 242 15 85 42 # ‡ ‡ ‡ ‡

Wyoming 4 223 34 66 15 96 244 12 88 44 # ‡ ‡ ‡ ‡

Other jurisdictions

District of Columbia 4 206 64 36 7 96 211 55 45 10 # ‡ ‡ ‡ ‡

DoDEA1 7 224 32 68 15 93 240 14 86 36 # ‡ ‡ ‡ ‡
Mathematics 2005 43

TECHNICAL AND DATA 

APPENDIX

Table A-9. Average mathematics scale scores and achievement-level results, by race/ethnicity, grade 8 public schools: By state, 2005

White Black Hispanic

Percentage of students Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or

above 

Basic

At or 

above 

Profi cient

Nation (public) 60 288 21 79 37 17 254 59 41 8 17 261 50 50 13

Alabama 59 276 32 68 22 37 240 73 27 3 2 ‡‡‡‡

Alaska 57 288 21 79 38 5 266 48 52 19 4 272 36 64 21

Arizona 50 288 21 79 38 5 261 50 50 15 38 260 52 48 13

Arkansas 71 281 25 75 28 23 243 70 30 4 4 266 44 56 15

California 33 284 26 74 34 8 248 65 35 7 45 254 58 42 9

Colorado 64 292 18 82 43 7 256 56 44 11 25 260 52 48 10

Connecticut 66 293 17 83 46 15 249 63 37 6 14 254 59 41 10

Delaware 56 291 15 85 40 33 264 47 53 13 7 268 43 57 16

Florida 52 286 22 78 36 22 251 61 39 8 22 265 44 56 16

Georgia 51 284 24 76 34 37 255 57 43 8 6 258 52 48 12

Hawaii 15 277 31 69 25 2 ‡‡‡‡ 3 257 53 47 9

Idaho 85 284 23 77 33 1 ‡‡‡‡ 12 261 52 48 11

Illinois 61 289 18 82 39 21 249 66 34 6 14 265 45 55 13

Indiana 81 286 20 80 34 12 257 56 44 9 4 261 51 49 14

Iowa 88 286 22 78 36 4 256 59 41 8 5 264 46 54 9

Kansas 77 289 17 83 39 8 256 56 44 12 9 266 44 56 14

Kentucky 86 276 33 67 24 10 255 57 43 9 1 ‡‡‡‡

Louisiana 53 281 23 77 25 44 252 63 37 5 2 ‡‡‡‡

Maine 96 281 26 74 30 2 ‡‡‡‡ 1 ‡‡‡‡

Maryland 50 292 18 82 43 40 258 54 46 11 4 262 53 47 19

Massachusetts 76 297 14 86 49 8 263 50 50 15 10 265 45 55 15

Michigan 73 285 23 77 36 20 247 66 34 6 4 265 48 52 16

Minnesota 81 296 15 85 49 8 251 63 37 9 4 263 47 53 10

Mississippi 46 279 26 74 24 51 247 69 31 4 1 ‡‡‡‡

Missouri 77 284 23 77 32 19 247 68 32 4 2 ‡‡‡‡

Montana 86 290 16 84 39 # ‡‡‡‡ 2 ‡‡‡‡

Nebraska 83 289 19 81 40 5 243 75 25 2 9 261 52 48 10

Nevada 55 280 27 73 29 10 247 66 34 7 29 256 56 44 10

New Hampshire 94 286 22 78 35 1 ‡‡‡‡ 2 ‡‡‡‡

New Jersey 57 295 15 85 47 20 260 50 50 11 15 264 42 58 15

New Mexico 34 279 28 72 26 2 257 56 44 13 51 255 57 43 8

New York 55 290 17 83 41 19 259 54 46 11 18 262 49 51 14

North Carolina 60 292 18 82 42 29 263 47 53 12 6 265 41 59 16

North Dakota 88 290 16 84 37 1 ‡‡‡‡ 1 ‡‡‡‡

Ohio 80 289 19 81 38 15 255 58 42 7 1 259 47 53 11

Oklahoma 62 278 29 71 26 11 249 65 35 4 7 257 55 45 11

Oregon 76 287 23 77 38 3 258 50 50 9 13 257 56 44 10

Pennsylvania 78 287 20 80 36 15 250 65 35 7 5 267 40 60 13

Rhode Island 73 281 27 73 30 8 249 66 34 5 15 244 71 29 4

South Carolina 57 294 14 86 44 39 263 49 51 10 3 269 42 58 19

South Dakota 86 291 15 85 40 1 ‡‡‡‡ 2 ‡‡‡‡

Tennessee 75 278 30 70 26 22 246 70 30 3 2 ‡‡‡‡

Texas 43 295 14 86 46 15 264 47 53 13 39 271 37 63 19

Utah 84 283 25 75 33 1 ‡‡‡‡ 10 255 55 45 9

Vermont 96 288 21 79 39 2 ‡‡‡‡ 1 ‡‡‡‡

Virginia 61 293 16 84 43 26 263 48 52 9 6 270 37 63 20

Washington 74 289 20 80 39 4 265 44 56 15 10 262 50 50 15

West Virginia 95 270 39 61 18 4 251 64 36 6 1 ‡‡‡‡

Wisconsin 79 291 16 84 42 11 246 70 30 5 6 265 44 56 16

Wyoming 87 284 21 79 32 1 ‡‡‡‡ 7 265 43 57 11

Other jurisdictions

District of Columbia 4 317 6 94 69 88 241 73 27 4 7 252 61 39 9

DoDEA1 45 292 15 85 41 20 267 42 58 16 13 280 28 72 28

See notes at end of table.
44 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

Table A-9. Average mathematics scale scores and achievement-level results, by race/ethnicity, 

grade 8 public schools: By state, 2005—Continued

Asian/Pacifi c Islander American Indian/Alaska Native

Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 5 294 19 81 46 1 266 45 55 14

Alabama 1 ‡‡‡‡ 1 ‡‡‡‡

Alaska 7 270 40 60 19 26 264 47 53 15

Arizona 2 ‡‡‡‡ 5 259 53 47 10

Arkansas 1 ‡‡‡‡ 1 ‡‡‡‡

California 12 293 20 80 45 1 ‡‡‡‡

Colorado 2 ‡‡‡‡ 1 ‡‡‡‡

Connecticut 4 292 22 78 46 # ‡‡‡‡

Delaware 3 306 9 91 59 # ‡‡‡‡

Florida 2 299 13 87 51 # ‡‡‡‡

Georgia 3 301 16 84 52 # ‡‡‡‡

Hawaii 68 264 47 53 17 # ‡‡‡‡

Idaho 1 ‡‡‡‡ 1 ‡‡‡‡

Illinois 4 300 10 90 50 # ‡‡‡‡

Indiana 1 ‡‡‡‡ # ‡‡‡‡

Iowa 2 ‡‡‡‡ 1 ‡‡‡‡

Kansas 2 ‡‡‡‡ 2 ‡‡‡‡

Kentucky 1 ‡‡‡‡ # ‡‡‡‡

Louisiana 1 ‡‡‡‡ 1 ‡‡‡‡

Maine 1 ‡‡‡‡ # ‡‡‡‡

Maryland 5 304 13 87 55 1 ‡‡‡‡

Massachusetts 5 314 9 91 68 # ‡‡‡‡

Michigan 2 ‡‡‡‡ # ‡‡‡‡

Minnesota 5 285 28 72 34 2 ‡‡‡‡

Mississippi 1 ‡‡‡‡ # ‡‡‡‡

Missouri 1 ‡‡‡‡ # ‡‡‡‡

Montana 1 ‡‡‡‡ 10 259 52 48 11

Nebraska 1 ‡‡‡‡ 1 ‡‡‡‡

Nevada 6 281 27 73 30 1 ‡‡‡‡

New Hampshire 2 ‡‡‡‡ # ‡‡‡‡

New Jersey 7 309 8 92 63 # ‡‡‡‡

New Mexico 1 ‡‡‡‡ 12 253 61 39 4

New York 7 298 17 83 50 # ‡‡‡‡

North Carolina 2 303 13 87 53 1 ‡‡‡‡

North Dakota 1 ‡‡‡‡ 9 261 51 49 9

Ohio 2 ‡‡‡‡ # ‡‡‡‡

Oklahoma 2 ‡‡‡‡ 18 267 40 60 15

Oregon 4 299 18 82 50 2 274 37 63 23

Pennsylvania 2 297 18 82 49 # ‡‡‡‡

Rhode Island 3 278 26 74 26 # ‡‡‡‡

South Carolina 1 ‡‡‡‡ # ‡‡‡‡

South Dakota 1 ‡‡‡‡ 10 260 52 48 11

Tennessee 1 ‡‡‡‡ # ‡‡‡‡

Texas 3 308 10 90 61 # ‡‡‡‡

Utah 3 273 37 63 26 2 ‡‡‡‡

Vermont 1 ‡‡‡‡ # ‡‡‡‡

Virginia 6 300 14 86 53 # ‡‡‡‡

Washington 8 294 19 81 45 2 273 36 64 26

West Virginia # ‡‡‡‡ # ‡‡‡‡

Wisconsin 3 286 30 70 32 1 ‡‡‡‡

Wyoming 1 ‡‡‡‡ 3 262 46 54 8

Other jurisdictions

District of Columbia 1 ‡‡‡‡ # ‡‡‡‡

DoDEA1 8 290 20 80 41 1 ‡‡‡‡

# The estimate rounds to zero. 

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: Results are not shown for students whose race/ethnicity was “unclassifi ed.” Detail may not sum to totals because of rounding.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational 

Progress (NAEP), 2005 Mathematics Assessment. 
Mathematics 2005 45

TECHNICAL AND DATA 

APPENDIX

1 Department of Defense Education Activity.

NOTE: Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational 

Progress (NAEP), 2005 Mathematics Assessment. 

Table A-10. Average mathematics scale scores and achievement-level results, by gender, grade 8 

public schools: By state, 2005

Male Female

Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale

 score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 51 278 32 68 30 49 277 33 67 27

Alabama 49 261 48 52 15 51 264 46 54 15

Alaska 53 280 30 70 30 47 278 32 68 27

Arizona 52 274 36 64 26 48 274 36 64 25

Arkansas 51 270 38 62 22 49 273 34 66 22

California 51 269 42 58 23 49 268 44 56 20

Colorado 49 281 30 70 33 51 281 29 71 31

Connecticut 50 281 31 69 35 50 281 30 70 34

Delaware 50 283 26 74 32 50 279 29 71 27

Florida 52 276 33 67 28 48 272 37 63 23

Georgia 51 273 38 62 24 49 272 38 62 23

Hawaii 54 265 45 55 19 46 266 44 56 18

Idaho 50 280 28 72 30 50 282 25 75 30

Illinois 51 279 30 70 30 49 276 34 66 27

Indiana 51 283 25 75 32 49 280 27 73 28

Iowa 50 283 25 75 34 50 284 24 76 33

Kansas 51 285 23 77 35 49 283 23 77 33

Kentucky 51 275 34 66 24 49 273 37 63 21

Louisiana 51 267 42 58 16 49 268 40 60 16

Maine 49 282 26 74 31 51 280 26 74 29

Maryland 48 278 35 65 31 52 278 33 67 28

Massachusetts 49 291 21 79 43 51 292 19 81 43

Michigan 50 279 30 70 31 50 275 34 66 27

Minnesota 50 291 22 78 45 50 289 20 80 41

Mississippi 49 263 48 52 15 51 262 49 51 12

Missouri 52 278 31 69 28 48 275 33 67 24

Montana 52 286 22 78 36 48 287 19 81 36

Nebraska 50 285 24 76 37 50 283 26 74 33

Nevada 51 270 39 61 23 49 269 40 60 20

New Hampshire 50 286 23 77 36 50 285 22 78 33

New Jersey 51 286 25 75 39 49 282 27 73 33

New Mexico 50 264 47 53 15 50 262 48 52 13

New York 50 280 30 70 31 50 280 30 70 30

North Carolina 51 281 29 71 32 49 282 26 74 32

North Dakota 51 287 20 80 36 49 287 19 81 33

Ohio 50 284 25 75 34 50 282 26 74 32

Oklahoma 50 272 37 63 22 50 271 37 63 19

Oregon 52 284 27 73 35 48 281 28 72 32

Pennsylvania 52 283 26 74 33 48 279 30 70 29

Rhode Island 51 272 37 63 24 49 273 36 64 23

South Carolina 50 282 29 71 31 50 281 28 72 29

South Dakota 51 287 20 80 36 49 287 20 80 37

Tennessee 49 270 39 61 21 51 271 39 61 20

Texas 50 283 26 74 33 50 279 29 71 28

Utah 52 280 29 71 32 48 278 29 71 27

Vermont 50 287 23 77 38 50 287 22 78 38

Virginia 50 285 25 75 35 50 283 26 74 32

Washington 51 285 26 74 37 49 285 24 76 35

West Virginia 51 268 40 60 18 49 270 40 60 18

Wisconsin 49 285 24 76 36 51 284 24 76 36

Wyoming 52 283 24 76 31 48 281 23 77 27

Other jurisdictions

District of Columbia 47 246 68 32 7 53 245 71 29 6

DoDEA1 52 285 23 77 34 48 283 25 75 31
46 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

# The estimate rounds to zero. 

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment. 

Table A-11. Average mathematics scale scores and achievement-level results, by eligibility for free/reduced-price school lunch, grade 8 

public schools: By state, 2005 

Eligible Not eligible Information not available

Percentage of students Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 39 261 49 51 13 59 288 21 79 39 3 277 34 66 28

Alabama 50 248 63 37 5 48 276 31 69 24 2 ‡‡‡ ‡

Alaska 34 264 46 54 14 64 287 23 77 37 2 ‡‡‡ ‡

Arizona 40 260 52 48 12 45 285 25 75 35 15 ‡‡‡ ‡

Arkansas 47 260 49 51 13 53 282 24 76 30 # ‡‡‡ ‡

California 45 254 58 42 10 50 282 29 71 33 5 ‡‡‡ ‡

Colorado 31 261 51 49 13 68 290 19 81 41 1 ‡‡‡ ‡

Connecticut 29 255 57 43 10 71 292 19 81 44 # ‡‡‡ ‡

Delaware 32 265 48 52 13 65 288 19 81 36 3 305 13 87 61

Florida 44 260 50 50 13 55 285 23 77 36 # ‡‡‡ ‡

Georgia 45 257 56 44 9 52 285 23 77 35 3 ‡‡‡ ‡

Hawaii 41 251 60 40 7 58 276 33 67 26 # ‡‡‡ ‡

Idaho 36 272 37 63 20 63 286 21 79 36 1 ‡‡‡ ‡

Illinois 38 258 54 46 10 62 290 18 82 40 1 ‡‡‡ ‡

Indiana 37 268 41 59 16 62 290 17 83 39 2 ‡‡‡ ‡

Iowa 29 269 39 61 17 71 290 18 82 40 # ‡‡‡ ‡

Kansas 37 270 39 61 19 63 293 14 86 43 # ‡‡‡ ‡

Kentucky 46 264 48 52 14 53 283 25 75 31 1 ‡‡‡ ‡

Louisiana 56 258 53 47 8 42 280 26 74 27 2 ‡‡‡ ‡

Maine 30 269 39 61 18 68 286 21 79 35 2 ‡‡‡ ‡

Maryland 28 258 55 45 10 67 287 24 76 39 5 ‡‡‡ ‡

Massachusetts 29 273 36 64 22 69 299 13 87 52 2 ‡‡‡ ‡

Michigan 27 258 53 47 13 72 285 24 76 36 1 ‡‡‡ ‡

Minnesota 27 270 39 61 22 73 297 14 86 50 # ‡‡‡ ‡

Mississippi 63 253 61 39 7 37 279 27 73 25 # ‡‡‡ ‡

Missouri 38 262 48 52 13 60 286 21 79 35 2 ‡‡‡ ‡

Montana 31 272 36 64 21 67 293 13 87 43 2 ‡‡‡ ‡

Nebraska 31 268 43 57 17 68 291 17 83 43 1 ‡‡‡ ‡

Nevada 32 256 56 44 10 65 277 32 68 27 3 ‡‡‡ ‡

New Hampshire 16 271 35 65 17 83 288 20 80 38 1 ‡‡‡ ‡

New Jersey 27 262 46 54 14 68 292 19 81 44 6 ‡‡‡ ‡

New Mexico 61 254 59 41 7 35 278 28 72 25 5 ‡‡‡ ‡

New York 45 267 44 56 19 50 291 17 83 41 5 ‡‡‡ ‡

North Carolina 39 266 43 57 15 60 293 17 83 43 1 ‡‡‡ ‡

North Dakota 28 274 33 67 20 71 292 14 86 40 1 ‡‡‡ ‡

Ohio 30 265 45 55 16 64 290 18 82 39 7 ‡‡‡ ‡

Oklahoma 50 260 50 50 10 50 283 23 77 31 # ‡‡‡ ‡

Oregon 33 270 40 60 20 63 289 21 79 41 3 ‡‡‡ ‡

Pennsylvania 30 262 47 53 12 69 289 19 81 39 2 ‡‡‡ ‡

Rhode Island 31 252 61 39 7 69 282 25 75 31 # ‡‡‡ ‡

South Carolina 47 267 43 57 15 53 294 16 84 43 # ‡‡‡ ‡

South Dakota 36 276 31 69 24 64 294 13 87 44 # ‡‡‡ ‡

Tennessee 45 256 56 44 9 55 282 25 75 30 # ‡‡‡ ‡

Texas 46 268 41 59 17 53 293 17 83 43 1 ‡‡‡ ‡

Utah 31 268 42 58 20 69 284 23 77 34 # ‡‡‡ ‡

Vermont 27 272 36 64 21 72 293 17 83 44 1 ‡‡‡ ‡

Virginia 27 263 48 52 11 73 292 17 83 41 # ‡‡‡ ‡

Washington 31 269 40 60 20 62 294 16 84 44 7 ‡‡‡ ‡

West Virginia 48 259 54 46 10 52 278 28 72 25 # ‡‡‡ ‡

Wisconsin 27 263 46 54 15 73 292 16 84 43 # ‡‡‡ ‡

Wyoming 30 272 35 65 17 70 287 19 81 34 # ‡‡‡ ‡

Other jurisdictions

District of Columbia 72 241 74 26 4 25 261 54 46 16 3 ‡‡‡ ‡

DoDEA1 # ‡‡‡ ‡ # ‡‡‡ ‡ 100 284 24 76 33
Mathematics 2005 47

TECHNICAL AND DATA 

APPENDIX

# The estimate rounds to zero. 

1 Department of Defense Education Activity.

NOTE: SD = students with disabilities. The results for students with disabilities are based on students who were assessed and cannot be generalized to the total population of such students. Detail may 

not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment. 

Table A-12. Average mathematics scale scores and achievement-level results, by students with disabilities (SD), grade 8 public 

schools: By state, 2005

SD Not SD

Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 11 244 69 31 7 89 281 28 72 31

Alabama 12 221 82 18 6 88 268 42 58 16

Alaska 12 248 67 33 6 88 283 26 74 32

Arizona 7 242 69 31 6 93 277 33 67 27

Arkansas 12 227 83 17 1 88 277 30 70 25

California 8 228 82 18 5 92 272 40 60 23

Colorado 9 244 70 30 5 91 284 26 74 35

Connecticut 11 248 63 37 10 89 285 26 74 38

Delaware 6 251 66 34 11 94 283 25 75 31

Florida 14 248 63 37 13 86 278 31 69 28

Georgia 10 241 71 29 6 90 276 35 65 25

Hawaii 12 224 89 11 1 88 271 38 62 21

Idaho 10 242 73 27 3 90 285 21 79 33

Illinois 13 244 69 31 5 87 283 26 74 32

Indiana 12 250 63 37 8 88 286 21 79 33

Iowa 13 245 74 26 4 87 290 17 83 38

Kansas 11 251 62 38 8 89 288 19 81 37

Kentucky 8 243 75 25 5 92 277 32 68 24

Louisiana 11 236 77 23 3 89 272 37 63 18

Maine 14 247 66 34 4 86 287 20 80 34

Maryland 7 245 68 32 10 93 281 31 69 31

Massachusetts 12 264 49 51 17 88 295 16 84 47

Michigan 10 243 69 31 4 90 281 28 72 32

Minnesota 10 250 66 34 10 90 295 16 84 47

Mississippi 6 228 84 16 2 94 265 46 54 14

Missouri 11 245 70 30 5 89 280 27 73 29

Montana 11 252 64 36 7 89 291 15 85 40

Nebraska 12 248 67 33 5 88 289 19 81 39

Nevada 9 233 80 20 5 91 274 35 65 23

New Hampshire 16 258 56 44 11 84 290 16 84 39

New Jersey 14 242 68 32 4 86 291 19 81 41

New Mexico 14 226 87 13 1 86 269 41 59 16

New York 12 249 63 37 7 88 284 25 75 34

North Carolina 13 253 60 40 10 87 286 23 77 35

North Dakota 12 260 54 46 7 88 291 14 86 38

Ohio 9 251 62 38 9 91 286 22 78 35

Oklahoma 13 237 76 24 3 87 276 31 69 23

Oregon 11 248 66 34 7 89 286 23 77 37

Pennsylvania 13 245 68 32 6 87 286 22 78 35

Rhode Island 15 241 74 26 3 85 278 30 70 27

South Carolina 8 251 63 37 7 92 284 25 75 32

South Dakota 10 250 65 35 6 90 291 15 85 40

Tennessee 10 237 79 21 3 90 274 35 65 23

Texas 8 249 64 36 8 92 284 25 75 33

Utah 9 237 77 23 3 91 283 24 76 32

Vermont 15 257 57 43 12 85 293 16 84 42

Virginia 11 256 58 42 9 89 288 21 79 36

Washington 10 244 71 29 6 90 289 20 80 39

West Virginia 14 235 83 17 2 86 275 33 67 21

Wisconsin 12 250 63 37 9 88 289 19 81 39

Wyoming 13 251 64 36 5 87 287 18 82 33

Other jurisdictions

District of Columbia 12 208 94 6 # 88 250 66 34 8

DoDEA1 8 247 66 34 4 92 287 20 80 35
48 The Nation’s Report CardTM TECHNICAL AND DATA APPENDIX

Table A-13. Average mathematics scale scores and achievement-level results, by English language learners (ELL), grade 8 public 

schools: By state, 2005

ELL Non-ELL Formerly ELL

Percentage of students Percentage of students Percentage of students

State/jurisdiction

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Percentage 

of all 

students

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Nation (public) 6 244 71 29 6 93 280 30 70 30 1 276 34 66 24

Alabama 1 ‡‡‡‡ 99 262 47 53 15 # ‡‡‡‡

Alaska 15 260 52 48 11 85 282 27 73 32 # ‡‡‡‡

Arizona 13 245 72 28 5 87 279 31 69 29 1 ‡‡‡‡

Arkansas 1 ‡‡‡‡ 99 272 36 64 22 # ‡‡‡‡

California 20 241 74 26 5 74 275 35 65 26 5 278 33 67 25

Colorado 6 246 71 29 5 94 283 27 73 34 # ‡‡‡‡

Connecticut 3 242 74 26 9 97 282 29 71 35 # ‡‡‡‡

Delaware 3 ‡‡‡‡ 97 282 27 73 30 # ‡‡‡‡

Florida 5 243 70 30 4 93 276 33 67 27 2 257 52 48 7

Georgia 2 ‡‡‡‡ 98 273 38 62 23 # ‡‡‡‡

Hawaii 6 229 83 17 3 94 268 42 58 19 # ‡‡‡‡

Idaho 6 254 58 42 7 94 283 25 75 31 # ‡‡‡‡

Illinois 2 249 70 30 8 98 278 31 69 29 # ‡‡‡‡

Indiana 2 ‡‡‡‡ 98 282 25 75 31 # ‡‡‡‡

Iowa 2 ‡‡‡‡ 98 285 24 76 34 # ‡‡‡‡

Kansas 3 251 67 33 3 97 285 22 78 35 # ‡‡‡‡

Kentucky 1 ‡‡‡‡ 99 274 35 65 23 # ‡‡‡‡

Louisiana 1 ‡‡‡‡ 99 268 41 59 16 # ‡‡‡‡

Maine 1 ‡‡‡‡ 99 281 26 74 30 # ‡‡‡‡

Maryland 2 ‡‡‡‡ 98 278 33 67 30 # ‡‡‡‡

Massachusetts 2 242 73 27 8 97 293 19 81 44 1 255 60 40 11

Michigan 2 ‡‡‡‡ 98 278 32 68 30 # ‡‡‡‡

Minnesota 6 ‡‡‡‡ 93 292 19 81 45 # ‡‡‡‡

Mississippi 1 ‡‡‡‡ 99 263 48 52 14 # ‡‡‡‡

Missouri 1 ‡‡‡‡ 99 277 32 68 26 # ‡‡‡‡

Montana 4 243 73 27 3 96 288 18 82 37 # ‡‡‡‡

Nebraska 3 242 78 22 2 97 285 23 77 36 # ‡‡‡‡

Nevada 9 236 79 21 4 90 273 36 64 23 1 ‡‡‡‡

New Hampshire 1 ‡‡‡‡ 99 286 22 78 35 # ‡‡‡‡

New Jersey 1 ‡‡‡‡ 98 284 25 75 36 1 ‡‡‡‡

New Mexico 16 239 77 23 2 84 268 42 58 16 # ‡‡‡‡

New York 4 237 77 23 4 87 282 28 72 32 9 278 33 67 27

North Carolina 3 252 58 42 8 96 283 27 73 33 1 ‡‡‡‡

North Dakota 1 ‡‡‡‡ 99 287 19 81 35 # ‡‡‡‡

Ohio 1 ‡‡‡‡ 99 284 25 75 33 # ‡‡‡‡

Oklahoma 4 252 60 40 12 96 272 36 64 21 # ‡‡‡‡

Oregon 7 253 60 40 10 93 285 25 75 35 # ‡‡‡‡

Pennsylvania 1 ‡‡‡‡ 99 281 27 73 31 # ‡‡‡‡

Rhode Island 4 224 89 11 1 96 274 34 66 24 # ‡‡‡‡

South Carolina 1 ‡‡‡‡ 99 282 28 72 30 # ‡‡‡‡

South Dakota 2 ‡‡‡‡ 98 288 19 81 37 # ‡‡‡‡

Tennessee 1 ‡‡‡‡ 99 271 39 61 21 # ‡‡‡‡

Texas 6 242 74 26 3 92 284 25 75 33 1 276 29 71 20

Utah 6 249 63 37 8 93 281 26 74 31 1 ‡‡‡‡

Vermont 1 ‡‡‡‡ 99 288 22 78 38 # ‡‡‡‡

Virginia 4 260 49 51 13 96 285 24 76 34 # ‡‡‡‡

Washington 4 249 68 32 11 96 287 23 77 37 # ‡‡‡‡

West Virginia # ‡‡‡‡ 100 269 40 60 18 # ‡‡‡‡

Wisconsin 3 269 44 56 19 97 285 23 77 36 # ‡‡‡‡

Wyoming 4 251 61 39 3 96 283 22 78 30 # ‡‡‡‡

Other jurisdictions

District of Columbia 3 ‡‡‡‡ 97 246 69 31 7 # ‡‡‡‡

DoDEA1 4 260 54 46 10 96 285 23 77 33 # ‡‡‡‡

# The estimate rounds to zero. 

‡ Reporting standards not met. Sample size is insuffi cient to permit a reliable estimate. 1 Department of Defense Education Activity.

NOTE: ELL = English language learners. Formerly ELL = students who passed their state’s English-language profi ciency examination within the past 2 years. The results for English language learners are 

based on students who were assessed and cannot be generalized to the total population of such students. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment. 
Mathematics 2005 49
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Mathematics 2005

October 2005

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http://nces.ed.gov/pubsearch.

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or order online at http://www.edpubs.org SUGGESTED CITATION

Perie, M., Grigg, W., and Dion, G. (2005). 

The Nation’s Report Card: Mathematics 2005

(NCES 2006–453). U.S. Department of Education, 

National Center for Education Statistics. Washington, 

D.C.: U.S. Government Printing Office.

CONTENT CONTACT

Arnold Goldstein 

202-502-7344 

Arnold.Goldstein@ed.gov