National Assessment of Educational Progress

The Nation’s Report CardTM

U.S. Department of Education

Institute of Education Sciences

NCES 2006–457r

CONTENTS

Mathematics 2005

Trial Urban District Assessment

Executive Summary 1

Introduction and 

Overall Performance 2

Student Group Results 4

Changes in Performance 12

Framework and 

Sample Questions 15

Technical Notes 

and Data Appendix 23
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

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 

Director

Learning Sciences Institute

Peabody College

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

Mark Schneider

Commissioner 

February 2006

The National Assessment Governing Board

For More Information...

The NAEP initial release website (www.nationsreportcard.gov) 

provides:

• Interactive displays of trial urban district results

• NAEP Data Explorer for statistical testing

• Snapshot reports for individual urban districts

• NAEP released questions tool 

The Nation’s Report CardTM informs the 

public about the academic achievement of 

elementary and secondary students in the 

United States. Report cards communicate 

the findings of the National Assessment 

of Educational Progress (NAEP), the only 

continuing and nationally representative 

measure of achievement in various subjects 

over time. The Nation’s Report CardTM

compares performance among states, urban 

districts, public and private schools, and 

student demographic groups.

 For over three decades, NAEP assessments have 

been conducted periodically in reading, mathematics, 

science, writing, history, geography, and other subjects. 

By making objective information available on student 

performance 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. The privacy of individual 

students 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. By law, the Commissioner of Education 

Statistics is responsible for carrying out the NAEP 

project. The National Assessment Governing Board 

(NAGB) oversees and sets policy for NAEP. NAGB 

is an independent, bipartisan group composed of 26 

representatives from throughout the U.S., including 

state and local officials, educators, business leaders, and 

members of the general public. 

The Nation’s Report CardTM Trial Urban District Assessment
Mathematics 2005 1

Executive Summary

EXECUTIVE SUMMARY

NAEP is a sample-based survey assessment that provides 

periodic reports on student academic performance at 

the national and state levels. The Trial Urban District 

Assessment (TUDA), a special project in NAEP, began 

assessing performance in selected large urban districts in 

2002 with reading and writing assessments, and continued in 2003 and 2005 with reading and mathematics 

assessments. Eleven large urban school districts participated in 2005, with Austin participating for the first time. 

This report provides the 2005 NAEP mathematics results 

for the participating districts. The report compares results 

to public school students’ performance in the nation and 

in large central cities, and to results for the previous mathematics assessment in 2003, where applicable, using a 

.05 significance level.

Mathematics Results for Grade 4 

In 2005, public school students in Austin and Charlotte 

had higher average scale scores than students nationally; 

average scores in the other districts were lower than the 

national average. Compared with students in large central city public schools nationwide, students in Austin, 

Charlotte, Houston, New York City, and San Diego had 

higher average scores and higher percentages performing at or above Basic. Boston had higher percentages at 

or above Basic. Students in Austin, Charlotte, and San 

Diego had higher percentages performing at or above 

Proficient. Atlanta, Chicago, Cleveland, the District of 

Columbia, and Los Angeles had lower average scores and 

lower percentages performing at or above Basic and at or 

above Proficient.

 Compared to students of the same race/ethnicity 

in large central city schools, Black students in Austin, 

Boston, Charlotte, Houston, and New York City had 

higher average scores and higher percentages performing 

at or above Basic. Black students in Chicago, the District 

of Columbia, and Los Angeles had lower average scores 

and lower percentages performing at or above Basic. 

Hispanic students in Austin, Charlotte, Houston, and 

New York City had higher average scores and higher percentages performing at or above Basic. Hispanic students 

in Chicago, the District of Columbia, and Los Angeles 

had lower average scores and lower percentages performing at or above Basic.

 Between 2003 and 2005, both the average scores and 

the percentages performing at or above Basic increased 

in Atlanta, Boston, Cleveland, the District of Columbia, 

Houston, Los Angeles, New York City, and San Diego. 

The same districts, except for Atlanta and Cleveland, also 

showed increases in the percentage of students performing at or above Proficient between 2003 and 2005.

Mathematics Results for Grade 8

In 2005, average scores for students in Austin and 

Charlotte were higher than the average score for public 

school students in the nation, with average scores in the 

other districts lower. Compared with students in large 

central cities, students in Austin, Boston, Charlotte, and 

San Diego had higher average scores and higher percentages performing at or above Basic. Austin, Boston, 

and Charlotte also had higher percentages of students 

performing at or above Proficient. Houston had a higher 

percentage at or above Basic, but a lower percentage at or 

above Proficient. Students in Atlanta, Chicago, Cleveland, 

the District of Columbia, and Los Angeles had lower 

average scores and lower percentages performing at or 

above Basic and at or above Proficient.

 Compared to students of the same 

race/ethnicity in large 

central city schools, 

Black students in 

Austin, Boston, 

Charlotte, Houston, 

and New York City 

had higher average 

scores and higher percentages at or above 

Basic. Black students 

in Atlanta, Chicago, 

Cleveland, and the 

District of Columbia had lower average scores and lower 

percentages performing at or above Basic. Black students in Los Angeles had lower average scores. Hispanic 

students in Austin, Chicago, and Houston had higher 

average scores and higher percentages performing at or 

above Basic than their large central city peers. Hispanic 

students in Los Angeles had lower average scores and 

lower percentages performing at or above Basic. 

 Between 2003 and 2005, the average scores and the 

percentages of students performing at or above Basic and 

at or above Proficient increased in Boston, Houston, Los 

Angeles, and San Diego.

At grade 4, between 

2003 and 2005, average scores improved 

in 8 of the 10 districts 

that participated in both 

years. At grade 8, during 

the same period, average 

scores improved in 4 of 

the 10 districts.
✓ KEY FINDINGS

! Compared with student 

performance in large central 

city schools...

 students in Austin, Charlotte, 

Houston, New York City, and 

San Diego had higher average 

scores and higher percentages 

performing at or above Basic.

 Austin, Charlotte, and San 

Diego had higher percentages 

performing at or above 

Profi cient.

 Boston had a higher percentage 

of students performing at or 

above Basic.

 students in Atlanta, Chicago, 

Cleveland, the District of 

Columbia, and Los Angeles had 

lower average scores and lower 

percentages performing at or 

above Basic and at or above 

Profi cient.

! Compared with student 

performance in large central 

city schools...

 students in Austin, Boston, 

Charlotte, and San Diego had 

higher average scores and 

higher percentages performing 

at or above Basic.

 Austin, Boston, and Charlotte 

had higher percentages 

performing at or above 

Profi cient.

 Houston had a higher percentage of students performing 

at or above Basic, but a 

lower percentage at or above 

Profi cient.

 students in Atlanta, Chicago, 

Cleveland, the District of 

Columbia, and Los Angeles had 

lower average scores and lower 

percentages performing at or 

above Basic and at or above 

Profi cient.

GRADE 4

GRADE 8

2 The Nation’s Report CardTM Trial Urban District Assessment

NAEP Achievement Levels 

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.

See pages 16 and 20 for brief descriptions of the achievement levels for mathematics. Detailed descriptions of the NAEP achievement levels for each subject can 

be found on the NAGB website (http://www.nagb.org/pubs/pubs.html). 

In 2005, ten urban school districts participated in the TUDA in mathematics 

at grades 4 and 8. The participating cities 

were Atlanta, Austin, Boston, Charlotte, 

Chicago, Cleveland, Houston, Los 

Angeles, New York City, and San Diego. 

(See the Technical Notes section for the 

full names of the school districts.) Austin 

participated for the first time in 2005.

Results for District of Columbia public 

school students, normally included along 

with NAEP’s state assessment results, are 

also reported. The results for these districts are for public school students only.

 In this report, NAEP results are presented in two ways: as average scale scores and 

as the percentage of students performing 

at or above three standards called achievement levels. NAEP mathematics scores are 

reported for grades 4 and 8 on a 0–500 

scale. Separate scales are created for other 

subjects, so even when a subject’s scale has 

the same numerical range (0–500), average scores should not be compared across 

subjects.

 Achievement levels are performance 

standards set by NAGB in a national 

process based on recommendations from 

panels of educators and members of the 

public. These performance standards 

indicate what students should know and 

be able to do in school subjects. The 

standards define basic, proficient, and 

advanced performance, providing a context for interpreting student results. 

 Urban district results are compared with 

results for public school students in the 

Introduction and Overall Performance: Grades 4 and 8

nation and in large central cities (population of 250,000 or more). As shown in 

figure 1, average scores for large central 

cities are lower than average scores for the 

nation. In many cases, students in participating urban districts also scored lower, 

on average, than those in the nation. In 

2005, grade 4 students in Austin and 

Charlotte had higher average scores than 

those in the nation, and all other districts 

had lower average scores. At grade 8, students in Austin and Charlotte also had 

higher average scores than students in the 

nation. The average scores in all other districts were lower than the nation’s average 

score. 

 The focus of the “Key Findings” boxes 

throughout the report is on comparing students in urban districts and large 

central city schools, because these schools 

represent a peer group, and are a more 

appropriate comparison than the nation 

as a whole for these urban districts. 

 Overall performance results for districts can be seen in figure 1; apparent 

differences between districts may not be 

statistically significant (at the .05 level). 

Note that the differences marked can 

indicate either higher or lower scores or 

percentages for the district. Figures A-1 to 

A-4 in the appendix display the statistically significant differences in performance 

among the districts. The rates of exclusion 

of students with disabilities and English 

language learners vary across districts 

and could affect comparisons of district 

performance. These rates are displayed in 

tables A-2 and A-3 in the appendix.
Mathematics 2005 3

INTRODUCTION AND

OVERALL PERFORMANCE

A Note on Achievement Levels

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 affi rmed the usefulness of these performance standards for understanding trends in achievement. NAEP achievement levels have been widely used by national and state offi cials. 

Information about what students at each grade level should know and be able to do at each achievement level is 

provided in the “Framework and Sample Questions” section.

# The estimate rounds to zero.

* Average score signifi cantly different from large central city public schools.

** Average score signifi cantly different from nation (public schools).

NOTE: 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 Trial Urban District 

Mathematics Assessment.

Figure 1. Average mathematics scale scores and percentage of students within each achievement level, grades 4 and 8 public 

schools: By urban district, 2005

Nation

Large central city

Charlotte

Austin

Houston

San Diego

New York City

Boston

Atlanta

Los Angeles

Cleveland

Chicago

District of Columbia

Average

score

Grade 4 Grade 4

Nation

Large central city

Charlotte

Austin

Houston

San Diego

New York City

Boston

Atlanta

Los Angeles

Cleveland

Chicago

District of Columbia

District District

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

21 44 30 5

32 43 21 3

14 41 35 9

15 45 33 7

23 51 23 3

26 45 25 4

27 47 23 3

28 50 20 2

43 40 14 3

42 39 16 2

40 47 12 #

48 38 12 1

55 35 8 1

237*

228**

244*,**

242*,**

233*,**

232*,**

231*,**

229**

221*,**

220*,**

220*,**

216*,**

211*,**

Below Basic Basic Proficient Advanced

Percentage below Basic Percentage at Basic, Proficient, and

Advanced

Percentage below Basic Percentage at Basic, Proficient, and

Advanced

Nation

Large central city

Austin

Charlotte

San Diego

Boston

Houston

New York City

Chicago

Los Angeles

Cleveland

District of Columbia

Atlanta

District

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

32 39 23 6

47 34 15 4

32 35 24 9

31 36 24 9

39 39 18 4

42 35 16 6

42 41 14 2

46 34 16 5

55 34 9 2

62 27 9 2

66 28 6 #

69 24 5 2

69 24 5 1

Grade 8 Grade 8

Nation

Large central city

Austin

Charlotte

San Diego

Boston

Houston

New York City

Chicago

Los Angeles

Cleveland

District of Columbia

Atlanta

Average

District score

278*

265**

281*,**

281*,**

270*,**

270*,**

267**

267**

258*,**

250*,**

249*,**

245*,**

245*,**

Below Basic Basic Proficient Advanced
✓ KEY FINDINGS

! Compared to students of the 

same race/ethnicity in large 

central city schools...

 Black students in Austin, 

Boston, Charlotte, Houston, 

and New York City had higher 

average scores and higher 

percentages performing at or 

above Basic.

 Black students in Chicago, the 

District of Columbia, and Los 

Angeles had lower average 

scores and lower percentages 

performing at or above Basic.

 Hispanic students in Austin, 

Charlotte, Houston, and New 

York City had higher average 

scores and higher percentages 

performing at or above Basic.

 Hispanic students in Chicago, 

the District of Columbia, 

and Los Angeles had lower 

average scores and lower 

percentages performing at or 

above Basic.

 Asian/Pacifi c Islander 

students in Boston, Charlotte, 

and New York City had higher 

average scores.

 Asian/Pacifi c Islander 

students in Boston and 

New York City had higher 

percentages performing at or 

above Basic.

GRADE 4

4 The Nation’s Report CardTM Trial Urban District Assessment

Table 1. Percentage of students by race/ethnicity in mathematics, grade 4 public schools: 

By urban district, 2005

District White Black Hispanic

Asian/Pacifi c 

Islander

American 

Indian/Alaska 

Native Unclassifi ed1

Nation 57 17 20 4 1 1

Large central city 21 32 39 6 1 1

Atlanta 11 84 3 1 # 1

Austin 28 14 55 3 # #

Boston 13 45 32 9 # #

Charlotte 41 40 11 5 # 3

Chicago 8 47 42 3 # #

Cleveland 20 70 7 1 # 3

District of Columbia 4 86 8 1 # #

Houston 10 28 59 3 # #

Los Angeles 10 10 74 6 # #

New York City 14 35 39 12 # #

San Diego 23 14 44 17 1 #

# The estimate rounds to zero.

1 “Unclassifi ed” students are those whose school-reported race/ethnicity was “other” or “unavailable,” or was missing, and whose race/ethnicity 

category could not be determined from self-reported information.

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 Trial Urban District Mathematics Assessment.

Student Group Results

District Mathematics Results by 

Race/Ethnicity: Grade 4

NAEP obtains information on a student’s 

race/ethnicity from school rosters and 

reports it as one of six categories: White, 

Black, Hispanic, Asian/Pacific Islander, 

American Indian/Alaska Native, and 

Unclassified. Black includes African 

American, Hispanic includes Latino, and 

Pacific Islander includes Native Hawaiian. 

Race categories exclude Hispanic origin 

unless specified. If the school roster was 

left blank for a student, student-reported 

race/ethnicity was used.

 Table 1 shows the percentages of 

students in grade 4 in each of the participating districts for 2005 by race/ethnicity. 

In each of the urban districts assessed, 

Black students and/or Hispanic students 

constituted the majority in grade 4. For 

the 2005 national assessment in public 

schools, White students constituted a 

majority—57 percent of the grade 4 

sample.

 Table 2 shows the average scale scores 

and the percentages of students performing below Basic, at or above Basic,

and at or above Proficient in 2005 for 

White, Black, Hispanic, and Asian/Pacific 

Islander students in grade 4. Performance 

results are not presented for American 

Indian/Alaska Native and Unclassified 

categories because of small sample sizes.

Districts are rank-ordered by average scale 

score within each racial/ethnic category. 

Asterisks in the table mark statistically 

significant differences between results for 

students in the urban districts and their 

counterparts in the nation and in large 

central cities. Information on average 

score gaps between White and Black students and between White and Hispanic 

students for each district, for 2005 and 

previous assessments, can be found in 

figure A-5 in the appendix. For more 

information on results by race/ethnicity, 

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

naepdata.
Mathematics 2005 5

STUDENT GROUP 

RESULTS

Table 2. Average scale scores and achievement-level results in mathematics, by race/ethnicity, grade 4 public schools: By urban 

district, 2005

White Black

Percentage of students Percentage of students

District

Average 

scale 

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient District

Average 

scale

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient

Nation 246 11 89 47* Nation 220* 40* 60* 13*

Large central city 247 12 88 50** Large central city 217** 45** 55** 11**

District of Columbia 266*,** 1 99 78*,** Charlotte 230*,** 26*,** 74*,** 21*,**

Atlanta 263*,** 4*,** 96*,** 72*,** Austin 228*,** 26*,** 74*,** 18

Austin 262*,** 1*,** 99*,** 75*,** Houston 224* 33*,** 67*,** 14

Houston 262*,** 3*,** 97*,** 73*,** Boston 223*,** 35* 65* 13

Charlotte 261*,** 3*,** 97*,** 70*,** New York City 222* 37* 63* 14

San Diego 249 6*,** 94*,** 50 San Diego 221 40 60 15

Los Angeles 247 13 87 49 Atlanta 215** 49** 51** 9**

New York City 245 13 87 46 Cleveland 215** 48** 52** 8**

Boston 244 12 88 43 Los Angeles 209*,** 58*,** 42*,** 9

Chicago 243 12 88 43 Chicago 208*,** 59*,** 41*,** 6*,**

Cleveland 233*,** 19 81 25*,** District of Columbia 207*,** 59*,** 41*,** 5*,**

‡ Reporting standards not met.

* Signifi cantly different from large central city public schools.

** Signifi cantly different from nation (public schools).

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

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

Mathematics Assessment.

Hispanic Asian/Pacifi c Islander

Percentage of students Percentage of students

District

Average 

scale 

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient District

Average 

scale

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient

Nation 225* 33* 67* 19* Nation 251* 11 89 54*

Large central city 223** 36** 64** 17** Large central city 247** 13 87 49**

Austin 234*,** 20*,** 80*,** 27*,** Boston 256* 2*,** 98*,** 65*

Charlotte 234*,** 19*,** 81*,** 27 Charlotte 256* 4 96 62

Houston 232*,** 22*,** 78*,** 23* New York City 253* 8* 92* 60*

New York City 226* 30* 70* 18 Los Angeles 246 12 88 45

Boston 225 30 70 14 San Diego 245** 13 87 46

Cleveland 224 32 68 18 Atlanta ‡‡‡ ‡

San Diego 222** 37** 63** 16 Austin ‡‡‡ ‡

Chicago 217*,** 45*,** 55*,** 13 Chicago ‡‡‡ ‡

Los Angeles 216*,** 47*,** 53*,** 13*,** Cleveland ‡‡‡ ‡

District of Columbia 215*,** 49*,** 51*,** 11*,** District of Columbia ‡‡‡ ‡

Atlanta ‡‡‡‡ Houston ‡‡‡ ‡
✓ KEY FINDINGS

! Compared to students of the 

same race/ethnicity in large 

central city schools...

 Black students in Austin, 

Boston, Charlotte, Houston, 

and New York City had higher 

average scores and higher 

percentages performing at or 

above Basic.

 Black students in Atlanta, 

Chicago, Cleveland, and the 

District of Columbia had lower 

average scores and lower 

percentages performing at or 

above Basic.

 Black students in Los Angeles 

had lower average scores.

 Hispanic students in Austin, 

Chicago, and Houston 

had higher average scores 

and higher percentages 

performing at or above Basic.

 Hispanic students in Los 

Angeles had a lower average 

score and a lower percentage 

performing at or above Basic.

 Asian/Pacifi c Islander 

students in Boston had a 

higher average score and a 

higher percentage performing 

at or above Basic.

GRADE 8

6 The Nation’s Report CardTM Trial Urban District Assessment

District Mathematics Results by Race/Ethnicity: Grade 8

Table 3, similar to table 1, shows the 

percentages of students in grade 8 by 

race/ethnicity for each of the participating districts. In each of the urban districts 

assessed, Black students and/or Hispanic 

students constituted the majority in grade 

8. For the 2005 national assessment in 

public schools, White students constituted a majority—60 percent of the grade 

8 sample. Table 4 displays the average 

scores and percentages performing below 

Basic, at or above Basic, and at or above 

Proficient in 2005 for the same racial/ethnic groups as in table 2. The districts are 

rank-ordered by average scale score within 

each racial/ethnic category. 

 Information on average score gaps 

between White and Black students and 

between White and Hispanic students for 

each district, for 2005 and previous assessments, can be found in figure A-6 in the 

appendix.

District White Black Hispanic

Asian/Pacifi c 

Islander

American 

Indian/Alaska 

Native Unclassifi ed1

Nation 60 17 17 5 1 1

Large central city 24 32 36 8 1 1

Atlanta 5 93 2 # # #

Austin 33 13 51 3 # #

Boston 16 45 28 11 # 1

Charlotte 38 48 9 4 1 1

Chicago 12 45 38 4 # #

Cleveland 18 70 10 1 # 1

District of Columbia 4 88 7 1 # #

Houston 10 28 58 4 # #

Los Angeles 9 13 72 6 # #

New York City 15 35 38 13 # #

San Diego 26 15 41 17 1 #

# The estimate rounds to zero.

1 “Unclassifi ed” students are those whose school-reported race/ethnicity was “other” or “unavailable,” or was missing, and whose race/ethnicity 

category could not be determined from self-reported information.

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 Trial Urban District Mathematics Assessment.

Table 3. Percentage of students by race/ethnicity in mathematics, grade 8 public schools: 

By urban district, 2005
Mathematics 2005 7

STUDENT GROUP 

RESULTS

Table 4. Average scale scores and achievement-level results in mathematics, by race/ethnicity, grade 8 public schools: By urban 

district, 2005

White Black

Percentage of students Percentage of students

District

Average 

scale 

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient District

Average 

scale

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient

Nation 288 21 79 37 Nation 254* 59* 41* 8*

Large central city 288 22 78 39 Large central city 250** 64** 36** 7**

District of Columbia 317*,** 6*,** 94*,** 69*,** Charlotte 264*,** 46*,** 54*,** 14*,**

Austin 305*,** 10*,** 90*,** 61*,** Austin 262* 48* 52* 12

Charlotte 304*,** 10*,** 90*,** 60*,** Houston 257* 53* 47* 7

Boston 299*,** 17 83 54*,** New York City 257* 56* 44* 10

Houston 294 15 85 50 Boston 256* 55* 45* 9

San Diego 292 17 83 42 San Diego 253 60 40 8

New York City 286 23 77 38 Chicago 245*,** 72*,** 28*,** 3*,**

Chicago 281 29 71 33 Cleveland 244*,** 71*,** 29*,** 3*,**

Los Angeles 280* 32 68 32 Atlanta 242*,** 72*,** 28*,** 4*,**

Cleveland 265*,** 46*,** 54*,** 17*,** District of Columbia 241*,** 73*,** 27*,** 4*,**

Atlanta ‡‡‡‡ Los Angeles 239*,** 71** 29** 7

‡ Reporting standards not met. 

* Signifi cantly different from large central city public schools.

** Signifi cantly different from nation (public schools).

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

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

Mathematics Assessment.

Hispanic Asian/Pacifi c Islander

Percentage of students Percentage of students

District

Average 

scale 

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient District

Average 

scale

score

Below

Basic

At or 

above

Basic

At or 

above

Profi cient

Nation 261* 50* 50* 13* Nation 294* 19* 81* 46*

Large central city 258** 54** 46** 11** Large central city 289** 24** 76** 40**

Austin 267*,** 44* 56* 17* Boston 309*,** 8* 92* 61*,**

Houston 265*,** 44* 56* 12 Houston 299 15 85 55

Chicago 263* 48* 52* 11 New York City 295 21 79 50

Charlotte 262 47 53 15 Chicago 292 17 83 38

Boston 261 49 51 12 Los Angeles 291 18 82 43

New York City 259 53 47 12 San Diego 282** 26 74 31**

San Diego 258 51 49 11 Atlanta ‡ ‡‡‡

District of Columbia 252** 61 39 9 Austin ‡ ‡‡‡

Cleveland 251 67** 33** 7 Charlotte ‡ ‡‡‡

Los Angeles 245*,** 68*,** 32*,** 6*,** Cleveland ‡ ‡‡‡

Atlanta ‡‡‡‡ District of Columbia ‡ ‡‡‡
✓ KEY FINDINGS

! Compared to students 

eligible for free/reducedprice lunch in large central 

city schools...

 eligible students in Austin, 

Boston, Charlotte, Houston, 

New York City, and San Diego 

had higher average scores and 

higher percentages performing 

at or above Basic.

 eligible students in Atlanta, 

Chicago, the District of 

Columbia, and Los Angeles 

had lower average scores and 

lower percentages performing 

at or above Basic.

! Compared to students 

eligible for free/reducedprice lunch in large central 

city schools...

 eligible students in Austin, 

Boston, Charlotte, Houston, 

and New York City had higher 

average scores.

 eligible students in Austin, 

Boston, Charlotte, Houston, 

New York City, and San Diego 

had higher percentages 

performing at or above Basic.

 eligible students in Atlanta, 

Cleveland, the District of 

Columbia, and Los Angeles 

had lower average scores and 

lower percentages performing 

at or above Basic.

GRADE 4

GRADE 8

8 The Nation’s Report CardTM Trial Urban District Assessment

District Mathematics Results by Eligibility for Free/Reduced-Price 

School Lunch: Grade 4

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 

under the NSLP. Those with incomes 

between 130 percent and 185 percent of 

the poverty level are eligible for reducedprice 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.) 

District

Percentage of students

Percentage of 

all students

Average 

scale score

Below 

Basic

At or above 

Basic

At or above 

Profi cient

Eligible

Nation 46* 225* 33* 67* 19*

Large central city 71** 221** 40** 60** 15**

Austin 63*,** 232*,** 23*,** 77*,** 23*

Charlotte 44* 230*,** 25*,** 75*,** 20*

Houston 78*,** 228*,** 27*,** 73*,** 18

New York City 84*,** 228*,** 30* 70* 22*

Boston 84*,** 227*,** 29*,** 71*,** 19*

San Diego 64*,** 225* 34* 66* 19

Cleveland 100*,** 220** 39** 61** 13**

Los Angeles 86*,** 216*,** 47*,** 53*,** 13*,**

Atlanta 76*,** 213*,** 52*,** 48*,** 6*,**

Chicago 87*,** 212*,** 52*,** 48*,** 9*,**

District of Columbia 76*,** 206*,** 62*,** 38*,** 5*,**

Not eligible

Nation 52* 248* 10* 90* 50*

Large central city 27** 246** 14** 86** 47**

Austin 37*,** 260*,** 2*,** 98*,** 70*,**

Charlotte 55* 256*,** 6*,** 94*,** 63*,**

Houston 22*,** 251 9* 91* 55

Los Angeles 14*,** 248 12 88 51

Atlanta 23*,** 247 16** 84** 49

San Diego 36*,** 246 11 89 47

Boston 13*,** 244 14 86 45

New York City 15*,** 243 13 87 42

Chicago 13*,** 237*,** 22** 78** 40

District of Columbia 22*,** 229*,** 32*,** 68*,** 27*,**

Cleveland 0 ††† †

† Not applicable. In Cleveland, all students were categorized as eligible for free/reduced-price school lunch.

* Signifi cantly different from large central city public schools.

** Signifi cantly different from nation (public schools).

NOTE: Detail may not sum to totals because of rounding. Results are not shown for students whose eligibility status for free/reduced-price lunch 

was not available; percentages in this category ranged from 0 to 2 percent.

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

Educational Progress (NAEP), 2005 Trial Urban District Mathematics Assessment.

Table 5. Average scale scores and achievement-level results in mathematics, by eligibility for 

free/reduced-price school lunch, grade 4 public schools: By urban district, 2005
Mathematics 2005 9

STUDENT GROUP 

RESULTS

 Average mathematics scale scores and achievementlevel results by students’ eligibility for free/reduced-price 

school lunch are shown in table 5 for grade 4 and in table 

6 for grade 8. Districts are rank-ordered by average scale 

score within the “eligible” and “not eligible” categories.

For comparison purposes, data are also provided for the 

nation and for large central cities. At grades 4 and 8, all 

districts except Austin, Charlotte, and San Diego had 

higher percentages of eligible students than did large 

central cities. 

District

Percentage of students

Percentage of 

all students

Average 

scale score

Below 

Basic

At or above 

Basic

At or above 

Profi cient

Eligible

Nation 39* 261* 49* 51* 13*

Large central city 62** 256** 57** 43** 11**

Boston 74*,** 264* 47* 53* 17*

New York City 84*,** 264* 49* 51* 18*

Houston 70*,** 262* 47* 53* 10**

Austin 50*,** 261* 51* 49* 13

Charlotte 45*,** 261* 49* 51* 12

San Diego 55*,** 258 51* 49* 10

Chicago 81*,** 254** 60** 40** 8*,**

Cleveland 100 249*,** 66*,** 34*,** 6*,**

Los Angeles 77*,** 245*,** 68*,** 32*,** 6*,**

District of Columbia 72*,** 241*,** 74*,** 26*,** 4*,**

Atlanta 78*,** 240*,** 74*,** 26*,** 3*,**

Not eligible

Nation 59* 288* 21* 79* 39*

Large central city 35** 282** 29** 71** 34**

Cleveland 0 ††† †

Austin 49*,** 301*,** 12*,** 88*,** 54*,**

Charlotte 54*,** 297*,** 16*,** 84*,** 51*,**

Boston 25*,** 288 27 73 41

New York City 12*,** 286 26 74 39

San Diego 45*,** 285 24 76 36

Houston 30*,** 279** 31** 69** 30**

Chicago 18*,** 275** 35** 65** 27**

Los Angeles 23*,** 270*,** 41*,** 59*,** 25*,**

Atlanta 19*,** 266*,** 48*,** 52*,** 22*,**

District of Columbia 25*,** 261*,** 54*,** 46*,** 16*,**

† Not applicable. In Cleveland, all students were categorized as eligible for free/reduced-price school lunch.

* Signifi cantly different from large central city public schools.

** Signifi cantly different from nation (public schools).

NOTE: Detail may not sum to totals because of rounding. Results are not shown for students whose eligibility status for free/reduced-price lunch 

was not available; percentages in this category ranged from 0 to 4 percent. 

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

Educational Progress (NAEP), 2005 Trial Urban District Mathematics Assessment.

Table 6. Average scale scores and achievement-level results in mathematics, by eligibility for 

free/reduced-price school lunch, grade 8 public schools: By urban district, 2005
✓ KEY FINDINGS

! Compared to students of the 

same gender in large central 

city schools...

 male students in Austin, 

Charlotte, Houston, New York 

City, and San Diego had 

higher average scores and 

higher percentages performing 

at or above Basic; male 

students in all other districts, 

except for Boston, performed 

lower on both measures.

 female students in Austin, 

Boston, Charlotte, Houston, 

New York City, and San Diego 

had higher average scores; 

female students in all other 

districts scored lower.

! Compared to students of the 

same gender in large central 

city schools...

 male students in Austin and 

Charlotte had higher average 

scores and higher percentages 

performing at or above Basic; 

male students in Atlanta, 

Chicago, Cleveland, the 

District of Columbia, and Los 

Angeles performed lower on 

both measures.

 female students in Austin, 

Boston, Charlotte, and San 

Diego had higher average 

scores and higher percentages 

performing at or above Basic; 

female students in Atlanta, 

Chicago, Cleveland, the 

District of Columbia, and Los 

Angeles performed lower on 

both measures.

GRADE 4

GRADE 8

10 The Nation’s Report CardTM Trial Urban District Assessment

Table 7. Average scale scores and achievement-level results in mathematics, by gender, grade 4 

public schools: By urban district, 2005

Percentage of students

Percentage 

of all students

Average 

scale score

Below

Basic

At or above

Basic

At or above

District Profi cient

Nation 

Male 51 238* 20* 80* 37*

Female 49 236* 21* 79* 33*

Large central city

Male 51 229** 32** 68** 26**

Female 49 227** 33** 67** 23**

Atlanta

Male 51 222*,** 42*,** 58*,** 18*,**

Female 49 219*,** 45*,** 55*,** 15*,**

Austin

Male 49 242*,** 15*,** 85*,** 41*

Female 51 242*,** 14*,** 86*,** 39*,**

Boston

Male 53 228** 29** 71** 23**

Female 47 230*,** 25* 75* 22**

Charlotte

Male 50 244*,** 15*,** 85*,** 43*

Female 50 245*,** 14*,** 86*,** 45*,**

Chicago

Male 53 217*,** 47*,** 53*,** 15*,**

Female 47 214*,** 50*,** 50*,** 11*,**

Cleveland

Male 52 220*,** 41*,** 59*,** 14*,**

Female 48 220*,** 38** 62** 12*,**

District of Columbia

Male 49 212*,** 56*,** 44*,** 11*,**

Female 51 211*,** 55*,** 45*,** 9*,**

Houston

Male 48 234*,** 22* 78* 28**

Female 52 232*,** 23* 77* 24**

Los Angeles

Male 48 222*,** 40*,** 60*,** 21*,**

Female 52 219*,** 44*,** 56*,** 16*,**

New York City 

Male 50 232*,** 26*,** 74*,** 28**

Female 50 229*,** 28*,** 72*,** 23**

San Diego

Male 48 234*,** 25* 75* 31**

Female 52 231*,** 27*,** 73*,** 27*,**

* Signifi cantly different from large central city public schools. 

** Signifi cantly different from nation (public schools). 

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 Trial Urban District Mathematics Assessment.

District Mathematics Results by Gender: Grades 4 and 8

The percentages of male and female students, their average scale scores, and the 

percentages performing below Basic, at or 

above Basic, and at or above Proficient are 

presented by district in table 7 for grade 4 

and in table 8 for grade 8. At both grades 

4 and 8, there were no significant differences between the average scores of male 

and female students within any of the 

districts in 2005.
Mathematics 2005 11

STUDENT GROUP 

RESULTS

Table 8. Average scale scores and achievement-level results in mathematics, by gender, grade 8 public schools: 

By urban district, 2005

Percentage of students

Percentage 

of all students

Average 

scale score

Below

Basic

At or above

Basic

At or above

District Profi cient

Nation 

Male 51* 278* 32* 68* 30*

Female 49* 277* 33* 67* 27*

Large central city 

Male 49** 266** 46** 54** 20**

Female 51** 264** 48** 52** 18**

Atlanta

Male 48 244*,** 70*,** 30*,** 7*,**

Female 52 246*,** 68*,** 32*,** 7*,**

Austin

Male 47 282* 32* 68* 34*

Female 53 279* 32* 68* 32*,**

Boston

Male 50 267** 45** 55** 20**

Female 50 272*,** 39*,** 61*,** 25*

Charlotte

Male 51 279* 34* 66* 32*

Female 49 282*,** 29* 71* 34*,**

Chicago

Male 48 258*,** 54*,** 46*,** 12*,**

Female 52 258*,** 56*,** 44*,** 10*,**

Cleveland

Male 48 249*,** 66*,** 34*,** 6*,**

Female 52 249*,** 65*,** 35*,** 7*,**

District of Columbia

Male 47 246*,** 68*,** 32*,** 7*,**

Female 53 245*,** 71*,** 29*,** 6*,**

Houston

Male 50 267** 42** 58** 16*,**

Female 50 267** 43** 57** 17**

Los Angeles

Male 49 252*,** 61*,** 39*,** 12*,**

Female 51 249*,** 64*,** 36*,** 9*,**

New York City 

Male 50 265** 47** 53** 19**

Female 50 268** 45** 55** 21

San Diego

Male 50 268** 41** 59** 21**

Female 50 272*,** 37* 63* 23*

* Signifi cantly different from large central city public schools.

** Signifi cantly different from nation (public schools).

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 Trial Urban District 

Mathematics Assessment.
✓ KEY FINDINGS

! Between 2003 and 2005, 

average scores increased in 

8 of the 10 urban districts 

that participated in both 

years: Atlanta, Boston, 

Cleveland, the District of 

Columbia, Houston, Los 

Angeles, New York City, and 

San Diego. 

! The same 8 districts showed 

increases in the percentages 

of students performing at or 

above Basic.

! Boston, the District of 

Columbia, Houston, Los 

Angeles, New York City, and 

San Diego showed increases 

in the percentages of 

students performing at or 

above Profi cient.

! Between 2003 and 2005, 

average scores increased in 

4 of the 10 urban districts 

that participated in both 

years: Boston, Houston, Los 

Angeles, and San Diego. 

! The same 4 districts showed 

increases in the percentages 

of students performing at or 

above Basic and at or above

Profi cient.

GRADE 4

GRADE 8 (page 14)

12 The Nation’s Report CardTM Trial Urban District Assessment

Of the 11 urban districts with assessment 

results for 2005, ten have comparison 

data from the 2003 assessment (Austin 

first participated in 2005). The vertical 

bars in figure 2 represent the average scale 

scores for grade 4 in 2003 and 2005 for 

public schools in the nation, in large central cities, and in each of the participating 

districts. An asterisk below the score in 

2003 indicates that it is statistically different from the corresponding average score 

in 2005.

 Table 9 presents the achievement-level 

results for each of the assessment years 

by district for grade 4. Percentages for 

2003 that are statistically different from 

the corresponding percentage in 2005 are 

marked with an asterisk (*).

 On page 14, figure 3 shows the average scale scores across years by district for 

grade 8. Table 10 displays the achievement-level results by district for 2003 and 

2005 for grade 8.

Changes in Performance

For More Information...

More information on average scores and achievement-level results for a particular district or student group is 

available at http://nces.ed.gov/nationsreportcard/naepdata. This interactive site provides a data tool for exploring results and calculating the statistical signifi cance of differences.
Mathematics 2005 13

CHANGES IN 

PERFORMANCE 

* Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

2 The district did not participate in 2003.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.

Figure 2. Average mathematics scale scores, grade 4 public schools: By urban district, 2003 and 2005

Table 9. Percentage of students by mathematics achievement level, grade 4 public schools: By urban district, 2003 and 2005

Below

Basic

At or above

Basic

At or above

Profi cient

At

Advanced

District 2003 2005 2003 2005 2003 2005 2003 2005

Nation 24* 21 76* 79 31* 35 4* 5

Large central city1 37* 32 63* 68 20* 24 2 3

Atlanta 50* 43 50* 57 13 17 2 3

Austin — 15 — 85 — 40 — 7

Boston 41* 28 59* 72 12* 22 1 2

Charlotte 16 14 84 86 41 44 6* 9

Chicago 50 48 50 52 10 13 1 1

Cleveland 49* 40 51* 60 10 13 # #

District of Columbia 64* 55 36* 45 7* 10 1 1

Houston 30* 23 70* 77 18* 26 1 3

Los Angeles 48* 42 52* 58 13* 18 1 2

New York City 33* 27 67* 73 21* 26 2 3

San Diego 34* 26 66* 74 20* 29 2* 4

— Not available. The district did not participate in 2003. 

# The estimate rounds to zero.

* Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

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), 2003 and 2005 Trial Urban 

District Mathematics Assessments.

0

200

210

220

230

240

500

District

Austin2

234

*

Nation

216

*

Atlanta

220

*

Boston

242

Charlotte

214

Chicago

215

*

ClevelandDistrict of Columbia

227

*

Houston

216

*

Los Angeles

226

*

New York City

226

*

San Diego

Large central city1

237

228

221

242

229

244

216

220

211

233

220

231 232

2003

2005

205

*

Scale score

224

*
14 The Nation’s Report CardTM Trial Urban District Assessment

* Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

2 The district did not participate in 2003.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.

Figure 3. Average mathematics scale scores, grade 8 public schools: By urban district, 2003 and 2005

Table 10. Percentage of students by mathematics achievement level, grade 8 public schools: By urban district, 2003 and 2005

Below

Basic

At or above

Basic

At or above

Profi cient

At

Advanced

District 2003 2005 2003 2005 2003 2005 2003 2005

Nation 33* 32 67* 68 27* 28 5* 6

Large central city1 50* 47 50* 53 16* 19 3* 4

Atlanta 70 69 30 31 6 7 1 1

Austin — 32 — 68 — 33 — 9

Boston 52* 42 48* 58 17* 23 4 6

Charlotte 33 31 67 69 32 33 7 9

Chicago 58 55 42 45 9 11 1 2

Cleveland 62 66 38 34 6 6 # #

District of Columbia 71 69 29 31 6 7 1 2

Houston 48* 42 52* 58 12* 16 2 2

Los Angeles 68* 62 32* 38 7* 11 1 2

New York City 46 46 54 54 20 20 4 5

San Diego 47* 39 53* 61 18* 22 2* 4

— Not available. The district did not participate in 2003. 

# The estimate rounds to zero.

* Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

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), 2003 and 2005 Trial Urban 

District Mathematics Assessments.

0

240

250

260

270

280

500

District

Scale score

276

*

Nation

244

Atlanta

Austin2

262

*

Boston

279

Charlotte

254

Chicago

253

Cleveland

243

District of Columbia

264

*

266

Houston

245

*

Los Angeles

New York City

264

*

San Diego

Large central city1

278

265

245

281

270

281

258

249

245

267

250

267 270

2003

2005

262

*
Mathematics 2005 15

Item Maps

The item maps presented on pages 17 and 21 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.

Framework and Sample Questions: Grade 4

The content of the NAEP mathematics assessment 

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 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 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. 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.

 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.

Number properties 

and operations Measurement Geometry

40% 20% 15%

Data analysis and 

probability Algebra

10% 15%

FRAMEWORK AND 

SAMPLE QUESTIONS
16 The Nation’s Report CardTM Trial Urban District Assessment

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
Mathematics 2005 17

FRAMEWORK AND 

SAMPLE QUESTIONS

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 Given a solution, determine the numbers in the problem

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
18 The Nation’s Report CardTM Trial Urban District Assessment

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

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
Mathematics 2005 19

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/.

Framework and Sample Questions: Grade 8

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 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.

 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.

Number properties 

and operations Measurement Geometry

20% 15% 20%

Data analysis and 

probability Algebra

15% 30%

FRAMEWORK AND 

SAMPLE QUESTIONS
20 The Nation’s Report CardTM Trial Urban District Assessment

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
Mathematics 2005 21

FRAMEWORK AND 

SAMPLE QUESTIONS

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.

Basic

262

Profi cient

299

Advanced

333

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 multistep story problem

NAEP Mathematics Scale

500

370

360

350

340

330

320

310

300

290

280

270

260

250

240

 O
22 The Nation’s Report CardTM Trial Urban District Assessment

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 five additional squares in 

a grid that has three 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.

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.
Mathematics 2005 23

TECHNICAL NOTES 

AND DATA APPENDIX

Technical Notes and Data Appendix

About This Revised Report

The initial version of this TUDA report was released 

on December 1, 2005. In the national report card for 

mathematics for 2005, the “type of location” variable 

was not reported with across year trends because the US 

Census classifications of too many schools had changed. 

Consequently, the “large central city” variable, one of 

the categories in “type of location,” was not reported for 

2003 in the initial TUDA mathematics report. However, 

subsequent analyses showed that while the overall “type 

of location” variable was not sufficiently consistent to 

report student performance trends, the “large central city” 

school classifications had remained stable enough across 

2003 and 2005 to permit reporting of trend results within this category. The main difference between this revised 

report and the original is the addition of large central city 

performance data in 2003.

Participating Districts

In 2005, ten urban public school districts participated 

in the TUDA in mathematics at grades 4 and 8. The 

school district names, as used in the NCES Common 

Core of Data, are Atlanta City School District, Austin 

Independent School District, Boston School District, 

Charlotte-Mecklenburg Schools, City of Chicago School 

District 299, Cleveland Municipal School District, 

Houston Independent School District, Los Angeles 

Unified School District, New York City Public Schools, 

and San Diego Unified School District. Results for the 

District of Columbia public school students, normally 

included along with NAEP’s state assessment results, are 

also reported. The results for these districts are for public 

school students only. 

NAEP Sampling Procedures

The sample of students in the participating TUDA 

school districts represents an augmentation of the sample 

of students who would usually be selected by NAEP as 

part of state samples. These augmented samples allow 

reliable reporting of student groups within these districts. 

Students in the TUDA samples are also included in 

“higher-level” samples. For example, data from students 

tested in the Los Angeles sample were used to report 

results for Los Angeles, and also contributed to the 

California and the national samples.

 In the same way that schools and students participating 

in national NAEP assessments are chosen to be nationally representative, samples of schools and students in 

the urban districts were selected to be representative of 

their districts. The results from the assessed students are 

combined to provide accurate estimates of overall district 

performance. Results are weighted to take into account 

the fact that schools within districts represent different 

proportions of the overall district population. Table A-1 

displays the sample sizes and target populations for the 

districts for 2003 and 2005.

Accommodations

It is important to assess all selected students from the target population, including students with disabilities (SD) 

and students classified by their schools as English language learners (ELL). To accomplish this goal, students 

who receive accommodations in their state’s assessments, 

such as extra testing time or individual rather than group 

administration, are offered most of the same accommodations in NAEP. One notable exception is that students 

may not use calculators in NAEP in the sections where 

questions are not intended for calculator use. 

Exclusion Rates

Some students identified as SD or ELL who are sampled for NAEP participation may be excluded from 

the assessment according to carefully defined criteria. 

School personnel, guided by the student’s Individualized 

Education Program (IEP), as well as by section 504 

eligibility, make decisions regarding inclusion in the 

assessment of students with disabilities. Based on NAEP’s 

guidelines, they also make the decision whether to 

exclude students identified as ELL. The process includes 

evaluating the student’s capability to participate in the 

assessment in English, as well as taking into consideration the number of years the student has been receiving 

instruction in English. The percentages of students 

excluded from NAEP may vary considerably across states 

and districts, as well as across years. Comparisons of 

achievement results across districts and within a district 

across years should be interpreted with caution if the 

exclusion rates vary widely. (See tables A-2 and A-3 for 

exclusion rates in 2003 and 2005.)
24 The Nation’s Report CardTM Trial Urban District Assessment

School and Student Participation Rates

In order to ensure reportable samples, NCES and NAGB 

established participation rate standards that states and 

jurisdictions are required to meet in order for their results 

to be reported. The same standards were applied to the 

urban districts. Participation rates before substitution 

needed to be at least 80 percent for schools and at least 

85 percent for students in each subject and grade. Results 

are not reported in any instances in which participation 

rates did not meet the established standards for certain 

student groups or jurisdictions. In the 2005 mathematics assessment, all states, jurisdictions, and participating 

urban districts met NAEP participation rate standards at 

both grades 4 and 8 (see table A-1). 

Interpreting Statistical Significance

Comparisons over time or between groups in this report 

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 measures 

of the margin of error in samples. Estimates based on 

smaller samples are likely to have larger margins of error 

than estimates based on large samples. The size of the 

standard errors may also be influenced by other factors, 

such as how representative the assessed students 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 Asian/Pacific Islander 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, asterisks are 

used to indicate that a score or percentage in 2005 is 

significantly different from the comparable measure in 

a previous assessment year, or to indicate differences 

from national or large central city results. Any difference 

between scores or percentages that is identified in the text 

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

within-group differences not marked in tables and charts, 

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.

“Large central city” in this report includes public 

schools located in large central cities (with populations of 

250,000 or more) throughout the United States within 

metropolitan statistical areas as defined by the federal 

Table A-1. School and student participation rates and target populations, grades 4 and 8 public schools: By urban district, 2005

District

School participation Student participation

Target 

population

Student-weighted percent 

before substitution

Number of 

schools participating 

Student-weighted 

percent

Number of 

students assessed

Grade 4

Atlanta 100 100 95 1,200 6,000

Austin 100 100 94 1,300 7,000

Boston 99 100 93 1,200 5,000

Charlotte 100 100 94 1,500 9,000

Chicago 100 100 95 2,100 36,000

Cleveland 100 100 90 1,000 7,000

District of Columbia 100 100 93 2,200 6,000

Houston 100 100 96 2,000 18,000

Los Angeles 100 100 93 2,100 63,000

New York City 100 100 92 2,000 81,000

San Diego 100 100 95 1,400 12,000

Grade 8

Atlanta 100 < 50 90 1,100 4,000

Austin 100 < 50 90 1,200 6,000

Boston 99 < 50 91 1,100 5,000

Charlotte 100 < 50 90 1,400 8,000

Chicago 100 100 93 1,900 35,000

Cleveland 100 < 50 80 900 5000

District of Columbia 100 < 50 86 1,900 3,000

Houston 100 < 50 88 1,700 14,000

Los Angeles 99 100 89 1,900 50,000

New York City 100 100 83 1,800 70,000

San Diego 100 < 50 89 1,300 10,000

NOTE: The numbers of schools and students are rounded to the nearest hundred, or indicated as < 50 where the value was between 1 and 49. The target population is rounded to the nearest 

thousand.

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

Mathematics Assessment.
Mathematics 2005 25

TECHNICAL NOTES 

AND DATA APPENDIX

Table A-2. Percentage of all students identified as students with disabilities and/or English language learners, excluded, and

assessed, grade 4 public schools: By urban district, 2003 and 2005 

District

Percentage of all students 

identifi ed

Percentage of all students 

excluded

Percentage of all students 

assessed with 

accommodations

Percentage of all students 

assessed without 

accommodations

2003 2005 2003 2005 2003 2005 2003 2005

SD and/or ELL

Nation 22 23 4 3 8 10 10 10

Large central city1 31 32 5 4 9 11 17 17

Atlanta 9 11114643

Austin — 37 — 10 — 14 — 12

Boston 33 33 5 6 17 15 11 11

Charlotte 21 22 4 3 12 12 5 7

Chicago 31 29 8 4 7 9 16 15

Cleveland 15 17765932

District of Columbia 18 20 4 6 10 10 4 4

Houston 45 46 8 7 18 21 19 17

Los Angeles 60 59 3 5 8 7 48 47

New York City 22 24 6 4 12 17 4 2

San Diego 41 43 2 4 4 6 34 33

SD only

Nation 14 14 3 3 7 8 4 4

Large central city1 13 13 3 3 6 7 4 3

Atlanta 89114632

Austin — 15 — 7 — 6 — 2

Boston 20 22 3 5 12 14 4 3

Charlotte 17 13 3 2 10833

Chicago 15 13546743

Cleveland 12 13555821

District of Columbia 13 16457822

Houston 18 12753483

Los Angeles 11 11234553

New York City 12 14 1 2 10 11 1 1

San Diego 11 11123474

ELL only

Nation 11 10 1 1 2 3 7 7

Large central city1 21 21 3 2 4 5 14 14

Atlanta 22###111

Austin — 25 — 5 — 9 — 11

Boston 18 15337389

Charlotte 8 10214424

Chicago 20 18 5 2 2 4 13 12

Cleveland 44111212

District of Columbia 75113221

Houston 35 37 4 4 17 18 14 15

Los Angeles 56 54 2 4 6 5 47 45

New York City 13 12634831

San Diego 34 36 2 3 2 3 30 30

— Not available. The district did not participate in 2003. 

# The estimate rounds to zero.

1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

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.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.

Office of Management and Budget. The term is not 

synonymous with “inner city.” Urban districts are school 

districts that include schools in their large central cities. 

Some districts (Austin, Charlotte, Cleveland, Houston, 

and Los Angeles) encompass a small percentage of schools 

not classified as large central city. In these cases, the data 

from the entire district were used in statistical comparisons 

to large central city schools. Further comparisons of urban 

district student group data with large central city data 

are available from the online data explorer on the NAEP 

website (http://nces.ed.gov/nationsreportcard/naepdata). 

Selecting the variable “Large central city for urban district 

comparisons” when making statistical comparisons for 

urban districts will allow comparisons to large central city 

data and will permit the software user to replicate results 

in this report and to explore additional comparisons.
26 The Nation’s Report CardTM Trial Urban District Assessment

Table A-3. Percentage of all students identified as students with disabilities and/or English language learners, excluded, and

assessed, grade 8 public schools: By urban district, 2003 and 2005 

Percentage of all students 

identifi ed

Percentage of all students 

excluded

Percentage of all students 

assessed with 

accommodations

Percentage of all students 

assessed without 

accommodations

District 2003 2005 2003 2005 2003 2005 2003 2005

SD and/or ELL

Nation 19 19 4 4 7 8 8 7

Large central city1 24 24 5 4 7 8 13 12

Atlanta 11 12215843

Austin — 26 — 10 — 4 — 12

Boston 31 25 7 9 15997

Charlotte 18 18 3 3 9 10 5 5

Chicago 22 21 7 3 7 12 8 5

Cleveland 21 20999923

District of Columbia 20 19 6 6 9 11 5 2

Houston 26 24 8 6 3 4 16 14

Los Angeles 37 39 2 3 6 6 29 30

New York City 24 20 5 2 14 16 6 2

San Diego 29 28 4 4 4 7 22 17

SD only

Nation 14 13 3 3 6 7 5 3

Large central city1 14 13 3 3 5 6 5 3

Atlanta 10 11115743

Austin — 14 — 8 — 2 — 5

Boston 24 18 4 7 13873

Charlotte 14 12328842

Chicago 17 16 5 2 7 11 6 3

Cleveland 17 18986713

District of Columbia 16 17 5 5 8 10 3 2

Houston 16 1174#295

Los Angeles 12 12225555

New York City 15 12 2 1 10 10 3 1

San Diego 11 11133474

ELL only

Nation 66111144

Large central city1 13 13 2 2 3 3 9 9

Atlanta 211##11#

Austin — 14 — 4 — 2 — 8

Boston 13 10544145

Charlotte 77113234

Chicago 86322232

Cleveland 5311321#

District of Columbia 54112221

Houston 16 15 5 3 2 3 9 10

Los Angeles 33 34 2 2 4 4 27 28

New York City 13 10426732

San Diego 23 21 3 3 2 4 18 14

— Not available. The district did not participate in 2003. 

# The estimate rounds to zero.

1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

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.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.
Mathematics 2005 27

TECHNICAL NOTES 

AND DATA APPENDIX

Figure A-1. Cross-district comparisons of average mathematics scale scores, grade 4 public schools: 2005

Charlotte

Austin

Houston

San Diego

New York City

Boston

Atlanta

Los Angeles

Cleveland

Chicago

District of Columbia

NationLarge central cityCharlotteAustinHoustonSan DiegoNew York CityBostonAtlantaLos AngelesClevelandChicagoDistrict of Columbia

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

Center for Education Statistics, National Assessment of Educational Progress (NAEP), 

2005 Trial Urban District Mathematics Assessment.

District had higher average scale score than the district listed at 

the top of the column.

No statistically significant difference detected from the district 

listed at the top of the column.

District had lower average scale score than the district listed at 

the top of the column.

➤

➤

Figure A-2. Cross-district comparisons of percentage of students at or above Basic in mathematics, grade 4 public schools: 2005

Charlotte

Austin

Houston

San Diego

New York City

Boston

Cleveland

Los Angeles

Atlanta

Chicago

District of Columbia

NationLarge central cityCharlotteAustinHoustonSan DiegoNew York CityBostonClevelandLos AngelesAtlantaChicagoDistrict of Columbia

Cross-District Comparisons by Average Scale Score and Percentage at or Above Basic:

Grades 4 and 8

Figures A-1 though A-4 compare average scores and percentages of students performing at or above Basic in each 

district to those in the nation, in public schools in large 

central cities, and in each other district. Read across the 

row corresponding to a district listed to the left of any of 

the charts. Match the shading intensity to the chart’s key 

to determine whether the average score (or percentage 

at or above Basic) of this district was found to be higher 

than, not significantly different from, or lower than that 

of the district in the column heading. In addition, the 

direction of the arrowheads in the comparison cells indicates whether the district in the row is significantly higher 

than (up arrow), lower than (down arrow), or not different from (blank cell) the district in the column heading. 

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

Center for Education Statistics, National Assessment of Educational Progress (NAEP), 

2005 Trial Urban District Mathematics Assessment.

District had higher percentage than the district listed at the top 

of the column.

No statistically significant difference detected from the district 

listed at the top of the column.

District had lower percentage than the district listed at the top of 

the column.

➤

➤
28 The Nation’s Report CardTM Trial Urban District Assessment

Figure A-4. Cross-district comparisons of percentage of students at or above Basic in mathematics, grade 8 public schools: 2005

Figure A-3. Cross-district comparisons of average mathematics scale scores, grade 8 public schools: 2005

Austin

Charlotte

San Diego

Boston

Houston

New York City

Chicago

Los Angeles

Cleveland

District of Columbia

Atlanta

NationLarge central cityAustinCharlotteSan DiegoBostonHoustonNew York CityChicagoLos AngelesClevelandDistrict of ColumbiaAtlanta

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

Center for Education Statistics, National Assessment of Educational Progress (NAEP), 

2005 Trial Urban District Mathematics Assessment.

District had higher average scale score than the district listed at 

the top of the column.

No statistically significant difference detected from the district 

listed at the top of the column.

District had lower average scale score than the district listed at 

the top of the column.

➤

➤

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

Center for Education Statistics, National Assessment of Educational Progress (NAEP), 

2005 Trial Urban District Mathematics Assessment.

Charlotte

Austin

San Diego

Boston

Houston

New York City

Chicago

Los Angeles

Cleveland

Atlanta

District of Columbia

NationLarge central cityCharlotteAustinSan DiegoBostonHoustonNew York CityChicagoLos AngelesClevelandAtlantaDistrict of Columbia

District had higher percentage than the district listed at the top 

of the column.

No statistically significant difference detected from the district 

listed at the top of the column.

District had lower percentage than the district listed at the top of 

the column.

➤

➤
Mathematics 2005 29

TECHNICAL NOTES 

AND DATA APPENDIX

Charlotte

Austin

San Diego

Houston

New York City

Boston

Los Angeles

Atlanta

Chicago

Cleveland

District of Columbia

NationLarge central cityCharlotteAustinSan DiegoHoustonNew York CityBostonLos AngelesAtlantaChicagoClevelandDistrict of Columbia

Charlotte

Austin

Boston

San Diego

New York City

Houston

Chicago

Los Angeles

District of Columbia

Atlanta

Cleveland

NationLarge central cityCharlotteAustinBostonSan DiegoNew York CityHoustonChicagoLos AngelesDistrict of ColumbiaAtlantaCleveland

Figure A-6. Cross-district comparisons of percentage of students at or above Proficient in mathematics, grade 8 public schools: 

2005

Figure A-5. Cross-district comparisons of percentage of students at or above Proficient in mathematics, grade 4 public schools: 

2005

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

Center for Education Statistics, National Assessment of Educational Progress (NAEP), 

2005 Trial Urban District Mathematics Assessment.

District had higher average scale score than the district listed at 

the top of the column.

No statistically significant difference detected from the district 

listed at the top of the column.

District had lower average scale score than the district listed at 

the top of the column.

➤

➤

District had higher percentage than the district listed at the top 

of the column.

No statistically significant difference detected from the district 

listed at the top of the column.

District had lower percentage than the district listed at the top of 

the column.

➤

➤

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

Center for Education Statistics, National Assessment of Educational Progress (NAEP), 

2005 Trial Urban District Mathematics Assessment.
30 The Nation’s Report CardTM Trial Urban District Assessment

25th percentile 50th percentile 75th percentile

District 2003 2005 2003 2005 2003 2005

Grade 4

Nation 215*** 219* 235*** 239* 254*** 257*

Large central city1 204*** 207** 224*** 228** 244*** 248**

Atlanta 195*** 200*,** 214*** 219*,** 234*** 240*,**

Austin — 224*,** — 242*,** — 260*,**

Boston 203*** 212*,** 219*** 230** 236*** 247**

Charlotte 223 225*,** 242 245*,** 261 265*,**

Chicago 196 195*,** 214 215*,** 232 236*,**

Cleveland 197 202*,** 215*** 221*,** 232 237*,**

District of Columbia 185*** 192*,** 204*** 210*,** 224*** 230*,**

Houston 210*** 216*,** 226*** 233*,** 243*** 250**

Los Angeles 196 198*,** 215*** 221*,** 235*** 242*,**

New York City 207*** 212*,** 226*** 231*,** 246 250**

San Diego 207*** 213*,** 226*** 234*,** 244*** 252*,**

Grade 8

Nation 253*** 254* 278*** 279* 301*** 303*

Large central city1 237 240** 262*** 265** 287*** 291**

Atlanta 220 221*,** 244 245*,** 267 268*,**

Austin — 255* — 281* — 308*,**

Boston 236*** 243** 260*** 270*,** 287*** 296*,**

Charlotte 252 254* 280 282* 307 308*,**

Chicago 233 236*,** 255 258*,** 277 281*,**

Cleveland 233 228*,** 252 251*,** 272 270*,**

District of Columbia 219 222*,** 243 244*,** 267 267*,**

Houston 244 246*,** 263*** 268*,** 283*** 289**

Los Angeles 219 225*,** 245*** 250*,** 270*** 275*,**

New York City 241 241** 266 266** 293 292**

San Diego 239*** 247*,** 265*** 272*,** 290*** 295**

— Not available. The district did not participate in 2003. 

* Signifi cantly different from large central city public schools in 2005. 

** Signifi cantly different from nation (public schools) in 2005.

*** Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.

Table A-4. Scale score percentiles in mathematics, grades 4 and 8 public schools: By urban district, 2003 and 2005
Mathematics 2005 31

TECHNICAL NOTES 

AND DATA APPENDIX

Table A-5. Average scale scores and achievement-level results in mathematics, by race/ethnicity, grade 4 public schools: By urban 

district, 2003 and 2005 

District

Average 

scale score

Percentage of students in each race/ethnicity category

Below 

Basic

At or above 

Basic

At or above 

Profi cient

2003 2005 2003 2005 2003 2005 2003 2005

White

Nation 243*** 246 13*** 11 87*** 89 42*** 47*

Large central city1 243*** 247 14 12 86 88 42*** 50**

Atlanta 258 263*,** 11 4*,** 89 96*,** 70 72*,**

Austin — 262*,** — 1*,** — 99*,** — 75*,**

Boston 234*** 244 23 12 77 88 32 43

Charlotte 257 261*,** 4 3*,** 96 97*,** 66 70*,**

Chicago 235 243 18 12 82 88 31 43

Cleveland 233 233*,** 20 19 80 81 27 25*,**

District of Columbia 262 266*,** 3 1 97 99 71 78*,**

Houston 254*** 262*,** 4 3*,** 96 97*,** 63 73*,**

Los Angeles 241 247 17 13 83 87 44 49

New York City 244 245 12 13 88 87 42 46

San Diego 243*** 249 13*** 6*,** 87*** 94*,** 41 50

Black

Nation 216*** 220* 46*** 40* 54*** 60* 10*** 13*

Large central city1 212*** 217** 53*** 45** 47*** 55** 8*** 11**

Atlanta 211*** 215** 55 49** 45 51** 7 9**

Austin — 228*,** — 26*,** — 74*,** — 18

Boston 216*** 223*,** 45*** 35* 55*** 65* 6*** 13

Charlotte 229 230*,** 27 26*,** 73 74*,** 20 21*,**

Chicago 207 208*,** 61 59*,** 39 41*,** 4 6*,**

Cleveland 210*** 215** 56*** 48** 44*** 52** 5 8**

District of Columbia 202*** 207*,** 67*** 59*,** 33*** 41*,** 4 5*,**

Houston 221 224* 38 33*,** 62 67*,** 12 14

Los Angeles 208 209*,** 58 58*,** 42 42*,** 6 9

New York City 219 222* 42 37* 58 63* 12 14

San Diego 216 221 46 40 54 60 8 15

Hispanic

Nation 221*** 225* 38*** 33* 62*** 67* 15*** 19*

Large central city1 219*** 223** 41*** 36** 59*** 64** 13*** 17**

Atlanta ‡ ‡ ‡ ‡ ‡‡ ‡‡

Austin — 234*,** — 20*,** — 80*,** — 27*,**

Boston 215*** 225 49*** 30 51*** 70 7*** 14

Charlotte 233 234*,** 20 19*,** 80 81*,** 26 27

Chicago 217 217*,** 45 45*,** 55 55*,** 10 13

Cleveland 220 224 42 32 58 68 14 18

District of Columbia 205*** 215*,** 61*** 49*,** 39*** 51*,** 7 11*,**

Houston 226*** 232*,** 30 22*,** 70 78*,** 15*** 23*

Los Angeles 211*** 216*,** 54*** 47*,** 46*** 53*,** 7*** 13*,**

New York City 220*** 226* 40*** 30* 60*** 70* 13 18

San Diego 216*** 222** 47*** 37** 53*** 63** 9*** 16

Asian/Pacifi c Islander

Nation 246*** 251* 13*** 11 87*** 89 48*** 54*

Large central city1 246 247** 14 13 86 87 47 49**

Atlanta ‡ ‡ ‡ ‡ ‡‡ ‡‡

Austin — ‡ — ‡ —‡ —‡

Boston 243*** 256* 13*** 2*,** 87*** 98*,** 43*** 65*

Charlotte 252 256* 10 4 90 96 60 62

Chicago ‡ ‡ ‡ ‡ ‡‡ ‡‡

Cleveland ‡ ‡ ‡ ‡ ‡‡ ‡‡

District of Columbia ‡ ‡ ‡ ‡ ‡‡ ‡‡

Houston ‡ ‡ ‡ ‡ ‡‡ ‡‡

Los Angeles 241 246 14 12 86 88 38 45

New York City 247 253* 11 8* 89 92* 47 60*

San Diego 238*** 245** 16 13 84 87 32*** 46

— Not available. The district did not participate in 2003. 

‡ Reporting standards not met. 

* Signifi cantly different from large central city public schools in 2005. 

** Signifi cantly different from nation (public schools) in 2005.

*** Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

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

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.
32 The Nation’s Report CardTM Trial Urban District Assessment

Table A-6. Average scale scores and achievement-level results in mathematics, by race/ethnicity, grade 8 public schools: By urban 

district, 2003 and 2005 

District

Average 

scale score

Percentage of students in each race/ethnicity category

Below 

Basic

At or above 

Basic

At or above 

Profi cient

2003 2005 2003 2005 2003 2005 2003 2005

White

Nation 287*** 288 21 21 79 79 36*** 37

Large central city1 285 288 23 22 77 78 36 39

Atlanta 298 ‡ 17 ‡ 83 ‡ 54 ‡

Austin — 305*,** — 10*,** — 90*,** — 61*,**

Boston 289 299*,** 23 17 77 83 48 54*,**

Charlotte 301 304*,** 9 10*,** 91 90*,** 55 60*,**

Chicago 276 281 32 29 68 71 25 33

Cleveland 269 265*,** 37 46*,** 63 54*,** 14 17*,**

District of Columbia ‡ 317*,** ‡ 6*,** ‡ 94*,** ‡ 69*,**

Houston 293 294 20 15 80 85 47 50

Los Angeles 277 280* 33 32 67 68 29 32

New York City 289 286 21 23 79 77 40 38

San Diego 284*** 292 24 17 76 83 35 42

Black

Nation 252*** 254* 61*** 59* 39*** 41* 7*** 8*

Large central city1 247 250** 66 64** 34 36** 5 7**

Atlanta 241 242*,** 74 72*,** 26 28*,** 3 4*,**

Austin — 262* — 48* — 52* — 12

Boston 251 256* 64*** 55* 36*** 45* 6 9

Charlotte 258*** 264*,** 53 46*,** 47 54*,** 11 14*,**

Chicago 245 245*,** 71 72*,** 29 28*,** 4 3*,**

Cleveland 249 244*,** 68 71*,** 32 29*,** 5 3*,**

District of Columbia 240 241*,** 74 73*,** 26 27*,** 3 4*,**

Houston 259 257* 53 53* 47 47* 7 7

Los Angeles 234 239*,** 79 71** 21 29** 2 7

New York City 253 257* 60 56* 40 44* 9 10

San Diego 252 253 61 60 39 40 7 8

Hispanic

Nation 258*** 261* 53*** 50* 47*** 50* 11*** 13*

Large central city1 256 258** 57 54** 43 46** 10 11**

Atlanta ‡‡ ‡‡ ‡‡ ‡‡

Austin — 267*,** — 44* — 56* — 17*

Boston 252*** 261 62*** 49 38*** 51 7 12

Charlotte 262 262 54 47 46 53 18 15

Chicago 259 263* 52 48* 48 52* 8 11

Cleveland 249 251 65 67** 35 33** 2 7

District of Columbia 246 252** 67 61 33 39 3 9

Houston 261*** 265*,** 51 44* 49 56* 9 12

Los Angeles 240*** 245*,** 74 68*,** 26 32*,** 3 6*,**

New York City 260 259 52 53 48 47 15 12

San Diego 248*** 258 66*** 51 34*** 49 6 11

Asian/Pacifi c Islander

Nation 289*** 294* 23*** 19* 77*** 81* 42*** 46*

Large central city1 281 289** 29 24** 71 76** 33 40**

Atlanta ‡‡ ‡‡ ‡‡ ‡‡

Austin —‡ —‡ —‡ —‡

Boston 300 309*,** 13 8* 87 92* 57 61*,**

Charlotte 293 ‡ 19 ‡ 81 ‡ 43 ‡

Chicago 286 292 22 17 78 83 36 38

Cleveland ‡‡ ‡‡ ‡‡ ‡‡

District of Columbia ‡‡ ‡‡ ‡‡ ‡‡

Houston ‡ 299 ‡ 15 ‡ 85 ‡ 55

Los Angeles 275*** 291 36 18 64 82 25*** 43

New York City 286 295 26 21 74 79 38 50

San Diego 278 282** 31 26 69 74 28 31**

— Not available. The district did not participate in 2003. 

‡ Reporting standards not met. 

* Signifi cantly different from large central city public schools in 2005. 

** Signifi cantly different from nation (public schools) in 2005.

*** Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

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

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.
Mathematics 2005 33

TECHNICAL NOTES 

AND DATA APPENDIX

‡ Reporting standards not met.

1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

2 The district did not participate in 2003.

NOTE: Score gaps 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), 2003 and 2005 Trial Urban 

District Mathematics Assessments.

Figure A-7. Gaps in average mathematics scores, by race/ethnicity, grade 4 public schools: By urban district, 2003 and 2005

White average score minus Black average score

Score gaps

0 10 20 30 70 80 40 50 60

29

27

23

25

38

38

33

58

60

18

24

35

29

32

28

21

19

34

48

47

31

26

27

27

27

18

24

30

30

30

28

51

57

14

9

26

19

28

24

19

20

28

‡

‡

24

21

21

White average score minus Hispanic average score

Score gaps

0 10 20 30 70 80 40 50 60

 Nation

 2003

 2005 

 Large central city 1

 2003

 2005

 Atlanta

 2003

 2005

 Austin 2

 2005

 Boston 

 2003

 2005

 Charlotte 

 2003

 2005

 Chicago

 2003

 2005

 Cleveland 

 2003

 2005

 District of Columbia

 2003

 2005

 Houston

 2003

 2005

 Los Angeles

 2003

 2005

 New York City

 2003

 2005

 San Diego 

 2003

 2005

 Nation

 2003

 2005 

 Large central city 1

 2003

 2005

 Atlanta

 2003

 2005

 Austin 2

 2005

 Boston 

 2003

 2005

 Charlotte 

 2003

 2005

 Chicago

 2003

 2005

 Cleveland 

 2003

 2005

 District of Columbia

 2003

 2005

 Houston

 2003

 2005

 Los Angeles

 2003

 2005

 New York City

 2003

 2005

 San Diego 

 2003

 2005

31 24

33
34 The Nation’s Report CardTM Trial Urban District Assessment

Figure A-8. Gaps in average mathematics scores, by race/ethnicity, grade 8 public schools: By urban district, 2003 and 2005

White average score minus Black average score

39

33

29

36

41

43

37

34

76

‡

21

20

36

31

41

43

43

39

43

‡

38

38

33

35

34

36

27

29

35

37

29

32

65

‡

14

20

19

17

42

40

38

37

38

‡

‡

30

30

26

28*

White average score minus Hispanic average score

Score gaps

0 10 20 30 70 80 40 50 60

Score gaps

0 10 20 30 70 80 40 50 60

 Nation

 2003

 2005 

 Large central city 1

 2003

 2005

 Atlanta 

 2003

 2005

 Austin 2

 2005

 Boston 

 2003

 2005

 Charlotte 

 2003

 2005

 Chicago

 2003

 2005

 Cleveland 

 2003

 2005

 District of Columbia

 2003

 2005

 Houston

 2003

 2005

 Los Angeles

 2003

 2005

 New York City

 2003

 2005

 San Diego 

 2003

 2005

 Nation

 2003

 2005 

 Large central city 1

 2003

 2005

 Atlanta 

 2003

 2005

 Austin 2

 2005

 Boston 

 2003

 2005

 Charlotte 

 2003

 2005

 Chicago

 2003

 2005

 Cleveland 

 2003

 2005

 District of Columbia

 2003

 2005

 Houston

 2003

 2005

 Los Angeles

 2003

 2005

 New York City

 2003

 2005

 San Diego 

 2003

 2005

57

‡ Reporting standards not met. 

* Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

2 The district did not participate in 2003.

NOTE: Score gaps 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), 2003 and 2005 Trial Urban 

District Mathematics Assessments.
Mathematics 2005 35

TECHNICAL NOTES 

AND DATA APPENDIX

Table A-7. Average scale scores and achievement-level results in mathematics, by student-reported highest level of education 

of either parent, grade 8 public schools: By urban district, 2003 and 2005

Average 

scale score

Percentage of students in each parental education category

Below 

Basic

At or above 

Basic

At or above 

Profi cient

District 2003 2005 2003 2005 2003 2005 2003 2005

Less than high school

Nation 256*** 259* 56*** 52* 44*** 48* 9*** 11*

Large central city1 253 255** 60 58** 40 42** 7 9**

Atlanta 240 237*,** 74 84*,** 26 16*,** 3 2

Austin — 264* — 48 — 52 — 11

Boston 253*** 270*,** 63*** 45 37*** 55 13 22*,**

Charlotte ‡ 264 ‡ 48 ‡ 52 ‡ 18

Chicago 256 252** 57 64** 43 36** 10 6**

Cleveland 255 250** 58 64 42 36 5 6

District of Columbia 236 243*,** 75 73*,** 25 27*,** 2 4**

Houston 259 264*,** 54 44* 46 56* 7 12

Los Angeles 242 244*,** 72 68*,** 28 32*,** 5 4*,**

New York City 260 262* 51 52 49 48 14 16

San Diego 250 260 64 50 36 50 6 12

Graduated from high 

school

Nation 267 267* 42 42* 58 58* 16 17*

Large central city1 254 256** 59 56** 41 44** 10 11**

Atlanta 238 237*,** 80 77*,** 20 23*,** 2 3*,**

Austin — 267* — 45 — 55 — 18*

Boston 256*** 266* 61*** 45* 39*** 55* 11 17*

Charlotte 255 264* 59 46* 41 54* 11 15

Chicago 250 251*,** 63 62** 37 38** 6 7**

Cleveland 252 247*,** 63 69*,** 37 31*,** 4 6*,**

District of Columbia 235 238*,** 81 78*,** 19 22*,** 1 2*,**

Houston 257 262* 56 51** 44 49** 7 11

Los Angeles 240 245*,** 73 69*,** 27 31*,** 4 5*,**

New York City 260 264* 52 49* 48 51* 16 17*

San Diego 256 255** 57 55** 43 45** 9 11

Some education 

after high school

Nation 280 280* 27 27* 73 73* 28 28*

Large central city1 268 269** 42 40** 58 60** 19 19**

Atlanta 253 257*,** 60 58*,** 40 42*,** 6 8*,**

Austin — 283* — 24* — 76* — 30*

Boston 268 272** 43 36 57 64 19 21

Charlotte 281 282* 28 27* 72 73* 29 31*

Chicago 262 262*,** 50 48*,** 50 52*,** 11 12*,**

Cleveland 260 258*,** 52 56*,** 48 44*,** 10 9*,**

District of Columbia 252 252*,** 63 61*,** 37 39*,** 6 6*,**

Houston 270 273** 41 34 59 66 13 18**

Los Angeles 253 259*,** 58 54*,** 42 46*,** 10 16**

New York City 272 270** 36 39** 64 61** 23 21**

San Diego 270 273** 39 33 61 67 18 20

Graduated from 

college

Nation 287*** 289* 23*** 22* 77*** 78* 39*** 41*

Large central city1 272*** 277** 39 35** 61 65** 26*** 31**

Atlanta 250 252*,** 65 61*,** 35 39*,** 10 11*,**

Austin — 300*,** — 15*,** — 85*,** — 55*,**

Boston 273 278** 41 37** 59 63** 26 31**

Charlotte 289 291* 24 22* 76 78* 43 45*

Chicago 257 265*,** 57 48*,** 43 52*,** 12 18*,**

Cleveland 251 252*,** 67 62*,** 33 38*,** 6 7*,**

District of Columbia 250 253*,** 64 62*,** 36 38*,** 11 13*,**

Houston 274 277** 38 33** 62 67** 23 28**

Los Angeles 257 266*,** 54 45*,** 46 55*,** 15 22*,**

New York City 275 272** 38 42*,** 62 58*,** 27 26**

San Diego 278*** 286* 33 24* 67 76* 32 38*

— Not available. The district did not participate in 2003. 

‡ Reporting standards not met.

* Signifi cantly different from large central city public schools in 2005.

** Signifi cantly different from nation (public schools) in 2005.

*** Signifi cantly different from 2005. 1 Some of the TUDA districts include a few public schools located outside of large central cities as defi ned by the Census Bureau (population of 250,000 or more within metropolitan areas). These 

schools were included in the category of “large central city” in the present report for all years, but were not included in results published in previous reports. As a result, some numbers reported in this 

report may differ slightly from those reported in earlier ones. 

NOTE: Detail may not sum to totals because of rounding. Prior to 2005, parental education questions were presented to students at grade 4, but were not reported because their responses were 

highly variable. In 2005, parental education questions were not presented to students at grade 4.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 and 2005 Trial Urban 

District Mathematics Assessments.
36 The Nation’s Report CardTM Trial Urban District Assessment

District

Less than 

high school

Graduated from 

high school

Some education 

after high school

Graduated from 

college Unknown

Nation 8 18 18 45 11

Large central city 12 18 17 36 18

Atlanta 7 26 16 40 11

Austin 14 17 13 41 14

Boston 10 18 18 36 17

Charlotte 5 16 18 52 9

Chicago 13 21 19 29 18

Cleveland 12 27 20 28 13

District of Columbia 6 27 17 35 15

Houston 21 18 11 30 21

Los Angeles 19 13 14 25 30

New York City 9 16 15 39 21

San Diego 12 14 18 37 20

Table A-8. Percentage of students by student-reported highest level of education of either parent, grade 8 public schools: 

By urban district, 2005

NOTE: Detail may not sum to totals because of rounding. Parental education questions were not presented to students at grade 4.

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

Mathematics Assessment.

Table A-9. Average scale scores and achievement-level results in mathematics, by students with disabilities who could be 

assessed, grades 4 and 8 public schools: By urban district, 2005 

District

SD Not SD

Percentage of SD students Percentage of not SD students

Average 

scale score

Below 

Basic

At or 

above 

Basic

At or 

above

Profi cient

Average 

scale score

Below 

Basic

At or 

above

Basic

At or 

above

Profi cient

Grade 4

Nation 218* 44* 56* 16* 240* 17* 83* 38*

Large central city 209** 58** 42** 11** 230** 29** 71** 26**

Atlanta 198*,** 72*,** 28*,** 5** 223*,** 41*,** 59*,** 18*,**

Austin 227*,** 26*,** 74*,** 18 243*,** 14*,** 86*,** 42*,**

Boston 210** 57** 43** 6** 234*,** 21*,** 79*,** 26**

Charlotte 228*,** 34* 66* 26*,** 247*,** 12*,** 88*,** 46*,**

Chicago 198** 70** 30** 7** 218*,** 46*,** 54*,** 14*,**

Cleveland 204** 65** 35** 4** 222*,** 37*,** 63*,** 14*,**

District of Columbia 188*,** 83*,** 17*,** 4*,** 214*,** 52*,** 48*,** 10*,**

Houston 214 54 46 12 235*,** 20* 80* 28**

Los Angeles 195*,** 70*,** 30*,** 5*,** 223*,** 40*,** 60*,** 20*,**

New York City 207** 60** 40** 7** 234*,** 23*,** 77*,** 28**

San Diego 214 51 49 17 234*,** 23*,** 77*,** 30**

Grade 8

Nation 244* 69* 31* 7* 281* 28* 72* 31*

Large central city 230** 81** 19** 4** 269** 43** 57** 21**

Atlanta 202*,** 95*,** 5*,** # 250*,** 66*,** 34*,** 7*,**

Austin 250* 64* 36* 9 283* 29* 71* 34*,**

Boston 233** 83** 17** 3 275*,** 36*,** 64*,** 25*,**

Charlotte 242* 74 26 8 285*,** 26* 74* 36*,**

Chicago 226** 86** 14** 2 264*,** 50*,** 50*,** 13*,**

Cleveland 216*,** 96*,** 4*,** # 253*,** 62*,** 38*,** 7*,**

District of Columbia 208*,** 94*,** 6*,** # 250*,** 66*,** 34*,** 8*,**

Houston 232** 83** 17** 4 270** 39*,** 61*,** 17*,**

Los Angeles 210*,** 93*,** 7*,** 2** 255*,** 59*,** 41*,** 11*,**

New York City 231** 84** 16** 3 271** 41** 59** 22**

San Diego 234** 76 24 5 274*,** 36*,** 64*,** 24**

# The estimate rounds to zero. 

* Signifi cantly different from large central city public schools.

** Signifi cantly different from nation (public schools).

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 

Trial Urban District Mathematics Assessment.
Mathematics 2005 37

TECHNICAL NOTES 

AND DATA APPENDIX

Table A-10. Average scale scores and achievement-level results in mathematics, by English language learners who could be assessed, grades 4 

and 8 public schools: By urban district, 2005

ELL Non-ELL Formerly ELL

Percentage of ELL students Percentage of non-ELL students Percentage of formerly ELL students

District

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Average 

scale 

score

Below 

Basic

At or 

above 

Basic

At or 

above 

Profi cient

Grade 4

Nation 216* 46* 54* 11* 239* 18* 82* 38* 240 15 85 35

Large central city 214** 50** 50** 10** 231** 29** 71** 27** 242 13 87 38

Atlanta ‡ ‡ ‡ ‡ 221*,** 43*,** 57*,** 17*,** ‡ ‡ ‡ ‡

Austin 225*,** 32*,** 68*,** 14 247*,** 10*,** 90*,** 48*,** ‡ ‡ ‡ ‡

Boston 221*,** 39* 61* 14 229** 29** 71** 22*,** 237* 16 84 29

Charlotte 228*,** 24*,** 76*,** 16 246*,** 14*,** 86*,** 46*,** ‡ ‡ ‡ ‡

Chicago 201*,** 72*,** 28*,** 3*,** 218*,** 44*,** 56*,** 15*,** ‡ ‡ ‡ ‡

Cleveland ‡ ‡ ‡ ‡ 220*,** 40*,** 60*,** 13*,** ‡ ‡ ‡ ‡

District of Columbia 206** 64*,** 36*,** 7 211*,** 55*,** 45*,** 10*,** ‡ ‡ ‡ ‡

Houston 228*,** 27*,** 73*,** 16* 236* 21* 79* 31** 243 12 88 41

Los Angeles 210*,** 55*,** 45*,** 8** 232** 28** 72** 30** ‡ ‡ ‡ ‡

New York City 211** 52 48 5** 231** 27** 73** 26** 241 14 86 39

San Diego 217* 45* 55* 11 240* 17* 83* 38* ‡ ‡ ‡ ‡

Grade 8

Nation 244* 71* 29* 6* 280* 30* 70* 30* 276 34 66 24

Large central city 238** 77** 23** 4** 268** 43** 57** 21** 277 33 67 23

Atlanta ‡ ‡ ‡ ‡ 245*,** 69*,** 31*,** 7*,** ‡ ‡ ‡ ‡

Austin 240 79 21 2 286*,** 26*,** 74*,** 37*,** ‡ ‡ ‡ ‡

Boston 233 78 22 5 274*,** 37*,** 63*,** 25*,** 255*,** 60*,** 40*,** 11*,**

Charlotte 252* 62 38 9 282*,** 29* 71* 35*,** ‡ ‡ ‡ ‡

Chicago 235** 85** 15** 1 259*,** 53*,** 47*,** 12*,** ‡ ‡ ‡ ‡

Cleveland ‡ ‡ ‡ ‡ 250*,** 65*,** 35*,** 7*,** ‡ ‡ ‡ ‡

District of Columbia ‡ ‡ ‡ ‡ 246*,** 69*,** 31*,** 7*,** ‡ ‡ ‡ ‡

Houston 245* 71 29 6 270** 40** 60** 19** 273 32 68 16*,**

Los Angeles 225*,** 90*,** 10*,** #*,** 263*,** 49*,** 51*,** 15*,** ‡ ‡ ‡ ‡

New York City 232** 84** 16** 2 267** 45** 55** 20** 279 32 68 28*

San Diego 236** 78 22 2** 279* 30* 70* 30* 274 31 69 17

# The estimate rounds to zero. 

‡ Reporting standards not met. 

* Signifi cantly different from large central city public schools. 

** Signifi cantly different from nation (public schools).

NOTE: ELL = English language learners. Formerly ELL= students who passed their state’s English-language profi ciency examination within the past two 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 Trial Urban District 

Mathematics Assessment.
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SUGGESTED CITATION

Rampey, B.D., Lutkus, A.D., and Dion, G. (2006). 

The Nation’s Report Card: Trial Urban District 

Assessment Mathematics 2005 (NCES 2006–457r). 

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