the nation's report card mathematics 2009 trial urban district assessment (tuda)(2)

8/14/2019 The Nation's Report Card Mathematics 2009 Trial Urban District Assessment (TUDA)(2)

1/9201-MTUDA-FrntCov 11/18/09 sam

M h m2009trial urban districtassessMent

results at grades 4 and 8

U.S. Department of EducationNCES 2010452

I n s t i t u t e o f E d u c a t i o n S c i e n c e s

Embargoed until

December 8, 2009

DO NOT CITE


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What is Te Nations Report Card ?Te Nations Report Card informs the public about the academic achieve-ment of elementary and secondary students in the United States. Reportcards communicate the ndings of the National Assessment of EducationalProgress (NAEP), a continuing and nationally representative measure of achievement in various subjects over time.

Since 1969, NAEP assessments have been conducted periodically in reading,mathematics, science, writing, U.S. history, civics, geography, and other

subjects. NAEP collects and reports information on student performance atthe national, state, and local levels, making the assessment an integral partof our nations evaluation of the condition and progress of education. Only academic achievement data and related background information are collect-ed. Te privacy of individual students and their families is protected.

NAEP is a congressionally authorized project of the National Center forEducation Statistics (NCES) within the Institute of Education Sciences of theU.S. Department of Education. Te Commissioner of Education Statistics isresponsible for carrying out the NAEP project. Te National AssessmentGoverning Board oversees and sets policy for NAEP.

Contents

1 Executive Summary

4 Introduction

7 Grade 4

19 Grade 8

31 District Proles

68 Technical Notes

70 Appendix Tables

Photo Credits:

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Among the 18 urban districts that participated in the 2009 mathematics assessment, scores for both fourth- and eighth-graders in 10 districts were lower than the scores for public school students attending schools in large cities overall. Scores forve districts, however, were higher than the scores for fourth- and eighth-graders in large cities nationally.

In comparison to the average scores in 2009 for large cities in the nation,

Austin, Boston, Charlotte, Houston, and San Diego had higher scores at both grades;

Atlanta, Baltimore City, Chicago, Cleveland, Detroit, the District of Columbia, Fresno, Los Angeles, Milwaukee, andPhiladelphia had lower scores at both grades;

scores in Jefferson County (Louisville, KY) were not signicantly different at either grade; and

scores for Miami-Dade and New York City were higher at grade 4 and not signicantly different at grade 8.

Five districts score above large cities atboth grades in 2009

NOTE: DCPS = District o Columbia Public Schools.

MD

MA

TX

CA

WI

KY

MI

NY

PA

NC

GA

FL

OHILFresno

Los Angeles

AustinHouston

Milwaukee

Chicago

Detroit

ClevelandPhiladelphia

New York City

Boston

Atlanta

Charlotte

JefersonCounty

District oColumbia (DCPS)

Miami-Dade

Baltimore City

San Diego

Comparison of district and large city average mathematics scores in 2009

THE NATIONS REPORT CARD


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A Closer Look at District Results Comparedto Large CitiesDifferences in overall average scoresbetween participating districts andlarge cities were not always consis-tent across student groups. In Atlanta, for example, the overallaverage mathematics score waslower than the score for large citiesat both grades. However, the scorefor Black students in the district(who comprise most of the studentpopulation) was not signicantly

different from the score for Blackstudents in large cities at eithergrade.

Among the 10 districts whereaverage scores at both grades werelower than the score for large cities,only Cleveland had lower scores forWhite, Black, and Hispanic stu-dents, and for students eligible forschool lunch (an indicator of lowerfamily income) in both grades.

Among the ve districts whereoverall scores were higher than thescore for large cities at both grades 4and 8, only Charlotte and Houstonalso had higher scores for White,Black, and Hispanic students andfor lower-income students in bothgrades.

NOTE: DCPS = District o Columbia Public Schools.

Higher average score than large city.Lower average score than large city.

No signicant diference between the district and large cit Reporting standards not met. Sample size insu cient to

permit a reliable estimate.

Comparison of district and large city average mathematics scores in 2009

GRADE 4 GRADE 8Race/ethnicity Race/ethnicity

District Overall White Black HispanicEligible or

school lunchOverall White Black HispanicEligible

school lu

Atlanta Austin

Baltimore City Boston

Charlotte

Chicago Cleveland

Detroit District o Columbia (DCPS) Fresno

Houston

Jeferson County (KY) Los Angeles

Miami-Dade Milwaukee

New York City Philadelphia San Diego

Demographics vary among the nation, large cities, andindividual urban districtsWhen comparing the results or urban districts to results or the nation and large cities, it iimportant to consider how the demographics o the jurisdictions are diferent. Nationally, thpercentages o White students at both grades 4 and 8 were higher than the combined percen

ages o Black and Hispanic students in 2009, while the opposite was true or large cities amost participating urban districts.

Large cities and participating urban districts also difered rom the nation in the proportionstudents eligible or the National School Lunch Program. While the percentages o studeeligible or ree/reduced-price school lunch in the nation were 48 percent at grade 4 and percent at grade 8, the percentages o eligible students in the districts ranged rom 46 to percent in 2009.

More detailed in ormation about the demographic characteristics o ourth- and eighth-gin the nation, large cities, and participating districts is included in the report.

MATHEMATICS 2009TRIAL URBAN DISTRICT ASSESSMENT


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Mathematics Content Areas

Introduction A primary goal of the NAEP Trial Urban District Assessment (TUDA) is to measure whatstudents in the nations large urban school districts know and can do in academic subjects.Eighteen urban districts participated in the TUDA in mathematics in 2009, seven of themfor the rst time.

Te Mathematics FrameworkThe National Assessment Governing Board oversees thecreation o the NAEP rameworks, which describe the specicknowledge and skills that should be assessed. Frameworksincorporate ideas and input rom subject area experts, schooladministrators, policymakers, teachers, parents, and others.NAEP rameworks also describe the types o questions thatshould be included and how they should be designed andscored. Collectively, the questions are to span a range odemands on students thinking. To ensure an appropriatebalance o content along with allowing or a variety o ways oknowing and doing mathematics, the Mathematics Framework

for the 2009 National Assessment of Educational Progress species that each question in the assessment measure oneo ve mathematical content areas.

Although the names o the content areas, as well as some othe topics in those areas, have changed over the years, therehas been a consistent ocus across rameworks on collectingin ormation on students per ormance in ve areas: numberproperties and operations; measurement; geometry; dataanalysis, statistics, and probability; and algebra.

Number properties and operations measuresstudents understanding o ways to represent,calculate, and estimate with numbers.

Measurement assesses students knowledge ounits o measurement or such attributes ascapacity, length, area, volume, time, angles, andrates.

Geometry measures students knowledge andunderstanding o shapes in two and three dimen-sions, and relationships between shapes such assymmetry and trans ormations.

Data analysis, statistics, and probabilitymeasures students understanding o datarepresentation, characteristics o data sets,experiments and samples, and probability.

Algebra measures students understanding opatterns, using variables, algebraic representation,and unctions.



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Levels of Mathematical ComplexityLow complexityquestions typically speci y what a student is todo, which is o ten to carry out a routine mathematical procedure.

Moderate complexityquestions involve more lexibility othinking and o ten require a response with multiple steps.

High complexityquestions make heavier demands and o tenrequire abstract reasoning or analysis in a novel situation.

Three levels o mathematical complexity (low, moderate,and high) described in the ramework orm an ordereddescription o the demands that questions make on stu-dents thinking. Mathematical complexity involves what aquestion asks students to do and not how they might under-take it. The complexity o a question is not directly relatedto its ormat, and there ore it is possible or some multiple-choice questions to assess complex mathematics and orsome constructed-response questions (i.e., open-ended)to assess routine mathematical ideas.

Reporting NAEP ResultsThe 2009 mathematics results are reported or public schoolstudents in 18 urban districts. The ollowing 11 districts par-ticipated in 2009 as well as in earlier assessment years:

Atlanta Public SchoolsAustin Independent School DistrictBoston Public SchoolsCharlotte-Mecklenburg SchoolsChicago Public SchoolsCleveland Metropolitan School DistrictDistrict o Columbia Public SchoolsHouston Independent School DistrictLos Angeles Unied School DistrictNew York City Department o EducationSan Diego Unied School District

The ollowing seven districts participated or the rst timein 2009:

Baltimore City Public SchoolsDetroit Public SchoolsFresno Unied School DistrictJeferson County Public Schools (Louisville, KY)Miami-Dade County Public SchoolsMilwaukee Public SchoolsSchool District o Philadelphia

Representative samples o between 900 and 2,200ourth-graders and between 900 and 2,100 eighth-graders

were assessed in each district. Sample sizes are proportion-ate to district enrollment (see appendix table A- 1 or thenumber o participating schools and the number o studentsassessed in each district).

Some charter schools that operate within the geographicboundaries o a school district are independent o the dis-trict and are not included in the districts Adequate YearlyProgress (AYP) report to the U.S. Department o Educationunder the Elementary and Secondary Education Act. Begin-ning in 2009, charter schools o this type are no longerincluded in the results or TUDA districts as they had beenin past NAEP assessments. Additional in ormation in this

report can be ound in the Technical Notes.

The complete mathematics ramework or 2009 isavailable at http://www.nagb.org/publications/ rameworks/math- ramework09.pd .



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Scale scoresNAEP mathematics results or grades 4 and 8 are reportedas average scores on a 0500 scale. Because NAEP scalesare developed independently or each subject, scorescannot be compared across subjects.

In addition to reporting on changes in overall mathematicsscores or those districts that participated in previousassessment years, re erences are also made to changes atve percentiles. These results show whether lower-per ormingstudents (at the 10th and 25th percentiles), middle-per orming students (at the 50th percentile), and higher-per orming students (at the 75th and 90th percentiles)are showing the same trends as the district overall.

Achievement levelsBased on recommendations rom policymakers, educators,and members o the general public, the Governing Board setsspecic achievement levels or each subject area and grade.Achievement levels are per ormance standards showing whatstudents should know and be able to do. NAEP results arereported as percentages o students per orming at or abovethe Basic and Procient levels and at the Advanced level.

As provided by law, NCES, upon review o congressionallymandated evaluations o NAEP, has determined that achieve-ment levels are to be used on a trial basis and should beinterpreted with caution. The NAEP achievement levels havebeen widely used by national and state o cials.

Interpreting the ResultsThe per ormance o students in each urban district iscompared to the per ormance o public school studentsin the nation and in large cities (i.e., cities with populationso 250,000 or more). The comparison to the nations largecities is made because students in these cities represent a

peer group with characteristics that are most similar to thecharacteristics o students in the 18 TUDA districts. Compari-sons in per ormance over time are made or those districtsthat participated in earlier assessment years.

NAEP reports results using widely accepted statistical stan-dards; ndings are reported based on a statistical signicancelevel set at .05 with appropriate adjustments or multiplecomparisons, as well as adjustments or the part-wholerelationship when individual districts are compared to results

or large cities or the nation (see the Technical Notes ormore in ormation). The symbol (*) is used in tables andgures to indicate that the scores or percentages beingcompared are signicantly diferent.

When scores signicantly increase or decrease rom oneassessment year to the next, we are condent that studentper ormance has changed. However, NAEP is not designedto identi y the causes o these changes. Further, the many

actors that may inuence average student achievementscores also change across time. These include educationalpolicies and practices, the quality o teachers, availableresources, and the demographic characteristics o thestudent body.

Accommodations and exclusions in NAEPMany o the same testing accommodations allowed on stateand district assessments (e.g., extra testing time or individualrather than group administration) are provided or studentswith disabilities or English language learners participating inNAEP. Even with the availability o accommodations, somestudents may still be excluded. Variations in exclusion andaccommodation rates, due to diferences in policies andpractices or identi ying and including students with disabili-ties and English language learners, should be consideredwhen comparing students per ormance over time and acrossdistricts. Districts also vary in their proportions o special-needs students (especially English language learners). Whilethe efect o exclusion is not precisely known, comparisons oper ormance results could be afected i exclusion rates aremarkedly diferent among districts or vary widely over time.See appendix tables A- 2 through A- 5 or the percentages ostudents accommodated and excluded in each district.

More in ormation about NAEPs policy on the inclusion ospecial-needs students is available at http://nces.ed.gov/nationsreportcard/about/inclusion.asp.

NAEP Achievement LevelsBasic denotes partial mastery o prerequisite knowledge andskills that are undamental or pro icient work at each grade.

Proficient represents solid academic per ormance. Studentsreaching this level have demonstrated competency overchallenging subject matter.

Advanced represents superior per ormance.



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Grade 4Scores increase since 2007 fortwo districts, while the nationalaverage shows no change Although there was no change in the overall average score since 2007 forfourth-graders in the nation, scores did increase for students in large citiesand two participating urban districts. In comparison to 2003, scores werehigher in 2009 for students in the nation, large cities, and 8 of the 10districts that participated in both years. Even though overall scores in 2009were lower for most participating districts than in the nation, districtssometimes showed higher scores for student groups when compared to

their peers nationally.



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SOURCE: U.S. Department o Education, Institute o Education Sciences, National Center or Education Statistics, National Assessment o Educational Progress (NAEP), various years, 200309 Mathemati

* Signicantly diferent (p < .05) rom 2009.1 District did not participate in 2003.NOTE: Beginning in 2009, i the results or charter schools are not included in the school districts AdequateYearly Progress (AYP) report to the U.S. Department o Education under the Elementary and SecondaryEducation Act, they are excluded rom that districts TUDA results. DCPS = District o Columbia Public Schools.

Figure 1. Trend in average scores for fourth-grade public school studentsin NAEP mathematics, by jurisdiction

0 190 200 210 220 230 240 250 500

Year

2003

2003

2003

2003

2003

2003

2003

2003

2003

2003

2003

2003

234*

224*

216*

220*

242

214*

215

205*

227*

216*

226*

226*

2005

2005

2005

2005

2005

2005

2005

2005

2005

2005

2005

237*

228*

221*

242

229*

244

216*

220*

2005 211*

233

220

231*

2005 23220072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

239239

230*231

224225

241240

233*236

244245

220222

20072009

215213

20072009

214*220

234236

221222

236237

234236

Scale score

Nation

Large city

Atlanta

Austin1

Boston

Charlotte

Chicago

Cleveland

District ofColumbia (DCPS)

Houston

Los Angeles

New York City

San Diego

Most districts show nosignifcant change since 2007In comparison to 2007 , average mathematicsscores were higher in 2009 or ourth-gradepublic school students in large cities even thoughthere was no signicant change in the score orstudents in the nation ( gure 1 ). Among the11 urban districts that participated in 2007 and2009, scores increased or Boston and the Districto Columbia and showed no signicant changein the other 9 districts. Gains in Boston werereected in higher scores or lower-per ormingstudents at the 25th percentile, and in the Districto Columbia or students at the 25th, 50th, 75th,and 90th percentiles (see appendix table A- 6 ).

In comparison to 2003 , scores were higher in 2009or all but 2 o the 10 districts that participated in

both years (scores or Charlotte and Cleveland

showed no signicant change). Scores increasedor students across the per ormance range (i.e.,

those at the 10th, 25th, 50th, 75th, and 90thpercentiles) in Atlanta, Boston, the District oColumbia, Houston, and New York City (seeappendix table A- 6 ). Scores increased or allstudents but those at the 10th percentile inChicago, Los Angeles, and San Diego.

4



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* Signicantly diferent (p < .05) rom large city.** Signicantly diferent (p < .05) rom the nation.NOTE: DCPS = District o Columbia Public Schools.

Figure 2. Average scores for fourth-grade public school students in NAEPmathematics, by jurisdiction: 2009

0 190 200 210 220 230 240 250 500260Scale score

239*

231**

225*,**

240*

222*,**

236*,**

245*,**

222*,**

213*,**

200*,**

220*,**

219*,**

Nation

Large city

Atlanta

Austin

Baltimore City

Boston

Charlotte

Chicago

Cleveland

Detroit

District o Columbia (DCPS)

Fresno

Houston

Jeferson County (KY)

236*,**

233**

222*,**

236*,**

220*,**

Los Angeles

Miami-Dade

Milwaukee

237*

222*,**

236*

New York City

Philadelphia

San Diego

Explore Additional ResultsAdditional results or the 18 districts that participated in the 2009 mathematics ament can be ound in the NAEP Data Explorer at http://nces.ed.gov/nationsreportnaepdata/.

In 2009, public school students attending

schools in large cities scored 8 points loweron average than public school students inthe nation ( gure 2 ). With ew exceptions,scores in most o the participating urbandistricts were also lower than the score

or the nation. Charlotte was the onlydistrict to score higher than the nationalaverage. Scores in Austin, New York City,and San Diego were not signicantlydiferent rom the nation, and scores inthe remaining 14 districts were lower.

When compared to the average score orlarge cities nationally, scores were higher inAustin, Boston, Charlotte, Houston, Miami-Dade, New York City, and San Diego. Thescore or Jeferson County was not signi-cantly diferent rom the score or largecities, and scores or the remaining10 districts were lower.

Seven districts scorehigher than large citiesnationally

SOURCE: U.S. Department o Education, Institute o Education Sciences, National Center or Education Statistics, National Assessment o Educational Progress (NAEP), 2009 Mathematics Assessment.



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Figure 3. Achievement-level results for fourth-grade public school students in NAEP mathematics, by jurisdiction: 2009

# Rounds to zero.NOTE: Detail may not sum to totals because o rounding. DCPS = District o Columbia Public Schools.

Nation

Large city

Boston

Jefferson County (KY)

New York City

San Diego

30 20 10 0 10 20 30 40 50 60 70 80 90100 60 5070 40

Percent

not signicantly different

lower

Miami-Dade

CharlotteAustin

Houston

higher

100

Compared to large city, the% at or aboveBasic is

Atlanta 37 42 17 4

19 48 29 3

28 41 26 6

21 44 29 6

23 41 30 6

44Chicago 38 16 2

Los Angeles 39 42 17 2

Milwaukee 41 44 14 1

Fresno 42 44 14 1

Cleveland 49 43 8 #

19 43 33 6

28 24 5

Detroit 69 28 3 #

18 52 27 3

19 50 26 4

14 41 35 10

17 45 32 6

Baltimore City 36 51 12 1

District of Columbia (DCPS) 38 15 443

Philadelphia 39 45 15 2

43

BelowBasic Basic Procient Advanced

Districts show range o knowledge and skills


Across the 18 districts that participated inthe 2009 assessment, the percentages ostudents per orming at or above the Basic level ranged rom 31 percent in Detroit to86 percent in Charlotte ( gure 3 ). All thedistricts had some students per orming ator above the Procient level.

The same 7 districts with scores higherthan the score or large cities alsohad higher percentages o studentsper orming at or above Basic (Austin,Boston, Charlotte, Houston, Miami-Dade,New York City, and San Diego), and thesame 10 districts with scores lower thanlarge cities also had lower percentagesat or above Basic (Atlanta, Baltimore City,Chicago, Cleveland, Detroit, the District

o Columbia, Fresno, Los Angeles,Milwaukee, and Philadelphia).

4

0 THE NATIONS REPORT CARD


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When comparing the results or urbandistricts to results or the nation and largecities, it is important to consider thediferences in their demographic makeup.In the nation, the percentage o White

ourth-graders was higher than thecombined percentages o Black andHispanic students in 2009. However, theopposite was true or large cities and ormost o the 18 participating districts.Almost all o the districts had highercombined percentages o Black andHispanic students than White students(table 1 ). Jeferson County was the onlydistrict where the percentage o Whitestudents was higher.

Table 1. Selected characteristics of fourth-grade public school students in NAEP mathematics, by jurisdiction: 2009

Jurisdiction

Number oourth-

graders

Number ostudentsassessed

Percentage o students

White Black Hispanic

Asian/Pacic

Islander

Eligible orree/

reduced-price school

lunch

Identied asstudents

withdisabilities

Identied asEnglish

languagelearners

Nation 3,485,000 163,000 54 16 22 5 48 12 1

Large city 570,000 37,800 20 29 42 7 71 11 2

Atlanta 4,000 1,200 13 79 5 1 74 9 2

Austin 6,000 1,500 25 11 60 3 65 12 3

Baltimore City 6,000 1,100 8 87 3 1 84 9 2

Boston 4,000 1,100 14 39 37 8 78 18 1

Charlotte 10,000 1,500 36 39 16 5 47 11

Chicago 29,000 1,900 9 45 42 4 87 12 1

Cleveland 3,000 900 15 68 13 1 1001 11 6

Detroit 6,000 900 3 84 11 1 81 12 6

District o Columbia (DCPS) 3,000 1,300 9 77 12 2 72 11

Fresno 5,000 1,400 14 10 63 12 89 8 3

Houston 15,000 2,200 7 25 64 4 83 5 3

Jeferson County (KY) 7,000 1,400 53 36 5 3 60 13

Los Angeles 48,000 2,200 9 7 77 7 84 10 4

Miami-Dade 24,000 2,200 10 25 62 1 68 11

Milwaukee 6,000 1,300 13 56 22 5 78 14 1

New York City 71,000 2,200 15 28 40 16 87 18 1

Philadelphia 13,000 1,300 12 61 19 6 87 12

San Diego 9,000 1,300 27 12 43 17 61 10 31 In Cleveland, all students were categorized as eligible or the National School Lunch Program.NOTE: The number o ourth-graders is rounded to the nearest 1,000. The number o students assessed is rounded to the nearest 100. Black includes A rican American, Hispanic includes Latino, and PacicRace categories exclude Hispanic origin. The race/ethnicity categories listed do not sum to 100 percent because the percentages or American Indian/Alaska Native and unclassied students are not shown. DCPSchools.

Districts vary in demographic makeupLarge cities and districts also difered romthe nation in the proportion o studentseligible or the National School LunchProgram. Forty-eight percent o ourth-graders were eligible or ree/reduced-

price school lunch nationally compared to71 percent in large cities. Charlotte wasthe only participating district where thepercentage o eligible students wascomparable to the nation. The percent-ages o eligible students in the otherdistricts were all higher than the nationranging rom 60 percent in JefersonCounty to 100 percent in Cleveland,where all students were categorized aseligible.

Large cities in general, and some o theparticipating districts, were also morelikely to have higher percentages oEnglish language learners (ELL). Thepercentage o identied ELL students in

large cities was 20 percent comparedto 10 percent in the nation overall. Thepercentages o ELL students in Austin,Fresno, Houston, Los Angeles, andSan Diego were higher than the percent-ages in both the nation and large cities.



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NOTE: Black includes A rican American, Hispanic includes Latino, and Pacic Islander includes Native Hawaiian. Race categories exclude Hispanic origin. DCPS = District o Columbia Public Schools.

Figure 4. Comparison of district and national average scores for fourth-grade public school students in NAEP mathematics, by selectegroups: 2009

Higher average score than the nation.Lower average score than the nation.

No signicant diference between the district and the nation. Reporting standards not met. Sample size insu cient to permit a reliable est imate.

Race/ethnicity

Eligibility orree/reduced-price

school lunch

Jurisdiction Overall White Black HispanicAsian/Pacic

Islander Eligible Not eligible

Nation 239 248 222 227 255 228 250Large city Atlanta Austin Baltimore City Boston

Charlotte

Chicago Cleveland Detroit District o Columbia (DCPS) Fresno

Houston


Los Angeles Miami-Dade Milwaukee

New York City

Philadelphia

San Diego

A Closer Look at District Results Compared to the NationMiami-Dade were higher than the score or lower-income studentsnationally, even though the overall average scores or these districtswere lower than the nation.

Among the three districts where overall scores did not difer signi -icantly rom the national average (Austin, New York City , andSan Diego), scores or at least one racial/ethnic group were higherthan the nation. Results or lower-income students showed higheraverage scores than the nation in Austin and New York City and alower score in San Diego.

Even though most participating districts per ormed below thenational average overall, scores or student groups in some districtswere higher than the scores or their peers in the nation. Among the14 districts where overall average scores were lower than thenational average, scores were higher or White students in Atlantaand the District o Columbia; or both White and Hispanic studentsin Miami-Dade; or Black and Hispanic students in Boston; and or

White, Black, Hispanic, and Asian/Pacic Islander students inHouston ( gure 4 ). Scores or lower-income students (i.e., thoseeligible or ree/reduced-price school lunch) in Boston, Houston, and

4



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Race/ethnicity

Eligibility orree/reduced-priceschool lunch



Large city 231 250 219 226 253 225 248Atlanta Austin Baltimore City Boston

Charlotte

Chicago Cleveland Detroit District o Columbia (DCPS) Fresno

Houston

Jeferson County (KY) Los Angeles

Miami-Dade Milwaukee

New York City

Philadelphia

San Diego

Figure 5. Comparison of district and large city average scores for fourth-grade public school students in NAEP mathematics, by selectgroups: 2009


No signicant diference between the district and large city. Reporting standards not met. Sample size insu cient to permit a reliable est imate.


A Closer Look at District Results Compared to Large Citiesprogram were also lower than the score or eligible students inlarge cities. O these 10 lower-per orming districts, only 3 also hadlower scores than large cities or students who were not eligible;scores were not signicantly diferent rom large cities in 5 districtsand higher in 1 district.

Among the seven districts where overall average scores werehigher than the score or large cities, only Houston showed higherscores or all the racial/ethnic groups with samples large enoughto report results. Scores or students eligible or the school lunchprogram were higher than the score or eligible students in largecities or all o the higher-per orming districts except San Diego,where there was no signicant diference between the scores orthe district and large cities.

Diferences in overall average scores between participatingdistricts and large cities sometimes varied when results wereexamined or student groups. Among the 10 districts whereaverage scores were lower than the score or large cities, onlyCleveland and Detroit showed lower scores or all the categories

o students by race/ethnicity and eligibility or ree/reduced-price school lunch with samples large enough to report results(gure 5 ). Although the scores or Atlanta and the District oColumbia were lower than the score or large cities overall, theaverage scores or White students in these districts were higherthan the score or White students in large cities.

In all 10 o the districts where overall scores were lower than inlarge cities, scores or students eligible or the school lunch



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NAEP Mathematics Achievement-Level Descriptions for Grade 4The policy denitions o achievement levels provided in the Introduction apply to all NAEP subjects. The specic descrip-tions o what ourth-graders should know and be able to do at the Basic , Procient , and Advanced mathematics achieve-ment levels are presented below. NAEP achievement levels are cumulative; there ore, students per orming at the Procient level also display the competencies associated with the Basic level, and students at the Advanced level also demonstratethe skills and knowledge associated with both the Basic and the Procient levels. The cut score indicating the lower end o

the score range or each level is noted in parentheses.

Basic (214)Fourth-grade students performing atthe Basic level should show someevidence of understanding the math-ematical concepts and procedures inthe ve NAEP content areas.

Fourth-graders per orming at the Basic level should be able to estimate anduse basic acts to per orm simplecomputations with whole numbers;show some understanding o ractionsand decimals; and solve some simplereal-world problems in all NAEPcontent areas. Students at this levelshould be able to usealthough notalways accurately our- unctioncalculators, rulers, and geometricshapes. Their written responses areo ten minimal and presented withoutsupporting in ormation.

Procient (249)Fourth-grade students performing at theProcient level should consistently applyintegrated procedural knowledge andconceptual understanding to problemsolving in the ve NAEP content areas.

Fourth-graders per orming at theProcient level should be able to usewhole numbers to estimate, compute,and determine whether results arereasonable. They should have aconceptual understanding o ractionsand decimals; be able to solve real-world problems in all NAEP contentareas; and use our- unction calcu-lators, rulers, and geometric shapesappropriately. Students per orming atthe Procient level should employproblem-solving strategies such asidenti ying and using appropriatein ormation. Their written solutionsshould be organized and presented bothwith supporting in ormation andexplanations o how they were achieved.

Advanced (282)Fourth-grade students performingat the Advanced level should applyintegrated procedural knowledge andconceptual understanding to complexand nonroutine real-world problemsolving in the ve NAEP content areas.

Fourth-graders per orming at theAdvanced level should be able to solvecomplex nonroutine real-world prob-lems in all NAEP content areas. Theyshould display mastery in the use o

our- unction calculators, rulers, andgeometric shapes. These students areexpected to draw logical conclusionsand justi y answers and solutionprocesses by explaining why, as well ashow, they were achieved. They shouldgo beyond the obvious in theirinterpretations and be able tocommunicate their thoughts clearlyand concisely.



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GRADE 4 NAEP MATHEMATICS ITEM MAP

A d v a n c e

d

P r o

c i e n

t

B a s i c

500

300 Data analysis, statistics, and probability Find the median price from a table299 Algebra Identify the expression that models a scenario295 Geometry Identify parallel and perpendicular lines291 Number properties and operations Solve a story problem involving remainders

288 Measurement Indicate measurements on a ruler288 Number properties and operations Identify the fraction closest to the given value285 Algebra Reason using equivalences to make and explain a conclusion (calculator available)282

281 Number properties and operations Identify a pictorial representation of equivalent fractions277 Geometry Plot points on a grid to satis y the given conditions ( shown on page 18 )273 Number properties and operations Reason about odd and even numbers270 Data analysis, statistics, and probability Read and interpret a line graph265 Number properties and operations Divide a three-digit number by a one-digit number257 Measurement Identify the gure with the greatest area on a grid252 Geometry Identify the shape of a shaded region250 Data analysis, statistics, and probability Determine the probability of a particular event249

246 Measurement Solve a story problem involving quarts and cups243 Number properties and operations Subtract a two-digit number from a three-digit number (shown on page 17 )241 Algebra Determine the missing shapes in a pattern237 Number properties and operations Determine a ratio from a diagram233 Algebra Determine the value o an unknown in a number sentence230 Number properties and operations Use place value to write a number228 Geometry Determine how many given pieces cover a shape222 Number properties and operations Represent the same whole number in diferent ways222 Data analysis, statistics, and probability Make a pictograph o the given in ormation214

207 Number properties and operations Recognize the result of multiplying by 10205 Number properties and operations Compute the product of a two-digit number and a one-digit number202 Measurement Identify an appropriate unit for measuring length (calculator available)199 Algebra Find the unknown in a whole number sentence188 Number properties and operations Compute a value using multiplication and division (calculator available)183 Geometry Identify the gure that is not symmetric (calculator available)176 Measurement Identify the appropriate measuring device

0

Scale score Content area Question description

NOTE: Regular type denotes a constructed-response question.Italic type denotes a multiple-choice question. The position of a question on the scale represents the average score attained by students who had a 65 percentprobability of successfully answering a constructed-response question, or a 74 percent probability of correctly answering a four-option multiple-choice question. For constructed-response questions, the question descrirepresents students performance rated as completely correct. Scale score ranges for mathematics achievement levels are referenced on the map.SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.

What Fourth-Graders Know and Can Do in MathematicsThe item map below is use ul or understanding per ormanceat diferent levels on the NAEP scale. The scale scores on thele t represent the average scores or students who were likelyto get the items correct. The cut score at the lower end o therange or each achievement level is boxed. The descriptions

o selected assessment questions are listed on the right alongwith the corresponding mathematics content areas.

For example, the map on this page shows that ourth-gradersper orming in the middle o the Basic range (students with anaverage score o 230) were likely to be able to use place valueto write a number. Students per orming in the middle o theProcient range (with an average score o 265) were likely tobe able to divide a three-digit number by a one-digit number.

4


4



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30175

226235236374

A

B

C

D

SAMPLE QUESTION:

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.

Percentage correct or ourth-grade public school students,by jurisdiction: 2009

NOTE: DCPS = District of Columbia Public Schools.

59

45

71

53

70

53

48

70

69

64

52

67

60

54

33

51

65

49

63

67

San Diego

Philadelphia

New York City

Milwaukee

Miami-Dade

Los Angeles


Houston

Fresno

Detroit

Cleveland

Chicago

Charlotte

Boston

Baltimore City

Austin

Atlanta

Large city

Nation

0 30 40 50 60 70 80 100Percent


This sample question rom the 2009 ourth-grade assess-ment measures students per ormance in the numberproperties and operations content area. The question asksstudents to subtract a two-digit number rom a three-digitnumber, which requires regrouping to obtain the correctanswer o 226 (Choice A). Students were not permitted touse a calculator to answer this question.

Sixty-seven percent o ourth-grade public school studentsin the nation selected the correct answer to this question.The percentage o correct responses in each o the districtsranged rom 33 percent in Detroit to 71 percent in Houston.The national average score or students likely to select thecorrect answer was 243 on the item map.

Sample Question: Number Properties and Operations

MATHEMATICS 2009TRIAL URBAN DISTRICT ASSESSMENTTRIAL URBAN DISTRICT ASSESSMENT MATHEMATICS 2009


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SAMPLE QUESTION:

On the grid below, plot the points thathave coordinates (B, 1), (B, 3), and (D, 5).

Plot 3 more points on the grid so thatwhen you connect all 6 points you will

make a rectangle.List the coordinates for the 3 new points.

________ ________ ________

Connect the 6 points to show yourrectangle.

s c r a s r w

__ ___ ____ ___ ________

6

7

5

4

3

2

1

A B C D E F G



Percentage o answers rated asSatis actory and Extended ourth-grade public school students, by jurisdiction: 2009

11

16

9

14

20

6

19

22

18

36

20

18

10

14

24

11

20

24

19

27

San Diego

Philadelphia

New York City

Milwaukee

Miami-Dade

Los Angeles


Houston

Fresno

Detroit

Cleveland

Chicago

CharlotteBoston

Baltimore City

Austin

Atlanta

Large city

Nation

0 10 20 30 40 50 60 100Percent

Satisfactory Extended

8

8

8

6

5

7

7

6

13

5

6

4

7

14

7

10

9

8

10

6


This sample constructed-response question measures ourth-graders per ormance in the geometry content area. It is amultistep problem that requires students to plot and identi ypoints in the plane, and to use visualization skills to determineadditional points that could be connected to orm a rectangle.Students were not permitted to use a calculator to answerthis question.

Student responses to this question were rated using vescoring levels.

Extended responses correctly plotted the three given points, (B,1), (B,3),

and (D,5), correctly plotted three other points that ormed a

rectangle and gave their coordinates, and connected the dots to orm a rectangle.

Satisfactory responses met all o the criteria or anextended rating, but contained a minor error or omission.

Sample Question: GeometryPartial responses correctly plotted the three given pointsand partially plotted three other points that ormed arectangle and gave their coordinates.

Minimal responses plotted three points clearly (either the

given points, the new points, or some combination), orpartially met one o the criteria specied or an extendedrating.

All other responses were rated as incorrect .

The sample student response shown with the question wasrated as Extended because it correctly answered all partso the question. Twenty-seven percent o ourth-grade publicschool students in the nation gave a response rated asExtended or this question. The percentages o studentresponses rated Satis actory and Extended are presentedbelow or the nation, large cities, and participating districts.

The national average score or students likely to provideExtended responses was 277 on the item map.

4


4



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* Signicantly diferent (p < .05) rom 2009.1District did not participate in 2003.NOTE: Beginning in 2009, i the results or charter schools are not included in the school districts AdequateYearly Progress (AYP) report to the U.S. Department o Education under the Elementary and SecondaryEducation Act, they are excluded rom that districts TUDA results. DCPS = District o Columbia Public Schools.

Figure 6. Trend in average scores for eighth-grade public school studentsin NAEP mathematics, by jurisdiction

0 240 250 260 270 280 290 300 500

Year

2003

2003

2003

2003

2003

2003

2003

2003

2003

2003

2003

2003

276*

262*

244*

262*

279*

254*

253

243*

264*

245*

266*

264*

2005

2005

2005

2005

2005

2005

2005

2005

2005

2005

2005

278*

265*

245*

281*

270*

281

258*

249*

2005 245*

267*

250*

267*

2005 270*20072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

20072009

282280*

269*271

256259

283*287

276279

283283

260264

20072009

257256

20072009

248251

273277

257258

270273

272*280

Scale score

Nation

Large city

Atlanta

Austin1

Boston

Charlotte

Chicago

Cleveland

District ofColumbia (DCPS)

Houston

Los Angeles

New York City

San Diego

Most districts show nosignifcant change since 2007In comparison to 2007 , average mathematicsscores were higher in 2009 both or eighth-gradepublic school students in the nation and in largecities; however, two participating urban districtsshowed gains. Among the 11 participating districts,scores increased or Austin and San Diego andshowed no signicant change in the remaining9 districts ( gure 6 ). Apparent increases since2007 or some districts (e.g., Chicago andHouston) were not statistically signicant.(Note that charter schools within TUDA districtboundaries that the districts exclude rom theirAdequate Yearly Progress (AYP) reporting to theU.S. Department o Education under the Elemen-tary and Secondary Education Act were excluded

rom the 2009 sample. See the Technical Notes or

more in ormation.)Gains since 2007 in Austin were reected inhigher scores or middle-per orming students atthe 50th percentile, and in San Diego or studentsat the 10th, 25th, and 75th percentiles (seeappendix table A- 6 ). Although there were nosignicant changes in the overall scores or theDistrict o Columbia and Houston, scores werehigher in 2009 than in 2007 or higher-per ormingstudents at the 90th percentile in the District oColumbia, and or students at the 25th and 50thpercentiles in Houston.

In comparison to 2003 , scores were higher in 2009or 9 o the 10 districts that participated in bothyears (there was no signicant change in the score

or Cleveland). Scores increased or studentsacross the per ormance range (i.e., those at the10th, 25th, 50th, 75th, and 90th percentiles) inAtlanta, Boston, Chicago, Houston, Los Angeles,and San Diego (see appendix table A- 6 ). Scoresalso increased or students at the 10th percentile inCharlotte; at the 50th, 75th, and 90th percentiles inthe District o Columbia; and at the 10th, 25th,50th, and 90th percentiles in New York City.


8


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* Signicantly diferent (p < .05) rom large city.** Signicantly diferent (p < .05) rom the nation.NOTE: DCPS = District o Columbia Public Schools.

Figure 7. Average scores for eighth-grade public school students in NAEPmathematics, by jurisdiction: 2009

0 500230 240 250 260 270 280 290 300Scale score

282*

271**

259*,**

287*,**

257*,**

279*

283*

264*,**

256*,**

238*,**

251*,**

258*,**

277*,**

271**

258*,**

273**

251*,**

273**

265*,**

280*

Nation

Large city

Atlanta

Austin

Baltimore City

Boston

Charlotte

Chicago

Cleveland

Detroit


Fresno

Houston


Los Angeles

Miami-Dade

Milwaukee

New York City

Philadelphia

San Diego

In 2009, public school students attendingschools in large cities scored 11 points loweron average than public school students in

the nation ( gure 7 ). With ew exceptions,scores in most o the participating urbandistricts were also lower than the score orthe nation. Austin was the only district toscore higher than the national average.Scores in Boston, Charlotte, and San Diegowere not signicantly diferent rom thenation, and scores in the remaining14 districts were lower.

When compared to the average score orlarge cities nationally, scores were higherin Austin, Boston, Charlotte, Houston,

and San Diego. The scores or JefersonCounty, Miami-Dade, and New York Citywere not signicantly diferent rom thescore or large cities, and scores or theremaining 10 districts were lower.

Five districts score higherthan large cities nationally




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Figure 8. Achievement-level results for eighth-grade public school students in NAEP mathematics, by jurisdiction: 2009

# Rounds to zero.NOTE: Detail may not sum to totals because o rounding. DCPS = District o Columbia Public Schools.

Nation

Large city

Philadelphia

Boston

New York City

Miami-Dade

ChicagoAtlanta

District of Columbia (DCPS)Cleveland

Milwaukee

Detroit

Fresno

100 30 20 10 0 10 20 30 40 50 60 70 8060 507080 40

Percent

not signicantly different

lowerLos Angeles

Baltimore City

San Diego

AustinCharlotte

Houstonhigher

100

Compared to large city, the% at or aboveBasic is

49 36 2

32 36 26 7

40 35 19 7

36 41 19 3

Jefferson County (KY) 40 37 18 5

54 34 10 1

54 31 12 3

58 35

57 33 9 1

7 1

63 30 6 #

29 39 25 7

40 18 5

77 18 4 #

31 45 19 5

33 36 23 9

25 36 28 11

28 39 24 8

48 36 13

13

3

26 9 362

54 32 11 2

36

BelowBasic Basic Procient Advanced

Districts show range o knowledge and skills


Among the 18 districts that participatedin 2009, the percentages o students per orm-ing at or above the Basic level ranged rom23 percent in Detroit to 75 percent in Austin(gure 8 ). All the districts had some studentsper orming at or above the Procient level.

The same ve districts with scores higher thanthe score or large cities also had higherpercentages o students per orming at orabove Basic (Austin, Boston, Charlotte,Houston, and San Diego). In addition, thepercentage o students at or above Basic inMiami-Dade was higher than in large cities.The percentages o students at or above Basic in Jeferson County and New York City werenot signicantly diferent rom large cities, andthe percentages in the remaining 10 districts

were lower.


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Table 2. Selected characteristics of eighth-grade public school students in NAEP mathematics, by jurisdiction: 2009

Jurisdiction

Number oeighth-graders

Number ostudentsassessed

Percentage o students

White Black Hispanic

Asian/Pacic

Islander

Eligible orree/

reduced-price school

lunch

Identied asstudents

withdisabilities

Identied asEnglish

languagelearners

Nation 3,504,000 156,200 56 16 21 5 43 10

Large city 539,000 34,600 21 27 42 8 66 11 1

Atlanta 3,000 900 7 88 4 # 78 10

Austin 5,000 1,300 31 11 55 3 55 11 1

Baltimore City 4,000 900 6 91 2 1 82 8

Boston 4,000 1,100 14 40 33 11 73 16

Charlotte 9,000 1,300 32 46 15 4 46 9

Chicago 28,000 1,800 9 48 40 3 86 14 Cleveland 3,000 900 15 71 12 1 1001 13 6

Detroit 6,000 1,000 2 89 8 1 70 13

District o Columbia (DCPS) 2,000 900 5 82 11 2 75 13

Fresno 5,000 1,300 14 11 58 16 86 9 2

Houston 12,000 1,900 8 29 60 3 78 8 1

Jeferson County (KY) 7,000 1,400 55 36 4 3 55 9

Los Angeles 48,000 2,000 8 10 75 7 82 10 2

Miami-Dade 23,000 2,000 10 22 65 1 63 11

Milwaukee 5,000 1,000 11 62 20 4 78 18

New York City 69,000 2,100 16 32 39 14 79 14

Philadelphia 11,000 1,200 16 57 18 8 85 12

San Diego 8,000 1,000 28 12 41 18 55 8 1# Rounds to zero.1In Cleveland, all students were categorized as eligible or the National School Lunch Program.NOTE: The number o eighth-graders is rounded to the nearest 1,000. The number o students assessed is rounded to the nearest 100. Black includes A rican American, Hispanic includes Latino, and Pacic Race categories exclude Hispanic origin. The race/ethnicity categories listed do not sum to 100 percent because the percentages or American Indian/Alaska Native and unclassied students are not shown. DCPSchools.

Districts vary in demographic makeupIn ormation about the demographicmakeup o eighth-graders in the nation,large cities, and the 18 participating urbandistricts helps to provide context whenmaking comparisons. In the nation, the

percentage o White eighth-graders washigher than the combined percentages oBlack and Hispanic students in 2009.However, the opposite was true or largecities and or most districts. Almost all othe districts had higher combined percent-ages o Black and Hispanic students thanWhite students ( table 2 ). JefersonCounty was the only district where the

percentage o White students was higherthan the combined percentage o Black andHispanic students.

Large cities and districts also difered romthe nation in the proportion o studentseligible or the National School LunchProgram. Forty-three percent o eighth-graders were eligible or ree/reduced-price school lunch nationally compared to66 percent in large cities. The percentageso eligible students in the districts wereall higher than the national percentageranging rom 46 percent in Charlotte to

100 percent in Cleveland where all studentswere categorized as eligible.

Large cities in general and some o theparticipating districts were also more likelyto have higher percentages o Englishlanguage learners (ELL). The percentageo identied ELL students in large cities was12 percent compared to 6 percent in thenation overall. The percentages o ELLstudents in Austin, Fresno, Los Angeles,and San Diego were higher than thepercentages in both the nation and largecities.



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Figure 9. Comparison of district and national average scores for eighth-grade public school students in NAEP mathematics, by selectegroups: 2009


Higher average score than the nation.Lower average score than the nation.

No signicant diference between the district and the nation. Reporting standards not met. Sample size insu cient to permit a reliable estimate.

Race/ethnicity

Eligibility orree/reduced-price

school lunch



Nation 282 292 260 266 300 266 293Large city Atlanta Austin Baltimore City Boston

Charlotte Chicago Cleveland Detroit District o Columbia (DCPS) Fresno

Houston Jeferson County (KY) Los Angeles

Miami-Dade Milwaukee New York City Philadelphia

San Diego

Even though most TUDA districts per ormed below the nationalaverage overall, scores or student groups in some districts werehigher than the scores or their peers in the nation. Among the 14districts where overall average scores were lower than the nationalaverage, scores were higher or White, Black, and Hispanicstudents in Houston; or Hispanic students in Miami-Dade; and or

Asian/Pacic Islander students in New York City when comparedto their peers in the nation ( gure 9 ). Scores or lower-incomestudents (i.e., those eligible or ree/reduced-price school lunch) in

Houston and New York City were higher than the score orlower-income students nationally, even though the overall averagescores or the districts were lower than the nation.

Among the three districts where overall scores did not difersignicantly rom the national average (Boston, Charlotte, andSan Diego), scores or at least one racial/ethnic group were higherthan in the nation.

A Closer Look at Districts Compared to the Nation


8


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Figure 10. Comparison of district and large city average scores for eighth-grade public school students in NAEP mathematics, by selecgroups: 2009


No signicant diference between the district and large city. Reporting standards not met. Sample size insu cient to permit a reliable est imate.

Race/ethnicity

Eligibility orree/reduced-priceschool lunch



Large city 271 294 256 264 299 262 289Atlanta Austin Baltimore City Boston

Charlotte Chicago Cleveland Detroit

District o Columbia

(DCPS) Fresno

Houston Jeferson County (KY) Los Angeles

Miami-Dade Milwaukee New York City Philadelphia San Diego

A Closer Look at District Results Compared to Large CitiesDiferences in overall average scores between participatingdistricts and large cities sometimes varied when results wereexamined or student groups. Among the 10 districts whereaverage scores were lower than the score or large cities, therewere no signicant diferences in scores or White students

in 3 districts, or Black students in 4 districts, and or Hispanicstudents in 5 districts when compared to their peers in largecities ( gure 10 ). Scores or students who were eligible or

ree/reduced-price school lunch in Chicago and Philadelphiawere also not signicantly diferent rom the score or eligiblestudents in large cities.

Among the ve districts where overall scores were higher than thescore or large cities, Austin, Boston, Charlotte, and Houston also

had higher scores or all racial/ethnic groups with samples largeenough to report results, and or lower-income students.

Among the three districts where overall average scores did notdifer signicantly rom the score or large cities, district scoreswere higher or Hispanic students in Miami-Dade and or Blackand Asian/Pacic Islander students in New York City, and lower

or White and Black students in Jeferson County. In comparisonto the score or students eligible or ree/reduced-price schoollunch in large cities, scores were higher or eligible students inMiami-Dade and New York City and lower in Jeferson County.



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NAEP Mathematics Achievement-Level Descriptions for Grade 8The policy denitions o achievement levels provided in the Introduction apply to all NAEP subjects. The specic descrip-tions o what eighth-graders should know and be able to do at the Basic , Procient , and Advanced mathematics achieve-ment levels are presented below. NAEP achievement levels are cumulative; there ore, students per orming at the Procient level also display the competencies associated with the Basic level, and students at the Advanced level also demonstratethe skills and knowledge associated with both the Basic and the Procient levels. The cut score indicating the lower end o

the score range or each level is noted in parentheses.

Basic (262)Eighth-grade students performing atthe Basic level should exhibit evidenceof conceptual and procedural under-standing in the ve NAEP content areas.This level of performance signiesan understanding of arithmeticoperationsincluding estimationonwhole numbers, decimals, fractions,

and percents.Eighth-graders per orming at the Basic level should complete problemscorrectly with the help o structuralprompts such as diagrams, charts, andgraphs. They should be able to solveproblems in all NAEP content areasthrough the appropriate selection anduse o strategies and technologicaltoolsincluding calculators, computers,and geometric shapes. Students at thislevel also should be able to use

undamental algebraic and in ormalgeometric concepts in problem solving.

As they approach the Procient level,students at the Basic level should beable to determine which o the availabledata are necessary and suf cient orcorrect solutions and use them inproblem solving. However, theseeighth-graders show limited skill incommunicating mathematically.

Procient (299)Eighth-grade students performingat the Procient level should applymathematical concepts and proceduresconsistently to complex problems inthe ve NAEP content areas.

Eighth-graders per orming at theProcient level should be able toconjecture, de end their ideas, andgive supporting examples. They shouldunderstand the connections among

ractions, percents, decimals, and othermathematical topics such as algebraand unctions. Students at this levelare expected to have a thoroughunderstanding o Basic level arithmeticoperationsan understanding suf cient

or problem solving in practicalsituations.

Quantity and spatial relationships inproblem solving and reasoning shouldbe amiliar to them, and they should beable to convey underlying reasoningskills beyond the level o arithmetic.They should be able to compare andcontrast mathematical ideas andgenerate their own examples. Thesestudents should make in erences romdata and graphs; apply properties oin ormal geometry; and accurately usethe tools o technology. Students at thislevel should understand the process

o gathering and organizing data andbe able to calculate, evaluate, andcommunicate results within thedomain o statistics and probability.

Advanced (333)Eighth-grade students performingat the Advanced level should beable to reach beyond the recognition,identication, and application ofmathematical rules in order togeneralize and synthesize concepts andprinciples in the ve NAEP contentareas.

Eighth-graders per orming at theAdvanced level should be able to probeexamples and counterexamples in orderto shape generalizations rom whichthey can develop models. Eighth-graders per orming at the Advanced level should use number sense andgeometric awareness to consider thereasonableness o an answer. They areexpected to use abstract thinking tocreate unique problem-solvingtechniques and explain the reasoningprocesses underlying their conclusions.



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GRADE 8 NAEP MATHEMATICS ITEM MAPScale score Content area Question description

500

361 Data analysis, statistics, and probability Determine the complete sample space350 Algebra Find the coordinates o collinear points347 Measurement Identi y the gures with equivalent areas342 Geometry Use the given pieces to make a shape with certain properties339 Data analysis, statistics, and probability Read and interpret the in ormation in a graph337 Algebra Use an algebraic model to make a prediction (calculator available)336 Algebra Find the next term in a geometric sequence333

332 Algebra Set up and solve an algebraic equation331 Algebra Find the change in y given the change in x or a linear equation330 Geometry Find the length o a hypotenuse324 Measurement Solve a problem involving unit conversions (calculator available)319 Geometry Identi y the piece used to orm a gure312 Number properties and operations Solve a problem using division306 Algebra Represent the length o a rectangle in terms o the width (shown on page 30 )300 Number properties and operations Determine a number that satises the given conditions299

292 Geometry Identi y the steps in a trans ormation288 Number properties and operations Identi y the number with the given digit in the hundredths place285

Measurement Determine the possible dimensions o a rectangle, given the area283 Geometry Identi y the side with the same length in congruent gures281 Algebra Identi y the solution rom a graph o linear equations278 Number properties and operations Determine a quantity based on a given percent267 Data analysis, statistics, and probability Determine the probability o a particular outcome (shown on page 29 )264 Algebra Read in ormation rom a graph262

260 Data analysis, statistics, and probability Recognize misrepresented data259 Measurement Solve a problem involving rates (calculator available)257 Geometry Identi y the result o combining two shapes253 Number properties and operations Use estimation to nd a diference236 Number properties and operations Find the greatest number that can be bought (calculator available)233 Measurement Measure the length o a line segment

224 Algebra Determine the value o the unknown in a number sentence

0

A d v a n c e

d

P r o

c i e n

t

B a s i c

NOTE: Regular type denotes a constructed-response question.Italic type denotes a multiple-choice question. The position of a question on the scale represents the average score attained by students who had a 65 percenprobability 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 amultiple-choice question. For constructed-response questions, the question description represents students performance rated as completely correct. Scale score ranges for mathematics achievement levels are rthe map.SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.

What Eighth-Graders Know and Can Do in MathematicsThe item map below illustrates the range o mathematicalknowledge and skills demonstrated by eighth-graders. Forexample, students per orming near the middle o the Basic range (with an average score o 285) were likely to be able to

determine the possible dimensions o a rectangle, given thearea. Students per orming near the top o the Procient range(with an average score o 332) were likely to be able to set upand solve an algebraic equation.


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Marty has 6 red pencils, 4 green

pencils, and 5 blue pencils.If he picks out one pencil withoutlooking, what is the probability thatthe pencil he picks will be green?

1 out of 31 out of 41 out of 154 out of 15

A

B

C

D

SAMPLE QUESTION:


Sample Question: Data Analysis, Statistics, and Probability


Percentage correct or eighth-grade public school students,by jurisdiction: 2009

0 30 40 50 60 70 80 100Percent

70San Diego

61Philadelphia

72New York City

62Milwaukee

68Miami-Dade

57Los Angeles

72Jeferson County (KY)

72Houston

56Fresno

34

District o Columbia (DCPS) 64

Detroit

61Cleveland

59Chicago

74Charlotte

73Boston

69Baltimore City

81Austin

Atlanta 66

Large city 67

Nation 77

This sample question from the 2009 eighth-grade assess-ment measures students performance in the data analysis,statistics, and probability content area. It asks students todetermine the probability of a simple event. Obtaining thecorrect answer requires rst determining that there is a totalof 15 pencils to choose from (6 red plus 4 green plus 5 blue).Since 4 of these pencils are green, the correct answer is 4out of 15 (Choice D). Students were not permitted to use acalculator to answer this question.

Seventy-seven percent of eighth-grade public school stu-dents in the nation selected the correct answer to thisquestion. The percentage of correct responses in each ofthe districts ranged from 34 percent in Detroit to 81 percentin Austin. The national average score for students who werelikely to select the correct answer was 267 on the item map.



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SAMPLE QUESTION:


Percentage correct or eighth-grade public school students,by jurisdiction: 2009


34

29

41

25

45

42

55

58

48

36

22

39

32

45

34

39

49

41

42

49

San Diego

Philadelphia

New York City

Milwaukee

Miami-Dade

Los Angeles


Houston

Fresno

Detroit

Cleveland

Chicago

Charlotte

Boston

Baltimore City

Austin

Atlanta

Large city

Nation

0 20 30 40 50 60 70 100Percent


NAEP Questions ToolExplore other sample questions from themathematics assessment athttp://nces.ed.gov/nationsreportcard/itmrlsx/

This sample question measures eighth-graders per ormancein the algebra content area. The question asks students toidenti y an algebraic expression that models a relationshipthat is given in a geometric context. Students were not per-mitted to use a calculator to answer this question.

Forty-nine percent o eighth-grade public school studentsin the nation selected the correct answer (Choice E) to thisquestion. The percentage o correct responses in each o thedistricts is presented below. The national average score orstudents who were likely to select the correct answer was306 on the item map.

Sample Question: Algebra

The length of a rectangle is 3 feetless than twice the width, w (in feet).What is the length of the rectanglein terms of w ?

3 2w2(w + 3)2(w 3)2w + 32w 3

A

B

C

E

D


8


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District Profiles

Individual district proles provide a closer look at some key ndings for each district,including how districts scores compare to scores in their home states, how theperformance of lower-income students in the districts compares to similar students in thenation, how racial/ethnic groups within the districts compare, and how the performance of students has changed in those districts that participated in earlier assessment years.

TRIAL URBAN DISTRICT ASSESSMENT MATHEMATICS 2009


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For Atlanta fourth-graders in 2009, the overall score was higher than in 2003 but not

signicantly diferent rom 2007.

the average score o 225 was at the 30th percentile orthe nation.

The district-to-state comparison showed

a lower overall score than or Georgia.

no signicant change in the gap compared to 2003 and2007.

Results for lower-income students showed

a higher average score compared to 2003 but nosignicant change compared to 2007.

a lower average score compared to lower-incomestudents in the nation.

Results for racial/ethnic groups showed

a higher average score or Black students compared to2003 but no signicant change compared to 2007.

no signicant change in the average score or Whitestudents compared to 2003 and 2007.

Achievement-level results showed

an increase in the percentage at or above Basic comparedto 2003 but no signicant change compared to 2007.

an increase in the percentage at or above Procient compared to 2003 but no signicant change comparedto 2007.

Atlanta, Grade 4Trendin NAEP mathematics average scores for fourth-gradersin Atlanta and Georgia

* Signicantly diferent (p < .05) rom 2009.

Trendin NAEP mathematics average scores for lower-income

fourth-graders in Atlanta and the nation

* Signicantly diferent (p < .05) rom 2009.NOTE: In NAEP, lower-income students are students identied as eligible or the NationalSchool Lunch Program.

Trendin NAEP mathematics average scores for fourth-gradersin Atlanta, by race/ethnicity

* Signicantly diferent (p < .05) rom 2009.1 Sample sizes insu cient to permit reliable estimates or Hispanic students in 2003 and 2005.NOTE: Results are not shown or all race/ethnicity categories because o insu cient sample sizes.Black includes A rican American, and Hispanic includes Latino. Race categories exclude Hispanicorigin.

Trendin NAEP mathematics achievement-level results for fourthgraders in Atlanta

* Signicantly diferent (p < .05) rom 2009.NOTE: Detail may not sum to totals because o rounding.

BelowBasic Ba si c Proci en t Adva nced

200320052007

Large city2009

Nation2009

50* 37* 11*43* 40 14*

2*

39 41 33

2009 37 42 17

17

4

28 43 24 5

19 43 33 6

Percent belowBasic

AtlantaPercent at Basic , Procient , and Advanced

Year03 05 07 090

210

240

230

220

500Scale score

234230*

235 236

216*224 225221*

250

Georgia

Atlanta

Year03 05 07 090

200

230

220

250

240

210

500Scale score

225*

213*209*

222*

216

227

216

228Nation

Atlanta

215*

263258

217

223

211*

218

222

266

0503 07

266White

Hispanic 1Black

09 Year0

210

240

230

260

500Scale score

270

250

220


4


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For Atlanta eighth-graders in 2009, the overall score was higher than in 2003 but not

signicantly diferent rom 2007.



a lower overall score than or Georgia.

a narrowing o the gap compared to 2003 but nosignicant change compared to 2007.


a higher average score compared to 2003 but nosignicant change since 2007.

a lower average score compared to lower-incomestudents in the nation.


a higher average score or Black students compared to2003 but no signicant change since 2007.


an increase in the percentage at or above Basic comparedto 2003 but no signicant change since 2007.

an increase in the percentage at or above Procient compared to 2003 but no signicant change since 2007.

Atlanta, Grade 8

Trendin NAEP mathematics average scores for eighth-gradin Atlanta, by race/ethnicity

* Signicantly diferent (p < .05) rom 2009.NOTE: Results are not shown or all race/ethnicity categories because o insu cient samplesizes. Black includes A rican American and excludes Hispanic origin.

Trendin NAEP mathematics average scores for lower-inco

eighth-graders in Atlanta and the nation

* Signicantly diferent (p < .05) rom 2009.NOTE: In NAEP, lower-income students are students identied as eligible or the NationalSchool Lunch Program.

Trendin NAEP mathematics average scores for eighth-gradin Atlanta and Georgia

* Signicantly diferent (p < .05) rom 2009.

Trendin NAEP mathematics achievement-level results for eighth-graders in Atlanta

* Signicantly diferent (p < .05) rom 2009.NOTE: Detail may not sum to totals because o rounding.

BelowBasic Basic Procient Advan ced

200320052007

Large city2009

Nation2009

70* 24*24*

5*5*

10

69*59 29 9

2009 54 34 12

11

40 36 18 5

29 39 25 7

Percent belowBasic Percent at Basic , Procient , and Advanced

Atlanta

272*270*275*

244*

256

278

259

245*

Georgia

Atlanta

Year03 05 07 090

240

270

260

250

500Scale score

280

240*

261*

239*

258*265*

251

266

253

Year03 05 07 090

230

260

250

280

270

240

500Scale score

Nation

Atlanta

242*

253

241*

255

0503 07 090

220

250

240

270

260

230

280

500Scale score

Year

Black

TRIAL URBAN DISTRICT ASSESSMENT MATHEMATICS 2009


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SOURCE: U.S. Department o Education, Institute o Education Sciences, National Center or Education Statistics, National Assessment o Educational Progress (NAEP), 2005, 2007, and 2009 Mathematics

For Austin fourth-graders in 2009, the overall score was not signicantly diferent rom

2005 and 2007.



no signicant diference rom the overall score or Texas.


no signicant change in the average score compared to2005 and 2007.

a higher average score compared to lower-incomestudents in the nation.


no signicant change in the average scores or White,Black, and Hispanic students compared to 2005 and2007.


no signicant change in the percentage at or above Basic compared to 2005 and 2007.

no signicant change in the percentage at or aboveProcient compared to 2005 and 2007.

Austin, Grade 4Trendin NAEP mathematics average scores for fourth-gradersin Austin and Texas

Trendin NAEP mathematics average scores for lower-incomefourth-graders in Austin and the nation

* Signicantly diferent (p < .05) rom 2009.NOTE: In NAEP, lower-income students are students identied as eligible or the National

School Lunch Program.

Trendin NAEP mathematics average scores for fourth-gradersin Austin, by race/ethnicity

NOTE: Results are not shown or all race/ethnicity categories because o insu cient samplesizes. Black includes A rican American, and Hispanic includes Latino. Race categories excludeHispanic origin.

Year05 07 090

220

the nation's report card mathematics 2009 trial urban district assessment (tuda)(2)

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