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Schools, Achievement, and Inequality: A Seasonal PerspectiveAuthor(s): Karl L. Alexander, Doris R. Entwisle, Linda S. OlsonSource: Educational Evaluation and Policy Analysis, Vol. 23, No. 2 (Summer, 2001), pp. 171-191Published by: American Educational Research AssociationStable URL: http://www.jstor.org/stable/3594128

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EducationalEvaluationandPolicy AnalysisSummer2001, Vol.23, No. 2, pp. 171-191

Schools, Achievement, and Inequality: A Seasonal Perspective

Karl L. Alexander, Doris R. Entwisle, and Linda S. Olson

TheJohnsHopkins University

Are there socioeconomicdifferences n theseasonality of children's earningovertheschoolyearand

summermonths? The achievementgap across social lines increases duringtheprimarygrades, as

much researchindicates,butdescriptiveanalysesandHLMwithin-persongrowthmodels or a rep-

resentativepanel of Baltimoreschool childrendemonstrate hatthe increasecan be tracedmainlytothe out-of-schoolenvironment i.e., influencessituated in home and community).School-yearverbal

andquantitativeachievementgains are comparableor uppersocioeconomic status(SES)andlower

SESchildren,but summergains, when children are outof school, evidencelarge disparities.Duringthesummer,upperSESchildren'sskills continueto advance(albeitat a slower rate thanduringthe

school year), but lower SES children'sgains, on average, areflat. Thisseasonalpatternof achieve-

mentgains impliesthatschooling plays an important ompensatoryrole, one that is obscuredwhen

achievementscompared n an annualbasis,as is typical.Policyimplications ftheseasonalityoflearn-

ingarediscussed, ncluding upportforpreventivemeasuresover thepreschoolyearsandforprograms,

possibly includingcalendarreformsand summer chool, tosupportdisadvantaged hildren's earning

year-round.

"Pupils Lose Ground in City Schools: The

LongerChildrenStayin the System, [the]More

They Fall Behind"reads a recentheadline from

Baltimore's local newspaper (Holmes, 1997).Baltimore is where our research s situated,but

the headline could as well be about Chicago,

Philadelphia,he District of Columbia,oranyof

the nation's other arge-city,high-poverty choolsystems. The accompanying article compares

citywide readingand math achievementtest re-

sults from Grades 1 through5 againstnational

norms,comparisonswhich, as the headlinesig-nals, prove none too flattering.This hardlysur-

prises.Whenevaluatedagainstnationalachieve-

ment standards,these school systems almost

always farebadly:theirpupils lag behind in the

earlygradesand fall fartherback overtime(e.g.,

EducationWeek,1998). Suchcomparisonsden-tify a problem of immense proportions,but

whether heschool systems nthose communities

arefailingourneediestchildren,as the headline

seemsto imply, is much less certain.

When testresultsforplaceslike Baltimoreare

comparedagainstnationalnorms, t hardlycan be

said that like is beingcomparedwith like. Balti-

more'spublicschoolenrollmentn 1999was86%

AfricanAmerican Maryland tateDepartment f

Education,1999a,p.l), two thirdsof its students

received free or reduced-pricemeals, indicatinglow familyincome relative o familysize (Mary-landStateDepartment f Education,1999b),and

in morethanhalfthecity's elementary chools thelow-incomeenrollment xceeded80%(TheSun,

1999)-hardly thenationalprofile.

Recognizing that"place" s a proxy for eco-

nomic standingand other dimensions of social

advantageor disadvantageputs the headline's

comparisonof test scores in broaderperspective.The out-of-school context necessarily explainsthelag in achievement evels of low-income and

minorityyouth over the preschool period.This

has been documented recently at the nationallevel in theEarlyChildhoodLongitudinalStudy

(U.S. Department f Education,2000) and in the

Prospectsfirstgradecohort (e.g., Karweit,Ric-

ciuti, & Thompson,1994). Comparisonswithin

the city system show much the same pattern:lower socioeconomic status (SES) children in

171



Alexander,Entwisle,and Olson

ourBaltimoreresearch est well below the level

of higherSES children at the startof firstgrade

(e.g., Entwisle,Alexander,& Olson, 1997).1That the out-of-school social context directs

children'sacademicdevelopmentbeforethey get

to "realschool" seems self-evident;yet the samelife circumstances hatundercut chool readiness

areeverpresent nyoung people'slives. Thedragof poverty, family stress,andcommunitydecaydoesn't suddenlyturnoff when childrenreach 6

and the school's influence begins to weigh in.

This has implications for the social patterningof achievement differentialsamong school-agechildren ust as it does among preschoolers: he

achievementgapacrosssocial lines would be ex-

pected to widen over time for reasons having

nothing at all to do with the schools.2

Thisexpectationholdsespeciallyfor thefoun-

dational curriculum hat dominates the primary

grades.Not manychildrenwill learn differential

calculus athome,oranalyzeclassicalimagery n

17th-centuryBritishliterature,but rudimentary

readingand number kills arequiteanothermat-

ter.These kinds of skills arerehearsed t home-

albeitmore so in some kinds of householdsthan

others e.g.,Hess &Holloway,1984;Scott-Jones,1984;Slaughter& Epps,1987)-and areinfused

in daily experience outside the household as

well-although, again, not in equal measure

across social lines (e.g., Entwisle,Alexander,&

Olson,1994).

Simple time trends like those at issue in the

headlinequotedaboveconfoundeffects of home,

school, and community.Do schools exacerbate

unequal choolperformance crosssocial lines or

dotheymitigatesuch nequality?Schools' contri-bution olearningroma stratificationerspective

hangson the answer,but achievementof clarity

requiressomehowbreaking hrough he family-home-schoolentanglement. ypically, his s done

piecemealthrough tatisticalmeans,as when the

influence of specific school resourcesor experi-ences (e.g., class size, perpupilexpenditures,or

curriculum lacement)s assessedconditionalon

family background.This is fine for evaluating

specificprogram ffects,butholisticunderstand-ing of the role of schoolingrequiresa different

approach e.g., Ceci, 1991).A seasonalperspectiveon learning achieves

clarityon thematterby exploiting heintermittentnatureof schooling.Children re"in" heirhomes

andcommunitiesyear-round, ut are "in"school

172

only partof the time. The long summerbreak-

currently nderassaultasantiquatede.g.,Barrett,

1990;Gewertz,2000; White, 1999)-constitutestimeout from school. For childrenwho do not at-

tendsummerschool, thispartitioning f the cal-

endarapproximatesa "schooled"-"unschooled"naturalexperiment.By this logic, differences n

the patterningof achievementgains across the

"schooled"-"unschooled"ivide oughtto impli-catetheexperienceof schooling.

How, then,does learningdifferon a seasonal

basis, and what do any such differences implyabout the schools' role with respectto achieve-

ment differences across social lines? To address

these questions,we analyzeCaliforniaAchieve-

mentTest(CAT)data romtheBeginningSchool

Study(BSS). TheBSS, an ongoing panel study,has been monitoring he academic andpersonal

developmentof a representativeandomsampleof children N= 790) whobeganfirstgrade n the

fall of 1982 in 20 of Baltimore'spublicschools.

The achievement data span 5 years, from fall

1982 (first grade for everyone) through spring1987. This period predatesrecent increases in

summer emediationprograms or children nthe

primarygrades (e.g., Cooper,Charlton,Valen-tine,&Muhlenbruck, 000), andfew membersof

the studygroupattendedsummerschool duringtheyearsatissue. Theanalysis n thatregard s a

relatively lean mplementationf the"schooled"-

"unschooled"ogic that directs attention o sea-

sonal differences n learning. n today'senviron-

ment, with summer programs proliferating,3t

would be muchharder o achievesuchclarity.

Testingwas done in the fall and springeach

year,covering5 schoolyearsand4 summers.Thistimeframespansall of elementary chool for chil-

drenpromoted achyear(about60%of thetotal)and s alignedwith the time frameof thenewspa-

perarticlewith whichwe began(Holmes, 1997).

Higherscores in the fall of the new school year(relativeo scores rom heprevious pring) eflect

summergains;higher scores towardyear's end

(relativeto scores fromthe previousfall) reflect

schoolyear gains.Figure1 illustrateshe calcula-

tionsinvolved. It is a simplematterat the level ofoperations:for summer gains, subtractspringscores from fall scores across adjacentschool

years;for school-year gains, subtract all scores

fromspringscores within schoolyears.Two kinds of assessments arereportedusing

this generalframework.The first is descriptive.



Schools, Achievement,andInequality

Fall Spring Fall Spring FallYear 1 Year 1 Year 2 Year 2 Year 3

TestingSchedule Il I1 IFirst First Second Second

Winter Summer Winter Summer

Winter Gains:

FirstWinter: [SpringYear1 - FallYear1]Second Winter: SpringYear2 - FallYear2]

SummerGains:

FirstSummer: [FallYear2 - SpringYear1]Second Summer: FallYear3 - SpringYear2]

FIGURE 1. Illustrative imelinefor seasonal comparisonsof cognitivegrowth.

Itplotsachievement evels annuallyandon a sea-

sonalbasis for the5 schoolyears.Thesedescrip-tivecomparisons ighlighthowcomparisonsrack

acrosssocial lines, andespeciallythe insightsaf-

fordedby takinga seasonalapproachn contrast

tothemoretypicalapproachhatmonitorsperfor-

mance levels at year's end. The second assess-ment s analytic.Within-personrowthcurvetra-

jectoriesareestimatedorthe 5 years nawaythat

allows for summer "deflections"off the annual

growthtime line and for socioeconomic differ-

ences in the magnitudeof those deflections.The

descriptive omparisons,we will see, seem to im-

plicateout-of-school earningdifferencesas driv-

ing the achievementgap acrosssocial lines. The

growthcurveanalysisprovidesa rigorous est of

thisproposition.

Previous Studies

BarbaraHeynswasamong he first o articulate

theequity implicationsof a seasonalperspectiveon learning,andatthe level of issues herempir-ical work-in theprimarygradesusing nationaldata (1987) and throughgrades 5 to 7 in At-

lanta'spublic schools (1978)-is the direct-line

lineage of BSS inquiries n this area. Interest n

the seasonalityof learningdid notoriginatewithHeyns, however. Cooper, Nye, Charlton,Lind-

sey, andGreathouse(1996) review 39 relevant

studies, the oldest datingback to 1906 (White,

1906). Most of the olderstudieswere interested

specificallyin summer earning oss, though(asdistinct from summer-winterdifferentials),and

few would pass muster against contemporary

methodologicalstandards.

Such concernsled Cooperet al. (1996) to re-

stricttheirmeta-analysis o 13 studiespublishedsince 1975.TheBSS is one of the 13,represented

by two analyses(EntwisleandAlexander, 1992,

1994).Heyns'stwo studies(1978, 1987)arealsoincluded.4Cooper et al. conclude that summer

losses averageaboutonegradeequivalentmonth

across these 13 studies (on the order of .1 stan-

darddeviation[SD]relative o springscores),but

this differs across performancedomains (mathlosses exceedreading osses), grade evel (lossesarelargerat the uppergrades),andas a function

of pupil background e.g., middle-classchildren

registerreadinggainsover summer; ower-class

childrenregister osses).Here we areparticularlynterested n the sea-

sonalpatterningf achievement ains(and osses)across social lines, andthe Cooperet al. (1996,

pp.227-268) reviewrightly indsbroad imilarityto Heyns's results and those of the BSS: "The

[BSS] analyseslargelyparalleled hatof Heyns(1978).... For math concepts, the authors re-

ported a difference in achievement between

Whites andBlacks thatincreased over time and

waslargelydue to differences n summer hange.Summereffects were also stronglyrelated o the

economicstatusof children's amilies. Lower n-

come children showed greatersummer osses."

And (p. 262): "Theresults of the meta-analysis

supportHeyns's (1978) andEntwistle [sic] and

Alexander's(1992, 1994) contention hat socio-

173




economic inequitiesareheightenedby the sum-

mer break."

In point of fact, the BSS conclusion is that

practically the entire gap increase across socio-

economiclines tracesto summer earningdiffer-

entials, and Heyns (1987, p.1154) finds similarresults for the Black-White earninggapnation-

ally and much the same in Atlanta (1978) for

achievementdisparitiesnvolvingbothfamilyin-

come andrace/ethnicity.Thesestudiesfindlittle

(or no) school-yeardifferentiationof achieve-

mentgainsby raceor family SES level and siz-

able summer differentiation.5 chooling, under

this accounting,mitigateseffects of social dis-

advantage n thatchildren's sizable school-year

achievementgainsdependmuch ess on home re-sources than do gains over the summermonths.

And it is impressive,we think, that this broad

agreementacross studies s evidentdespite many

methodologicaldifferences,ncludingpopulation

coverage(Atlanta, he UnitedStates,Baltimore),the achievementtests, domains of performanceandmetrics used to measure earning (quantita-tive andverbal n all instances,butotherwisedis-

similar),andgradelevel andtime framecover-

age (Grades5 and 6 at baseline in Atlantafor18 months, 18 monthsfor successive gradeco-

hortsthrough he elementary chool yearsin the

SESproject,and24 months n theBSS, withfall

of firstgradeas baseline).ThetwoBSS reports EntwisleandAlexander,

1992, 1994)reviewedby Cooperet al. (1996) ex-

aminethe first2 school yearsand2 summersof

children'sschooling, using repeatedMANOVA

measures oestimate easonaldifferencesnlearn-

ing and possible interactions nvolving schoolcontext(i.e., segregation rintegrationtatus)and

studentbackground e.g., race/ethnicity, amilysocioeconomic background). BSS work since

(e.g., Alexander& Entwisle, 1996a, 1996b;Ent-

wisle, Alexander, & Olson, 1997), largely de-

scriptive,hasplotted easonaldifferencesnlearn-

ing for 5 years, the same time frame as in the

presentinquiry.So far as we know, there is no

other tudyof seasonal earningpatternshatspans

allof elementary chool for a representativeam-ple of school beginners(in the case of the BSS,thatsample s urbanand ow income),andforthat

reason BSS research on the topic has attracted

considerable ttentione.g., Krueger,2000).6In lightof all thiswork,why revisit the issues

here?Todate,seasonal earningdifferencesnthe

174

BSS havebeen evaluatedanalytically or 2 yearsanddescriptively or 5. Thepresentpaperreports

descriptiveandanalyticresultsforthe full 5-year

period n parallel,and in so doingaddressescer-

tain questions more authoritativelythan here-

tofore. From the longer term descriptivecom-

parisons, for example, it appearsthat summer

differentialsarelarger he first 2 yearsthan ater,but this has not been evaluatedanalytically.The

growthcurveanalyses reportedhere embraceall

of theelementaryyearsin a comprehensiveway,

somethingnot done heretofore.Also, theseanaly-ses test the primacyof race versus family SES

level versus gender as the source explainingsummerlearning disparities. Ourintroductory

comments have been cast broadly in terms ofachievement differentials"across social lines,"but whether there is one "line of divide" that

dominates the others remainsto be determined.

We knowfromearlierBSS studies,forexample,that Whites register greaterachievement gainsover the summermonthsthan do African Amer-

icans,and thatupper ncome children n theBSS

registergreatersummerachievementgains than

dolower income children.But we haveyet totest

forrace differences n theseasonalityof learningnet of family socioeconomic level or for socio-

economic differences n theseasonalityof learn-

ing net of race. Theanalysesthat follow inform

all theseissues.

Methods

The BSS Research Design

Childrenwere selected forparticipationn the

BSS study througha two-stage process. First,20 schools were chosen randomlyfrom within

strata defined by racial mix (6 predominantlyAfricanAmerican;6 predominantlyWhite;8 in-

tegrated)andby socioeconomic status(14 inner

city or workingclass; 6 middleclass); then stu-

dentswererandomly ampledusing kindergartenrostersfrom the previous school year, supple-mented by first-gradeclass rostersafterschool

began in the fall. Ninety-seven percentof chil-

drenand families so selected were successfullyrecruitedntotheproject.

The Baltimorecontext is low-income urban,andthis is reflectedin the studygroup's"high-risk"makeup e.g.,Kaufman,Bradby,&Owings,

1992).TheBaltimoreCityPublicSchool(BCPS)enrollment in the early 1980s was about 77%




African American;the originalBSS sample of

790 first-time (nonrepeater)first graders was

55%African American,45%White (to sustain

comparisonsby race,Whites wereoversampled).Mother'seducationforthe groupaverageda lit-

tle more than 11years,withalmost40% consist-ing of high school dropouts 44%of Whites and

34%of AfricanAmericans).According o school

records, wo thirdsof BSS families received free

or reduced-price chool meals (aboutthe same

percentageas in the school system at the time),andmanyfirstgraderswere ivingin single-parenthouseholds44%overall,ncluding30%of Whites

and 56% of AfricanAmericans).The analysis uses achievement data from

school records,demographicnformation race/ethnicityandsex) fromschool records,anddata

onfamilysocioeconomicstandingobtained rom

parent nterviews and school records.Thesedata

sources are describednext.

Data Sources

California Achievement Test (CAT) scores. When

the BSS commenced n fall 1982, theBCPS sys-

temwasadministeringheCATbattery wice an-nually, fall and spring.Two subtestsfrom the

CAT batteryareused:ReadingComprehension(CAT-V:20 items in the fall of firstgrade),and

Math Concepts and Applications(CAT-M: 36

itemsin the fall of firstgrade).Severalconsidera-

tions directedus to these particulardomainsof

performance,mainlythe importanceof the skill

areas hemselves.Additionally, eilingconstraints

wereaproblem or othercomponentsof theCAT

battery. n the springof firstgrade,for example,16.6%of the cohortreceived the highest score

possible on the MathComputation ubtestcom-

paredwith 3.5%on the MathConceptsandAp-

plicationssubtest.The correspondingiguresfor

Vocabulary notused)andReadingComprehen-sion (used) were 17.3%and3.7%,respectively.Also, modules to assesscompetence n thesetwo

areasare ncluded n all versionsof theCAT bat-

teryfromfirstgrade throughhigh school, which

means that the same cognitive domains can bemonitored hroughout.TrendsarereportedusingCAT scale scores. Theseareverticallycalibratedacrossversions of the CATbatterydesignedfor

administrationt differentgrade evels, approxi-matinga singlecontinuum f performance crossallpointsof comparison.

Sociodemographic data. Race (White = 0; African

American = 1) and gender (male = 0; female = )

are from school records,supplementedby self-

reports.FamilySESis measuredas a composite,

using informationon mother's and father'sedu-

cational evels, arankingof mother'sandfather'soccupationaltatus Featherman Stevens,1982),and receipt of reduced-price school meals, in-

dicative of low familyincomerelativeto familysize.Thefirst our ndicatorswereself-reported y

parents;he last is fromschoolrecords.Thecom-

posite is constructedas the averageof available

measures, after conversion to Z scores. Scale

scoresareavailable or787 of the 790 group,with

justunder70%calculatedon 4 or5 indicators nd

5.4%on asingle ndicator.Alphareliabilityor the386 youngsterscoveredby all five items is .86.

Fordescriptivecomparisons,a three-categoryversionof theSEScomposites used.With he cut-

tingpointsselected,mother'seducationaverages10.0yearsforthe lower SESgroup,12.0yearsfor

the middle group, and 14.6 years for the upper

group;the respectivepercentagesfor participa-tion in themeal subsidyprogram orlow-income

families are95.1, 53.4, and 13.1. There are few

genuinely wealthyhouseholds n theBSS, anditshould be understood hat the descriptorsused,

e.g., "lower"and"higher" r"upper" rerelative

to thesample's makeup. nfact,halfthecohort s

locatedin thelower SES category,a reflectionof

the study group's low socioeconomic standingoverall.

Sample Attrition

Coverageonthebackgroundmeasures s virtu-

ally complete.Sex andrace/ethnicityare knownforeveryone,andonly threecases lack scores on

the scale thatranks amilysocioeconomic stand-

ing. The CAT data,however,come from 10 test

administrationsver5 years,andmissingdataare

a concern. Coverage is sparsefor the children

(25%)whotransferredut of Baltimore's chools

during the primary grades, but absences, lost

records,and the like alsocontribute o gapsin the

testingrecord.Thereare ust 368 children of the

original790) with all 10scoresonthe CAT-V and371 with all 10 scores on the CAT-M.This has

obligedus toconsider heconsequencesof sampleattrition arefully.The firstand thirdcolumns of

the Appendixshow how youngsterswith com-

plete testingdatacomparewiththeoriginalsam-

ple on various measures from first grade. The

175




comparisons rereassuring: espiteahighdegreeof sample oss, attritions not selectivealongaca-

demic lines andonly moderatelyselectivealongsociallines.

Accordingly,all availabledataareusedin the

analysis.The only cases screened out arethosefor whom growth trajectories annotreasonablybe estimated:those with fewer than threeover-

time datapointsperachievementdomain(three

beingtheminimumnumberrequired o estimate

a growthtrajectory,allowingfor curvature)and

those lacking "anchoring" aseline scores from

the fall of firstgrade.These restrictionsyield a

(maximum) case base of 665 for the CAT-V

analysisanda base of 678 forthe CAT-Manaly-

sis.7 These "restrictedcoverage" samples like-wise evidencelittle attritionbias (see Appendix).

Results

AnnualversusSeasonalAchievementGains

What,then,does theachievementpatternook

like in the BSS when assessed spring-to-spring,thestandard pproach?Table 1 shows that ower

SES youth already lag behind theirupperSES

peers n firstgrade byabout0.7 SD on bothCAT

subtests),and after 5 years they arefartherback

still (by more than 0.9 SD). Raw score differ-

ences (i.e., numberof CATpoints)likewise start

outlargeandincrease,but these arenotadjustedfor theincreasingdispersionon scores overtime

andso must be interpretedwithcare.8

LowerSESyoungstersn the BSS thus arenot

keepingup.This s thepatternypicallyseenwhen

achievements assessedatyear'send-indeed the

newspaper rticlewithwhich webegancouldwell

have been writtenabout the experience of our

studygroup.Withthese resultsas a frameof ref-

erence,how does thepicturechangewhenschool-

year and summerachievementgains are calcu-latedseparately?Thisis done in Table2,9andthe

exerciseinformsa whole hostof issueshavingto

do with schools andachievement.

First,CAT gainspostedwhile childrenare in

school (tophalf of Table2) exceedgainsoverthe

summermonths(lowerhalf of Table2), with the

school-yearmarginof advantage arge whether

calculated s raw scoregainsorgainspermonth.10

TABLE1

SpringCATPerformanceLevels Over Five Years,by FamilySocioeconomic Status

(RestrictedSamples,N = 665, 678)

FamilySES evel Spring83 Spring84 Spring85 Spring86 Spring87

CAT-Vmean

(Reading)LowSES 329.15 375.95 397.92 433.58 461.17(N) (329) (308) (282) (274) (292)Mid SES 348.68 388.43 423.93 467.52 495.51

(N) (161) (144) (120) (118) (129)HighSES 361.01 418.09 460.81 506.20 534.60(N) (150) (137) (109) (99) (93)High-lowdifference 31.86 42.14 62.88 72.62 73.43Pooled SD 45.65 48.39 57.85 69.77 73.92

Difference/pooledSD .70 .87 1.09 1.04 .99

CAT-Mmean

(Math)Low SES 331.27 371.87 397.80 427.63 357.76

(N) (339) (315) (289) (281) (295)Mid SES 350.45 387.08 418.88 457.76 491.66

(N) (162) (146) (122) (122) (134)High SES 357.39 407.30 448.09 487.02 514.62

(N) (147) (135) (110) (98) (91)High-lowdifference 26.12 35.42 50.29 59.39 56.85Pooled SD 36.53 38.54 48.25 54.64 60.97

Difference/pooledSD .72 .92 1.04 1.09 .93

CAT,California chievementest.

176




TABLE2

CATAchievementGainsbySeasonandSocioeconomicLevel:Five Winters,Four Summers

(RestrictedSamples,N = 665 [Verbal],678 [Quantitative])

CAT-V Reading) CAT-MMath)

Season Low SESa Mid SESaHigh

SESa Low SESa Mid SESaHigh

SESa

Wintergains1st 55.94 (2.64) 69.86 (3.55) 60.09 (3.37) 48.84 (1.64) 53.79 (2.11) 43.71 (2.46)2nd 46.00 (2.31) 43.19 (3.06) 39.82 (3.50) 42.35 (1.42) 44.06 (2.06) 42.92 (2.22)

3rd 30.46 (2.17) 34.34 (3.48) 34.68 (3.76) 35.50 (1.56) 35.68 (2.27) 35.96 (2.39)4th 33.57 (2.24) 41.29 (3.15) 28.52 (4.26) 32.94 (1.50) 32.88 (2.49) 34.71 (2.76)

5th 25.28 (2.22) 27.86 (3.37) 23.58 (4.19) 24.35 (1.82) 30.90 (2.72) 26.35 (3.31)

Totalgain 191.25 216.54 186.69 183.98 197.31 183.65

Meangain/ 4.78 5.41 4.67 4.60 4.93 4.59

monthb

Summergains1st -3.67 (2.49) -3.11 (3.46) 15.38 (3.05) -4.89 (1.59) -8.22 (2.22) 7.18 (2.66)2nd -1.70 (2.26) 4.18 (3.60) 9.22 (4.00) -5.18 (1.67) -.50 (2.50) 3.14 (2.74)3rd 2.74 (2.21) 3.68 (3.82) 14.51 (4.33) -1.25 (1.57) 6.15 (2.74) 2.28 (2.78)4th 2.89 (2.56) 2.34 (3.21) 13.38 (4.42) 5.50 (1.59) 4.31 (2.67) 6.30 (3.39)Totalgain .26 7.09 52.49 -5.82 1.74 18.90

Meangain/ .02 .44 3.28 -.36 .11 1.18

monthb

Note.Standardrrors rereportednparentheses.CAT,Californiachievementest.a

Samplesize rangesfor seasonalgains:Low SES N= 264-339; Mid SESN= 113-162; High SES N= 85-150.bBased on 8 monthsof winter(Oct-May),4 months of summer June-Sept).

Children, t is reassuring o see, learn more and domain losses predominateand are especiallylearnmoreefficientlywhentheyare nschool.Sec- largeover the first wo summers.Thismeans that

ond,verbalgainsover the summergenerallyex- lower SES children generally start the new

ceedquantitative ains, suggesting hat,at leastin school year aboutwhere they had been the pre-the early grades, quantitative earning is more vious springor even behindtheirspring evels of

school-dependent hanverbal learning.Cooper performance.

et al.(1996)reachasimilar onclusion.Third, on- UpperSES children's cores,on the otherhand,sistentwiththe dea that heperiodof earlyschool- improveover the summermonths lowerpanel) n

ing is foundationalEntwisle& Alexander,1989, both domains,which means thatthey begin the1993), school-year gains generallyarelarger he new school year aheadof where they had been

first woyearsthan ater. thepreviousspring.And the summerdifferences

Theseinsightsalone would be amplereasonto comparingowerandupperSES youtharelarge.examinelearningon a seasonalbasis;however, This is easiest to see when the year-by-yeardif-

ourpresent nterest centers on a fourth ssue in- ferences are summedacrossyears(i.e., the"total

formedby Table 2:howCATgainsdifferby sea- gain"entriesnthe lowerpanelof Table2). These

son accordingto children'sfamily background. totalsfavorchildren romupperSES households

School-yeargains yearby yearare not very dif- by sizable margins,with the differences largeferentacross SES levels (upperpanel).Indeed, n enoughto account or almost the entireCATgap

theearlyyearsthecomparisons ometimes favor increase hatemergesoverthe first5 yearsof thelower andmiddleSES childrenover upper.The panel'sschooling.Comparehe scalescorediffer-

summerpatterns strikinglydifferent hough,es- ences from springof 1983 to springof 1987 in

pecially across the SES extremes.In the verbal Table 1 againstthe cumulativesummer differ-

area, then, lower SES youth essentially tread ences in Table2." At the endof 5 years,theper-water,some summersgainingafew points,some formanceof lower SES children ags farbehind,summers osing a few, while in the quantitative but Table2 clarifieswhatis at issue. Duringthe

177




schoolyearthese childrenkeep up,buttheybeginfirstgradealreadybehindandduring he summer

months,when they are not in school, their skills

registerverylittleimprovement.These descriptivecomparisonsthus seem to

implicate helong summerbreakas the sourceoflower SES children's achievementshortfalldur-

ing theprimarygrades.Theanalysesreported n

the next sectiontest whether the summer short-

fall sufferedby lower SES childrenrelative to

upper s statisticallyreliable.

Modeling the Time Line of Cognitive Growth

on a Seasonal Basis

Analysis plan. Hierarchical linear modeling

(HLM) s used to estimatewithin-person chieve-ment growth models (Bryk, Raudenbush,and

Congdon, 1996; Bryk and Raudenbush, 1992).12

Person-specificgrowthparameters re estimated

at the within-person, r Level 1, stage.These re-

sultsdefine the time line of CATgainsacrossthe

entiresample-essentially the averageortypical

pattern.Thebetween-person,or Level 2, param-etersevaluatevariabilityn theLevel 1parametersinrelationo traits hatvaryacrosspersons.So, for

example,do school-yearand summerCATgainsdifferfor lowerandhigherSESyouth?Ourmajorinterest centers on family SES, but effects of

race/ethnicityand gender are also controlled at

Level 2 to guardagainstconfounding.Two variantsof the model are evaluated.Both

specifications fit three growth parameters at

Level 1: a baseline ntercept erm;alineargrowthterm;and a quadraticermto allow for curvature

in the growth trajectory the rate of gain is ex-

pectedto decline over ime,e.g., Schneider,1980;Stephens,1956). The two models differ in how

adjustmentso theschool-yearpattern f achieve-

mentgainsare estimated.The first mplementsa

single summer adjustment erm to gauge how

summergainsdiffer fromwintergains on aver-

age. However,because the summergain differ-

entialby family SES level seems to vary across

years (see Table 2), the second growth model

estimates a separate adjustmentterm for each

summer.The datarequirements or estimating he sec-

ond specificationof summer deflections are se-

vere,however.At Level 1,person-specific rowth

trajectories re derived.Withseparate odingfor

each summer, hese models fit seven parameters

(intercept, rowth,growthsquared, ndfoursum-

178

meradjustmenterms)to a maximumof 10 data

points(fall andspringCAT scores over 5 years).Thisapproacheshe limit of the nformation vail-

able,andHLMscreensoutmanycases becauseof

strategic aps n thetestingrecord.Numbers ange

from 448 to 458 when fourseparate ummerad-

justmentparameters re estimatedversus 646 to

656 when a single, averagesummeradjustmentis estimated. Notwithstanding such technical

concerns, attritionbias owing to missing CAT

dataseemsminor(see Appendix),and allmodels

converged.Maximum ikelihood estimatesof parameters

in the Level 1 andLevel 2 equations or the four

summer ermmodels areas follows:13

Level 1 Model: Within-PersonGrowth

Trajectories

Yti = Pi + PliSlti + 2iS2ti + 3iS3ti + 4iS4ti

+ P5T5ti+ 6iT2i+ ?ti,

where

Ytis CATlevel at time t for student ,

SltiS4tiare summeradjustmentdummyvari-

ables,

Ttis time, coded at 0 for fall 1982 and incre-

mentedby unit steps thereafter or each testingoccasion(springandfall),

T, is time squared o allow fornonlinearityn

the growthtrajectory,

P0i s the expected baseline CAT value for

child i,

pli... p4i are summer adjustments to the

school-year earningrate for student ,

P5i and p6i map the learning rate during the

school year,

?ti is an estimate of person-level disturbance.

Level2 Model: Between-Person

BackgroundContingencies14

3oi =Too + TcoiSES, TC02RACE/

+n;o3SEX, + Voi

P-i ...iP4= .10.. T740 + T-11 ... 741SESi

+712 ... t42RACE,

+713 ... 7143SEXi + V...4i



Schools, Achievement,andInequality'

35i = t50 + 7i51SESi+ t52RACE,

+7153SEXi + V5i

p6i=

T60 + V6i

where

o0i,Pli ... 4i, I5i, 36i reperson-levelparam-eterestimatesfromthe Level 1 model,

it'sareLevel 2 parameter stimates(interceptand slopes), and Voi .. . v6i are Level 2 random

effects.

Growth models with a single summer adjustment.

Table3reports stimates orgrowthcurvemodelsthat ncludeasingle,average, ummer-adjustmentterm.Resultsfor CAT-V arereportedon the left

side of the table,for CAT-Mon the rightside.15

The firstLevel 1 equation(columnI) fits linear

and quadraticgrowth terms,with time set to 0

at baseline (fall 1982, or fall of firstgrade)and

incrementing one unit per subsequent testingoccasion.

Children'sCAT averagesat the start of first

gradeare n thevicinityof 300 scalepoints nbothdomains.Both baseline means are significantlydifferentrom0, as areall fourgrowth erms,with

coefficientestimates orthequadraticermsnega-

tivelysigned(-.96 forCAT-V; .47 forCAT-M).This indicatesthat the rateof growthslows over

time,asexpected.Thesedetailsof thegeneral ime

line of achievementgrowthall areunexceptional.

However,the specification n column I does not

adjust or summerdifferences,whichmeans that

theparameter stimatesdescribe hegrowthpathperiodby period N= 10)withoutregard opossi-ble differencesby season.

The second column of results evaluates

between-person variability in these growth

parametersn relationto family SES (heremea-

suredusingthefull scale metric),sex (withgirlscoded "1") and race/ethnicity (with African

Americanscoded"1").Becauseof thewayLevel

1andLevel 2 parameterstimatesare"linked"n

the HLMframework, he Level 1 coefficientsincolumn IIareanalogous o interceptestimates n

OLS regression-they represent the expectedvalueof thedependentvariable or thegroupde-

finedby the intersectionof Level 2 predictorsat

score0. In thepresent nstance,thatcorrespondsto White males with average family SES

scores-recall that the SES scores are standard-

ized. Theinterceptestimateof 292.11 in column

II of the CAT-Vresultsthus s theexpectedscore

of suchyoungstersat baseline(fallof firstgrade).The associatedLevel 2 coefficients arenet incre-

mentsor decrements o thatlevel of test perfor-mance at school entry associatedwith, respec-

tively, contrastingvalues of SES, race/ethnicity,andsex. ForCAT-V, effects of family SES and

sex aresignificant.WithSES scaledin SD units,its associated coefficient in Table 3 indicates a

16.25-pointCAT-Vdifferenceat thestartof first

grade orchildren1 SD apartn familySES. The

SD of the CAT-Vdistributionat baselineis 40.8

points, so 16.25 points corresponds to about

.40 SD.16 The difference, as expected, favorschildren n upperSES households.The CAT-V

results also show girls' scores slightly above

boys' at baseline.

TheLevel 2 SES difference s much the same

for CAT-Mperformanceas for CAT-V, exceptthat the CAT-Mgenderdifference s not signifi-cant and the racedifference s. AfricanAmerican

children n thissamplestartschool a littlebehind

their White counterpartsn the quantitativedo-

main.The4.8pointdifference,net of SESandsex,correspondsoroughly 15CAT-MSD,about he

samemagnitudeas theboy-girldifference n the

verbaldomain.

The SES differences are the largest of these

Level 2 effects on baseline performance.The

growth ermsshowwhathappens rom thatpointforward.Because the trend s nonlinear, he two

terms that describe the growth pathhave to be

evaluatedointly.However,becausepreliminary

analysesrevealed no Level 2 effects on the de-celerationparameters, n Table 3 (and later, in

Table4) only the "main-effect" erms arespeci-fied as contingenton Level 2 influences. Under

thatframework, ower SES youths' rate of gainover theelementaryyears agsbehindupperSES

youths' in both domains, African American

youths' ratelags behindWhite youths' in both

domains,and,boys' rate lags behindgirls', all

significantat the .01 level.

In theseresults, hen,lower SESyouthfall far-therback overtime,as seenby plotting averages

(Table 1).However,these estimatesdo notallow

for seasonal differences in growth trajectories.Whether herearesuchdifferences,andhowtheyaffect growth patternsacross social lines, is as-

sessed in columnsIIIandIV of Table 3.

179



TABLE 3

GrowthCurveAnalysisEstimatedWitha Single AverageSummerAdjustment

CAT-V (Reading)

Model I Model II Model III Model IV Model I

Intercept 293.63 (1.45) 292.11 (2.39) 286.84 (1.49) 285.70 (2.45) 302.40 (1.19) 3

SES 16.25 (1.63) 17.56 (1.67)Race -1.26 (2.59) -1.34 (2.66)

Sex 6.05 (2.53) 5.57 (2.60)Lineargrowthterm 29.56 (0.71) 29.90 (0.79) 48.17 (1.06) 47.34 (1.68) 23.36 (0.43)

SES 3.11 (0.33) -.34 (1.08)Race -1.98 (0.51) -1.44 (1.69)

Sex 1.72 (0.50) 2.91 (1.64)

Quadratic rowthterm -.96 (0.07) -.94 (0.07) -.93 (0.07) -.91 (0.07) -.47 (0.04)Summeradjustment -38.93 (1.62) -36.38 (3.03)

SES 7.11 (2.10)Race -1.25 (3.29)Sex -2.44 (3.20)

Note. Standard rrorsare shown in parentheses.Bolded entriesaresignificantat the .05 level. Within-person,Level 1 growthcurveestimatesare talicized.Coefficients fo

fects. Forthe CAT-V analyses,Ns rangefrom646 to 665; for the CAT-Manalyses,Ns rangefrom656 to 678.



Schools, Achievement,andInequalit'

ColumnIII addsa single summeradjustmentterm to the general time trend to representan

averageeffectacross hefoursummers ubsumed

underthe model's 5-year time frame.The sum-

meradjustment oefficientsfor bothCAT-Vand

CAT-Marenegativelysignedandhighlysignif-icant,but smallerthan the correspondinginear

growth coefficients. The descriptivepattern n

Table2 suggestedthatgrowthslows duringthe

summerrelativeto school-year growth,and the

resultshereareconsistentwith thispattern.How-

ever, because the summercoefficients are ad-

justments to the per period growth that would

otherwisebe expectedover the intervalat issue,the summerdeflection coefficientsin Table3 do

notrepresent ummerdrop-offorgainperse. Tocomparewinterandsummergainspreciselyre-

quiressome additionalcalculations.

"Time,"as construedin this analysis, is di-

vided into incrementsin which one unit corre-

sponds to one season, fall to spring, spring to

fall. To see themodel's implicationsin terms of

actualsummergrowth(orloss), we firstneed to

derive the growth implied at time "t" by the

general growth specification (i.e., linear and

quadratic erms)andthen correctthat estimate

for the summer-winter differential. The first

partof the calculation is accomplishedby tak-

ing the first derivative of the equationimplied

by column III at time t. Evaluatingthe CAT-V

equationat t= 2, forexample, yields anestimate

of (instantaneous)growth n the fall of year2 of

44.45 CAT-V points. Adjustedfor the averagesummer deflection (-38.93, from Table 3), the

average expected gain for the first summeris

5.52 CAT-V points.17 Similar calculations

could be done throughout,and in general themodel indicatesa slower rate of cognitive gainover the summer months compared with the

school-yearrateof gain.ColumnsIV of Table 2 add Level 2 predictors

to the model to test whetherthe within-personLevel 1 interceptestimates,growth-termparam-eters, and summeradjustmentcoefficientsjustreviewed vary significantlyin relation to SES,

race/ethnicity,and sex. Adding these terms ad-

dressesourmainsubstantive oncern:TheLevel2effects in column II establish that the SES gapwidens over time, but does this happen to the

samedegreesummerand winter?

SeveralchangesareevidentcomparingLevel2

effects acrosscolumnsII and IV. The race coeffi-

cient in the CAT-V growthtermresultsis non-

significant,orexample,as is thesex coefficient n

the CAT-Mresults.However, consequencesfor

the family socioeconomicstatuseffect standout

especially:whereaspreviously he SES effect on

growthwas largein bothdomains, n columnIV

both SES effects arenonsignificantandtriviallysmall.The frameof referencen the two instances

is different,hough,andthis is fundamentalo the

interpretation:hegrowthparametersncolumnII

describethepatternof growthacrossall periods;in columnIV, with the summeradjustmenterm

included n themodel,thegrowth ermspertaino

school-yeargrowth specifically.Socioeconomic

statusthusapparentlyhas no bearingon achieve-

mentgainsduring heschoolyear.Not soforsum-

mergains-the Level2 SES effect on the summeradjustmentoefficient s highly significantnboth

the CAT-V andthe CAT-Mresults(see column

IV). Andbothcoefficientsarepositivelysigned,whichmeans hat henegativesummeradjustmentis attenuatedor upperSES childrenrelative to

lower SES children.

Theimplicationsof thisadjustment re easiest

to seewhenexactsummergainsarecalculated,as

above. As an example, for childrenscoringone

standarddeviation below the samplewideSESmean,thepredictedCAT-Vchangeoverthefirst

summeris +.55 points;for children at the SES

mean, the predictedfirst-summergain is +7.32

points; and for children one standarddeviation

above theSESmean,thepredictedgainis +14.09

CAT-Vpoints.18As mentioned,race andgenderdifferences n-

volving school-year growth are also attenuated

when the summeradjustments implemented, l-

thoughAfricanAmericans' chool-yeargainsstill

lagbehindWhites'school-yeargainson theCAT-

M, and there s aborderline ignificantdifference

favoringgirlsontheCAT-V. But the seasonalad-

justmenthas itsgreatest ffecton the size andpat-

terningof SESdifferences,with achievementdis-

parities largeraltogetheracross socioeconomic

lines than across racial/ethnicand genderlines.

Whenthemetriccoefficientsreportedn Table3

arestandardizedn overallverbalgrowth o com-

pareeffect sizes across Level 2 predictors,the

effect coefficients n columnII become:SES, .32;race, .23; sex, .17. However,becausesignificantSES differencesemerge only during hesummer,

theymustbe traced o sourcesoutsideschool.

Growth models with separate summeradjust-ments. Table 4 reportsresults for the growth

181




TABLE 4

GrowthCurveAnalysis WithFour SeparateSummerAdjustments

CAT-V Reading) CAT-MMath)

Model I Model II Model I ModelII

Intercept 283.23 (1.54) 282.63 (2.55) 293.10 (1.20) 297.42 (1.92)SES 16.58 (1.75) 16.86 (1.33)Race -.82 (2.78) -4.26 (2.12)Sex 3.77 (2.72) -1.62 (2.08)

Lineargrowthterm 57.22 (1.51) 56.03 (1.96) 49.24 (0.96) 49.85 (1.31)SES -.62 (1.06) -.51 (0.75)Race -.87 (1.66) -2.04 (1.18)Sex 3.16 (1.61) .97 (1.15)

Quadratic rowthterm -2.01 (0.14) -2.01 (0.14) -1.35 (0.09) -1.35 (0.09)1stSummer -48.80 (2.50) -47.79 (3.99) -47.70 (1.76) -47.12 (2.81)

SES 11.04 (2.58) 4.48 (1.82)

Race -3.32 (4.10) -.01 (2.89)Sex 2.90 (3.99) -.33 (2.83)

2nd Summer -47.96 (2.10) -38.89 (3.83) -43.74 (1.43) -43.40 (2.63)SES 5.90 (2.62) 6.94 (1.81)Race -7.72 (4.12) 1.55 (2.85)Sex -7.70 (4.00) -.85 (2.79)

3rdSummer -31.79 (2.13) -33.10 (3.95) -33.55 (1.51) -33.32 (2.76)SES 7.95 (2.68) 3.60 (1.86)Race 2.94 (4.21) -.42 (2.92)Sex 0.00 (4.09) .93 (2.85)

4th Summer -20.14 (2.52) -15.66 (4.26) -22.30 (1.79) -25.63 (2.97)

SES 5.90 (2.74) 3.04 (1.89)Race -1.19 (4.25) 2.83 (2.92)Sex -5.98 (4.11) 4.19 (2.84)

Note.Standardrrors reshownnparentheses.Bolded ntries re ignificanttthe 05 evel.Within-person,evel1growthurve stimates re talicized.CoefficientsorSES,race,and sex arebetween-person,Level 2 effects. ForCAT-Vanalysis,N= 448; forCAT-M,N= 458.

model specification that implements separatesummeradjustments or each summer.Despitethereducedsamplesize because of missingdata

when summersare indexedindividually,the re-sults that arecomparableacrossTables 3 and 4aresimilar(e.g., school-yearCAT gains still donotrespond o familySESin eitherdomain).

And whatof the moredetailedspecificationofthe summeradjustmentcoefficients? All eightsummeradjustment ffects are significant(withthe estimates for summers 1 and 2 largerthanthose forsummers3 and4 inbothdomains),andfor six of the eight, the Level 2 effect of family

SES is also significant.These summeradjust-ments all favor upperSES children.However,the evidence thatsummergains areconditionalon SES is morecompellingforthe firsttwo sum-mersthan or the lasttwo, atleast forquantitativeachievement.These results husgive limitedsup-portfor the idea that the first2 yearsof elemen-

182

taryschool aredistinctive,butstrongsupport ordifferential summerlearningover the primarygradesas thescaffolding hatsupportsdisparitiesin school achievementacross social lines. LowerSESyouthstartout behind(i.e., the baselinedif-ferences are significant)and duringthe school

year they keep up, but duringthe summerperi-ods theirgains fall short of those registered byupperSES youth. These details of the seasonal

patterningof disparities n achievement n read-

ing and math all accordwiththedescriptivepat-ternseen earlier,but they arespecific to familysocioeconomic level: none of the summer ad-

justmentcoefficients for sex or race/ethnicitysfully significantundereitherspecification.

Discussion

The seasonalpatternof learning,documented

here in Baltimore,but also at the national level

(e.g., Heyns, 1987;Karweit,Ricciuti,& Thomp-



Schools,Achievement,andInequality

son, 1994) andin otherlocalities, includingAt-

lanta Heyns,1978),NewHaven Mumane,1975),andTexas(O'Brien,1998),undercuts omelong-

standingbut mistakendeasaboutschools andso-

cialinequality:hatschoolsare neffectualandun-

abletoequalizeeducational pportunity,rworsestill that they actively handicapdisadvantagedchildren.The "ineffectual" otiontraces o a mis-

readingof the Colemanreport(Coleman,et al.,

1966)that "schoolsmake no difference; amilies

make the difference"(quote attributedo D. P.

Moynihan n Hodgson, 1973), and has been re-

inforced inceby overstated laimsthatschoolre-

sources have little bearingon achievementout-

comes (e.g., see, on the one hand, Hanushek,

1994 and 1997 against,on theother,Finn, 1998;Hedges,Laine,& Greenwald,1994;Wenglinsky,

1997),while the"complicity" rgumentindssup-

port n glaring undingdisparitiesacrosswealthyandpoorcommunities e.g., Kozol, 1991).

Families and communities ndeed shapechil-

dren's academic development. Their power is

evident in the large learningdifferences across

family SES levels seen in the present results

for the summermonths;but schooling, too, is a

powerfulforcebehindchildren'sacademicdevel-opment. Certainlymanydisadvantaged hildren

areheld backby inequitiesin the distributionof

school resourcesand associated"opportunitiesto learn" (e.g., Dougherty, 1996; Murphy &

Hallinger,1989;Oakes,Gamoran,&Page,1992),but this piecemeal approachmisses schooling'smoregeneralized,salutaryeffects. Thenearpar-

ity of school-year earningacrosssocial lines es-

tablishes hat schoolsplayanimportant ompen-

satory ole,carrying longdisadvantagedhildrenat a pace close to that of their more advantagedclassmates.

Schools do matter,andthey matterthe most

when support for academic learning outside

school is weak. School-basedpublic resources

do notcompletelyoffset themanyandvariedad-

vantagesthataccrueto childrenof privilegebyvirtue of privatefamilyresourcesoutsideschool

(e.g., Coleman, 1990). It is a stretch o thinkthat

theywould,but thisis theimplicitstandardwhentest results in Baltimore's schools are found

wantingagainstnationalnorms.

The powerful role of schools in fosteringachievement of all children is one lesson in-

formedby a seasonalperspectiveon learning.A

second is that disadvantagedchildren, on the

whole, arecapable earners.Theykeepup duringthe school year,but before they startfirstgradeand in summers between grades the out-of-

school resourcesavailableto themarenot suffi-

cient to supporttheir achievement. When our

study groupstartedschool theirpre-readingand

pre-math kills reflected heir unevenfamily sit-

uations,andthese initial differenceswere mag-nifiedacrosstheprimarygradesbecauseof sum-

mer setback despite the equalizing effect of their

school experiences.

No doubt,material esources,amilyprocesses,and affectivecontext all are implicated n these

summerdifferences see Entwisle,Alexander,&

Olson, 1997, 2000). If theproblem racesto dis-

advantaged children's out-of-school resource

shortfallalong these lines, as appearsthe case,thenextendingthe school's reachthroughyear-roundschooling(Gandara& Fish, 1994),home-

schoolpartnershipshatcontinuewhen school is

closed (Epstein, 1991, 1992), and high-qualitysummerprograms Cooper,Charlton,Valentine,& Muhlenbruck,2000) would seem promisingavenues.Indeed,all hold promise,but no single

programor intervention s

likelyto

provesuffi-

cient.Accordingly,we concludebysketchingour

thoughtson what a morecomprehensiveagenda

mightentail.

Prevention,as a rule, is easier thanremedia-

tion. Accordingly, minimizingthe achievement

gap at the point of school entry should be the

firstpriority.We know thatgood preschoolscan

improve disadvantagedchildren's later school

success-not just in test performance,but also

in reductionof retentionrisk,assignment o spe-cial education, and even high school dropout

(Ramey,Campbell,& Blair, 1998;Schweinhart

& Weikart, 1998; Temple, Reynolds, & Ou,

2000).19At present,though,disadvantaged hil-

drenarethe ones least likely to attendpreschool

(NCES, 1998).

Disadvantagedchildren also need to attend

high-quality, full-day kindergartenprograms.

Today kindergartens nearlyuniversal-on the

orderof 98%of childrenattend,20with the ma-jority in full-day programs(59% in 1998, e.g.,U.S. Bureauof the Census, 1999b).And owingto targeted ederal and statesupplemental und-

ing (e.g., Title I), lower income children,not

upper,moreoftenattend ull-dayprograms e.g.,

Rothenberg,1995; U.S. Bureauof the Census,

183




1999b).The situation was quitedifferentin the

early eighties, though,whentheBSS cohortwas

kindergarten ge.Thenpart-timeprogramswere

thenorm(U.S. Census, 1999a).21Tenpercentof

BSS first-graders ad no kindergarten ndmore

of those fromthepoorestfamiliesattendedhalf-

dayprograms.Does this matter? Our evidence certainly

suggests that it does. The benefits of full-dayas

compared to half-day kindergartensfor BSS

children are considerable. With family back-

ground and many other variables allowed for,firstgraderswho attended ull-daykindergartenwere absent fewer days in firstgrade,were less

oftenretained,and earnedhighermarksandtest

scores in first grade than half-day attendees

(Entwisle,Alexander,Cadigan,& Pallas, 1987;see also Cryan, Sheehan, Weichel, & Bandy-Hedden, 1992; Karweit, 1989).

Preschool and kindergartencan reduce the

achievementgapassociatedwithSES when chil-

dren startfirstgrade,but to help them keep uplater will requireextraresourcesandenrichment

experiences, often of the sort thatmiddle class

parentsroutinelyprovidefortheirchildren.This

leads us to supportsummer school or extended

year programs ustfor poor children as well as

supplemental chool-yearservicesfor these chil-

drenduring heearly grades.The Chicago LongitudinalStudy shows that

intensesupplementation f learningresources n

theearlygradeshelps poorchildrenmaintain he

academic edge they get from attendinga good

preschooland that these benefitsthen continue

into theuppergrades(Reynolds,1994;Reynolds& Temple, 1998;Temple, Reynolds,& Miedel,

1998). It is importanthat, n the Chicagostudy,neitherpreschoolalone nor school-yearsupple-mentationalone proved sufficient.Rather,theyare most effective in combination,one buildingon the other.

TheChicago ntervention s not a summerpro-

gram,but in light of the presentresultsit seems

reasonablethat summer enrichmentprograms

specifically for disadvantagedstudents beforeandafterfirstgradewould confersimilar, f not

greater,benefits. But how shouldthese summer

programsbe designed?Certainlynot like sum-

merprogramsof thepast,whichfunctionedso asto magnify,not shrink,disparitiesacrosssocio-

economic lines (e.g., Cooper, Charlton,Valen-

tine, & Muhlenbruck,2000; Entwisle, Alexan-

der,& Olson, 2000; Heyns, 1978).A strongcurriculumcomes first, focused on

reading, t being the foundation or all that fol-

lows. Heyns(1978)foundthat hesinglesummer

activitymost stronglyandconsistentlyrelated o

summerearnings reading,whethermeasuredbythe numberof booksread,by the timespentread-

ing, orby theregularity f libraryusage.Reading

during he summer ncreased he vocabulary est

scores of childrenand had a substantial ffect on

achievement argely ndependent f familyback-

ground.Likewise, BSS children's use of the li-

braryn summer,

specially akingoutbooks,

pre-dictedsummergains n achievement.Educational

policies that increaseaccess to books, perhaps

through ncreased ibraryservices,stand to have

animportantmpacton achievement,particularlyfor less advantagedhildren.

But summerschools shouldnot be limitedto

traditionalacademics. Summerprogramsso far

have not addressed the unique contribution that

parentsandneighborhoodsmakewhen school is

cut off. We found thatbetteroff children n theBSS moreoften wenttocityandstateparks, airs,or carnivalsandtookdayorovernight rips.Theyalso took swimming,dance, andmusic lessons;visited ocalparks,museums, ciencecenters,and

zoos; and more often went to the library n sum-

mer. And childrenwho lived in betterneighbor-hoods alsoplayedmoreorganizedsports n sum-

mer.Sports ike soccer,fieldhockey,and softball

require hildren olearncomplicated ulesystems

and takemultipleroles. They also can stimulateinterestntopicslikebattingpercentages,oddsof

winningorlosing,andthelike.22These activities

surelyare not the only ones thatmatter,buttheyall support earningoutside the traditional lass-

roomsetting,and thatgives childrenanedge.

Buildingon suchleads,probably ummerpro-

gramsfordisadvantagedhildrenshouldsupple-ment academics with a heavy dose of physical

activityandenrichment xperiences.Suchanex-

panded agendais important or anotherreasonalso:to make summer choolfun.Learningworks

best when children feel they arepartners n the

enterprise.Torealizetheirpotential, ummerpro-

gramsshouldbe engagingandnon-punitive.For

manydisadvantaged,poor-performinghildren,

184




"school" s synonymouswith"failure." or them

school is not fun, it is punishing.This may be a

particularproblemin mandatoryprogramsfor

children who fall short of promotionguidelines

(e.g., Bracey, 2000; White & Johnston,1999).

Puttingapositivespinon thatwill not beeasy,butit could well be key.

Thesesuggestionshighlight he need to supple-ment"regular chooling" hrough long-term, o-

ordinatedprogramof interventionsembodying"bestpractice"principles.For such interventions

to counteract he powerful out-of-school forces

thatkeep too many disadvantaged hildren rom

achievingat the level of theirpotential, heywill

have to betargeted t low-incomechildren pecif-

ically (e.g., universalpreschoolor summersup-

plementationorallstudentswould notbe consis-

tent with thismodel;see Entwisle, Alexander,&

Olson,2000).Suchprogramswillneedtobeginas

early as age 3 and continue thereafter n a sus-

tainedway.And eventhen,"reasonablerogress"

oughtto be therealisticexpectation.We say this because even the best of today's

remedies all fall shortof achieving"successfor

all"(e.g., Farkas,Fischer, Dosher,

&Vicknair,1998; Pinnell,Lyons, DeFord,Bryk, & Seltzer,

1994;Ross,Smith,Casey,&Slavin,1995).There

are some children,andin high-poverty settings

perhapsmany,whose academicproblemsarenot

redressedby ourcurrent epertoire f well-crafted

programs,and to helpthemprobablywill requireeven morefar-reaching eforms.Onesthatbreak

the strangleholdof the clock andcalendar e.g.,Cuban, 1989; Tyack & Cuban, 1995; Tyack &

Tobin, 1994) may merit special attention. TheNational EducationCommission on Time and

Learning 1994, p. 7) putsit thisway:"Decadesof schoolimprovement fforts have

founderedon a fundamentaldesignflaw,the as-

sumptionthatlearningcan be doled out by the

clock anddefinedby thecalendar ... Some stu-

dents takethreeto six timeslongerthanothersto

learnthesamething.Yet studentsarecaught n a

timetrap-processed on an assemblyline to the

minute.Ourusage of time virtuallyassures thefailureof manystudents."

The challenge-a dauntingone-is to build

more flexibility into the system and to put that

added lexibilityto gooduse. Butdespitepovertyandfamily disruption,t is importantorecognize

thatyoung children'sabilityto learnduringthe

school yearseems little impairedby scarce fam-

ily resources.Recognizing the efficacy of ele-

mentary chools nlevelingtheplaying ield s yetanother trategy orclosingthe achievementgap

between rich andpoor. Most press coverage ofAmericaneducationtoday emphasizes the sys-tem'sfailures,especiallywithrespect o themost

disadvantagedtudents.Missed in thesereports s

theextentto which schoolsalreadyhelpmakeupfordeficitsin poorchildren'sbackgrounds.

Recognitionof thepowerof schoolsto makea

differencein the lives of poor studentsneeds to

be coupled with efforts to involve parentsand

communities n the schoolingprocessso thatall

parents,notjust middle-classparents,are active

collaboratorsn the education of their children.

Thephysicalpossessionsof betteroff families-

computers,booksand the like-may be of some

importance n producing he summeradvantage,butprobablymoreimportants thatparentsview

themselves as partners n the learning processandpossessthepsychologicalresources hatsup-

port learning.Parentsalso contribute o the am-

bience of theneighborhood,

fonly by selectingthemselves ntogoodonesandavoidingbadones.

This lackofresources nfamilyandneighborhood

poses a double burden for poor children.Pre-

schoolandsummerprograms, roperly rganized,canhelptopotentiate conomicallydisadvantaged

parents nd heirneighborhoodsnsupport f chil-

dren's academicdevelopment.

Notes

This is a revisedversionof a paperpreparedor"Summer earningndthe AchievementGap:FirstNationalConference,"uly17-18,2000,Baltimore,MD,anearlier ersion f whichwaspresentedtthe1998AnnualMeeting f theAmerican ssociationorthe Advancementf Science,February2-17,Phila-

delphia, A.WethankMikeSeltzer orhelp nwork-

ing throughetails f theHLManalysis.SeealsoPhillips,Crouse, ndRalph,1998.

2Likewise,heBlack-Whiteap n achievementn-

creasesromheelementaryradeshroughigh chool

(Phillipstal.,1998).3In1996 U.S.DepartmentfEducation,999)al-

most 10%of all school-age hildren ttendedum-mer chool,ncluding.5%ofchildrennGrades -7.

Accordingo a recent urveyBorman, 001), hena-tion's 100largestschooldistrictsall offersummer

185




programs.Ninety-two percentprovide remedial in-

structionduring he summer,and28% of those entail

some form of mandatoryattendance(personalcom-

munication).4 Counting"studies" s complicated n quantitative

literaturereviews. The two BSS paperscovered byCooperet al. (1996) use the same datasourceandso

constitute one "study"for their purposes, whereas

Heyns's two papersuse differentdatasourcesand so

constitute two studies. In fact, the data analyzed in

Heyns's 1987report,heSustainingEffectsStudydata,havebeenanalyzed roma seasonalperspectiveby sev-

eralresearchers e.g., Carter,1984; Ginsburg,Baker,

Sweet,&Rosenthal,1981;Klibanoff&Haggart,1981;

Bryk & Raudenbusch,1988). Cooperet. al.'s (1996)

meta-analysisuses 10 effect sizes from one of these

reports (Klibanoff & Haggart, 1981) to reflect the

SustainingEffects Studyevidence on the matter.5Karweit, Ricciuti, and Thompson (1994), also

analyzingnationaldata(i.e., theProspectsfirstgrade

cohort), find much the same duringfirst grade and

the summerbetween first and second grade. How-

ever, in second grade, school-year gains favor chil-

drenin low-poverty schools.

6 Thestudyby Phillips,Crouse,andRalph 1998) is

broader n scope, covering Black-Whitedifferences

throughGrades1 to 12, butit is synthetic, .e., draws

togetherdatafromdifferentsources.7 For these groups,datacoverage is good. In both

domains,more thanhalf havecompleteCATdata,and

justunder hreequarters73.5%on theCAT-V;73.6%

on theCAT-M)have at least 8 of the 10 scores.8 A given achievementgap,say20 points,will seem

more impressiveif scores rangeover a narrowband

(e.g., from 0 to 100) than if they rangeover a broad

band(e.g., 0 to 1000). As withtestingdatagenerally,CAT variability n the BSS increaseswith children's

age, such thata constantpoint gap implies a smallerrelative difference.9Variations of Table 2 have been reportedprevi-

ously (Alexander&Entwisle,1996a, 1996b;Entwisle,

Alexander,& Olson, 1997).Thisversionincorporatesrecentdataenhancements,one being the inclusion of

achievementdata or somechildrenwhotransferredo

schools outsidethe BCPS.

10Gains per monthare only approximate.Testingwas donein OctoberandMay,butexact dates arenot

known. The 8-monthand 4-month ntervalsusedthus

lack precision,butthe consequencesof this probablyareconservative e.g., someschool-yeargainis "cred-

ited"to the summer,so raw summergains andgains

permonthlikely err on thehigh side).

1Muchthe same is observed when the exercise is

repeatedon a full-panel (i.e., listwise-data-present)basis.

12 The only other strictly comparableanalysis of

which we areaware s didactic:BrykandRaudenbush

(1988, 1992) model seasonaleffects on achievementgrowth to illustrate within-person applications of

HLM. An unpublished aperby Karweit,Ricciuti,and

Thompson 1994)reports rowthcurveresultsoverone

summer and two wintersusing a repeated-measuresANOVAapproachhat s similar n intent.

13The specifications for the single summer-

adjustmentmodel are the same except thatonly one

summer-adjustmentarameters estimatedat Level 1.

Accordingly,at Level2, between-personffects arees-

timated or four rather han seven Level 1 parameters.14 In the Level 2 specification,the Level 1 param-

etersthatrepresent urvature rnonlinearityn therate

of achievementgains (i.e., p6i)are not allowed to varyin relationto studentSES, race, andsex. Preliminary

analysesdetectedno suchconditionalitynvolvingthe

deceleration erm.15A baseline model that fits just the grandmean

is used to partitionthe variance in test scores into

between-personand within-personcomponents.For

CAT-V,25.4%of the variance s between-person;or

CAT-M,22.6%of the variance sbetween-person.16 A 1-SD difference in family SES corresponds,

roughly,to thedifferencebetweenhaving high school

dropoutparentsandhavingparentswithsomecollege.17 By way of comparison,the actualdrop-off ob-

servedfor the firstsummer s 1.12 pointsforthe sam-

ple as a whole. The estimated effect is much larger,butthe estimate derives fromanaveragesummerad-

justmentacross all summersand so sacrifices preci-sion.

18 Recall that the summeradjustmentn the model

fromwhichtheseestimatesarederived s constrainedto be the same all four summers.That constraint s re-

laxed in Table 4.19For a generaloverview, see Barett, 1995.20 In 1991, though,4% of firstand second graders

whose parents were high school dropouts had not

attendedkindergartenversus 1%or 2% for all other

educationcategories(U.S. Departmentof Education,

1992).21 And half-day programsremained the majority

into the early 1990s (e.g., Love & Logue, 1992;U.S.

Department f Education,1992).22For a discussion of the link between organized

sportsandacademicprogress, ee Entwisle,Alexander,andOlson, 1994.

186




APPENDIX

Seasonal AttritionChecks:Backgroundand OtherCharacteristicsrom First Grade or Cross-Sectional,

Restricted,and Full Panel Samples

Samplecharacteristics Cross-sectionalcoveragea Restrictedcoverageb Fullpanel coveragec

FamilySESlevel -.04/(787) -.05/(665) -.13/(368)Pooled SD [.80]Mother'syearsof education 11.67/(750) 11.72/(635) 11.60/(353)PooledSD [2.55]

Proportionow income .67/(701) .67/(627) .68/(366)Pooled SD [.47]

Proportionwo-parenthousehold .56/(754) .56/(637) .54/(355)PooledSD [.50]

ProportionAfrican American .55/(790) .57/(665) .62/(368)Pooled SD [.50]

Proportionemale .51/(790) .51/(665) .53/(368)

Pooled SD [.50]CATV, fall 1stgrade 280.62/(691) 280.71/(665) 280.74/(368)Pooled SD [40.81]CATM, fall 1stgrade 292.49/(708) 293.50/(653) 294.38/(362)PooledSD [31.94]Academicself-image, spring1stgrade 4.17/(717) 4.17(627) 4.20/(355)PooledSD [60]

Marks, all 1stgrade 2.06/(704) 2.07/(623) 2.12/(354)PooledSD [.71]

Absences, 1stgrade 13.28/(702) 13.23/(622) 13.15/(355)PooledSD [11.64]

Work habitratings,fall 1stgrade 10.03/(702) 10.08/(620) 10.25/(352)PooledSD [2.12]

Note. Samplesizes are shown in parentheses; tandarddeviationsare shownin brackets.

aAll possiblecases.

bSample coverageis cross-sectionalbut screened on CAT availability or fall of Grade1 and scores for at least two other time

points.Samplesare drawnseparately orverbal andquantitativedomains.Resultsreportedhereare for the verbalsample.The full panel sample screenson complete CAT coverage (5 wintersand4 summers),separatelyby verbal andquantitative

domains.Resultsreportedhereare for the verbalsample.

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Authors

KARL L. ALEXANDERis the JohnDewey Pro-

fessor of Sociology at The JohnsHopkinsUniversity,3400 N. CharlesStreet,Baltimore,MD 21218;e-mail:

[email protected] interests center on problems of

educationalstratificationhat canbe addressedvia or-

ganizational, ocial-psychological,and ife courseper-

spectives. The Beginning School Study (BSS) has

been his primaryresearchactivity since the projectcommencedin 1982. With Doris Entwisle and Susan

Dauber,he is revising andupdatinga monographongrade retention, On the Success of Failure: A Re-

assessmentof theEffectsof Retention n the PrimaryGrades(CambridgeUniversityPress, 1994). He also

is workingon severalprojectsthatexaminethe earlyadulttransition hrough he lens of theBSS; one proj-ect focuses on mode of high school exit.

DORIS R. ENTWISLE is professor emerita of

sociology at The JohnsHopkins University. She has

been interested ormanyyearsin theeffects of social

structure n humandevelopment n middle childhood

andadolescence.Her currentresearchconcernshowyouthin the BeginningSchool Studymanageto jug-

gle their work and school roles as theymake the tran-

sition to adulthood. She recently published a book

(with Karl L. Alexanderand Linda S. Olson) titled

Children,Schools,andInequality Westview-Perseus,

1997), which discusses the ways in which social and

190




financialdisadvantage lters he life paths hatchildren

take through elementaryschool. A formerGuggen-heim Fellow, in 1997 she receivedthe Society of Re-

search nChildDevelopmentAward orDistinguishedScientific Contributionso ChildDevelopment.

LINDA STEFFEL OLSON is a senior researchassistant n theDepartment f Sociology at TheJohns

HopkinsUniversity.Shehasbeen associatedwith the

Beginning School Study for the past 15 years. Her

interests center on the effects of social structureon

schoolingoutcomes.

Manuscript eceivedSeptember27, 1999Revision receivedNovember3, 2000

Accepted February , 2001

achievement and inequality a seasonal perspective[1]

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