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Policy, Research,and ExternalAffairs
WORKING
PAPERS
Educationand Employment
Populationand HumanResources Department TheWorldBank October1990 WPS525
School Effects on Achievement in Secondary Mathematics and Portuguese in Brazil MarlaineE. Lockheed
and BarbaraBruns
Students in Brazil's federal technical schools outperformed students in other schools in both mathematics and Portuguese. Important factors were class size (achievement was higher in larger classes), the number of hours math was taught (the more the better), the school's organizational comple;,ity, average family social class background,and the numberof hours students spent working. ThePolicy.Research. and ExternalAffairs Complex disuibutes PRE WorkingPapers todisesninatethefindings of woskin progrcss and to encourage the exchange of ideas among Bank staffand aU others interested in development issues. These papers cary the nanes of the authors, rflect only their views, and should be used and cited accordingly. The findings, interpreations, and cnclusions ars the authoras ownDThey should not be attributed to the World Bank, its Board of Directors, its management, or any of its mnenbercontries.
Policy,Research,'and ExternalAffairs
*
_S 1
tEducaion andEmployment WVPS 525
This paper - a product of the Education and Employment Division, Population and Human Resources Department - is part of a larger effort in PRE to understand differences in educational effectiveness. Copies are available free from the World Bank, 1818 H Street NW, WashingtonDC 20433. Please contact Cynthia Cristobal, room S6-033, extension 33640 (26 pages).
Lockheed and Bruns use a multilevel modeling procedure to explore (I) the percentage of variance in secondary school achievement in Brazil that could be attributed to the types of school attended, (2) differences between schools in students' achievement in mathematics and Portuguese, and (3) differences between schools in reducing achievement differences based on students' socioeconomic status. Students in federal technical schools outperformed students in general secondary, SENAI,* and teacher training schools in both mathematics and Portuguese, after holding constant for gender, age, family size, and the number of hours the student spent working. This could reflect differences in students' entry-level performance as admission to federal technical schools in Brazil is highly selective. For mathematics only, students in private schools outperforned those in public schools. To explain why students in federal technical and private schools outperformed students in
other schools, Lockheed and Bruns explored variations in their organization, quality, and social composition. Factors significantly related to average mathematics achievement were class size (achievement was higher in larger classes) and the number of hours math was taught (the more time, the higher average achievement), and the
school's averagestudentsocioeconomicstatus (family sociai O.Aass background), suggesting that student selection into the schools accounted for much of the observed difference. Factors significantly related to average achievement In Portuguese were the school's organizational complexity, the ,.verage sociocconomic status, and the average number of hours students spent working. Performance was not different for schools paying higher salaries, day schools, high-fee schools, or schools where teachers attended university.
*SENAI secondary schools are financed by the federal govcrnmerit but administered by the National Confederation of Industry (a private association of industrial employers).
The PRE Working Paper Series disseminates the findings of work under way in the Bank's Policy, Research, and Extemal AffairsComplex. Anobjectiveoftheseries is to getthcse findingsoutquickly, even if presentations are less than fullypolished. The findings, interpretations, and conclusions in these papers do not necessariiy represent official Bank policy. Produced by the PRE Dissemination Center
Table of Contents 2 ................................................................ Introduction 3 Method...................................................................... 4 Sample................................................................ 5 ........................................................... Instruments 5 Analytic sample....................................................... 6 AnalyticModels and Results................................................. 6 Models................................................................ 8 ......... School and individualcontributionto variance in achievement .10 School type effects on achievementand social class differentiation. 11 ............................ Studentbackgroundeffects on achievement 12 ............................................ Average achievement 14 SES-achievementgap............................................ 15 Differencesbetween schools.......................................... 17 School organizationaland quality factors............................ 17 ............................................ Average achievement 18 ................................... Social class differentiation 19 School compositionalfactors......................................... 20 ............................................ Average achievement 20 ................................... Social class differentiation 20 Final reduced model.................................................. 22 ................................................................. Conclusion 25 Annexes.................................................................... 26 ................................................................. References
The World Bank does not accept responsibilityfor the views expressedherein, which are those of the authors and should not bB attributedto the World Bank or to its affiliatedorganizations. The findings,interpretations,and conclusionsare the results of researchor analysissupportedby the Bank; they do not necessarilyrepresentofficialpolicy of the Bank. The authors gratefullyacknowledgethe contributionsof Mr. Qinghua Zhau for computational assistanceand of Dr. Heraldo Vianna of the Carlos Chagas Foundationfor designingand administeringthe test and making the data available to us. Support for this researchwas providedby RPO 674-84.
-2 -
1. Introduction
1.
The differentialeffect of schools on student achievementhas been a
matter of considerabledebate over the past quarter century. While early studies, typicallyutilizing cross-sectionaldesigns,sought to identify the relativecontributionof family backgroundversus school characteristicsto achievement,more recent research,often employingpanel data, has sought to identifythose elementsof schools that explain (i) differencesin student growth in achievement (e.g. Raudenbushand Bryk, 1986; Lockheed and Longford, 1989; Riddell, 1989), or (ii) differencesin schools'ability to reduce the effects of family backgroundon achievement(e.g. Lee and Bryk, 1988). Recent researchhas also differedfrom earlierwork insofaras it employs multi-level modelling techniquesappropriatefor hierarchicallyorganizeddata (see Aitken and Longford, 1986; Raudenbush,1988 for reviews).
2.
Key variables that have been examinedinclude school sector (public
or private, see Coleman,Hoffer and Kilgore, 1982); religiousaffiliation (Catholicor lay, see Lee and Bryk, 1988); and a variety of school-level inputs and processes (particularlypeer, organizational,and teachingprocess variables). While a number of studies in more developedcountrieshave erployedboth panel designs and multi-levelmodelling techniques,comparable researchon school effects on achievementin developingcountries is, to the
-3. best of o%r knowledge,limited to one study in Zimbabwe (Riddell,1989) and one in Thailand (Lockheedand Longford, 1989); even research employing crossectionaldesigns occurs infrequently. The two studies that examined school effects in developingcountries reached similar conclusions,however: that student backgroundand prior achievementhave significantlygreater impact on present achievementthan do school factors,and that different schools are relativelyconsistentin their transformationof prior achievement into present achievement.
3.
This study contributesto the literatureby providing evidencefor a
Latin American country and by exploringa larger variety of school types than previouslyexamined in either developedor developingcountries. The present study examines the relativeeffect of four types of secondaryschools (technical,SENAI, teacher training,and general secondary)and two sectors (publicand private)on student achievementin mathematicsand Portuguesein four cities in Brazil.
2. Method 4.
The Ministry of Educationand the World Bank commissionedthe Carlos
Chagas Foundationto design and administera standardizedtest of mathematics and Portugueseto a sample of secondarystudentsin four cities (Fortaleza, Salvador,Sao Paulo and Curitiba). The achievementtest was designedfor studentsat the end of their third (and final) year of secondary school, and comprised test items that had appearedpreviouslyon entrance examinationsfor Brazilianuniversities(yestibular). The test was accompaniedby a background questionnairefor each student and a questionnaireabout the school that was completedby the school director. Both tests and questionnaireswere
-4administeredin November, 1988. The overallpurpose of the study was to explore differencesin the relativeeffectivenessof various types of school in enhancingstudent achievementand in reducingperformancedifferences between students from differentsocial class backgrounds.
Sample
5.
For each city, a stratifiedrandom sample of schools was identified,
with replacements;stratificationwas based on school type (FederalTechnical, 1 ' teacher training SENAI schools, [magisterio]schools,and general secondary
schools),time of shift (day or night) and ownership (publicor private); it was desigred to be representativeof the actual distributionof schools and students in each state. Within each school, all studentspresent on the day of test administrationwere requestedto completethe test and accompanying questionnaire,althoughparticipationwas voluntary.
6.
The voluntary nature of participationmay have affected the overall
estimatesof achievementfor individuals,schools and cities. Private school and day shift studentswere slightlyoversampledin Fortalezabut undersampled in Sao Paulo. In Salvador,public schoolswere oversampled. Strong collaborationfrom the State Secretaryof Education in Parana resultedin the most representativesample for this city.
I/ SENAI secondary schools are financedby the federal governmentbut administeredby the National Confederationof Industry (a private association of industrialemployers). The 17 SENAI secondaryschools in Brazil offer a four-yearprogram that combines a full secondaryeducationwith technical specialization.
-5Instruments
7.
Four instrumentswere developed:a mathematicstest, a Portur *se
test, a student backgroundquestionniaire, and a school questionnaire. The mathematicsand Portuguesetests were designedto measure understandingof the basic secondaryschool curriculumin these areas, and includedone or more item for each area of content: for example,-.erb tenses and reading comprehensionin Portugueseand linear functionsand trigonometryin mathematics. Items were selected from a pool of items used on vestibular tests on the basis of "item facility",a statisticalmeasure of item discrimination. Reliabilitiesfor the total tests were high, with Cronbach's alpha - .84 for mathematicsand .75 for Portuguese. However,reliabilities calculatedseparatelyfor studentsin teacher trainingprograms (nmagisterio" students)were substantiallylower, .30 for mathematicsand .58 for Portuguese.
Analytic
8.
sample
Data were obtained from 2648 studentsand 66 schools;after cleaning
the data (range and logic checks) and making necessary corrections,usable data were obtained from 2611 studentsand 62 schools. Three schoolswere deleted for insufficientstudent-leveldata (9, 3 and 10 cases respectively) and a fourth school was deleted for insufficientschool-leveldata (all fields were blank).
-6 -
3. Analytic models and results
9.
When longitudinaldata are not available,an alternativeapproach is
to disaggregatethe variance in achievementinto a student-leveland a grouplevel component;it is then possible to model the group level variance in achievementwhile statisticallycontrollingfor student level characteristics. To do this, a multi-levelmodellingpackage, HIM, is used (Bryk, Raudenbush, Seltzer and Congdon, 1988). One advantageof the HLM procedureover ordinary least squares (OLS) is that is correctlyestimates the standarderrors for the school-levelcoefficients. This in turn means that the statistical significanceof school-levelvariables is correctlyestimated. A second advantage of the HIM procedure is that it can analyze the factors that influencedifferencesin student achievementwithin schools (e.g. it models within school relationships,such as the rel
onship between social class and
achievement)at the same time as it evaluates the factors that influence student achievementacross schools.
Models
10.
The multi-levelmodellingapproachused in these analyses enablesus
to model two elementsof the social distributionof achievementwithin schools. The student outcomesconsideredin these analysesare senior-year mathematicsand Portuguesetest scores. The within-schoolmodel holds constant sex, age, family size and the number of hours the student works, and regressesmathematicsand Portugueseachievementfor student i within school j as a functionof family social class background (SES) which is a composite
-7. index comprisingfather'soccupation,father'seducation,mother'seducation and family income;Annex A reports the factor loadings for the index:
MATHACNH-
jo +
pal SES +
e
PORTACHj- P' + PjlSES + ej
The social distributionof achievementin each school is characterizedin terms of two parameters:an interceptand one regressionslope. SES is a continuousvariable centeredaround its school mean. Tne two parametersm y be interpretedas follows:
dR - Mean mathematics (Portuguese)achievementfor students in school j.
fjl- The degree to which social class differencesamong students relate to achievement(the social class differe.atiation effect).
11.
The school that is effective in equalizingthe distributionof
achievementwould be characterizedas simultaneouslyhaving a high average level of achievement,pp and a weak differentiationeffect with regard to social class (i.e., a small value for Pj are hypothesizedto 1). These eff..cts vary acrors schools as a functionof school-leveldifferencesin management, organizationalstructureand peer group influence (compositionaleffects).
-8School and individualcontributionto variance in achievement
12.
The first step in the HLM estimationprocess involvesfitting an
unconditional,or random regressionmodel. We do this in two steps. In the first step, we partition the variance in the mathematicsand Portuguesetest scores into their between unit (school)and within unit (individual) components. The results are presentedin Table 1; they show that school level factors account for nearly two-thirdsof the variance in mathematics achievementbut only about one third of the variance in Portuguese achievement. This result is consistentwith research from other countries showing that, as one might expect, the more abstract the subject matter, the more importantformal schoolingis for developingstudent achievement.
Table 1: Results of variancecomponentanalysis: Brazil secondary,1988 Score
School
Mathematics Portuguese
13.
62.38 36.36
Individual 37.62 63.64
In the second step, we fit an unconditionalmodel that includesthe
SES-achievementgap. Table , presents the results. The averagemathematics score is 14.29 (out of a maximum possiblescore of 45) and the average Portuguesescore is 17.36 (out of a maximum possible score of 35). The average social class differentiation(the average within-schoolsocial classachievementslope) is .14 for mathematicsand .31 for Portuguese. All are significantat probabilitylevels less than .05. The school average achie.vement estimates are highly reliablefor both mathematicsand Portuguese, but the social class differentiationestimatesare considerablyless so. This
.9means that much of the observedvariability in regressioncoefficientiis samplingvariance and as a result unexplainableby school factors. Sufficient variabilityacross schools on both the mean achievementand the SES differentiationeffect does exist, however, to proceed. (The Chi-squarechart indicatesthat all but the Portuguesesocial class differenti&vioneffect estimatedparameter variances are significantlydifferent from zero).
Table 2: The HIM unconditionalmodeil Gamma coefficients
EstimatedEffects School mean Achievement Mean mathematics Mean Portuguese
Standard error
t-stat
p-value
14.29 17.36
.75 .41
19.04 42.39
.000 .000
.29 .31
.15 .12
1.99 2.54
.046 .011
Social Class Differentiation Mean mathematics Mean Portuguese The Chi Square Table Parameter Mean Achievement Mathematics Portuguese Differentiation SES Mathematics Portuguese
Estimated value
D/F
34.28 9.87
61 61
0.39 0.16
61 61
Reliabilityof School-LevelRandom Effect Mean Achievement Mathematics Portuguese -
.982 .948
SES Differentiation Mathematics Portuguese -
.223 .125
Chi-square
4028.2 1424.0 90.41 68.84
p-value
.000 .000 .009 .229
* 10 -
School tvoe effects on achievementand social class differentiation
14.
The major purpose of this study was to explore differencesin the
mathematicsand Portugueseachievementof studentsattendingdifferenttypes of secondaryschools. Comparisonswere made, therefore,between the scores of those attending federal technical,SENAI, teacher trainingand general secondaryschools;Table 3 presents the average achievementof studonts attendingvariot'stypes of schools.
Table 3: Mean achievementscores for studentsin differenttypes of secondary school, Brazil, 1l88 School type
Mathematics Mean S.D.
Portueuese Mean S.D.
Federal technical SENAI Teacher training General secondary
22.60 12 75 11.24 13.70
21.11 16.79 16.79 17.00
15.
2.18 0.53 1.56 5.79
0.88 0.82 2.04 3.28
On average,students in federal technicalschools scored
significantlyhigher on both mathematics(about 10 points) and Portuguese (about 5 points) than students in any of the other types of schools. Students in teacher trainingschools scored lowest in mathematics,w.th studentsin SENAI schools scoring about 1.5 points higher and studentsin general secondaryschools about 2.5 points higher than students in teacher training schools. In Portuguese,performanceat all types of schools other than the federal technicalschools was equivalent. Average differencesbetween schools,however, do not mean that the schools are responsiblefor the differences. Di£'farences in recruitmentpracticescan also account for differencesin achievement. Where some types of schools,such as the federal
-
11
-
technicalschools,SENAI schools and the best private schools are selective and others are not, it is likely that the average ability of studentswill differ across schools.
Student BackgroundEffects on Achievement
16.
In fact, the data clearly indicatethat the differenttypes of
schools attract differenttypes of students (Table 4). Students in federal technicalschools and SENAI secondaryschools are disproportionately male and come from higher social class backgrounds (SES is a composite index comprising father'soccupation,father'sschooling,family income and mother's schooling; Annex A reports the factor loadingsfor this index, which is standardizedwith a mean of 0), while students in teacher trainingschools are disproportionately female and come from lower social class backgrounds. The average socioeconomiclevel for studentsin general secondaryschools in this sample was in the mid-range,but it should be recalled that this average is composedof private (generallyhigh SES) and public (generallylower SES) school students. Other differencesare that students in general secondary schools spend more hours a week working (which presumablydetractsfrom time availablefor study), and studentsin federal technicalschools spend fewer hours working than either SENAI or teacher trainingstudents.
- 12 Table 4: Average characteristicsof studentsattendingdifferenttypes of secondary schools,Brazil 1988 School type Student characteristic Sex (% female) Age in years SES (factorscore) Family size Hours working weekly Sample size
17.
Federal technical SENAI 26.0 18.5 .18 4.7 5.8 192
6.8 19.4 .19 4.2 8.6 118
Teacher training 96.1 18.9 -.29 4.4 8.0 309
General secondary 58.7 18.7 .02 4.5 14.5 1992
To take into account these backgrounddifferencesbetween students
attendingdifferent schools,we entered five student characteristicvariables into the model: social class background,sex, age, family size, and number of hours per week that a studentworked. All backgroundcharacteristicswere allowed to vary within schools,but a random effect was observed for SES only. The other four variables were "fixed"and the residualvariances set to zero. Because general secondaryand teacher trainingschools are found in both the public and private sector,we also includeda dummy variable to test for sector effect on achievement.
18.
Average achievement. The results of these analysesare presented in
Table 5 (generalsecondaryschools and public schools are the two omitted categories);since we are modellingthe within-schoolSES-achievement relationship,the school average SES is entered into the achievementequation as a control variable. The results show that older studentsperformed less well on both mathematicsand Portuguesetests than did younger students,and girls outperformedboys in Portuguese,but boys outperformedgirls in mathematics. Studentswho worked less outperformedthose than studentswho
- 13 -
worked more hours per week. Family size was unrelated to achievementin either mathematicsor Portuguese,and was dropped for subsequentanalyses. Students from higher social class backgroundsoutperformedthose from lower social class backgrounds,on average,but the relationshipdifferedbetween schools.
19.
With student characteristicsheld constant,students in federal
technicalschools scored significantlyhigher in both mathematics(by about 9 points, or 1.5 standarddeviations)and Portuguese(by about 3 points, or one standarddeviation)than studentsin general secondaryschools;previously observedmodest differencesbetweeui students in general secondaryschools and those in both teacher trainingschools and SENAI schoolswere entirelydue to differencesin student background. Controllingfor school type and student background,students in private schools outperformedstudents in public schools on the mathematicstest, but not in Portuguese. School type explained 69.7% of the between school variance in mathematicsachievementand 64.9% of the between school variance in Portugueseachievement.
- 14 -
Table 5: School type effects on achievementand social class differentiation Mathematics Independentvariable Fixed Female Age Family size Working hours Mean achievement Intercept Average SES Federal technical SEtNAI Teacher training Private SES achievementgap Base Federal technical SENAI Teacher training Private *
p < .05, ** p < .01, ***
20.
Coeff.
t-stat
Portuguese Coeff.
t-stat
-1.48*** -0.37*** 0.05 -0.03***
-7.06 -5.84 0.27 -4.65
0.58** -0.48** 0.05 -0.02**
3.02 -8.24 1.11 -3.62
13.92*** 4.71*** 9.28*** -1.52 -1.37 3.20*
22.29 4.74 5.20 -0.63 -1.06 2.12
16.81*** 3.82*** 3.68** -0.84 -0.09 -0.20
43.71 6.42 3.44 -0.58 -0.12 -0.22
0.11 0.68 -0.69 -0.35 0.02
0.54 1.31 -1.07 -0.80 0.06
0.21 -0.25 -0.37 -0.28 0.22
1.26 -0.57 -0.70 -0.74 0.72
p < .001
SES-achievementgap. Although the SES-achievementrelationshipwas
significantlydifferent from zero for both mathematicsand Portuguese(Table 2), neither school type nor sector explainedthis relationship. However, for mathematics,the directionof the effect was positive for federal technical while it schools,suggestingthat they increasedsocial class differentiation, was negative for both SENAI and teacher trainingschools, suggestingthat they may have amelioratedthe effect. For Portuguese,effects of all three types of schoolswere negative,but statisticallyinsignificant. Private schools but weakly and statisticallynonincreasedsocial class differentiation, significantly.
-
15 -
DifferencesBetween Schools
21.
For this analysis,we classifiedschool characteristicsinto two
groups: (i) school organizationand quality and (ii) school composition. Four school organizationvariableswere examined: the school'sorganizational complexity (a composite index comprisingnumber of sessions (shifts),number of classes,and number of students in the school;Annex B reports the factor loadings for this index, which is standardizedwith a mean of 0), public or private sector (an indicatorof more decentralizedadministration),day or night session,and average class size. Four school quality variableswere examined:average teacher salary, average number of hours of mathematics instruction,average number of hours of Portugueseinstruction(indicatorsof the opportunityto learn), and whether or not the school charged a high tuition fee. In addition to the average social class backgroundof students in the school, two other school compositionvariableswere explored: the average hours worked by students in the school and the percent of studentswho were female.
22.
There were substantialdifferencesamong school types in these
variables (Table 6). On average,federal technicalschools were more organizationallycomplex,paid higher teacher salaries,but offered fewer hours of mathematicsand Portugueseinstructionthan other schools. SENAI schools were less organizationally complex, offeredmore hours of instruction and had smaller classes than other schools. Schools also differed in terms of the compositionof their student bodies.
- 16 Table 6: Organizationalquality and compositionalcharacteristicsof different types of secondaryschools,Brazil 1988
Federal technical
School characteristic
School Tvpe Teacher SENAI training
General secondary
Organization Complexity (factorscore) Number of classes School size Number of shifts Private (%) Day school (%) Class size
0.86 12.0 420.0 3.0 0 100.0 35.0
-1.40 6.0 180.0 2.0 0 100.0 25.0
0.20 10.25 400.0 2.4 25.0 87.5 37.5
-0.05 9.8 377.4 2.1 27.1 58.3 38.8
Quality
Teacher salaryaj Hours of Portuguese Hours of mathematics High fee private (%)
CZ250,000 CZ250,000 CZ112,100 CZ121,329 (US$425) (US$425) (US$191) (US$206) 1.75 3.0 2.63 2.58 2.0 3.0 2.38 2.29 0 0 12.5 20.8
ComPosition
Average SES (factor score) Average working hours Percent female Sample size (schools)
.11 4.98 19.3 4
.08 13.13 11.9 2
-.20 8.82 96.6 8
.04 14.53 56.5 48
a/ November 1988 Cruzeiros. The average exchangerate for that month was CZ588.1 - US$1.
23.
We next sought to explain the school type and sector effects on
achievement,by examiningthe extent to which differencesin school organization,quality or compositioninfluencedthe social distributionof achievement.
- 17 School Organizationaland Ouality Factors
24.
Our first hypothesiswas that differencesin the management,
organizationor quality of the schools accounted for the differencesobserved. Four school organizationand quality variableswere examined: the number of hours of mathematicsor Portugueseinstructionoffered, the average teacher's salary, and average class size. Table 7 presents the results of these analyses.
Table 7: School organizationand quality effects on secondaryachievement and social class differentiation, Brazil 1988 Mathematics Independentvariable
Coeff.
Fixed Female -1.51*** Age -0.37*** Working hours -0.03*** Mean achievement Intercept 2.73 Average SES 5.43*** Federal technical 8.87*** Private 1.66 Organizationalcomplexity 0.72 Class size 0.15* Hours of math/Port. 2.21** Teacher salary 0.05 SES achievementgap Base 0.08 Federal Technical -0.10 SENAI -1.14 Organizationalcomplexity 0.15 Teacher salary 0.05
t-stat
Portuguese Coeff.
t-stat
-7.24 -5.90 -4.64
0.57** -0.48*** -0.02**
2.99 -8.24 -3.58
1.01 5.66 4.73 1.08 1.53 2.57 3.73 0.69
12.52*** 3.79*** 3.34* 0.63* 0.05 0.72 0.05
8.14 7.93 2.66 2.54 1.52 1.91 0.88
0.08 -0.15 -1.49 0.84 1.69
0.23 - 0.09 0.01
0.29 -0.63 0.41
- 0.18
-0.91
0.01
0.46
Class size
-0.01
0.47
Hours of math/Port.
-0.11
-0.40
* p < .05, ** p < .01, *** p < .001
25.
Average achievement. For mathematics,two school organizationand
quality factorswere associatedwith higher achievement:class size and the
-
18
-
number of hours that mathematicswas taught in the school. Students in schoolswith larger classes and in those that taught mathematicsfor more hours scored higher on the mathematicstest; neither organizationalcomplexity nor teacher quality (as indicatedby teacher salary) had any impact on average achievement. For Portugueseachievement,however, organizationalcomplexity was stronglyand significantlyrelated to achievement;students in larger schools with more sessionsand classes outperformedstudents in schools that were less organizationallycomplex. However, the number of hours Portuguese was taught, class size and teacher salary were unrelated to achievement.
26.
The introductionof school organizationand quality variables into
the model did not diminish relationshipbetween federal technicalschools and achievement;these variables did, however, reduce the private school effect, suggestingthat the private school differencein mathematicsachievementcould in some part be attributedto more hours of mathematicsinstructionand larger classes.
This latter result may reflect the fact that the lower-achieving
SENAI schools also had substantiallysmaller classes than all other schools. School organizationaland quality factors added about 9% additionalvariance explainedfor mathematicsachievement(for a total of 78.3% of variance explained),and about 7% additionalvariance explainedfor Portuguese achievement(for a total of 72.3% of variance explained).
27.
Social class differentiation. For mathematicsonly, school
organizationfactors seemed to explain why federal technicalschools exaggeratedthis effect; these factors did not, however, account for the reductionof social class differentiationin SENAI schools.
-
19
-
School ComRositionalFactors
'!8.
A second hypothesiswas that differencesbetween schoolswas
accountedfor by peer effects:the compositionof the peer group differed between the types of schools. Three school compositionalvariables in additionto average student SES were examined:percent female students, average number of hours studentsworked, and average school achievementin mathematicsor Portuguese(for social class differentiationonly). The results of these analysesare presented in Table 8.
Table 8: School composition,organizationand quality effects on Secondaryachievementand social class differentiation, Brazil 1988 Mathematics Independentvariable Fixed Female Age Working hours Mean achievement Intercept Average SES Federal Technical Organizational complexity
Class size Hours of math/Port. Percent female Average working hours SES achievementgap Base Salary Percent female Average SES Average working hours Average math/Port.test
Portuguese
Coeff.
t-stat
Coeff.
-1.48*** -0.38*** -0.03***
-7.05 -5.95 -4.60
0.55** -0.49 -0.02**
2.86 -8.31 -3.58
7.15* 5.05*** 7.64***
2.17 C 66 4.24
17.30*** 3.06*** 2.55*
11.74 6.20 2.19
-
-
0.56*
t-stat
2.10
0.17** 1.67* -3.18 -0.09
3.69 2.69 -1.71 -1.94
0.55 -1.31 -0.09**
1.57 -1.1? -3.07
-1.62 0.04 1.06 -0.33 -0.00 0.04
-1.40 1.36 1.39 -0.93 -0.03 0.93
1.10 0.40 0.50 -0.01 -0.06
0.80 0.77 1.58 -0.32 -0.93
* p < .05, ** p < .01, *** p < .001
- 20 29.
Average achievement. School compositioneffects on average
achievementwere very significant. As noted previously,students in schools where the average SES of their peers was higher outperformedstudents in schools where the average SES of their peers was lower; schools in which the average SES of the stud6ntswas one standarddeviationabove the average SES scored 5 points higher in mathematicsand 3 points higher in Portuguese,other things constant. Studentsin schoolswhere few studentsworked outperformed students in schools where more studentsworked. And in mathematics,students in schoolswith a lower proportionsof female studentsoutperformedstudents in schoolswith higher proportionsof female students. School composition factors added an additional1% of explainedvariance in mathematics achievement(for a total of 79.2% of variance explained)and an additional3% of explainedvariance in Portugueseachievement(for a total of 75.4% of variance explained).
30.
Social class differentiation. School compositionvariables
completelywashed out the effects of school organizationon the social classachievementgap in mathematics,but themselvescontributednothing to explainingthe parametervariance.
Final Reduced Model
31.
We next excludednon-significantvariables from the models in Table
8. A final, simplifiedmodel presents the school and individuallevel variables that explain average achievementamong the schools in this sample (Table 9).
- 21 Table 9: Reduced model, Brazil secondary achievement,1988 Mathematics Independentvariable Fixed Female Age Number of hours working Mean achievement Intercept Average SES Federal technicalschool Class size Hours of mathematics Percent female Average working hours Organizational Complexity
SES AchievementGap Base
Coeff.
Portuguese
t-stat
Coeff.
t-stat
-1.47*** -0.37*** -O.03***
-7.04 -5.87 -4.63
0.52* -0.48*** -0.02**
2.72 -8.26 -3.61
7.18* .02*** 7.31*** 0.17** 1.71* -3.39 -0.09
2.19 6.66 4.09 3.71 2.77 -1.84 -1.92
17.92*** 3.17*** 2.68**
41.84 6.74 2.87
-
0.10
-
0.67
-
-0.08*
-3.42
0.40
1.55
0.18
1.43
*p
