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Teacher Effects on Minority and DisadvantagedStudents’ Grade 4 AchievementSpyros Konstantopoulos a & Vicki Chung ba Michigan State Universityb Long Wing Education ConsultingPublished online: 08 Feb 2011.

To cite this article: Spyros Konstantopoulos & Vicki Chung (2011) Teacher Effects on Minority and Disadvantaged Students’Grade 4 Achievement, The Journal of Educational Research, 104:2, 73-86, DOI: 10.1080/00220670903567349

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The Journal of Educational Research, 104:73–86, 2011Copyright C© Taylor & Francis Group, LLCISSN: 0022-0671 print / 1940-067 onlineDOI:10.1080/00220670903567349

Teacher Effects on Minority andDisadvantaged Students’ Grade 4

AchievementSPYROS KONSTANTOPOULOS

Michigan State UniversityVICKI CHUNGLong Wing Education Consulting

ABSTRACT. The authors examined the differential effectsof teachers on female, minority, and low-socioeconomic status(SES) students’ achievement in Grade 4. They used data froma randomized experiment (Project STAR) and its follow-upstudy (LBS). Student outcomes included Grade 4 SAT scoresin mathematics, reading, and science and student demograph-ics included gender, race, and SES. The authors used mul-tilevel models to determine how teacher effectiveness inter-acted with student gender, race, and SES. We also exploredwhether teacher effects were more pronounced in schoolswith high proportions of minority or female students. Re-sults indicated that all students benefited from having effec-tive teachers. The differential teacher effects on female, mi-nority, and low-SES students’ achievement, however, wereinsignificant. There is some evidence in mathematics thatteacher effects are more pronounced in high-minority schools.Finally, teacher effects seem to be consistent within and be-tween schools.

Keywords: minority students, school achievement, teachereffects

T eachers are a paramount factor of the U.S. educa-tion system, and their effectiveness is believed bythe substantial majority of educational researchers

to promote student achievement. The U.S. education sys-tem has, in principle, a dual objective: to provide oppor-tunities to all students to grow academically and to reduceinequality in achievement. It is appealing to think that ef-fective teachers can meet both objectives, that is, increaseacademic achievement for all students and simultaneouslyclose the achievement gap between female and male, mi-nority and White, and low- and high-socioeconomic status(SES) students.

One focus of the No Child Left Behind (NCLB) Act isto close the achievement gap and ensure that lower achiev-ers from disadvantaged backgrounds reach academic profi-ciency. Teachers can play a critical role in accomplishingthis objective, and NCLB has recognized the importance ofteachers in increasing student learning by mandating stateplans to improve teacher effectiveness. The underlying be-lief is that highly effective teachers can increase student

achievement, especially for minority and disadvantaged stu-dents. Thus, it is important to determine how teachers affectthe achievement of minority and disadvantaged students andwhether these types of students benefit more from effectiveteachers than other students.

A recent study provided evidence, using data from a ran-domized experiment, that teacher effectiveness, measuredas variability in achievement across classrooms, is criticalin promoting student achievement (Nye, Konstantopoulos,& Hedges, 2004). They found important teacher effectsin mathematics and reading achievement in early gradesthat were typically larger than small class effects. In addi-tion, that study provided some evidence that teacher ef-fects may be more pronounced in low-SES schools thanin other schools. Other studies have indicated that teach-ers’ race affects positively the achievement of students ofthe same race (Dee, 2004). Findings from nonexperimentalstudies have suggested that Black and White students benefitequally from teacher effectiveness (Sanders & Rivers, 1996).Nonetheless, some of the findings that have been reportedin the literature are somewhat mixed. For example, someresearchers have demonstrated that teacher characteristicssuch as experience are positively and significantly linkedto Black student achievement (Murnane & Philips, 1981),whereas other researchers have reported that teacher effectsare not associated with the achievement of Black or Latinostudents (Hanushek, 1971, 1992).

Overall, previous work has not documented well whetherteacher effectiveness influences student groups in differentways that result in additional gains for minority and disad-vantaged students in elementary school. In principle, teach-ers should respond to students’ learning needs and promotestudents’ academic progress especially for students from dis-advantaged backgrounds (Ferguson, 1998). In this study wedetermined whether female, minority, and disadvantagedstudents benefit more from having effective teachers in early

Address correspondence to Spyros Konstantopoulos, 459 EricksonHall, College of Education, Michigan State University, East Lansing,MI 48824, USA. (E-mail: spyros@msu.edu)

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grades. In particular, we examined the differential effectsof effective teachers on Grade 4 achievement of female,minority, and lower SES students, using high-quality exper-imental data from Project Student Teacher AchievementRatio (STAR) and the Lasting Benefits Study (LBS). ProjectSTAR was a well-executed, large-scale randomized experi-ment, and evidence derived from such data is likely to havehigher internal validity and to a lesser extent higher externalvalidity than small-scale studies (Nye, Hedges, & Konstan-topoulos, 2000). We also examined the cumulative effectsof teacher effectiveness on the academic achievement offemale, minority, and lower SES students, because the influ-ence that students receive over the early grades from theirteachers is presumably cumulative. For instance, female, mi-nority and disadvantaged students may benefit more thanother students from having highly effective teachers in con-secutive years in early grades.

We also examined teacher effects in schools with highproportions of minority or female students in an attemptto determine whether teacher effectiveness was more pro-nounced in those schools. Teachers are not randomly al-located to schools and thus selection mechanisms typicallytake place. In fact, schools with high proportions of low-income or minority students often have difficulty recruitingand retaining effective teachers (Darling-Hammond, 1995).In addition, low-income urban students are more likely tobe exposed to less effective teachers (Krei, 1998), and low-achieving, minority, and low-income students in urban set-tings typically attend schools with less competent teachers(Langford, Loeb, & Wyckoff, 2002). Ferguson (1998) alsoargued that less effective teachers are more likely to teachin schools with higher proportions of minority students. Inthe same vein, a more recent study provided evidence thatin lower SES schools there was larger variability in teachereffectiveness (Nye et al., 2004). Finally, NCLB targets suchdisadvantaged schools and urges school systems to staff theseschools with more effective teachers in order to improve stu-dent achievement. Hence, examining teacher effectivenessin high-minority schools is a timely task. Finally, we alsoinvestigated the inconsistency of teacher effects within andbetween schools in order to determine whether school con-text interacts with teacher effects.

Related Literature on Teacher Effectiveness

Overall, three related lines of research have discussedteacher effects on student achievement. The first tradition ofresearch examines variation between classrooms in achieve-ment, controlling for student background. These models typ-ically use prior achievement as a covariate, so they can beinterpreted as measuring the variance in residualized stu-dent achievement gain across classrooms. The results of suchstudies have suggested that teacher effects are evident (Gold-haber & Brewer, 1997; Murnane & Phillips, 1981; Rowan,Correnti, & Miller, 2002). For example, Rowan et al. (2002)documented considerable teacher effects measured as vari-

ability in achievement across classrooms on elementary stu-dents’ gains in mathematics and reading achievement. Amore recent study (Nye et al., 2004) defined teacher effectsin a similar way and also found that teacher effects were sub-stantial and as large as the cumulative effects of small classeson student achievement. Note that in such studies it is diffi-cult to identify which teacher characteristics are responsiblefor teacher effectiveness, because teacher effects are definedas a general construct.

The second tradition of research includes educationproduction function studies that attempt to determine therelation of specific teacher characteristics (e.g., experience,education, salary) to student achievement. These educa-tion production function studies (Coleman et al., 1966;Hanushek, 1971) use student and family background charac-teristics as covariates to adjust for student effects. A partic-ularly important covariate is prior achievement because it ishypothesized to summarize the effects of individual studentbackground and family background up to that time. Anotherimportant covariate is family background manifested by SES.Some reviewers of the education production function litera-ture have argued that measured teacher characteristics suchas educational preparation, experience, or salary are onlyslightly related to student achievement (Hanushek, 1986).Other reviewers have argued that some school resource char-acteristics such as teacher experience and teacher educationhave positive effects on student achievement (Greenwald,Hedges, & Laine, 1996; Murnane & Philips, 1981). Inparticular, Murnane and Philips (1981) found that teacherexperience was associated with increased achievement ofBlack students. Note that the two research traditions men-tioned previously compute teacher effects net of the effectsof student background (including previous achievementand SES) and thus, these models are part of the value-addedframework. Value-added models are a common way ofestimating teacher effects on students’ learning gains net ofstudent effects (e.g., prior achievement, family background).

The third tradition of research discusses what constitutesgood teaching practice and examines the association be-tween good teaching practice and student achievement.This line of work has provided evidence about the linkbetween teacher behavior (i.e., what teachers do in theclassroom) and student learning (Good & Brophy, 1987).In his pioneering work, Good (1979) discussed teacher ef-fectiveness as teachers’ ability to increase student perfor-mance on standardized tests. He reviewed findings on teachereffectiveness from process-product studies and concludedthat teachers matter and that teacher effectiveness mea-sured as teacher characteristics substantially influences aca-demic achievement for all students. Other reviewers reachedsimilar conclusions and argued that teachers vary in theireffectiveness in increasing student achievement (Brophy,1986, 1988). Within this tradition, recent work indicatedthat more effective teachers had higher classroom achieve-ment means and suggested that higher teacher evaluationscores closed the achievement gap, but only between lower

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and higher SES students in Grade 4 (Borman & Kimball,2005).

Validity Threats in Project STAR

The internal validity of estimates in Project STAR de-pend on whether random assignment was executed success-fully and eliminated effectively preexisting differences be-tween students and teachers assigned to different types ofclassrooms. Previous researchers examined whether randomassignment was successful in Project STAR and found thatthere were no preexisting significant differences across typesof classrooms for student characteristics such as SES, andminority group status (Krueger, 1999). Krueger (1999) alsofound that there were no significant differences across treat-ment types in teacher characteristics such as race, experi-ence, and education. Unfortunately, no pretest scores werecollected in Project STAR so it is not possible to examinedifferences in prekindergarten achievement.

Although there are no significant differences betweenclassrooms across treatment types, it is still possible thatthere may be differences between classrooms that were as-signed to the same treatment types within schools. A recentstudy examined this possibility and produced results thatwere consistent with what would be expected if randomiza-tion were successful. That is, no systematic differences werefound for observed student characteristics between class-rooms that where in the same treatment type within schools(Nye et al., 2004).

Attrition is another threat to the internal validity of theestimates. In Project STAR as in most large-scale longitu-dinal studies attrition took place. Some students who par-ticipated in Project STAR in one year dropped out of theexperiment the following year. Approximately 28% of thestudents who participated in Project STAR in kindergartenwere not part of the study in Grade 1. The attrition ratewas nearly 25% for students who participated in the studyin Grade 1, but were not present in Grade 2. Nearly 20%of the students dropped out of the study after Grade 2, and35% of the students dropped out of the study after Grade 3.Concerns about attrition in Project STAR were addressed inprevious studies, and the findings indicated that attrition didnot affect the small class effect much (Krueger, 1999; Nye etal., 2000). Attrition can potentially affect the teacher effectsestimates of the present study if, for instance, the studentswho dropped out in one year, and had received low effectiveteachers in the previous year, are systematically differentin achievement levels from students who dropped out andhad received high effective teachers. Such differential attri-tion could affect the teacher effects estimates positively ornegatively because of negative or positive selection.

Hence, we examined whether differential attrition af-fected the estimates of teacher effects and computed differ-ences in achievement between students who dropped out orstayed in the experiment and received higher or lower effec-tive teachers. For each year (kindergarten, Grades 1–3) we

compared the achievement scores of students who droppedout of or stayed in the study the following year (Grades1–4). First, we created three categories of teacher effective-ness: (a) high effective teachers (top quartile in the distribu-tion of teacher effectiveness), (b) medium effective teachers(middle 50% in the distribution of teacher effectiveness),and (c) low effective teachers (bottom quartile in the dis-tribution of teacher effectiveness). Second, for each grade,we constructed three binary indicators to represent thesecategories or teacher effectiveness and a binary variable forstudents who dropped out or stayed in the study. Third, weused a linear model and regressed mathematics, reading, orscience scores on each teacher effectiveness indicator, thedropout indicator, and the interaction between the teachereffectiveness and the dropout dummies. The estimates ofthe interaction effects represent differences in achievementfor dropouts and stayers who received high, medium, or loweffective teachers the previous year. Insignificant interac-tions would suggest no evidence of differential attrition foreach category of teacher effectiveness. We also examinedwhether the linear association between teacher effective-ness and achievement differed for dropouts and stayers.

The results of this analysis are summarized in Table 1.Specifically, the p values of the tests of the interaction effectsfor reading and mathematics for kindergarten and Grades1–3 and for science in Grade 3 are presented in Table 1. Onlythree out of the 36 p values (about 8%) reported in Table 1were smaller than .05, whereas all other p values were greaterthan .05. Two of the three significant interactions were inGrade 3, which had the larger attrition rate. The percentageof significant interactions is low (less than 10%) and thus itis possible that it could have occurred by chance. Overall,these results do not seem to suggest evidence of differentialattrition, and, hence, we argue that it seems implausible thatattrition biased the teacher effects substantially.

Method

Data

We used data from the Tennessee class size experiment,or Project STAR, a large-scale randomized experiment thatwas conducted in the State of Tennessee in the mid-1980s(Krueger, 1999; Nye et al., 2000). Over a 4-year period morethan 11,000 students in 79 elementary schools in 42 districtsin Tennessee participated in the experiment. In the first yearof the study, within each school, kindergarten students wereassigned randomly to classrooms in one of three treatmentconditions: small classes (with 13–17 students), larger classes(with 22–26 students), or larger classes with a full-time class-room aide. Teachers were also assigned randomly to classesof different types. Some students entered the study in Grade1 and subsequent grades and were assigned randomly to class-rooms at that time. Teachers at each subsequent grade levelwere assigned randomly to classes as the experimental co-hort passed through their grade. Districts had to agree to

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TABLE 1. Values of Interactions Between Teacher Effectiveness and Dropout Status, by Grade

Interaction Kindergarten 1 2 3

MathematicsHigh Teacher Effectiveness × Dropout 0.527 0.219 0.694 0.738Medium Teacher Effectiveness × Dropout 0.197 0.191 0.355 0.014Low Teacher Effectiveness × Dropout 0.752 0.223 0.932 0.645Teacher Effectiveness × Dropout 0.482 0.461 0.389 0.431

ReadingHigh Teacher Effectiveness × Dropout 0.981 0.332 0.985 0.017Medium Teacher Effectiveness × Dropout 0.229 0.452 0.811 0.218Low Teacher Effectiveness × Dropout 0.771 0.029 0.245 0.587Teacher Effectiveness × Dropout 0.989 0.124 0.721 0.780

ScienceHigh Teacher Effectiveness × Dropout 0.466Medium Teacher Effectiveness × Dropout 0.069Low Teacher Effectiveness × Dropout 0.325Teacher Effectiveness × Dropout 0.324

participate for 4 years, and allow site visitations for verifica-tion of class sizes, interviewing, and data collection, includ-ing extra student testing. They also had to allow the researchstaff to assign pupils and teachers randomly to class types andto maintain the assignment of students to class types fromkindergarten through Grade 3. Students who participated inProject STAR through Grade 3 were followed in subsequentgrades as part of a follow up study that examined the lastingbenefits of small classes (Nye, Hedges, & Konstantopoulos,1999). Nearly 4,000 students who were part of Project STARin Grade 3 were followed in Grade 4, and this is the samplewe used in some of our analyses.

Project STAR has high internal validity because withineach school students and teachers were assigned randomly toclasses of different sizes. In addition, because Project STARis a large-scale randomized experiment that includes a broadrange of schools and districts (urban, rural, wealthy, andpoor), it should have higher external validity than smallerscale studies that use convenient samples. Moreover, thestudy was part of the everyday operation of the schools thatparticipated, and, hence, there is a lower likelihood thatnovelty effects affected the class size estimates.

Analysis

Computation of teacher effects. The main objective of thisstudy was to examine whether teacher effects in early grades(e.g., kindergarten to Grade 3) influenced Grade 4 achieve-ment of specific student groups (e.g., female, minority, andlow-SES students). The first step of the analysis involvedthe computation of teacher effects in a specific grade. InProject STAR, within each school, students and teacherswere assigned randomly to classrooms, and, therefore, theclassrooms within classroom type and school are initiallyequivalent. Hence, within each school, any systematic dif-ferences in achievement among classrooms must be due to

one of two sources: the treatment effect (e.g., class size) anddifferences in teacher effectiveness (Nye et al., 2004). Thatis, any systematic differences in achievement between class-rooms in the same classroom type must be due to variationsin teacher effectiveness. However, note that students andteachers select their schools, and, therefore, it is importantto take into account possible differences among schools (e.g.,school effects) when computing teacher effects. It is essen-tial then to compute the distribution of teacher effectivenessnet of the distribution of school effectiveness. This is accom-plished by using a three-level model where school effects aremodeled separately of teacher effects as level 3 residuals.Following Nye et al. (2004), we operationalized teachereffects as classroom-specific residuals that are adjusted fortreatment effects and possible student (e.g., student SES)and school effects.

Because of the nested structure of the data, it is natu-ral to employ three-level hierarchical linear models (HLM)to compute teacher effects as classroom-specific random ef-fects or residuals (Raudenbush & Bryk, 2002). The first levelinvolves a between-student, within-classroom, and schoolmodel; the second level involves a between-classroom,within-school model; and the third level is a between-schoolmodel. First, we computed teacher effects in Grade 3. Specif-ically, in Grade 3, mathematics, reading, or science achieve-ment was regressed on a set of predictors such as studentgender (coded as 1 if female and 0 otherwise), race (codedas 1 if minority student and 0 otherwise), SES (coded as 1 ifeligible for free or reduced-price lunch and 0 otherwise), andclass type (coded as 1 if in small or in regular-size class witha full-time aide and 0 otherwise). The outcomes used in thisanalysis were Stanford Achievement Test (SAT) readingand mathematics scores (as well as science scores in Grade3) that were collected from kindergarten through Grade 3 aspart of Project STAR. We also computed teacher effects formathematics or reading in kindergarten and Grades 1–2 to

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be able to measure cumulative teacher effects. This part ofthe analysis was conducted for each grade separately. Thus,for each grade the one-level mixed effects equation for stu-dent i, in class j, in school k is

Yijk = γ000 + γ010SMALLjk + γ020AIDE jk

+ γ100FEMALE ijk + γ200LOWSES ijk

+ γ300MINORITY ijk + εijk + ξ0jk + η00k (1)

where Yi j k represents student achievement (e.g., mathemat-ics, reading, science) in a specific grade; γ000 is the averageachievement across students, classrooms, and schools for aspecific grade g; γ010 represents the overall small class effect;SMALL is a dummy variable for being in a small-size class-room; γ020 represents the overall regular class with a full-timeaide effect; AIDE is a dummy variable for being in a regular-size classroom having a full-time classroom aide; γ100 is theoverall gender effect; FEMALE is a dummy variable for gen-der; γ200 is the overall low-SES effect; LOWSES is a dummyvariable for free or reduced-price lunch eligibility; γ300 is theoverall minority effect; MINORITY is a dummy variablefor minority group membership (indicating that the studentwas African American, Hispanic, or Asian); εi j k is a student-specific random effect (residual); ξ0 j k is a classroom-specificrandom effect (residual); and η00k is a school-specific ran-dom effect (residual). In this model, the variance of the errorterm is divided into three parts: the within-classroom, thebetween-classroom within-school, and the between-schoolvariance. The classroom-specific random effects, ξ’s, rep-resent the teacher effects adjusted for student gender, SES,minority group status, and the treatment effect (small or reg-ular size classes). Within the value-added framework we alsocomputed residualized teacher effects (in Grades 1–3), con-trolling for previous achievement (in kindergarten, Grade 1,or Grade 2, respectively). Residualized teacher effects can-not be computed for kindergarten because achievement wasnot measured at the baseline of the experiment. In this casethe one-level mixed effects equation for student i, in class j,in school k is

Yi j k = γ000 + γ010SMALLjk + γ020AIDE jk

+ γ100FEMALE ijk + γ200LOWSES ijk

+ γ300MINORITY ijk

+ γ400PREVIOUSACHIEVEMENT ijk

+ εijk + ξ ∗0jk + η00k (2)

where PREVIOUSACHIEVEMENT represents studentachievement in the previous grade, ξ ∗

0 j k represent the resid-ualized teacher effects (adjusted for previous achievement),and all other terms were defined previously. The analysisillustrated in Equation 2 also used as outcomes the SATreading and mathematics scores. Again, we conducted sep-arate analyses for each dependent variable for each grade.

Nye et al. (2004) discussed the magnitude of these teachereffects (defined as between-teacher variance) for each grade(kindergarten, 1, 2, 3) using data from Project STAR.

Third grade differential teacher effects on fourth grade achieve-ment. The second step of the analysis was to model teachereffects as predictors of student achievement in Grade 4. Forexample, the teacher effects (residuals) computed in Grade 3were used as predictors of Grade 4 achievement for studentswho were in the sample both years. Students who were inthe same class in Grade 3 and were part of the sample inGrade 4 had the same teacher effect. This part of the analy-sis examines whether teacher effects in third grade impactsthe achievement of female, minority, and low-SES studentsin Grade 4 controlling for Grade 4 teacher effects. Differen-tial effects are typically represented in regression models asinteractions. The notion of interactions goes back to the pi-oneering work of Cronbach and Snow (1977). In this study,we followed Cronbach and Snow’s definition of interactionsand examined whether different groups of students (suchas female, minority and low-SES students) benefit morefrom having effective teachers. We created three interac-tion terms between teacher effectiveness and the female,minority, and low-SES variables. The model also includedthe main effects of all variables. All predictors were includedin the first or student level. We used again a three-levelHLM, and, for Grade 4, the one-level mixed-effects modelfor student i, in class j, in school k is

Yijk = γ000 + γ100FEMALE ijk + γ200LOWSES ijk

+ γ300MINORITY ijk

+ γ400TEACHEREFFECT ijk

+ γ500TEACHEREFFECT ijk × FEMALE ijk

+ γ600TEACHEREFFECT ijk × LOWSES ijk

+ γ700TEACHEREFFECT ijk × MINORITY ijk

+ εijk + ξ0 j k + η00k, (3)

where Yi j k represents SAT mathematics, reading, or sci-ence scores in Grade 4; γ000 is the average achievementacross students, classrooms, and schools; γ100, γ200, γ300,

and γ400 represent the overall FEMALE, MINORITY,LOWSES, and TEACHEREFFECT effects, respectively;γ500, γ600, and γ700 represent the overall interaction ef-fects between TEACHEREFFECT and FEMALE, MINOR-ITY, and LOWSES respectively; and εi j k , ξ0 j k , and η00k arelevel 1, level 2, and level 3 residuals, respectively. Note thatall predictors in the regression equation above are level 1predictors. We also examined interactions between gender,race/ethnicity, and SES and residualized teacher effects. Thisanalysis resembles value-added models because teacher ef-fects are adjusted for prior achievement as well. The resultsof this analysis are summarized in Tables 3–5 for differentcoding schemes of the teacher effects predictor.

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TABLE 2. Descriptive Statistics of the Sample:Grade 4

Variable M SD

Female 0.49 0.50Minority 0.20 0.40Low SES 0.38 0.49Inner city

school0.07 0.26

Urban school 0.08 0.28Suburban

school0.25 0.43

Rural school 0.60 0.49

Note that the teacher effect is modeled as a linear effect inEquation 3. However, the teacher effect can in principle benonlinear. One can model teacher effects as nonlinear, usingbinary indicators. For example, one could model the effectsof highly effective teachers on student achievement (those inthe top half or the top quartile of the distribution of teachereffectiveness). In this study, we modeled teacher effects bothas linear and nonlinear. The nonlinear effects were coded

as binary variables that took the value of 1 when a studentreceived a highly effective teacher (top half of the teachereffectiveness distribution) and 0 otherwise. We also codedteacher effects in different ways such as teachers being inthe top and bottom third or quartile of the teacher effective-ness distribution. Linear teacher effects were also examined.Gender, race, and SES were also coded as binary variables.

In the series of analyses described previously, it is im-portant to control for the effects of fourth grade teachersbecause they could affect student achievement and teachereffects in Grade 3 or cumulative teacher effects from kinder-garten through third grade. That is, the estimates reportedin Tables 3–7 indicate how teacher effects in Grade 3(or cumulative teacher effects) affect Grade 4 achieve-ment for student groups net of the effects of the currentteachers in Grade 4. To accomplish this in HLM, we cen-tered the level 1 predictors (that include teacher effectsand their interactions with female, minority and low SESstudents) at their classroom means (Raudenbush, 2004; Rau-denbush & Wilms, 1995). We tested this empirically usingregression models that included teacher fixed effects as dum-mies for Grade 4. The regression estimates were similar tothose obtained from the multilevel models. In addition, we

TABLE 3. Standardized Coefficients of Interactions Between Effective Teaching (Top 50%) and Student Groups in Grade 4Mathematics, Reading, and Science

Mathematics Reading Science

Variable Estimate SE Estimate SE Estimate SE

Teacher effect in Grade 3 (top 50%) 0.056∗ 0.027 0.093∗ 0.019 0.111∗ 0.024Female 0.069∗ 0.022 0.065∗ 0.021 −0.025 0.017Teacher effect by female interaction 0.027 0.021 −0.002 0.024 −0.037 0.021Minority −0.087∗ 0.028 −0.125∗ 0.031 −0.084∗ 0.032Teacher effect by minority interaction 0.038 0.024 0.011 0.020 −0.024 0.022Low SES −0.177∗ 0.020 −0.202∗ 0.028 −0.183∗ 0.023Teacher effect by low SES interaction 0.028 0.023 0.019 0.028 0.005 0.028Between-classroom variance component 0.109∗ 0.017 0.067∗ 0.012 0.078∗ 0.014Between-school variance component 0.111∗ 0.029 0.114∗ 0.027 0.119∗ 0.028Sample size: Schools 62 61 62Sample size: Classrooms 219 214 220Sample size: Students 4,042 3,976 4,173Residualized teacher effect in Grade 3 (top 50%) 0.036 0.025 0.055∗ 0.027Female 0.087∗ 0.023 0.073∗ 0.026Residualized teacher effect by female interaction −0.013 0.023 −0.019 0.033Minority −0.105∗ 0.029 −0.140∗ 0.041Residualized teacher effect by minority interaction 0.056 0.031 0.038 0.028Low SES −0.156∗ 0.024 −0.194∗ 0.023Residualized teacher effect by low SES interaction −0.016 0.030 0.007 0.026Between-classroom variance component 0.085∗ 0.016 0.050∗ 0.012Between-school variance component 0.138∗ 0.033 0.125∗ 0.028Sample size: Schools 62 61Sample size: Classrooms 215 213Sample size: Students 3,353 3,368

∗p < .05.

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TABLE 4. Standardized Coefficients of Interactions Between Linear Teacher Effects and Student Groups inGrade 4 Mathematics, Reading, and Science

Mathematics Reading Science

Variable Estimate SE Estimate SE Estimate SE

Teacher effect in Grade 3 0.102∗ 0.029 0.139∗ 0.022 0.123∗ 0.027Female 0.084∗ 0.016 0.065∗ 0.015 −0.045∗ 0.013Teacher effect by female interaction 0.001 0.017 −0.002 0.022 −0.029 0.018Minority −0.062∗ 0.027 −0.118∗ 0.029 −0.098∗ 0.028Teacher effect by minority interaction 0.013 0.023 −0.009 0.022 −0.043 0.024Low SES −0.160∗ 0.016 −0.190∗ 0.018 −0.181∗ 0.018Teacher effect by low SES interaction −0.011 0.021 0.005 0.027 0.007 0.027Between-classroom variance component 0.109∗ 0.017 0.067∗ 0.012 0.078∗ 0.014Between-school variance component 0.111∗ 0.029 0.114∗ 0.027 0.119∗ 0.028Sample size: Schools 62 61 62Sample size: Classrooms 219 214 220Sample size: Students 4,042 3,976 4,173Residualized teacher effect in Grade 3 (top 50%) 0.034 0.025 0.049 0.034Female 0.081∗ 0.018 0.063∗ 0.016Residualized teacher effect by female interaction −0.011 0.018 −0.001 0.029Minority −0.067∗ 0.026 −0.119∗ 0.034Residualized teacher effect by minority interaction 0.016 0.022 0.027 0.027Low SES −0.167∗ 0.018 −0.189∗ 0.018Residualized teacher effect by low SES interaction 0.036 0.025 −0.007 0.030Between-classroom variance component 0.085∗ 0.016 0.050∗ 0.012Between-school variance component 0.138∗ 0.033 0.125∗ 0.028Sample size: Schools 62 61Sample size: Classrooms 215 213Sample size: Students 3,353 3,368

∗p < .05.

ran multilevel models using grand-mean centering for stu-dent predictors to examine whether centering affected theestimates. In other sensitivity analyses we used two-levelmodels and controlled for school fixed effects via dummyindicators to take into account how differences in schoolscould affect main and interaction teacher effects.

Cumulative teacher effects. We also examined interactionsbetween cumulative teacher effects and gender, race, andSES effects. Nine to 10% of students who were in the studyfor all years had effective teachers who were in the top halfof the teacher effectiveness distribution successively fromkindergarten through Grade 3. The cumulative teacher ef-fects were defined as having effective teachers (in the tophalf of the teacher effectiveness distribution) in consecutivegrades (kindergarten through Grade 3). Specifically, the cu-mulative teacher effect was computed as a binary indicatorfor students who had teachers who were in the top half of theteacher effectiveness distribution in all grades (kindergartenthrough Grade 3). This binary indicator was then used as apredictor of mathematics or reading achievement in Grade4. The model was identical to that illustrated in Equation 3,and all predictors were again introduced at level 1. The onlydifference is that the teacher effect indicator represents now

the cumulative teacher effects from kindergarten throughGrade 3. Cumulative effects cannot be computed for sci-ence because students started taking the science exam inGrade 3. The idea was to examine whether certain studentgroups benefited more from receiving effective teachers (e.g.,top half of teacher effectiveness) in successive grades, andthus we included interaction terms between student groupsand cumulative teacher effects in the model. Notice thatthis analysis used the group of students who were part ofProject STAR and LBS from kindergarten through Grade4. This analysis was repeated to examine cumulative resid-ualized teacher effects (for Grades 1, 2, and 3) on studentgroups’ achievement as well. The results of this analysis aresummarized in Table 6. Again, in this analysis we controlledfor the effects of Grade 4 teachers by centering level 1 pre-dictors at their classroom means. We replicated this analysisusing grand-mean centering as well.

Teacher effects in high-minority and high-female schools. Asecondary objective of our study was to determine whetherteacher effects in Grade 3 were more pronounced in high-minority (top half of the % minority school distribution) orhigh-female (top half of the % female school distribution)schools in Grade 4. To that end we ran a three-level HLM

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TABLE 5. Standardized Coefficients of Interactions Between Top and Bottom 33% of Teaching Effectiveness and StudentGroups in Grade 4 Mathematics, Reading, and Science

Mathematics Reading Science

Variable Estimate SE Estimate SE Estimate SE

Teacher effect in Grade 3 (Top 33%) 0.064∗ 0.031 0.106∗ 0.031 0.045 0.028Teacher effect in Grade 3 (bottom 33%) −0.058∗ 0.028 −0.037 0.027 −0.092∗ 0.028Female 0.077∗ 0.026 0.080∗ 0.024 −0.055∗ 0.019Top teacher effect by female Interaction 0.003 0.025 −0.032 0.026 −0.021 0.021Bottom teacher effect by female Interaction 0.012 0.021 −0.003 0.025 0.038 0.022Minority −0.056 0.033 −0.087∗ 0.026 −0.111∗ 0.033Top teacher effect by minority interaction 0.010 0.023 −0.018 0.021 −0.014 0.025Bottom teacher effect by minority interaction −0.015 0.025 −0.040 0.022 0.039 0.030Low SES −0.139∗ 0.025 −0.152∗ 0.028 −0.168∗ 0.028Top teacher effect by low SES interaction −0.023 0.026 −0.024 0.028 0.001 0.030Bottom teacher effect by low SES interaction −0.019 0.026 −0.050 0.030 −0.029 0.028Between-classroom variance component 0.109∗ 0.017 0.067∗ 0.012 0.078∗ 0.014Between-school variance component 0.111∗ 0.029 0.114∗ 0.027 0.119∗ 0.028Sample size: Schools 62 61 62Sample size: Classrooms 219 214 220Sample size: Students 4,042 3,976 4,173Residualized teacher effect in Grade 3 (top 33%) 0.018 0.030 0.027 0.030Residualized teacher effect in Grade 3 (bottom 33%) −0.026 0.033 −0.008 0.039Female 0.071∗ 0.026 0.042 0.025Top residualized teacher effect by female interaction 0.002 0.020 0.025 0.027Bottom residualized teacher effect by female interaction 0.019 0.026 0.023 0.031Minority −0.054 0.035 −0.095∗ 0.040Top residualized teacher effect by minority interaction 0.005 0.025 −0.001 0.031Bottom residualized teacher effect by minority interaction −0.03 0.032 −0.050 0.030Low SES −0.136∗ 0.027 −0.210∗ 0.032Top residualized teacher effect by low SES interaction −0.021 0.025 0.019 0.028Bottom residualized teacher effect by low SES interaction −0.041 0.030 0.029 0.028Between-classroom variance component 0.085∗ 0.016 0.050∗ 0.012Between-school variance component 0.138∗ 0.033 0.125∗ 0.028Sample size: Schools 62 61Sample size: Classrooms 215 213Sample size: Students 3,353 3,368

∗p < .05.

that also included school composition of minority or femalestudents as a main effect and the teacher effect by school mi-nority or female interactions (see Equation 4). The schoolvariables and the teacher effects by school variables (in-teractions) were modeled at the third level as school-levelpredictors. For Grade 4 the one-level mixed effects modelfor student i, in class j, in school k is

Yijk = γ000 + γ100FEMALE ijk + γ200LOWSES ijk

+ γ300MINORITY ijk

+ γ400TEACHEREFFECT ijk

+ γ001SCHOOLMIN k

+ γ401TEACHEREFFECT ijk × SCHOOLMIN k

+ εijk + ξ0 j k + η00k, (4)

where Yi j k represents student SAT scores in mathemat-ics, reading, or science in Grade 4; γ000 is the aver-age achievement across students, classrooms, and schools;γ001 is the main effect for SCHOOLMIN; γ401 is theTEACHEREFFECT by SCHOOLMIN interaction effect;γ100, γ200, γ300, and γ400 represent the overall FEMALE,LOWSES, MINORITY, and TEACHEREFFECT effects, re-spectively; and εi j k , ξ0 j k , and η00k are level 1, level 2, andlevel 3 residuals, respectively. The variable SCHOOLMINwas coded as a binary indicator that took the value of 1 ifthe school was in the top half of the percentage of minorityschool distribution and 0 otherwise. Equation 4 was also usedto examine teacher effects in high-female schools. Insteadof SCHOOLMIN we included the variable SCHOOLFEMand its interaction in the model. Again, the variableSCHOOLFEM was coded as a binary indicator that took thevalue of 1 if the school was in the top half of the percentage

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TABLE 6. Standardized Coefficients of Interactions Between Cumulative Teaching Effects (Top 50% in K−3) and StudentGroups in Grade 4 Mathematics and Reading

Mathematics Reading

Variable Estimate SE Estimate SE

Teacher effect in Grades K–3 (top 50%) 0.062∗ 0.028 0.083∗ 0.034Female 0.057∗ 0.028 0.041 0.023Teacher effect by female interaction 0.024 0.025 −0.020 0.028Minority −0.072∗ 0.033 −0.136∗ 0.037Teacher effect by minority interaction 0.030 0.023 −0.024 0.013Low SES −0.132∗ 0.026 −0.155∗ 0.027Teacher effect by low SES interaction −0.020 0.022 0.021 0.030Between-classroom variance component 0.078∗ 0.018 0.034∗ 0.013Between-school variance component 0.127∗ 0.032 0.106∗ 0.026Sample size: Schools 62 61Sample size: Classrooms 208 205Sample size: Students 2,033 2,019Residualized teacher effect in Grades 1–3 (top 50%) 0.012 0.037 0.040 0.030Female 0.053 0.029 0.038 0.023Residualized teacher effect by female interaction 0.038 0.026 0.005 0.032Minority −0.065 0.034 −0.137∗ 0.036Residualized teacher effect by minority interaction −0.014 0.023 −0.012 0.024Low SES −0.134∗ 0.024 −0.156∗ 0.025Residualized teacher effect by low SES interaction −0.010 0.029 0.020 0.018Between-classroom variance component 0.077∗ 0.018 0.034∗ 0.012Between-school variance component 0.126∗ 0.032 0.106∗ 0.026Sample size: Schools 62 61Sample size: Classrooms 208 205Sample size: Students 2,050 2,036

∗p < .05.

of female school distribution and 0 otherwise. This analysiswas repeated, modeling the residualized main and interac-tion teacher effects. The results of all these analyses aresummarized in Table 7.

We also investigated whether teacher effects were incon-sistent across classrooms within schools or across schools.Because the teacher effect is a student-level predictor, it canbe modeled as a random effect in the second and third lev-els. Essentially, these random effects indicate interactionsbetween the teacher effect in Grade 3 and Grade 4 class-rooms and schools. The variances of these random effectssuggest whether teacher effects are impacted more by class-room or school context. The idea is to determine whetherthe teacher effect has a differential impact on achievementthat is more variable at the classroom or at the school level.The results of all this analysis are summarized in Table 8.

Results

Descriptive Statistics

Table 2 summarizes descriptive statistics for the variablesof interest included in the analysis. The Grade 4 sample in-cluded nearly 4,000 students. Fifty percent of the students in

the sample were female, about 40% of students were eligiblefor free or reduced-price lunch, and 20% of the students inthe sample were minorities. The majority of the studentsattended schools in rural areas, 25% of students attendedsuburban schools, and 15% of students attended inner cityor urban schools. The outcomes of interest were mathemat-ics, reading, and science scores that were standardized tohave a mean of 0 and a standard deviation of 1.

Predicting Fourth Grade Achievement

First we present results obtained from the model in whichteacher effects were coded as binary variables that took thevalue of 1 when a student had an effective teacher (top halfof the teacher effectiveness distribution) and 0 otherwise.We standardized outcomes and predictors to have a meanof 0 and a standard deviation of 1 in order to simplify in-terpretation of the regression coefficients. Specifically, allestimates can be interpreted as standardized regression coef-ficients expressed in standard deviation units. The regressionestimates and their robust standard errors for mathematics,reading, and science achievement are summarized in Table 3.In mathematics and reading female students outperformed

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TABLE 7. Standardized Coefficients of Interactions Between Effective Teaching (Top 50%) and High-Minority (Top 50%)or High-Female (Top 50%) Schools in Grade 4 Mathematics, Reading, and Science

Mathematics Reading Science

Variable Estimate SE Estimate SE Estimate SE

Teacher effect in Grade 3 (top 50%) 0.104∗ 0.018 0.115∗ 0.014 0.093∗ 0.016High-minority school (top 50%) −0.007 0.043 −0.059 0.030 −0.053 0.034Teacher effect by high-minority school interaction 0.078∗ 0.031 0.018 0.024 0.008 0.029Between-classroom variance component 0.086∗ 0.015 0.041∗ 0.009 0.063∗ 0.012Between-school variance component 0.052∗ 0.017 0.025∗ 0.009 0.033∗ 0.012Sample size: Schools 62 61 62Sample size: Classrooms 219 214 220Sample size: Students 4,042 3,976 4,173Residualized teacher effect in Grade 3 (top 50%) 0.049∗ 0.018 0.068∗ 0.017High-minority school (top 50%) −0.032 0.045 −0.057 0.033Residualized teacher effect by high-minority school interaction 0.088∗ 0.031 0.026 0.028Between-classroom variance component 0.069∗ 0.014 0.033∗ 0.009Between-school variance component 0.076∗ 0.021 0.030∗ 0.010Sample size: Schools 62 61Sample size: Classrooms 215 213Sample size: Students 3,353 3,368Teacher effect in Grade 3 (top 50%) 0.104∗ 0.019 0.116∗ 0.014 0.093∗ 0.016High-female school (top 50%) −0.020 0.039 −0.008 0.031 −0.014 0.034Teacher effect by high-female school interaction −0.018 0.031 0.007 0.024 0.024 0.027Between-classroom variance component 0.085∗ 0.014 0.041∗ 0.009 0.063∗ 0.012Between-school variance component 0.051∗ 0.017 0.026∗ 0.010 0.034∗ 0.012Sample size: Schools 62 61 62Sample size: Classrooms 219 214 220Sample size: Students 4,042 3,976 4,173Residualized teacher effect in Grade 3 (top 50%) 0.052∗ 0.020 0.068∗ 0.017High-female school (top 50%) 0.004 0.045 0.004 0.032Residualized teacher effect by high-female school interaction 0.038 0.034 0.019 0.028Between-classroom variance component 0.069∗ 0.014 0.033∗ 0.009Between-school variance component 0.072∗ 0.020 0.031∗ 0.010Sample size: Schools 62 61Sample size: Classrooms 215 213Sample size: Students 3,353 3,368

∗p < .05.

their male peers, whereas in science male and female studentsachieved similarly. Minority and low-SES students achievedsignificantly lower than White and higher SES students, re-spectively, across all achievement scores. The race and SESgap was more pronounced in reading. The main teachereffects estimates were all statistically significant. These es-timates indicated that one standard deviation increase ofthe teacher effect in Grade 3 corresponded to an increase ofGrade 4 achievement that was nearly one tenth of a stan-dard deviation in reading and science. The magnitude ofthe effect was much smaller in mathematics. The largestteacher effects were observed in science and in reading. Thedifferential effects of teacher effectiveness in Grade 3 andfemale, minority, or low-SES student were overall small inmagnitude and did not reach statistical significance. The in-

teraction coefficients were virtually zero and indicated thatboys, girls, minorities, Whites, low- and high-SES studentsall benefited equally from effective teachers in Grade 3.

The regression estimates and robust standard errors ofthe residualized teacher effects analysis are reported in thelower panel of Table 3 for mathematics and reading. Thefemale, minority, and low-SES achievement gaps were qual-itatively similar to those in the upper panel of Table 3.However, the teacher effects estimates were much smallerin magnitude by nearly 50% and statistically significant onlyin reading. That is, once Grade 2 achievement was con-trolled for, Grade 3 teacher effects were not as useful pre-dictors of Grade 4 mathematics achievement. All interac-tion effects were again virtually zero and insignificant. Notethat residualized teacher effects cannot be computed for

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TABLE 8. Variance Components Estimates of Teacher Effects at the Second and Third Levels

Mathematics Reading ScienceVariable estimate estimate estimate

Teacher effect in Grade 3 (top 50%)Between-classroom variance 0.019 0.002 0.026Between-school variance 0.015 0.001 0.000

Teacher effect in Grade 3 (top 33%)Between-classroom variance 0.015∗ 0.027 0.005Between-school variance 0.003 0.004 0.006

Teacher effect in Grade 3 (bottom 33%)Between-classroom variance 0.050∗ 0.006 0.028∗

Between-school variance 0.010 0.001 0.003Teacher effect in Grade 3 (linear)

Between-classroom Variance 0.016 0.014 0.339Between-school variance 0.101∗ 0.015 0.062

Cumulative teacher effects (K–3)Between-classroom variance 0.002 0.011Between-school variance 0.002 0.005

Residualized teacher effect in Grade 3 (top 50%)Between-classroom variance 0.001 0.001Between-school variance 0.015 0.004

Residualized teacher effect in Grade 3 (top 33%)Between-classroom variance 0.005 0.010∗

Between-school variance 0.007 0.034Residualized teacher effect in Grade 3 (bottom 33%)

Between-classroom variance 0.003 0.008Between-school variance 0.042 0.030

Residualized teacher effect in Grade 3 (linear)Between-classroom variance 0.001 0.169Between-school variance 0.027∗ 0.032

Residualized teacher effect in Grade 3 (K–3)Between-classroom variance 0.012 0.007Between-school variance 0.042 0.001

∗p < .05.

science because students started taking the science exam inGrade 3.

We also conducted analyses were we modeled the teachereffects as linear. The results of this analysis are summarizedin Table 4. Overall, the estimates reported in Table 4 aresimilar to those reported in Table 3. The teacher effects es-timates were somewhat larger than those reported in Table3; however, the residualized teacher effects estimates wereinsignificant. All interaction effects were small and insignifi-cant. We further coded teacher effects as nonlinear modelingteachers who were in the top or bottom third of the teachereffectiveness distribution in Grade 3. The results of this anal-ysis are reported in Table 5. Overall, these analyses producedestimates that were comparable to those reported in Tables3 and 4. Most importantly for this study, the interaction ef-fects were all small and insignificant. Finally, we also codedteacher effects as nonlinear modeling teachers who were inthe top or bottom quartile of the teacher effectiveness dis-tribution in Grade 3. These results are not reported here butproduced similar estimates as the analyses described.

Cumulative Teacher Effects

Only 1–2% of students who were part of the study all 4years had effective teachers who were in the top quartileof the teacher effectiveness distribution from kindergartenthrough Grade 3. A total of 3–4% of students who werepart of the study all 4 years had effective teachers who werein the top third of the teacher effectiveness distributionfrom kindergarten through Grade 3. A total of 9–10% ofstudents had effective teachers who were in the top halfof the teacher effectiveness distribution from kindergartenthrough Grade 3. We conducted analyses that computed thecumulative teacher effects of teacher who were in the tophalf of the teacher effectiveness distribution in all 4 years.The regression estimates and their robust standard errors aresummarized in Table 6.

Again, to simplify the interpretation of the regressioncoefficients outcomes and predictors were standardized tohave a mean of 0 and standard deviation of 1. Hence,the estimates are standardized regression coefficients. In

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mathematics female students outperformed their male peers,whilst in reading the female advantage was not statisticallysignificant. Minority and low-SES students achieved signif-icantly lower than White and higher SES students, respec-tively, both in mathematics and reading. The race and SESgap was more pronounced in reading than in mathematics.The main teacher effects estimates were significant in math-ematics and reading, and the effects were larger in reading.However, the interactions between cumulative teacher ef-fects and female, minority, or low-SES students were overallsmall in magnitude and did not reach statistical significance.The interaction coefficients were virtually zero and indicatedthat males, females, minorities, Whites, low- and high-SESstudents all benefited equally from having effective teachersin kindergarten through Grade 3.

The results of the residualized teacher effects analysis arereported in the lower panel of Table 6 for mathematics andreading. The female, minority, and low-SES achievementgaps were similar to those in the upper panel of Table 6.However, the teacher effects estimates were much smallerin magnitude and no longer statistically significant. All in-teraction effects were again virtually zero and insignificant.Overall, the results reported here were similar to those re-ported in the previous tables and this indicated that minorityand disadvantaged students do not benefit more from effec-tive teachers than other students.

Teacher Effects in High-Minority and High-Female Schools

The results of this analysis are summarized in Table 7. Allestimates reported are standardized regression coefficients.Also, for simplicity we report estimates of the teacher ef-fects, the minority or female school composition, and theirinteractions. The upper panel of Table 7 summarizes theresults for minority school composition. The main teachereffects were positive and significant as in the previous tables.The main high-minority school effect was negative as ex-pected but not significant. The interaction effect in readingwas virtually zero. However, the interaction effect in math-ematics was statistically significant and slightly smaller inmagnitude than the main teacher effect. This result suggeststhat teacher effects in mathematics are more pronouncedin high-minority schools. That is, in high-minority schoolsthere is an additional benefit in fourth grade mathematicsfrom having an effective teacher in Grade 3. The differentialresidualized teacher effects (adjusted for previous achieve-ment) on high-minority schools are comparable. The mainteacher effects were smaller in magnitude as expected, butthey were statistically significant. The main high-minorityschool effects were negative and not significant. In math-ematics the interaction effect was considerable and signifi-cant, whilst in reading the interaction was virtually zero andnot significant.

The lower panel of Table 7 summarizes the results forfemale school composition. The main teacher effects werepositive and significant as in the previous tables. The main

high-female school effect was negative but not significant.The interaction effects both in mathematics and readingwere virtually zero and not significant. The differential resid-ualized teacher effects (adjusted for previous achievement)on high-female schools are comparable. Only now, the mainteacher effects were smaller in magnitude as expected, butthey were still statistically significant. The main high-femaleschool effects were virtually zero. The interaction effectswere also virtually zero and not significant. That is, we foundno evidence that teacher effects are more pronounced inschools with higher proportions of female students.

The results from the analyses that examined the variabil-ity of teacher effects across classrooms and schools indicatedthat the estimates of teacher effects did not vary much be-tween classrooms within schools or between schools. Theseresults are reported in Table 8 and suggest that the estimatesof teacher effects are virtually similar across classrooms andschools and that there are not interactions between teachereffects and classroom and school context.

Discussion

The present study examined how teachers influence Grade4 achievement of female, minority, and low-SES students.We used high-quality data from Project STAR and its follow-up study, LBS. First, the results of our study indicate thatteacher effects in Grade 3 affect positively Grade 4 achieve-ment in mathematics, reading, and science for all studentsnet of the effects of Grade 4 teachers. In reading and sci-ence in particular the teacher effects were larger than thegender gap and similar in magnitude to the race gap whichis typically nontrivial. The estimates in reading and sci-ence indicated that having an effective teacher in Grade3 increases Grade 4 achievement by about one tenth of astandard deviation, which is a considerable effect in educa-tion. To put the magnitude of the teacher effect estimatein reading in context we compared it to estimates of annualgains in achievement provided by Hill et al. (Hill, Bloom,Black, & Lipsey, 2008). The comparison indicated that theteacher effect in reading is approximately one fourth of ayear’s growth in reading achievement, and we argue thatthis is a considerable effect. This finding supports the notionthat effective teachers in third grade can increase fourthgrade achievement significantly for all students. However,the residualized teacher effects were small and not signifi-cant both in mathematics and reading. That is, once Grade2 achievement is controlled for, teacher effects in Grade 3are not significant predictors of Grade 4 achievement giventhe effects of Grade 4 teachers. Our findings also indicatethat teacher effects are cumulative and that having effec-tive teachers in successive years (kindergarten to Grade 3)leads to larger gains in achievement in Grade 4 in math-ematics and reading. However, the residualized cumulativeteacher effects were insignificant. In addition, in all specifi-cations variance component estimates were significant indi-cating differences in achievement between classroom within

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schools and between schools. In all analyses we controlledfor Grade 4 teacher effects. We also ran models using grand-mean centering for student-level predictors and obtainedestimates that were similar to those reported here. That is,centering did not seem to affect the estimates much in ourstudy. In other sensitivity analyses we controlled for schoolfixed effects and obtained very similar regression coefficients.

Second, and most important for this study, there was noevidence of differential teacher effects on student achieve-ment. All interactions between Grade 3 teacher effects orcumulative teacher effects and gender, race, or SES werevery small in magnitude and insignificant. Our results suggestthat, overall, all student groups benefit equally from effectiveteachers. That is, it appears that minority and disadvantagedstudents do not benefit more from effective teachers thanother students. This replicates findings of Sanders and Rivers(1996), who reported that all types of students benefitedequally from effective teachers. This finding is unfortunate,because it is tempting to think of teachers as school resourceswho not only promote student achievement for all but closethe achievement gap at the same time.

It should be noted however, that the interaction effectswere not statistically significant likely because the over-whelming majority of the estimates were grossly underpow-ered. That is, the statistical power of the t tests for most ofthe interaction terms was overall small. The probability ofdetecting a significant interaction typically ranged from 5 to25% and in a few cases the probability of detecting an inter-action effect was around 40%. This is not surprising becauseinteraction effects are typically more likely to be underpow-ered than main effects. However, this is a limitation of thestudy, in that it is unclear that the interaction effects arenot important, but the majority of them are not statisticallysignificant.

Third, we also examined whether teacher effects are morepronounced in schools with higher proportions of minorityor female students. We did not find any evidence of inter-action effects in reading. However, the interaction effectin mathematics was statistically significant and considerablein magnitude. That is, teacher effects are more pronouncedin high-minority schools, or in high-minority schools thereis an additional benefit in mathematics from having effec-tive teachers. This finding is in congruence with results re-ported from Nye et al. (2004). The differential residualizedteacher effects adjusted for previous achievement on high-minority schools are comparable. In mathematics the in-teraction effect was considerable and significant, whereasin reading the interaction was virtually zero. However, wedid not detect any interactions between teacher effects andschools with high proportions of female students. Also, thedifferential residualized teacher effects adjusted for previousachievement on high-female schools are comparable. Ourresults suggest no evidence that teacher effects are morepronounced in schools with higher proportions of femalestudents. We also examined whether the teacher effects es-timates were consistent across classrooms and schools by

treating the teacher effects estimates as random effects at thesecond (classroom) and at the third (school) level. These re-sults indicated that overall, the estimates of teacher effectsdid not vary between classrooms or schools. This finding sug-gests that the magnitude of teacher effects is consistent anddoes not depend on the classrooms or schools that studentsattend in Grade 4.

Given that our results suggest that all students benefitequally from effective teachers, which demonstrates that ef-fective teachers can make a difference, and that the teachereffects are more pronounced in high-minority schools (inmathematics), it is important to mandate policies withinthe NCLB framework that encourage effective teachers toteach in schools with high proportions of minority and dis-advantaged students. Providing these students with greateraccess to effective teachers is crucial for improving equalityof educational opportunity. These policies should also helphigh-poverty and high-minority schools to recruit and retaineffective teachers.

To conclude, although this study demonstrates positiveteacher effects for all students, there is no evidence ofdifferential teacher effects for minority and disadvantagedstudents. However, there is some evidence that teachersmake more of a difference in mathematics in high-minorityschools. In addition, the study does not unravel the mech-anism through which teachers affect student achievement.This caveat is due to the definition of teacher effects, whichis general and does not allow examination of associations be-tween observed teacher characteristics or teaching practicesand student achievement. Unfortunately, data about teach-ing practices in classrooms are not available. Such detailedobservational data are necessary to unveil the mechanismof teacher effectiveness because they provide informationabout instructional processes and interactions between stu-dents and teachers. A well-designed study with the objec-tive of collecting high-quality observational classroom datawould provide invaluable information about the mechanismof teacher effectiveness.

REFERENCES

Borman, G. D., & Kimball, S. M. (2005). Teacher quality and educationalequality: Do teachers with higher standards-based evaluation ratings closestudent achievement gaps? Elementary School Journal, 106, 3–20.

Brophy, J. (1986). Teacher influences on student achievement. AmericanPsychologist, 10, 1069–1077.

Brophy, J. (1988). Research linking teacher behavior to student achieve-ment: Potential implications for instruction of Chapter 1 students. Edu-cational Psychologist, 23, 235–286.

Coleman, J. S., Campbell, E. Q., Hobson, C. J., McPartland, J., Mood,A. M., Weinfeld, F. D., & York, R. L. (1966). Equality of educationalopportunity. Washington, DC: U.S. Government Printing Office.

Cronbach, L. J., & Snow, R. E. (1977). Aptitudes and instructional methods.New York, NY: Irvington.

Darling-Hammond, L. (1995). Inequality and access to knowledge. InJ. A. Banks (Ed.), Handbook of research on multicultural education(pp. 465–483). New York, NY: Macmillan.

Dee, T. S. (2004). Teachers, race and student achievement in a randomizedexperiment. Review of Economics and Statistics, 86, 195–210.

Ferguson, R. F. (1998). Can schools narrow the Black-White test scoregap? In C. Jencks & M. Phillips (Eds.), The Black-White test score gap(pp. 318–374). Washington, DC: Brookings Institution Press.

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Goldhaber, D. D., & Brewer, D. J. (1997). Why don’t schools and teachersseem to matter? Assessing the impact of unobservables on educationalproductivity. Journal of Human Resources, 32, 505–523.

Good, T. (1979). Teacher effectiveness in the elementary school. Journalof Teacher Education, 30, 52–64.

Good, T., & Brophy, J. (1987). Looking in classrooms. New York, NY: Harper& Row.

Greenwald, R., Hedges, L. V., & Laine, R. D. (1996). The effect of schoolresources on student achievement. Review of Educational Research, 66,361–396.

Hanushek, E. A. (1971). Teacher characteristics and gains in studentachievement: Estimation using micro data. American Economic Review,61, 280–288.

Hanushek, E. A. (1986). The economics of schooling: Production andefficiency in public schools. Journal of Economic Literature, 24, 1141–1177.

Hanushek, E. A. (1992). The tradeoff between child quantity and quality:Some empirical evidence. Journal of Political Economy, 100, 84–117.

Hill, C. J., Bloom, H. S., Black, A. R., & Lipsey, M. W. (2008). Empiricalbenchmarks for interpreting effect sizes in research. Child DevelopmentPerspectives, 2, 172–177.

Krei, M. S. (1998). Intensifying the barriers—The problem of inequitableteacher allocation in low-income urban schools. Urban Education, 33,71–94.

Krueger, A. B. (1999). Experimental estimates of education productionfunctions. Quarterly Journal of Economics, 114, 497–532.

Langford, H., Loeb, S., & Wyckoff, J. (2002). Teacher sorting and the plightof urban schools: A descriptive analysis. Educational Evaluation and PolicyAnalysis, 24, 37–62.

Murnane, R. J., & Phillips, B. R. (1981). What do effective teachers ofinner-city children have in common? Social Science Research, 10, 83–100.

Nye, B., Hedges, L.V., & Konstantopoulos, S. (1999). The long-term ef-fects of small classes: A five-year follow-up of the Tennessee class sizeexperiment. Educational Evaluation and Policy Analysis, 21, 127–142.

Nye, B., Hedges, L. V., & Konstantopoulos, S. (2000). The effects of smallclasses on achievement: The results of the Tennessee class size experi-ment. American Educational Research Journal, 37, 123–151.

Nye, B., Konstantopoulos, S., & Hedges, L.V. (2004). How large are teachereffects? Educational Evaluation and Policy Analysis, 26, 237–257.

Raudenbush, S. W. (2004). What are value-added models estimating andwhat does this imply for statistical practice? Journal of Educational andBehavioral Statistics, 29, 121–129.

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models. Thou-sand Oaks, CA: Sage Publications.

Raudenbush, S. W., & Wilms, J. D. (1995). The estimation of school effects.Journal of Educational and Behavioral Statistics, 20, 307–335.

Rowan, B., Correnti, R., & Miller, R. J. (2002). What large-scale, surveyresearch tells us about teacher effects on student achievement: Insightsfrom the Prospects Study of elementary schools. Teachers College Record,104, 1525–1567.

Sanders, W. L., & Rivers, J. C. (1996). Cumulative and residual effects ofteachers on future student academic achievement. Knoxville, TN: Universityof Tennessee Value-Added Research and Assessment Center.

AUTHORS NOTE

Spyros Konstantopoulos is an Associate Professor of Mea-surement and Quantitative Methods at the College of Ed-ucation at Michigan State University. His empirical workfocuses on teacher, school, and class size effects, as well asthe achievement gap. His methodological work focuses onpower computations for nested designs.

Vicki Chung, PhD, works as a Quantitative Analyst forLong Wing Education Consulting. Her research interestsinclude education, teacher quality, and school accountabil-ity/standards.

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