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Race and Academic Achievement in Racially Diverse High Schools: Opportunity and Stratification

by Chandra Muller, Catherine Riegle-Crumb, Kathryn S. Schiller, Lindsey Wilkinson & Kenneth A. Frank - 2010

Background/Context: Brown v Board of Education fundamentally changed our nation’s schools, yet we know surprisingly little about how and whether they provide equality of educational opportunity. Although substantial evidence suggests that African American and Latino students who attend these schools face fewer learning opportunities than their White counterparts, until now, it has been impossible to examine this using a representative sample because of lack of data.

Purpose/Objective/Research Question/Focus of Study: This study uses newly available data to investigate whether racially diverse high schools offer equality of educational opportunity to students from different racial and ethnic groups. This is examined by measuring the relative representation of minority students in advanced math classes at the beginning of high school and estimating whether and how this opportunity structure limits the level of achievement attained by African American and Latino students by the end of high school.

Setting: This study uses data from the Adolescent Health and Academic Achievement Study (AHAA) and its partner study, the National Longitudinal Study of Adolescent Health (Add Health), a stratified, nationally representative study of students in U.S. high schools first surveyed in 1994–1995.

Population/Participants/Subjects: Two samples of racially diverse high schools were used in the analysis: one with African Americans, Whites, and Asians (26 schools with 3,149 students), and the other with Latinos, Whites, and Asians (22 schools with 2,775 students).

Research Design: Quantitative analyses first assess how high schools vary in the extent to which minority students are underrepresented in advanced sophomore math classes. Hierarchical multilevel modeling is then used to estimate whether racial-ethnic differences in representation in advanced math have an impact on African American and Latino students’ achievement by the end of high school, relative to the Whites and Asians in the school. Specifically, we estimate the effects of Whites’ and Asians’ overrepresentation in sophomore-year math (or Latino or African American underrepresentation) within the school on students’ senior-year grades and their postsecondary enrollment.

Findings/Results: Findings show that schools vary in the extent to which African American and Latino students are underrepresented in advanced sophomore math classes. This pattern of racial inequality in schools is associated with lower minority senior-year grades and enrollment in 4-year postsecondary institutions, net of students’ own background.

Conclusions/Recommendations. Evidence consistently suggests that schools can play an active role in the provision of opportunities for social mobility or in the exacerbation of social inequality, depending on how they are structured. It is important to consider racial stratification within schools as a mechanism of inequality of educational opportunity.

Academic success in high school has major consequences for adolescents socioeconomic status (SES) and well-being in adulthood and for the structure of social stratification among our next generation. Not only does our educational system teach skills, socialize students, and create opportunities for social interaction that contribute to positive outcomes, but it also allocates degrees, certifications, and credentials recognized by employers and others. As a major determinant of intergenerational stratification, the importance of equal access to educational opportunity has long been recognized, yet the complexity of accomplishing it in the stratified society of the United States has defied public policy efforts.

Over half a century ago, Brown vs. Board of Education focused attention on racial inequality in access to schools and decreed that separate was unequal and that racially integrated schools would offer greater educational opportunity for African American students. A decade after the Brown decision, the Coleman Report (Coleman et al., 1966) detailed the extent of inequality that stemmed from racially segregated schools and drew attention to the profound effects of social background on preparation and opportunities to learn. Several decades later, after the implementation of busing, magnet schools, and other policies to desegregate schools, attention turned to tracking, or within-school grouping of students, as a location of inequality in the opportunity to learn (Gamoran, 1987; Hallinan & Sorensen, 1983; Oakes, 1985). As our nation still struggles to integrate schools, our public schools are becoming more racially segregated because of the increasing number of school-age minority children in the United States (Logan, 2004). Similarly, although the Latino population has been attending U.S. schools for generations, rapid relative growth of this population demands that we recognize that school segregation and integration is more than a Black and White issue (Reardon, Yun, & Eitle, 2000).

Even racially diverse schools may be racially segregated internally, allowing for minimal interracial contact and possibly undermining the benefits of school desegregation (Mickelson, 2001). Further, if schools are academically segregated, such that minority students have less access to advanced-level courses, this indicates not only that minority students are being given fewer opportunities to learn but also that they are also subject to institutional messages about the different academic roles and expectations that pertain to them. This study empirically examines the opportunity structure of racially diverse schools by focusing on the relative representation of minority students in advanced math classes at the beginning of high school and subsequently examines how this structure limits the level of achievement attained by African American and Latino students by the end of high school.

It is worth emphasizing that we are able to address the measurement problems stemming from the strong association between race and social class for individual students as well as within schools by using new nationally representative longitudinal data of high schools and their students from the combined Adolescent Health and Academic Achievement Study (AHAA) and the National Longitudinal Study of Adolescent Health (Add Health). Although much research has suggested or alluded to the possibility of lower level opportunities to learn for minority students in many racially diverse schools, our data enable us to examine this systematically. Additionally, we consider the existence of academic segregation within schools and its consequences for Latino students, as well as Black students, and therefore extend beyond the scope of most existing literature.


Both the Brown decision and the Coleman Report underscored the potential advantages of racially integrated schools as a vehicle for achieving racial equality of educational opportunitiesBrown through equal access to the schools financial resources, facilities, and interracial contact, and Coleman through access to the resources available as a result of the SES of the schools parent community, and social contact more generally. Certainly there is evidence that integrated schools provide African American students better opportunities than racially segregated schools (Braddock & McPartland, 1988; Clotfelter, 2004; Rumberger & Willms, 1992), and evidence suggests that African American students in integrated schools earn better reading scores, though not necessarily better scores on math achievement tests (Cook & Evans, 2000).

A major concern about racially diverse schools is that African American and Latino students opportunities to learn will be reduced because the school will be racially segregated internally, with high levels of racial homogeneity in classrooms. Two decades ago, Jeannie Oakes (Oakes, 1985) provided compelling qualitative evidence that the experiences and opportunities of students in integrated schools were unequal because the schools tracking systems functioned to segregate African Americans from Whites. Shortly after, however, with nationally representative data from High School and Beyond (HSB), Gamoran and Mare (1989) found that background and preparation, rather than race alone, were the source of race differentials in track assignments. Effectively, they argued, race-based course assignment practices could be explained by family background and students academic preparation.

A significant body of recent research on schools has accumulated that calls into question the assertion that social class and academic preparation alone can explain racial stratification within schools. Racially diverse schools could have racially segregated courses, and even academically prepared African American and Latino students may end up in separate and lower level classes than Whites for several reasons. They may choose lower level classes because of oppositional culture (Fordham & Ogbu, 1986; Ogbu, 2003) or peer influence (Hallinan, 1982, 1983), or, in the case of the most advanced courses such as Advanced Placement (AP) classes, they may be subject to a stereotype threat and believe that minority students perform less well (Steele & Aronson, 1995). Finally, minority students may be placed in less advanced classes because of racial preferences of school personnel (Mickelson, 2001). Even if the practice of tracking has changed such that the mechanism for stratifying students involves a more nuanced sorting across multiple academic subjects (Lucas & Good, 2001), the allocation of students to courses may still be associated with race, or the presence of a de facto tracking system (Lucas & Berends, 2002).

Taken together, these studies suggest that contemporary integrated schools may be stratified internally according to race beyond stratification expected from SES differences within the school. Further, it suggests that this stratification may indicate differential educational opportunities for Whites relative to African American and Latino students in these schools. Ideally, the assessment of whether racially diverse schools offer educational opportunity to African American and Latino students would not only take the schools opportunity structure into account but also estimate the effect of that structure on students who move through the school, from the important early years to completion of the final years of preparation for postsecondary education. Such an assessment has not been possible on a national scale until now, with the high school transcript study linked to the Add Health data.


The structure of math curriculum in the United States is an ideal single indicator and starting point for studying mechanisms of stratification and opportunity within schools because of its sequenced nature through the use of gatekeeping courses and prerequisite knowledge (Schneider, Swanson, & Riegle-Crumb, 1998). Students who complete algebra as ninth graders and geometry the following year can progress to algebra II as juniors (Riegle-Crumb, 2006), a key course for preparation for college (Pallas & Alexander, 1983) Therefore, early course placement largely determines how far students go in math by the end of high school. The exception is that most states and school districts do not require students to take 4 years of high school math, though all require at least 2 years of math, and many require that students pass a minimum level of competency in algebra. By senior year, about 60% of U.S. high school students choose not to enroll in any math course (Schiller & Muller, 2003). Choosing to take less math may impact students preparation for postsecondary education.

We argue that the presenceor absenceof minority students in advanced math classes in the beginning of high school is a visible indication of the academic opportunities available to African American and Latino students within the school. If very few minority students are in such classes, this is a clear signal that elite academic positions both within high school and beyond are not the typical domain of students of color. The underrepresentation of minority students in advanced math classes is an indicator that opportunities to learn within the school are bounded by race and ethnicity, and this likely extends beyond math classes to how academic efforts and achievements are rewarded. Beyond the individual academic abilities and background of minority students, the existence of a limited opportunity structure is likely to shape their future educational efforts and experiences, perhaps by giving African American and Latino students little reason to expect that they can get ahead and be academically successful. Additionally, to the extent that the prevailing academic opportunity structure is racially stratified, teachers and other school personnel may also discourage the achievement of minority students, either overtly or more subtly. In short, an institutionalized system of constrained opportunities for minority students at the beginning of high school is likely to influence their subsequent achievement, regardless of their own degree of academic promise.  

The objective for this study is to assess whether racially diverse high schools offer equality of educational opportunity to students from different racial and ethnic groups. Additionally, because the race and social class backgrounds of students in the school may be linked to one another and to academic preparation, we must hold constant a students background on entry into the school and consider what the school adds to the students academic skills and preparation for future educational attainment. We begin with an investigation of the opportunity structure of racially diverse schools by considering whether schools vary in the extent to which minority students are underrepresented in advanced sophomore math classes. We consider what aspects of schools themselves may help to explain this variation. Next, we model whether racial-ethnic differences in representation in advanced math have an impact on African American and Latino students achievement by the end of high school, relative to the Whites and Asians in the school. Specifically, we estimate the effects of Whites and Asians overrepresentation in sophomore-year math (or Latino or African American underrepresentation) within the school on students senior-year grades and their postsecondary enrollment. We consider two types of racially diverse schoolsthose with a mix of African American and White/Asian students, and those with Latinos and Whites/Asiansand conduct separate analyses for each.


We used data from the National Longitudinal Study of Adolescent Health (Add Health) and the high school transcript study of Add Health respondents, the Adolescent Health and Academic Achievement Study (AHAA; Muller et al., 2007). Using a two-stage stratified sampling design, 80 high schools with an 11th grade and their feeder middle schools were selected for the Add Health study according to their region, urbanicity, sector, racial composition, and size. An In-School survey was administered to all students attending school on a survey day during the 19941995 school year. The roster from this sample was augmented with school records to draw a representative sample of boys and girls (in equal numbers) in Grades 712 to participate in the longitudinal study that currently includes three waves of data. Three waves of In-Home survey data were collected in 1995, 19951996, and 20002001; the Wave III sample includes 15,163 young adults.

In 20022003, when almost all Add Health respondents were no longer attending high school, the AHAA study collected the high school transcripts and other data from the high schools last attended by Wave III Add Health respondents. Transcripts were collected and coded for approximately 12,250 Wave III respondents, or 81% of the Wave III Add Health sample. Two special education schools from the original Add Health sample of high schools were excluded from AHAA because they did not keep transcripts for their students.

Each course that appeared on the transcripts was coded with a standard coding scheme, the Classification System for Secondary Courses (CSSC), using information provided by the schools about the courses offered at the particular school. Course grades were coded in a standard format, and the courses were assigned Carnegie Units for comparability across schools. The coding schemes were comparable with those used in the National Assessment of Educational Progress High School Transcript Studies (NAEP-HSTS) and are similar to those used in the National Education Longitudinal Study (NELS) of 1988 and HSB. Courses taken at an Add Health high school were coded as having been taken there even if the student subsequently transferred away, providing a representative sample of courses taken at each Add Health high school in the 19941995 school year.


Using the Add Health and AHAA data, we estimated multilevel models for two indicators of academic achievement. Our first dependent variable was the grade point average (GPA) of all senior-year courses, constructed from transcript data by the AHAA study. The second dependent variable was based on Wave III survey responses and measured whether the student was currently attending, or graduated from, a 4-year college. The reference category included students who graduated from high school, those who attended or graduated from 2-year colleges, and students who started at 4-year colleges and dropped out. These models were estimated for high school graduates only.


School-level measures. To capture the academic opportunity structure within high schools in racially diverse schools, we constructed a key school-level indicator to measure the underrepresentation of African American or Latino students in advanced math classes at the beginning of high school, relative to the representation of White and Asian students. We focused on the proportion of students of different race and ethnicities in advanced math as sophomores because not all Add Health high schools included a ninth grade. We used the math sequence variable from the AHAA study, which is an ordinal variable ranging from 0 to 9 that indicates the math course that students take in each year of high school (Riegle-Crumb, Muller, Frank, & Schiller, 2005). The modal category for sophomore year is geometry, a value of 5 on the variable. Thus, advanced math is defined as taking algebra II or above as a sophomore (which also indicates that the student usually began high school taking geometry). Sophomore algebra II students are positioned to advance to college and take calculus in their senior year of high school. Using indicators of students race from self-reports at Wave I (with missing values substituted from the In-School survey when possible) combined with the math sequence variable from AHAA, we measured minority underrepresentation with a log odds ratio defined as:


where Pr(Y=1|White or Asian) and Pr(Y=1|African American) represent the race-specific probabilities of advanced math course placement, and Pr(Y=0|White or Asian) and Pr(Y=0|African American) represent the race-specific probabilities of nonadvanced math placement. An analogous measure was constructed for the Whites and Asians compared with Latinos, substituting Latino for the African American group in the equation. The higher the positive value on this variable, the greater the African American or Latino underrepresentation in advanced math at the beginning of high school, or, conversely, the greater the White and Asian overrepresentation.

It is important to note that because of the low frequency of Asian students in many of the schools in our sample, estimating effects for these students across schools was problematic. Furthermore, Asian students were very similar to White students in terms of levels of academic coursework and grades. For these reasons, we chose to combine White and Asian students when estimates refer to academic indicators; we retained distinct categories for African American and Latino students.

To accurately measure this type of stratification, we needed a representative sample of students in each school. When sample weights are used, the AHAA data provide a representative sample of students enrolled in each Add Health high school during the 19941995 academic year. For these measures, we used data from all respondents who were in 10th grade in the school years 19941995 and 19951996. We extended the course enrollment window to 2 years rather than the single 19941995 academic year to obtain a larger sample of students for a more reliable estimate; we excluded students who repeated the course during the 2 academic years.1 To obtain representativeness, we included all sample members who were attending the school during the 19941995 academic year even if they later transferred out of the school before graduation.

Additionally, we controlled for the logit of the proportion of students enrolled in algebra II or above in 10th grade during the 19941996 academic years, which taps the distribution of sophomores in the school above the nations modal category of geometry. Thus, we controlled for the overall proportion of students in the school who were taking advanced math as sophomores, in addition to our key measure, described previously, which taps the extent to which African American and Latino students were underrepresented relative to Whites and Asians in these courses. The transcript sample weight was used to construct these indicators. Using data from the In-School survey and the In-School weight, we estimated the logit of the proportion of students in the school with college-educated parents. We also constructed a log odds ratio analogous to our minority underrepresentation in advanced math indicator to capture the difference between the proportion of White and Asian students in the school with a college-educated parent, and the proportion of either African American or Latino students with a similarly educated parent. The higher the positive value on this variable, the greater the White/Asian parental educational advantage, or, conversely, the greater the African American or Latino parental educational disadvantage. We controlled for the logit proportion of Latinos in the school and the logit proportion of African Americans in the school.2 Finally, we controlled for the school location (urban, suburban or rural)3 and region (South versus other).4

Individual-level measures. At the individual level, we controlled for students sex, parents highest level of education, and students score on the Add Health Peabody Picture Vocabulary Test (AH-PVT). Missing values for AH-PVT were imputed with the IMPUTE command in STATA using parents education, sex, and Wave I self-reported grades as predictors, and missing flags were included in all models. Our models also controlled for students GPA during freshman year of high school, which was constructed from the high school transcripts. Freshman year is an important transitional year and an early indicator of performance and potential that predicts academic achievement throughout high school (Roderick & Camburn, 1996; Schiller, 1999). Furthermore, grades capture the effort that students expend in the course and their ability to successfully complete course demands and other aspects of the teachers evaluations of performance, which could influence performance. Controlling for freshman grades in our models helped to isolate students achievement in high school that was independent of performance on arrival in the school and helped us focus on the effects of the school. The models of senior-year GPA and 4-year college enrollment included a control for students own level of sophomore-year math course taken. For Latino students, we also included in our models whether Spanish was the main language spoken at home and their generational status as background controls.


We restricted our analyses to schools that had diverse student populations, such that at least 7% of the student body was either African American or Latino, and White and Asian students represented at least 25% percent of the student body.5 In other words, schools that were homogenous with respect to race (i.e., all African American, all Latino, or all White) were excluded from the analysis. This criterion excluded 26 predominantly White schools, 5 predominantly Latino schools, and 6 predominantly African American schools out of 78 possible schools. Two schools that met the criteria of either 7% African American or Latino students based on the In-School survey were excluded because their transcript samples included no minority students in 10th grade in 19941996. It was essential to exclude these schools for the construction of our measure, described previously, of racial stratification in elite gatekeeping math courses. An additional outlier school was excluded from the analysis because of the overwhelmingly large proportion of students in the school who were classified as taking advanced math in 10th grade, such that there was no variation in the dependent variable for course-taking. Our final analytic sample includes 26 schools that met the criteria for African American and White/Asian students, and 22 schools for Latino and White/Asian students. These two groups of schools were used as separate analytic samples to model the distinct effects of school attributes on African American and Latino students, respectively. Ten schools were common to both samples because they had a sufficient representation of both African American and Latino students.6

Within these racially diverse schools, students were included in the longitudinal multilevel models if they last attended the Add Health school; however, they were excluded if they transferred and last attended another school because we were interested in estimating the contextual effects of the Add Health schools on students achievement at the end of high school. Furthermore, we excluded students who did not fall into one of our four racial categories of interest. To ensure that students in our analytic sample were representative of the high schools they were attending, we also excluded students who entered the Add Health survey as middle school students. In addition, we excluded students without a sample weight, freshman-year transcript-derived grades, or parents education level.7  Students were also excluded from analyses if they had missing data on the dependent variable in question. After these exclusions, we had 3,149 students for the African American/White sample and 2,775 students for the Latino/White analysis. The final sample sizes, along with descriptive statistics for all variables, are shown in the appendix.

Table 1 compares our two samples of racially diverse schools with the larger AHAA sample of schools. The columns for African American schools and Latinos schools show the particular subset of schools in each of those samples. Racially diverse schools were more likely to be in urban areas. The African American diverse schools were much more likely to be in the South, and the Latino diverse schools were disproportionately in the West and Northeast. On average, the three groups of schools were quite similar with respect to the proportions of college-educated parents and the proportion of students enrolled in advanced math classes.

Table 1. Comparison of AHAA School Samples (Weighted)


Complete Sample

(n = 78)

African American


(n = 26)

Latino Schools

(n = 22)

Proportion college-educated parents




Proportion in advanced math




Proportion African American




Proportion Latino




Proportion Asian




Proportion White

































We use hierarchical linear modeling (HLM) to account for the clustering of students within schools and to estimate the separate effects of students individual characteristics (level 1) on their academic status from those effects related to the characteristics of the school they attend (level 2). HLM is particularly useful because it allows us to estimate the extent to which racial stratification in a school contributes to racial gaps in educational opportunity independent of students own characteristics. In a model in which the dependent variable is GPA, for example, by introducing cross-level interactions between school-level characteristics and individual-level characteristics, we can determine whether the overall negative effect between African American (an individual-level attribute measured at level 1) and GPA varies according to the academic opportunity structure of the school (measured at level 2). Furthermore, HLM allows us to model the general effects of school context on the outcome for an average student across schools by modeling the level 1 intercept, β0j.

HLM simultaneously estimates coefficients at each level of analysis. The example described here is for predicting students’ GPA. The level 1 model estimates for each school j the coefficients for the individual variables for predicting the dependent variable (Equation 1). In our analyses, all the individual-level variables are grand-mean centered except those designated with an *, which are group-mean centered. This enables us to directly estimate the school mean effect by including the average of a separate school-level variable. This centering allows the intercept ß0j to be interpreted as the average outcome for a school adjusted for the characteristics of students in that school.

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The level 2 model estimates how the intercept (β0j), or the average outcome, and the race gaps (ß1j for African Americans or ß2j for Latinos) vary between schools based on school characteristics. To ensure sufficient within-school representation of racial groups for estimating the race gaps, we only modeled ß1j for the African American/White racially diverse schools and ß2j for the Latino/White schools. All the school characteristics were centered on their grand means. Equation 2 shows the equations describing the effects of school characteristics for our subsample of 26 African American racially diverse schools. The coefficients γ00 and γ10 for school characteristics are essentially the estimated β0j or ß1j for the average school. The coefficients for school characteristics are adjustments to either the estimated average outcome in a school, or the estimated race gap.

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The models are basically the same for the other outcome and attending a 4-year college. The major difference is that college enrollment is based on a level 1 logistic regression, coefficients from which are modeled as a linear variable on level 2.



A primary goal of this article is to examine the academic opportunities for African American and Latino students in racially diverse schools. As discussed, we tapped this institutional structure of school by measuring the underrepresentation of these minority students in advanced math classes as sophomores, or, conversely, the overrepresentation of White and Asian students. As seen in the appendix table, the mean for this variable was 1.32 for the measure of African American underrepresentation, and 1.41 for the measure of Latino underrepresentation. This indicates that the average school is characterized by minority students being underrepresented relative to White and Asian students in advanced sophomore math classes. Additionally, there is substantial variation in this measure, such that maximum of both variables is over a value of 4. Thus, it is clear that although on average, White and Asian students are overrepresented in advanced math, this is more the case in some schools than in others.

Table 2 displays correlations between this school-level measure of academic stratification and other school-level characteristics, including other academic characteristics, racial composition of the school, variables relating to the social class background of students within the school, and indicators of school size, sector, and location. All correlations with these school characteristics and the indicator of African American underrepresentation in advanced math are small and nonsignificant. For the indicator of Latino underrepresentation, there are modest correlations with the percent of students parents with a college degree and the mean GPA of students within the school. Additionally, there is a positive and significant correlation with suburban schools, and a negative significant correlation with urban schools. Thus, we can conclude that schools with higher levels of Latino underrepresentation in advanced math are characterized by slightly higher levels of social class and academic performance. Although the correlations are relatively modest in size, there is some evidence that the schools where Latino students have the most limited academic opportunities are schools that are somewhat privileged.  This stands in contrast to schools with higher levels of African American underrepresentation in sophomore advanced math classes, which are not characterized by higher levels of social class, nor by higher overall levels of student performance. In our subsequent analytic models, we controlled for these other school characteristics to discern the independent effects of the academic opportunity structure in the school on the subsequent individual achievement of African American or Latino students.8

Table 2. School-Level Correlations Between the Level of Black or Latino Underrepresentation in Advanced Sophomore Math Classes and Other School Characteristics


Black Underrepresentation

Latino Underrepresentation

Percent Black or Latino



Percent sophomores in advanced math



Percent of parents with a college degree



Disparity between White and minority students parent education level



Mean grade point average of students



Disparity between White and minority students grade point average



School size



Private school



Suburban school



Urban school




Number of schools



*p < .05. **p < .01. *** p < .001. Correlations are weighted.


We now consider the consequences for minority students of attending a school where access to advanced courses is racially stratified rather than equitable. In a society in which a college degree is a necessary step for access to professional occupations, a key role of high schools is to prepare students for postsecondary education. Thus, our next step is to estimate whether academic stratification in the school shapes the final academic performance and postsecondary matriculation of African American and Latino students.

Table 3 contains results from multilevel models predicting senior-year GPA and 4-year college enrollment for students in the African American racially diverse schools sample. The top rows of the table show coefficients for the school effects, the middle portion shows the cross-level interactions between school characteristics and the African American race gap (relative to Whites and Asian students), and the lower section has the individual-level controls.9 We focus on two main findings about equality of educational opportunity.

First, on average, there is no African American race gap in GPA net of background, verbal ability, freshman-year performance, and sophomore course placement, as indicated by the insignificant intercept for African American students. In fact, African Americans in these racially diverse schools are more likely than Whites and Asians to enroll in 4-year colleges after high school, once controlling for all other factors in the model (the intercept is .454 and significant).10

Second, in spite of the general absence of a negative race effect on the outcomes, we find that the race gaps for GPA and college enrollment vary across schools and are associated with the academic opportunity structure of the school. Specifically, the race gap in senior-year GPA is larger (and significant) in schools where Whites and Asians are overrepresented in advanced sophomore math courses (-.035). In addition, Whites and Asians overrepresentation in advanced sophomore math reduces the relative advantage of African Americans in 4-year college enrollment (-.136). This suggests a potential lasting effect on achievement. Other significant school-level effects indicated that African American students had lower GPAs in schools where White and Asian students had a parental educational advantage and more African Americans attended the school, and they had a lower probability of going to college when they attended schools with higher aggregate levels of parent education.

To get an idea of the meaning of the estimated effect of White/Asian overrepresentation in advanced math on students GPA, we calculated predicted values for the GPA of African Americans compared with Whites and Asians for otherwise average students in three types of schools: those that are average, and those that are one standard deviation above and below the mean on the overrepresentation of Whites in advanced sophomore math. In average schools, Whites and Asians earned an average GPA of 2.698, compared with African Americans GPA of 2.671, for an estimated race gap of .027. Table 3 shows that this gap (the African American intercept, -.027) is not significantly different from zero. Schools with low levels of overrepresentation indicate no race gap; on average, Whites and Asians are predicted to earn a GPA of 2.658, and African Americans are predicted to earn a GPA of 2.687 in these schools. In contrast, in schools where elite math classes are stratified along race lines, the predicted GPA for Whites and Asians is 2.739, compared with 2.655 for African American students. Although the gap of .084 in these schools is not large, it is triple that of students in average schools, and the statistical significance of the interaction term indicates that it is different from zero. Further, this is an estimated effect for all students in schools with stratified math course-taking and is net of individual background characteristics; thus, it potentially impacts a large number of students. With an increasing emphasis on class rank in college admissions, this gap has the potential to impact students academic success in the long-term.

Table 3. HLM Predicting Senior-Year GPA and 4-Year College Attendance for Students in African American/White and Asian Racially Diverse Schools

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Note. AH-PVT = Add Health Peabody Picture Vocabulary Test.

p ≤ .10. *p ≤.05. **p ≤.01. ***p ≤.001; two-tailed test.

Turning to the analysis of Latinos’ achievement at the end of high school, Table 4 shows models similar to those in Table 3, but for the sample of Latino racially diverse schools. The Latino intercept for the GPA model indicates that, on average, Latino students earn slightly lower GPAs in their senior year of high school when compared with White and Asian students. There is no gap in 4-year college attendance once background and early performance are taken into account. However, the cross-level interactions for 4-year college enrollment, shown in the middle section of the model predicting college attendance, suggest that once background and early performance are held constant, Latinos are more likely (compared with Whites and Asians) to attend a 4-year college if they attended schools with a higher proportion of Latinos or schools in the South.

Table 4. HLM Predicting Senior-Year GPA and 4-Year College Attendance for Students in Latino/White and Asian Racially Diverse Schools

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Note. AH-PVT = Add Health Peabody Picture Vocabulary Test.

p ≤. 10. *p ≤ .05. **p ≤  .01. ***p ≤ .001; two-tailed test.

Results for our key variable of the academic opportunity structure for minority students within schools indicate that both GPA and the probability of college enrollment are lower among Latinos attending schools in which Whites and Asians are overrepresented in sophomore-year math. As with African Americans, this suggests that attending schools where course-taking is racially stratified may have long-term consequences for Latinos achievement. As with the African American school sample, we calculated the predicted GPA for students in average schools, in schools one standard deviation above the mean, and in schools one standard deviation above the mean in the overrepresentation of Whites and Asians in advanced math, with all other variables set to the mean. In schools with less stratification in sophomore math, Whites and Asians earned a senior-year GPA of 2.698, on average, compared with a predicted GPA of 2.735 earned by Latinos. If anything, Latinos have a slight senior-year GPA advantage in these schools once background and early performance are held constant. In contrast, in schools with relatively high levels of academic stratification, the estimated GPA is 2.851, compared with 2.676 for Latinos, or a gap of .175. This is more than double the race gap of Latino and White/Asian students in schools with an average level of academic stratification, who have an estimated GPA of 2.775 and 2.705, respectively, or a gap of .070.


The Brown v Board of Education decision fundamentally changed our nations schools, yet we know little about racially diverse schools as engines of social mobility or agents of social reproduction. In bringing together students of different racial, socioeconomic, and academic backgrounds under one roof, it has been difficult to gauge whether these racially diverse high schools offer academic opportunity to all students. Our results contribute significant new evidence about these schools and the academic achievement of the students who attend them. Using a nationally representative longitudinal sample of schools and the students in them, we found that racially diverse high schools vary in the extent to which they appear to offer equality of educational opportunity to African American and Latino students, compared with Whites and Asians, in the early years of high school. This structure of opportunity in the school is associated with students achievement during the high school years and beyond. Where most of the policy and research attention has been devoted to stratification among African Americans and Whites, we have extended the analysis to the fastest growing segment of the U.S. population: Latinos.

A major obstacle to better understanding whether racially diverse high schools offer equality of educational opportunity has been the lack of national data with sufficiently large samples of students within schools to determine the variance of inequality across schools. The combined Add Health and AHAA data sets provide the first real chance to examine whether there is substantial variation between schools in the academic opportunity structures for students of different races and ethnicities. Capturing this variation was a key goal of this article. With respect to math course-taking early in high school, we found that, on average, African American and Latino students are underrepresented in advanced courses, but the extent of this inequality is greater in some schools than in others. Furthermore, there is little evidence that this school-level inequality is related to issues of social class or academic preparation.

Additionally, our results indicate that the academic opportunity structure of schools has lasting consequences for the individual achievement of African American and Latino students. The racial stratification that comes about through sophomore math course-taking patterns, such that in some schools, Latino and African American students are greatly underrepresented in advanced classes, was associated with lower GPAs and rates of 4-year college enrollment among these minority students compared with Whites and Asians. Such effects are net of powerful controls for background, preparation, early performance, and sophomore course placement. This suggests that how schools assign students to courses may contribute to racial inequality of educational opportunity in some racially diverse schools.

It is likely that the mechanisms that widen the race gap in achievement at the end of high school are different for African American and Latino students, and they may also vary among different Latino ethnic subgroups. Explanations for the widening of an achievement gap during the high school years include different choices made by students within the schools related to oppositional culture, peer influences, or stereotype threat, as well as practices of school personnel related to course placement, guidance and counseling, and even racial discrimination (Mickelson, 2001).

Another finding concerning school effects on equity deserves mention. Notably, we found that in schools where White and Asian students had much higher levels of parental education compared with parents of African American students, African American students tended to earn lower senior-year GPAs even after the individual background, preparation, and early performance variables were held constant. We did not find this pattern among Latinos in our Latino school sample. Our data do not allow us to pinpoint the detailed mechanisms that function to lower African American students GPAs in such a school context. Yet prior research indicates that college-educated parents are strong advocates for their childrens education. They influence course placement in high school (Baker & Stevenson, 1986), are involved in school decision making, and participate in fund-raising organizations (Lareau, 1989; Schneider & Coleman, 1993). If disparities in parents education fall along race linesfor example, if college-educated parents in a school are also predominantly White, and minority parents have much lower levels of educationthen the educational advantages held by White children may be amplified, and at the same time, positional disadvantages among African American students could be exacerbated. As admissions to selective colleges and universities become more competitive and more heavily based on class rank, the implications of our findings that show small advantages in GPA could have profound consequences for attainment of talented minority youth.

Several limitations of this study deserve mention. We do not consider who attends these racially diverse schools, as opposed to predominantly single-race schools. Clearly, attending a school with students of another race is a function of family resources and regional opportunity or individual choice. Although we have controlled some of these factors, there is no doubt that we have omitted variables that are crucial in shaping which students attend this sample of racially diverse schools. The danger is that these factors could also bias the estimates of our coefficients in ways that we are unaware. It is important to underscore that this analysis applies only to high school students who were attending racially diverse schools in the mid-1990s. We cannot generalize to the larger population of high school students or claim that we have identified any causal mechanisms that operate within these schools to bring about greater or lesser opportunity for the students who attend them. We do not know if students who were attending racially homogeneous high schools would have had experiences similar to the ones we observed had they attended racially diverse schools. Rather, we investigated the internal composition and organization among racially diverse high schools, and the association of that variation with students achievement. We argue that the centrality of school integration as an educational policy during the last half-century justifies our attention to the experiences of this population.

Our results suggest that as the demographic composition of our nations schools shifts within the context of school desegregation policy and demographic changes in our school-age population, it is crucial that we examine variations among racially diverse schools. This study has unique value as a contemporary longitudinal and nationally representative sample of schools with large enough within-school samples of students to estimate within-school stratification. Clearly, the mechanisms through which stratification influences adolescents academic achievement and attainment are complex. The processes are likely to be different for African Americans, Latinos, Whites, and Asians. Yet the evidence consistently suggests that schools can play an active role in the provision of opportunities for social mobility or in the exacerbation of social inequality, depending on how they are structured.


This research was funded by grants to the Population Research Center, University of Texas at Austin, from the National Institute of Child Health and Human Development (R01 HD4042802 [Chandra Muller, PI]; 5 R24 HD042849 [Mark Hayward, PI]), the National Science Foundation (REC-0126167 [Chandra Muller, PI], and HRD-0523046 [Chandra Muller, PI, and Catherine Riegle-Crumb, co-PI]). Additionally, this research uses data from Add Health, a program project designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris and funded by a grant from the National Institute of Child Health and Human Development (P01-HD31921), with cooperative funding from 17 other agencies. The authors greatly appreciate comments by Kelly Raley, AHAA project members, Roz Mickelson, and anonymous reviewers.


1. The stratification indicator based on the single year is similar to our measure.

2. The In-School survey was not administered in four Add Health high schools, so for these schools, we used data from the In-Home survey and applied the Wave I sample weight to construct our school composition indicators.

3. We combined suburban and rural schools for the Latino schools sample because there was only one rural school with sufficient numbers of Latinos to be included in our study.

4. In models not shown here, we controlled for school sector (public/private), magnet schools, school size, average school-level race differences (African American or Latino vs. White) in students GPA and AH-PVT scores, and the average income level of residents in the neighborhoods surrounding the school. We also conducted models in which region was coded into several categories, including West, Midwest, Northeast, and South. These variables were not included in the final models for parsimony; they were not significant predictors of the outcomes, and the results we present are consistent with the findings when these other variables were included in our models.

5. Our goal was to include as many schools as possible in the analysis and still have sufficient data numbers of both Whites and minority students within each school to allow for an analysis of the academic performance of each group. The choice of 7% African American or Latino students was primarily a practical one, providing us with this balance of maximum schools, each with a viable number of students. We also ran the analyses using only schools with 10% minority and 25% White and Asian student body and obtained consistent results.

6. In an analysis not shown, we compared the distribution of the AHAA high school sample with the 19941995 Common Core of Data (CCD), a census of public schools in the United States. Comparing all CCD public high schools with an 11th grade and using the criteria of 7% minority students and 25% White or Asian students, we found that the AHAA sample of diverse schools appears representative of the nations public schools. This represents approximately 56% of African American students in public schools with an 11th grade, 49% of Latino students, 65% of Asian students, and 43% of White students.

7. The numbers of students without a sample weight were 80 and 73 for the African American and Latino samples, respectively; 39 and 34, respectively, did not have freshman-year grades, and 59 and 48, respectively, had missing values for parents level of education.

8. We did not include measures for school mean GPA or the relative difference between the mean GPA for White/Asian students and African American or Latino students in the final models presented here. These variables did not significantly predict the slope for African American or Latino on our outcome variables, and in the interest of preserving degrees of freedom and parsimony, we did not include them in the final models.

9. For the analyses, we fixed the slope (β1j) for race (either African American or Latino) so that there is no residual. This approach allowed us to conserve degrees of freedom. In addition, the African American slope in Table 3 does not vary significantly for either outcome, and although the Latino slopes in Table 4 do vary, fixing the effect did not substantially alter the results.

10. As others have found, prior to inclusion of background controls, in analyses not shown, we found that African American students are more likely to enroll in 4-year colleges (Alexander, Holupka, & Pallas, 1987).


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Descriptive Statistics for Analysis Variables (Weighted)


African American Schools

(n = 26)

Latino Schools

(n = 22)








School-level variables


White overrepresentation in high math





Proportion college-educated parents (logit)





White parent education advantage





Proportion in advanced math (logit)





Proportion African American (logit)





Proportion Latino (logit)





















African American






Parents education





Spanish spoken in home



First generation








Freshman GPA





Sophomore math course level





Dependent variables






Senior GPA








Enrollment in 4-year college



Note. Descriptive statistics generated for individual-level variables based on senior-year GPA sample.

AH-PVT = Add Health Peabody Picture Vocabulary Test.

Cite This Article as: Teachers College Record Volume 112 Number 4, 2010, p. 1038-1063
https://www.tcrecord.org ID Number: 15659, Date Accessed: 10/23/2021 2:29:11 PM

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About the Author
  • Chandra Muller
    University of Texas at Austin
    E-mail Author
    CHANDRA MULLER is a professor of sociology and a faculty affiliate of the Population Research Center at the University of Texas at Austin. Her research interests are in the effects of high schools on adolescents’ transitions to adulthood. She is principal investigator of the Adolescent Health and Academic Achievement Study. Her recent publications (with colleagues Frank, Riegle-Crumb, Schiller, Wilkinson, and others) concern the effects of social relationships on math and science course-taking in Sociology of Education and American Journal of Sociology, and the course-taking patterns of immigrant students (with Rebecca Callahan and others) in Social Science Quarterly and Theory and Research in Social Education.
  • Catherine Riegle-Crumb
    University of Texas at Austin
    CATHERINE RIEGLE-CRUMB is an assistant professor of curriculum and instruction and a faculty research associate at the Population Research Center at the University of Texas at Austin. Her research interests include how social contexts influence gender and racial/ethnic inequality in educational trajectories from high school into postsecondary, with a particular focus on the fields of science, technology, engineering, and mathematics. Recent publications include “The Role of Gender and Friendship in Advanced Course-Taking” (with coauthors George Farkas and Chandra Muller) in Sociology of Education.
  • Kathryn S. Schiller
    University at Albany, State University of New York
    KATHRYN S. SCHILLER is an associate professor in the Department of Educational Administration and Policy Studies and the Department of Sociology at the University at Albany, State University of New York. Her main fields of interest are social stratification, math and science curriculum, academic trajectories, and school transitions. Recent publications include “Raising the Bar and Equity? State Policies and High School Students’ Mathematics Course Taking” in Educational Evaluation and Policy Analysis, and “Economic Development and the Effects of Family Characteristics on Mathematics Achievement” in the Journal of Marriage and Family.
  • Lindsey Wilkinson
    Portland State University
    LINDSEY WILKINSON is an assistant professor of sociology at Portland State University. Her research interests include educational inequality, immigrant adaptation, and the transition to adulthood. She has recently coauthored articles in Educational Policy and Social Science Quarterly that address the impact of high school ESL placement on math and science course-taking among immigrant youth. She is currently working on a project that examines the impact of high school processes on the language use of Asians and Latinos in young adulthood.
  • Kenneth Frank
    Michigan State University
    KENNETH A. FRANK is a professor of measurement and quantitative methods, counseling, educational psychology, and special education, and an associate professor of fisheries and wildlife at Michigan State University. His substantive interests include the diffusion of innovations, study of schools as organizations, social structures of students and teachers and school decision-making, social capital, and resource flow. His substantive areas are linked to several methodological interests: social network analysis, causal inference, and multilevel models. Recent publications, with collaborators, include “The Social Dynamics of Mathematics Coursetaking in High School” in American Journal of Sociology, and “Extended Influence: National Board Certified Teachers as Help Providers” in Education, Evaluation, and Policy Analysis.
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