Stable or Changing?: Racial/Ethnic Compositions in American Public Schools, 2000 to 2015

by Siri Warkentien - 2019

Background/Context: Trends in district and metropolitan school segregation over the past several decades have been well documented, but less attention has focused on the racial/ethnic composition changes at individual schools that generate aggregate trends. These shortcomings limit our ability to understand complex and dynamic patterns of racial/ethnic change within schools, which may in turn prevent policy interventions that could increase school diversity and direct needed educational resources to schools.

Purpose/Objective/Research Question/Focus of Study: This study identifies distinct trajectories of racial/ethnic change occurring in public elementary schools between 2000 and 2015 and describes the characteristics and prevalence of each trajectory. In addition, the study examines how initial levels of school poverty are associated with membership in different trajectories.

Research Design: This secondary data analysis relies on data from the National Center for Education Statistics Common Core of Data (CCD) and employs latent class growth analysis.

Findings/Results: Despite the rapidly changing demographics of the overall student population, approximately 45% of all public elementary schools in the sample had stable racial compositions between 2000 and 2015. Close to half of the remaining schools, about 25% overall, experienced racial change at such a pace that they will be completely minority isolated within the next several decades if the pace continues. In the remaining schools, the pace of racial change is sufficiently slow to maintain diverse schools for many decades. Schools experiencing rapid Hispanic growth tend to have initially higher proportions of low-income students, indicating where racial change may likely occur and where schools will become racially and socioeconomically isolated without proactive policies in place.

Conclusions/Recommendations: Results suggest that absent intentional interventions that target the type of change trajectories being experienced at the school level, the overall increasing diversity of the student population will not likely lead to sustainably diverse schools for the majority of students. Providing the benefits of a non-racially isolated education for all children is possible, but we must first identify the school trajectories of change and stability, then determine the most appropriate strategy for improving school diversity, and finally provide the resources and policies needed to foster and maintain diverse schools that are inclusive of all students.

Long before the 1954 Brown v. Board of Education decision and for many decades following it, many communities resisted racially integrated public schools. Although large declines in segregation occurred during the 1970s and 1980s, progress stalled in the early 1990s. In recent years, researchers have debated whether American schools are re-segregating. Some argue that public schools are becoming increasingly segregated, citing that higher percentages of minority students are attending minority-segregated schools today than in the previous 30 years (G. Orfield, 2009, 2014). Others contend that while minority isolation may be increasing, this is attributable to the increasing diversity of the student population, and that racial unevennessthe measure of how evenly students of different races are distributed across schools within a district or metropolitan areahas remained relatively flat or declined over the past several decades (Fiel, 2013; Stroub & Richards, 2013; see Reardon & Owens, 2014 for a review).

Regardless of the segregation measure used, these studies examine trends in racial/ethnic sorting over school districts and metropolitan areas but do not examine changes occurring within individual schools. Although composition changes at the school level determine district and metropolitan segregation indices, all schools may not be equal contributors to that change. Some schools maintain stable proportions of racial groups over timethe result of racial stability in the school catchment area or active efforts to exclude others (Fiel, 2013). Other schools may experience a rapidly increasing proportion of a racial group that exceeds overall district- or metropolitan-wide demographic changes, perhaps resulting from an influx of one group and the flight of another as occurred in the wake of desegregation (Smock & Wilson, 1991). Still other schools within the district may change slowly over a period of a decade or more.

Complex and dynamic processes occurring within schools cannot be understood without school-level analyses that allow for unique trajectories of racial/ethnic change. Few studies have focused directly on racial changes occurring in individual schools (Clotfelter, 2011; Frankenberg, 2010; Smock & Wilson, 1991). Those that have tend to rely on arbitrary percentage cutoffs at each time point to classify school racial/ethnic compositions (e.g., Jacobsen, Frankenberg, & Lenhoff, 2012). Furthermore, determining whether schools are stable or changing over time requires additional ad hoc decisions around which thresholds to use to define stability and change. If a school is experiencing racial/ethnic change, the classification still says little about exactly how the school changes and the pace of that change. These shortcomings limit our ability to understand patterns of racial/ethnic change in schools, which may in turn prevent policy interventions that could direct needed educational resources to schools.

This study explores racial/ethnic composition changes¹ occurring in public schools over a 15-year period. Using latent class growth analysis, I directly model the proportion of four racial groups over time to identify trajectories of change and then examine how school poverty is correlated with membership in different trajectories. The major contribution of this analysis is to document the substantial racial stability of American public schools. Despite the rapidly changing demographics of the overall student population, approximately 45% of all U.S. public elementary schools in the sample had stable racial compositions between 2000 and 2015. Close to half of the remaining schools are experiencing racial change at such a pace that they will be completely minority isolated, often defined as schools where minority students represent more than 90% of the student population (Frankenberg, Siegel-Hawley, Wang, & Orfield, 2010), within the next several decades if the pace continues. This analysis shows that the racial transformation in the United Statesfrom 36% minority in 1995 and projected to be 54% in 2024 (Snyder, de Brey, & Dillow, 2016, p. 102)is concentrated in a fraction of schools overall. Those schools experiencing rapid Hispanic growth tend to have initially higher proportions of low-income students, indicating where racial change may likely occur and where schools will become racially and socioeconomically isolated without proactive policies in place.

Decades of research have shown that school racial composition can affect student short- and long-term educational outcomes (Mickelson, 2008). Students attending diverse schoolsthose that are not racially isolatedtend to fare better across academic, labor market, and social emotional outcomes, including cross-racial knowledge, understanding, and empathy (see Wells, Fox, & Cordova-Cobo, 2016 for a review). As a result, policies that help to create and sustain diverse schools are in the interest of students of all backgrounds as well as the larger society. The current study describes the distribution of racial trajectories within public elementary schools which can begin to inform educational policies. With the necessary political will, enacting these policies can support currently diverse schools to remain diverse and prevent schools that are experiencing racial change from becoming racially isolated. Within-school racial compositions over timewhether stable or changingprovide a new lens through which policymakers, educators, and researchers can understand school racial dynamics. Results from this analysis suggest that absent some type of intervention, the overall increasing diversity of the student population will not likely lead to sustainably diverse schools for the majority of the student population.

BACKGROUND

SCHOOL RACIAL COMPOSITION

Origins: Past and Present Discrimination in Housing Policy

The demographic composition of public schools in the U.S. continues to be largely determined by where students live, with just over three quarters of students attending an assigned public school (Noel, Stark, & Redford, 2016). As a result, schools that are extremely racially isolated often reflect a similarly racially isolated surrounding neighborhood, while schools with diverse student bodies often draw from more integrated neighborhoods. The policies and factors that created racially segregated neighborhoods strongly influence the current state of school segregation, and in turn, the racial composition of different schools.

Most of the current racial residential segregation can be traced to housing discrimination that affected, and continues to affect, where minority families were able to buy and rent homes (Charles, 2003; Massey & Denton, 1993; Rothstein, 2017). A long history of federal and state policies sanctioned and promoted separate neighborhoods for white families and families of color in the United States (Rothstein, 2017). Discrimination and harassment by private citizens and racial steering by real estate agents also limited where families of color could live, further ensuring that the suburbs were limited to white families. Finally, though to a lesser extent, personal preferences shaped where families moved. Research shows that white families have a much stronger preference for living with same-race neighbors, while black and Hispanic families prefer more diverse neighborhoods (see Charles, 2003 for a review). The result of this mismatch was often that white families were quick to move out of diversifying neighborhoods and reluctant to move into them, thus creating and then maintaining racially isolated neighborhoods (Orser, 2015).

Since the passage of the 1968 Fair Housing Act, the factors shaping racial residential patterns have shifted to be less overtly discriminatory. Yet by the time the suburbs were opened to families of color, they were often prohibitively expensive because of growing racial wealth gaps (Kochhar & Fry, 2014; Oliver & Shapiro, 2006) and made less attainable by exclusionary zoning policies that restricted the building of more affordable multifamily units (Fischel, 2004; Rothwell, 2012). Krysan and Crowder (2017) suggest that segregation persists, even as peoples preferences change and become more tolerant and overt discrimination declines, because families decide where to live and move within racialized social, economic, cognitive, and spatial structuresall of which perpetuate patterns of segregation.

Mechanisms of Stability and Change

Although most students attend their zoned neighborhood school and are therefore affected by residential segregation, education policiesincluding decisions about district and school boundary lines, desegregation orders, and school choice programsalso shape school racial composition. The current section considers how each of these may contribute to schools racial stability or change, before discussing how larger demographic shifts in the student population affect school racial composition.

District Boundaries

District fragmentation, or the proliferation of independent school jurisdictions, creates many small homogeneous districts rather than a single larger school district (Bischoff, 2008) and has contributed to growing between-district segregation over the past half century, even while within-district segregation has lessened (Clotfelter, 2011). Fragmentation increases multiracial segregation between districts, suggesting that as the number of small districts in an area increases, so does the concentration of students of one racial/ethnic group within specific schools (Bischoff, 2008). This phenomenon is particularly prevalent in the Northeast and Midwest, but it has been growing in the South and West (Clotfelter, 2011). Its prevalence suggests the continuation of racially isolated schools that have stable student demographics, in part because high levels of fragmentation tend to lead to highly stratified districts. As school districts compete for prestige and standing by vying for the most affluent families, they often achieve exclusivity through exclusionary zoning practices that keep out lower-income residents (see Holme & Finnigan, 2013 for a review).

School Attendance Boundaries

School boundary lines within a district can also impact school racial composition, by either pulling students from a single homogeneous neighborhood to create a racially isolated school or by drawing students from several different neighborhoods resulting in a more diverse student body. Findings are mixed on whether irregularly shaped school boundaries, often referred to as gerrymandered, exacerbate or mitigate neighborhood segregation. Several studies find that gerrymandered school boundaries make schools more segregated than the neighborhoods in which they are located (Richards, 2014; Siegel-Hawley, 2013). Richards and Stroub (2015) further find that boundaries are most severely gerrymandered in districts experiencing rapid racial change. However, Saporito (2017) provides evidence that highly irregular boundaries may also provide a mechanism for district administrators to pull students of different racial/ethnic groups living in different neighborhoods together into one school, thus mitigating racial residential segregation.

Court-ordered Desegregation

After a series of Supreme Court decisions between 1969 and 1973 that declared delaying integration impermissible and allowed busing as a remedy to segregation (Epperson, 2013; G. Orfield & Monfort, 1992), school districts began dismantling their dual education systems. But between 1991 and 2009, a period of substantial overlap with this studys focus, over 200 school districts were released from court desegregation orders (Reardon, Grewal, Kalogrides, & Greenberg, 2012). Once released, many schools transitioned back to majority white or majority minority (Billings, Deming, & Rockoff, 2014; Lutz, 2011; Reardon et al., 2012), suggesting that schools in affected districts will have changing racial trajectories that reverse existing diverse schools and trend toward either majority white or majority minority.

School Choice Policies

School choice policies are often more local decisions as opposed to federal mandates, but they, too, affect school racial composition. Whether policies increase or decrease the racial isolation of schools depends on the specific choice policy and its aims. For instance, magnet programs, schools with special themes designed specifically to attract diverse students, are often located in racially segregated neighborhoods (Smrekar & Goldring, 1999). When focused on attracting and maintaining diverse students, these programs can increase the number of diverse schools in a district or region (Siegel-Hawley, 2014). Similarly, in controlled choice plans, districts offer families the option of ranking their school preferences but make the final match between student and school based in part on the demographic composition of the school and the demographic background of the student (Frankenberg & DeBray, 2011). On the other hand, color blind school choicesystems of choice where there are no explicit school diversity goals, including most charter schoolsaffect school racial composition, but most research finds that this type of choice has a segregating effect (Bifulco & Ladd, 2007; Booker, Zimmer, & Buddin, 2005; Kotok, Frankenberg, Schafft, Mann, & Fuller, 2017; Ni, 2012; Roda & Wells, 2012).

School choice, particularly choice related to charter schools, increased significantly across the country between 1999 and 2013, with enrollment in public charter schools rising from less than 1% of all public elementary and secondary students to 5% (Kena et al., 2016). By 2012, 37% of all parents reported public school choice was available to them, and 13% of all students in traditional public schools were in a chosen, as opposed to assigned, school (Kena et al., 2016). Given the above research findings, the rapid expansion of charter schools suggests schools with increasing racial isolation. Yet the number of districts exercising voluntary integration policies has also increased in the past two decades, with over 90 districts currently employing some form of voluntary integration strategy, up from just a handful in the late 1990s (Potter, Quick, & Davies, 2016), suggesting a growing number of schools with stable diversity. Many of these policies, however, employ socioeconomic status rather than race/ethnicity as the student factor, which may limit the extent of specifically racial diversity within the schools (Reardon, Yun, & Kurlaender, 2006).

Demographic Change and Residential Segregation

Perhaps the most consequential factor affecting school racial composition changes in the past two decades has been the rapid shifts in the racial/ethnic composition of the student population. Between 2000 and 2015, the elementary and secondary student population decreased from 61% to 49% non-Hispanic white, while the Hispanic population increased from 16% to 26%, the Asian population increased from 4% to 5%, and the black student population shifted slightly from 17% to 16% (Snyder et al., 2016, p. 102). If demographic changes were distributed evenly across all schools, we would expect to see a rising proportion of Hispanic and Asian students, a mostly stable proportion of black students, and a shrinking proportion of white students. But as described above, patterns of racial residential segregation affect school composition. In general, the period between 2000 and 2010 saw very modest decline in black-white segregation but intensifying isolated enclaves among the rapidly increasing Hispanic and Asian populations (Logan & Stults, 2011). At the same time, black exposure to Hispanic and Asian individuals increased (Logan, 2013). These changes suggest schools with increasing concentrations of students of color overall with strong Hispanic and Asian growth.

School Racial Composition and Poverty

The racial wealth gap and rising income inequality both contribute to where families can afford to buy homes. As of 2016, black and Hispanic families had average and median net worth less than 15% that of white families; Hispanic families had median net worth that was just slightly higher than black families (Dettling, Hsu, Jacobs, Moore, & Thompson, 2017). These gaps directly affect the amount of capital families can marshal for home purchases (Oliver & Shapiro, 2006). Research further demonstrates that individuals of different races but similar incomes often live in very different neighborhoods, with white families tending to live in much more affluent neighborhoods than their black or Hispanic peers (Reardon, Fox, & Townsend, 2015). Wealthier families increasingly leverage their assets to buy homes in desirable school districts (Holme, 2002; Lareau & Goyette, 2014), often defined as those with high achievement scores, a metric highly correlated with race (Logan, Minca, & Adar, 2012; Owens, 2016). Families with lower incomes and without significant wealth are unable to access similar school districts and often purchase or rent homes in higher minority and lower performing districts (Johnson, 2014; Rhodes & Warkentien, 2017).

In terms of school racial change patterns, we expect that schools with initially higher levels of student poverty may be destination schools for minority students, because they are likely located in neighborhoods with more affordable apartments or homes, and thus more attainable for minority families looking for schools (Johnson, 2014; Rhodes & DeLuca, 2014). This suggests that these schools would have rising shares of black and Hispanic students. Schools with initially low proportions of poor students are likely located in wealthier catchment areas that may be more difficult for families with limited financial resources to access because of exclusionary zoning policies and a lack of affordable housing. These schools are less likely to be sites of dynamic racial change and instead more likely to remain predominantly white and/or Asian.

SIGNIFICANCE OF SCHOOL RACIAL COMPOSITION

Decades of research have documented that ensuring that all students have access to diverse schools is critical for individual student outcomes, intergroup relations, and breaking the cycle of segregated housing and education. School racial composition affects student educational outcomes not because students of color benefit educationally from sitting next to white students in the classroom but because schools with high concentrations of minority students, on average, do not enjoy the same resources as schools with high concentrations of white students. Since the Brown decision, studies have shown that students attending predominantly minority schools are less likely to have access to qualified teachers, small class sizes, and challenging curriculum (e.g., Boozer, Krueger, & Wolkon, 1992; Crosnoe, 2005; Darling-Hammond, 2004; Gamoran, 1987). In addition to more limited academic resources, predominantly minority schools generally have higher percentages of low-income students and lower average academic achievement than schools with high concentrations of white and Asian students (Logan et al., 2012; G. Orfield, Kucsera, & Siegel-Hawley, 2012). As a result, research generally finds that attending more diverse schools, as opposed to minority-isolated schools, is beneficial for educational achievement and attainment (Goldsmith, 2009; Hanushek, Kain, & Rivkin, 2009; Hoxby, 2002; Mickelson, 2008; Mickelson & Nkomo, 2012; Wells & Crain, 1994; Yun & Kurlaender, 2004). Furthermore, a growing literature documents the value of diverse schools and classrooms for all students, finding that learning alongside a diverse group of peers improves all students critical thinking and problem-solving, as well as their intercultural and cross-racial knowledge, understanding, and empathy (Wells et al., 2016). Significant behavioral interactions and time spent with youth of different racial/ethnic groups has also been shown to improve cross-racial understanding and attitudes (see Davies, Tropp, Aron, Pettigrew, & Wright, 2011 for a review). Finally, research shows that attending diverse schools increases the likelihood that young adults will move to more diverse residential neighborhoods (Goldsmith, 2010, 2016; Mickelson, 2008). These residential decisions in turn have the potential to increase neighborhood racial composition patterns, which largely shape the racial composition of elementary schools.

RACIAL COMPOSITION AND SEGREGATION

Although school racial composition and school segregation levels are related, the concepts are distinct. Multiple indices are used to measure different aspects of segregation, including racial isolation and unevenness, and the differences, benefits, and drawbacks of each are well documented (Massey & Denton, 1988; for a recent review see Reardon & Owens, 2014). Segregation indices require a defined unit and geographical area (e.g., segregation of schools within a district), while school racial composition is simply determined by the students in a single school regardless of the larger context in which the school exists. Tracking within-school racial enrollment patterns does, however, provide a sense of how individual schools are changing or stable over timesomething consequential to the lived experiences of each schools students, teachers, and parentsand can potentially provide additional understanding for how larger patterns of district or metropolitan segregation evolve.

Motivating a School-Level Analysis: A Hypothetical Example

Consider a school district with 20 schools that has even proportions of white and Hispanic students. The district begins with completely segregated schools with a white-Hispanic dissimilarity index of 1.0, indicating that white and Hispanic students attend completely separate schools and that all of the white (or Hispanic) students would need to move to another school to achieve complete integration. Suppose 10 years later, the dissimilarity index has declined dramatically to 0.5, indicating that now only 50% of white (or Hispanic) students would need to switch school to achieve even distribution of white and Hispanic students across schools. As shown in Figure 1, this dissimilarity value can be achieved in multiple ways. In the first scenario shown in the top band, half of the schools remain completely segregated (i.e., have 100% white students or 100% Hispanic students) while the other half completely integrate (i.e., have 50% each of white and Hispanic students). In the second scenario shown in the bottom band, only two schools remain completely segregated while all other schools experience a range of racial change. Both versions yield a dissimilarity index of 0.5, but the specific changes within individual schools in each scenario are quite different. In the first scenario, half of the schools remain completely racially isolated, having experienced completely stable racial compositions. In the second scenario, the pace of change varies widely. If these changes are correlated with shifts in school resources, school climate, community support, or other factors that affect students outcomes, focusing only on segregation indices and neglecting to take an institutional view limits our understanding of the consequences of demographic change.

Figure 1. Two hypothetical scenarios of 20 schools within one district that result in identical segregation levels through different within-school racial change patterns.

DATA, SAMPLE, AND METHODS

To identify trajectories of racial change among the population of elementary schools in the United States over a period of 15 years, I use data from the Common Core of Data (CCD). The CCD is an annual universe survey of public schools administered by the National Center for Education Statistics (NCES) that collects fiscal and nonfiscal data from schools, school districts, and education agencies. The school surveys used in this analysis provide data on the demographics of the student body and other teacher and school characteristics between 200001 and 201415.

The analytic sample was restricted to include only regular elementary schools with at least 30 students. Elementary schools were chosen as the focus because enrollments are particularly sensitive to neighborhood racial change since they tend to draw from smaller catchment areas (Reardon et al., 2012). Elementary schools are defined as those where the lowest grade is between pre-kindergarten and third grade and the highest grade is between pre-kindergarten and eighth grade. The sample was further restricted to include only those schools that were open and functioning as elementary schools for at least 10 of the 15 academic years under study. Schools run by the Department of Defense (DoD) or the Bureau of Indian Affairs (BIA) are excluded, as are schools in all outlying areas. Alaska and Hawaii are excluded as in previous national analyses (e.g., Logan, Oakley, & Stowell, 2008). Because of these restrictions, the analytic sample differs slightly from the cross-sectional racial distribution from the universe of all public elementary and secondary schools (Snyder et al., 2016, p. 102).

ANALYTIC STRATEGY

This analysis documents racial changes occurring in individual schools over a 15-year period by directly and simultaneously modeling the racial changes of four racial groups using latent class growth analysis (LCGA). The direct modeling of four racial groups allows an explicit estimate of whether each racial group is stable or changing, and the direction and pace of any change. LCGA is an improvement over traditional growth models for the purposes of understanding racial change in the U.S. school population. Traditional growth models estimate one set of growth parameter estimates for the entire population. In a simple linear growth model, this model would estimate one intercept (initial racial composition) and one slope (or change in racial composition) (Raudenbush & Bryk, 2002). Although traditional growth models allow random variation around these sets of estimates, they assume that one set of estimates can sufficiently describe the population. LCGA relaxes this assumption and allows for a mixture of subpopulations to comprise the full population (Feldman, Masyn, & Conger, 2009; Kreuter & Muthén, 2008). Each subpopulation is latent in the sense that it must be modeled empirically with the data, and each latent class has its own set of growth parameter estimates.

School racial change trajectories are characterized by the initial level of each racial or ethnic group and the rate of change each group experiences over the 15-year period. These two parameters are estimated by the following equations. The level-1 equation is

                   (1)

for school i at time t in class k, where there exist K latent classes. The  estimate describes the initial racial proportion for racial group r, and the  estimates the change in that racial proportion over time.² Time is indexed such that  for 200001 academic year,  for the 200203 academic year, and so on. The level-2 equations are indexed by class as well but have no within-class variance estimates.

Because the within-class variances and covariances are zero, the individual school differences for racial proportion in initial level and change over time are modeled only by class membership. Prior research has shown that LCGA will sometimes identify more latent classes than would be identified using a method that allows for within-class variation (i.e., growth mixture modeling) (Feldman et al., 2009). However, in this analysis, allowing the inclusion of within-class variance collapsed schools with stable, but wildly disparate, racial compositions together. Constraining the variance to be zero in both intercept and slope discriminated between schools that were, for example, almost exclusively white for the entire duration and experienced virtually no change in any racial group, and schools that were almost exclusive black and also experienced extreme stability in the racial proportion of all groups.³

I model three racial proportions for every year in the studythe proportion non-Hispanic black, the proportion Hispanic, and the proportion Asian/Pacific Islander and American Indian (API/AI).⁴ The fourth racial groupnon-Hispanic whitewas not included in the model to avoid multicollinearity but was calculated by subtracting the sum of all other races from 1. The model includes estimates for the intercept and slope of each racial group. After testing whether a model including a quadratic term fit the data better, I concluded that although the model fit (according the Bayesian information criteria [BIC]) was slightly improved, the results were not substantially different and chose to present the more parsimonious model for this reason and for ease of interpretation.⁵

Determining The Number of Latent Classes

The literature documenting specific types of school-level racial changes is sparse, making specific a priori expectations for the exact number of latent classes difficult. I use a combination of statistical and substantive criteria to decide on the optimal number of latent classes. I begin with one latent class and add an additional latent class in each successive model run, comparing four indices of relative model fit across model runs (Muthén & Muthén, 2000). I first examine the Bayesian information criteria (BIC) for which lower values represent better-fitting models. I next examine the Lo-Mendell-Rubin likelihood ratio test (LMR-LRT) that compares the model fit of the current model to a model with one fewer class. P-values higher than 0.05 (the chosen alpha level in this analysis) indicate that adding the additional class does not improve the model fit. Third, the quality of classification is determined by the entropy value, which ranges from 0 to 1. Higher values indicate better classification of individuals into their most likely latent class. Finally, I consider the substantive interpretability of the model with an additional class versus the model with one fewer class.

Trajectory Membership as a Function of School Poverty

The LCGA framework also allows the modeling of the probability of trajectory membership as a function of covariates through a multinomial logistic regression, with one trajectory class as the reference group. This is useful for summarizing the most likely trajectory class for schools with different characteristics, but it can also help test hypotheses on the antecedents of different racial change patterns (Feldman et al., 2009). I specifically examine whether initial levels of school poverty are correlated with the schools racial change trajectory. I include two control covariates (school region and locale) to better estimate the contribution of school poverty given the relationship between school segregation and both region and locale (e.g., Bischoff, 2008). Following prior school segregation work (Logan et al., 2008; G. Orfield & Monfort, 1992), region is a five-category variable, with schools located in the Northeast, Midwest, West, South, or Border states.⁶ Locale is a four-category variable based on the schools locale in 2000: urban, suburban, town, or rural. The poverty level of the school is a five-category variable created from the percentage of students at the school eligible for free or reduced-price lunch in 2000: less than 10%, 10%24%, 25%49%, 50%74%, or 75% or higher. For those schools with a missing value on the 2000 measure, the earliest available value was used.

Equation (2) shows the model for a trajectory class c with K categories and a single covariate x.

            (2)

where is the probability of membership of trajectory group k conditional on x. By choosing a reference class, say class K, and setting  and , then we can interpret the coefficient from equation (2) as the change in log-odds of being in trajectory group k relative to reference group K for a unit change in .

 

(3)

To further simplify the interpretation, average marginal effects are presented in Table 1. The mixture model is estimated using Mplus 7 and the multinomial logit model is estimated using Stata 13 by regressing each schools most likely latent class on region, locale, and poverty level.⁷

Table 1. Average Marginal Effects of School Characteristics on Racial/Ethnic Change Trajectory Membership

	Stable Isolation				Minority isolating				Sustainable Diversity
	Stable Isolated White	Stable Isolated Black	Stable Isolated Hispanic		Diverse—Minority Growth	High Black—Hispanic Growth	Diverse—Strong Hispanic Growth		High White—Minority Growth	White and Black—Hispanic Growth
Percentage eligible for free or reduced-price lunch (<10% as ref.)
10–24%	−0.017** (0.006)	−0.013*** (0.002)	−0.016*** (0.002)		−0.034*** (0.004)	0.012*** (0.003)	0.042*** (0.003)		−0.063*** (0.007)	0.089*** (0.005)
25–49%	−0.075*** (0.006)	−0.003 (0.002)	−0.003 (0.002)		−0.045*** (0.003)	0.046*** (0.003)	0.130*** (0.004)		−0.164*** (0.007)	0.114*** (0.005)
50–74%	−0.186*** (0.006)	0.037*** (0.003)	0.067*** (0.003)		−0.029*** (0.004)	0.122*** (0.004)	0.195*** (0.004)		−0.271*** (0.007)	0.065*** (0.005)
75% or more	−0.298*** (0.007)	0.178*** (0.005)	0.205*** (0.005)		−0.001 (0.005)	0.135*** (0.005)	0.149*** (0.005)		−0.337*** (0.006)	−0.030*** (0.004)

Note. n=47,293 observations. Standard errors in parentheses. * p<0.05, ** p<0.01, *** p<0.001. School region and locale are included as control covariates in the model, but not shown. Full results can be requested from the author.

National Center for Education Statistics, Common Core of Data (CCD), State Nonfiscal Survey of Public Elementary and Secondary Education, 200001 through 201415.

RESULTS

OVERALL RACIAL CHANGES, 20002015

Between 2000 and 2015, the elementary school student population grew increasingly diverse. Table 2 shows that in 2000, 65% of public elementary school students were non-Hispanic white, 15% were non-Hispanic black, 15% were Hispanic, and about 5% were Asian, Pacific Islander or American Indian (hereafter API/AI). Over the next 15 years, the white student percentage declined steadily, so that by academic year 201415, white students accounted for just 55% of the student population. During the same period, the Hispanic student population increased to 24% of all studentsan increase of 64%. API/AI students also increased their share by 26%, accounting for 6% of the student population in 201415. The proportion of black students was stable, constituting 15% of the overall population in 201415. The overall changes make clear that the student population was growing increasingly diverse over this period, but these overall proportions tell us little about how that change was distributed among different schools.

Table 2. Sample Characteristics: Racial/Ethnic Distribution of Students in Public Elementary Schools, 20002015

	2000			2002			2004			2006			2008			2010			2012			2014
	Mean	SD		Mean	SD		Mean	SD		Mean	SD		Mean	SD		Mean	SD		Mean	SD		Mean	SD
Racial/Ethnic Proportion
White	0.646	0.333		0.627	0.337		0.608	0.341		0.586	0.346		0.575	0.346		0.563	0.345		0.555	0.343		0.546	0.342
Black	0.157	0.253		0.160	0.255		0.163	0.256		0.167	0.258		0.167	0.256		0.159	0.251		0.155	0.246		0.151	0.240
Hispanic	0.149	0.240		0.163	0.248		0.177	0.256		0.192	0.263		0.201	0.267		0.222	0.273		0.234	0.275		0.244	0.277
Asian/Pacific Islander and
American Indian/ Alaska Native	0.047	0.096		0.050	0.100		0.052	0.101		0.055	0.104		0.057	0.106		0.055	0.106		0.056	0.108		0.059	0.111
Number of Schools	44,314			45,595			46,587			49,782			49,970			48,542			47,352			46,436

National Center for Education Statistics, Common Core of Data (CCD), State Nonfiscal Survey of Public Elementary and Secondary Education, 200001 through 201415.

TRAJECTORIES OF STABILITY AND CHANGE

The model fit indices suggest that eight trajectories describe the racial change patterns within U.S. public elementary schools between 2000 and 2015 (Table 3). The area graphs shown in Figure 2 plot the estimated means for each racial group for all eight classes.

Table 3. Model Fit Statistics of Latent Class Growth Analysis Models of Racial Change

	Intercept and Slope Only
Number of Classes	BIC	adj BIC	Entropy	LMR-LRT (p-value)	Vuong LMR-LRT (p-value)
1	262875	262780	--	--	--
2	1	1	1	1	1
3	−548495	−548635	0.987	0.000	0.000
4	−779141	−779303	0.985	0.000	0.000
5	−998351	−998535	0.986	0.000	0.000
6	−1146681	−1146888	0.986	0.000	0.000
7	−1261667	−1261896	0.976	0.000	0.000
8	−1343499	−1343750	0.977	0.000	0.000
9	−1426480	−1426753	0.983	0.145	0.144

-- Not applicable.

¹ The two-class model did not converge.

Figure 2. Predicted racial change

Stable Isolation

Three classes experience very little racial change over the 15-year period, with no single racial group increasing or decreasing its representation by more than 8 percent, and all three classes are almost exclusively one racial group (as shown in the top row of Figure 2). Nearly half of all elementary schools in the sample (45%) can be characterized as having this type of prolonged racial isolation. The largest of theseand the largest class overallis the Stable Isolated White class, which accounts for 31% of all public elementary schools (Table 4). These schools have on average 96% white students in 2000; 15 years later white students are still 92% of the student body. The increased diversity comes from a very modest increase in the percentage of Hispanic students.

Table 4. Percentage Distribution of Trajectory Classes

Trajectory Description	Number of Schools	Percent
Stable Isolation
Stable Isolated White	14,653	31.0
Stable Isolated Black	2,717	5.7
Stable Isolated Hispanic	3,750	7.9
Minority isolating
DiverseMinority Growth	1,856	3.9
High BlackHispanic Growth	3,918	8.3
DiverseStrong Hispanic Growth	6,081	12.9
Sustainable Diversity
High WhiteMinority Growth	8,559	18.1
White and BlackHispanic Growth	5,759	12.2

National Center for Education Statistics, Common Core of Data (CCD), State Nonfiscal Survey of Public Elementary
and Secondary Education, 200001 through 201415.

The second and third classes of isolated schools are Stable Isolated Black and Stable Isolated Hispanic, which account for 6% and 8% of all public elementary schools in the sample, respectively. On average, the Stable Isolated Black schools are consistently over 90% black across the 15-year period. The percentage of white students declines from an average of 6% to 4%, leaving them almost exclusively minority. Schools in the Stable Isolated Hispanic class were about 82% Hispanic in 2000 and steadily increased about 8 percentage points by 2015. White students, who dropped from 12% to 6% of the student body over those years, lost the ground gained by Hispanic students. The other two racial groups experienced very little change.

Minority Isolating

The next three classes (shown in the middle row of Figure 2) differ from the stably isolated trajectories because they begin in 2000 with diverse student bodies, defined by the presence of multiple racial groups with no one racial group drastically outnumbering another. Although minority students are on average between 50% and 60% of the student population, there are nontrivial proportions of white students. A snapshot of their racial compositions in 2000 would suggest that these public elementary schools were a model of diversity, with substantial proportions of students of multiple racial groups learning together. But this snapshot neglects the dynamic pace of racial change. Should this pace continue, schools in these three trajectory classes will be entirely nonwhite within several decades. Altogether, these three classes account for 25% of elementary schools in the sample.

The first class, DiverseMinority Growth has no racial majority, with an average of 45% white students and 41% API/AI students. Over the next 15 years, the white student population declines while the API/AI and Hispanic student populations increase. Although the pace of change is modest for Hispanic alone or API/AI alone, taken together, these demographic shifts suggest that the schools will be entirely minority within three decades.

The second class, High BlackHispanic Growth, averages about 54% black students in 2000. Over the next 15 years, the Hispanic student population increases from about 9% to 21%, while the white student population falls from 34% to 22%. The third and largest class, DiverseStrong Hispanic Growth, is on average about 38% Hispanic in 2000. The Hispanic student population increases steadily and constitutes 59% of the student body by 2015. During this same period, white, black, and API/AI student enrollment shrinks. If this pace of Hispanic growth continues, the schools in this class will be entirely Hispanic-isolated within three decades. This rapid pace of change reflects experiences in approximately 13% of elementary schools nationwide.

Sustainable Diversity

The final two latent classes (shown in the bottom row of Figure 2) begin with multiple racial groups present and experience sufficiently slow racial change over the 15-year period to ensure that multiple racial groups will be present for many decades to come. Together, these two classes constitute approximately one third (30%) of all U.S. public elementary schools in the sample. The first of these latent classes, High WhiteMinority Growth, represents 18% of all elementary schools. These schools are predominantly white in 2000 (81%), but over the next 15 years, the percentage of white students shrinks so that, on average, they account for 68% of the school population in 2015. Meanwhile, the proportion of Hispanic students increases from 9% to 20% and the share of API/AI and black students makes small gains.

The second of these slowly diversifying classes represents 12% of the elementary school population. Labeled White and BlackHispanic Growth, the class begins with a larger population of black students (on average, about one in five students is black). Over the 15-year period, the percentage of Hispanic students increases from 5% to 14%, while white students decline from 72% to 60%.

In summary, profound and stable racial isolation or trends toward racial isolation characterize the majority of public elementary schools in the U.S. Nearly one third of elementary schools in this sample have been almost exclusively white over the past 15 years. An additional 14% of schools are either Hispanic isolated or black isolated and show no signs of racial change. Students attending nearly half (45%) of elementary schools in this sample experience very little contact with students of other racial backgrounds during their elementary years. Another 25% of schools have student populations that were diverse in 2000 but experience sufficiently strong minority growth, particularly Hispanic growth, that nearly four in five students are nonwhite by 2015. The pace of change, should it continue, guarantees that the schools will be entirely minority isolated within two or three decades. The last 30% of schools begin with a large white majority in 2000 and experience racial change at a sufficiently modest pace that the schools will likely have substantial proportions of each racial group for many decades.

SCHOOL POVERTY AND TRAJECTORY MEMBERSHIP

Bivariate distributions of school poverty and racial change trajectories follow patterns that one might predict given how strongly correlated race and socioeconomic status are in the United States (Table 5). Almost 9 out of 10 minority-isolated schools (Stable Isolated Black, Stable Isolated Hispanic) had school poverty rates above 50% in 2000 compared to just 17% of Stable Isolated White schools. More than 80% of predominantly white schools had less than 50% of students eligible for free or reduced-price lunch at the start of the study period. Although schools belonging to minority isolating trajectories were not, on average, as economically disadvantaged as minority-isolated schools in 2000, they had far higher percentages of poor students than white-isolated schools. Close to half (47%) of schools in the DiverseMinority Growth class, 62% of schools in DiverseStrong Hispanic Growth class, and 74% of High BlackHispanic Growth schools were high-poverty schools with a majority of students receiving free or reduced-price lunch in 2000. In contrast, schools experiencing slower racial change had relatively advantaged student populations in 2000. Approximately 86% of schools in the High WhiteMinority Growth class and 67% in the White and BlackHispanic Growth class had poverty levels less than 50%.

Table 5. Characteristics of Racial/Ethnic Change Trajectories

		Stable Isolation				Minority Isolating				Sustainable Diversity
	All Schools	Stable Isolated White	Stable Isolated Black	Stable Isolated Hispanic		DiverseMinority Growth	High BlackHispanic Growth	DiverseStrong Hispanic Growth		High WhiteMinority Growth	White and BlackHispanic Growth
Free or reduced-price lunch eligibility
Less than 10%	15.0	22.1	3.4	3.8		24.7	2.3	2.4		29.2	7.4
1024%	17.6	25.7	1.2	1.7		14.1	4.8	7.9		27.7	19.8
2549%	27.9	35.5	6.5	7.0		14.5	18.6	28.1		29.5	40.2
5074%	21.7	14.2	21.3	26.6		21.7	38.3	35.3		11.6	27.3
75% or more	17.8	2.4	67.5	60.9		24.9	36.1	26.3		2.0	5.2

Note. n=47,293 observations.

National Center for Education Statistics, Common Core of Data (CCD), State Nonfiscal Survey of Public Elementary and Secondary Education, 200001 through 201415.

Results from the multinomial logistic regression are shown in Table 1. For ease of interpretation, the table presents average marginal effectsthe effect (or predicted change) of school poverty in 2000 on the probability of belonging to a specific racial change trajectory, averaged across all observations. The model controls for school region and locale, but results confirm the bivariate relationship, with school poverty in 2000 strongly related to trajectory membership. Having the highest proportion of low-income students in 2000 (>75% students eligible for free or reduced-price lunch) decreases the probability of belonging to the Stable Isolated White trajectory by 30 percentage points relative to the lowest poverty schools (<10% poor students). Interestingly, the same pattern holds for schools in the High WhiteMinority Growth trajectory, but with even larger effects. Having initially higher levels of school poverty decreases the probability of belonging to this sustainably diversifying trajectory by between 6 and 34 percentage points. The reverse is true for Stable Isolated Black and Stable Isolated Hispanic trajectories as well as two of the three minority isolating trajectories (High BlackHispanic Growth, DiverseStrong Hispanic Growth): having higher poverty levels in 2000 increases the probability of belonging to these Hispanic growth trajectories relative to the lowest poverty level (<10% poor students).

These findings suggest that initial school poverty level is a strongly correlated with trajectory membership. Controlling for school region and locale, having higher levels of school poverty in 2000 increases the likelihood that schools experience strong Hispanic growth over the next 15 years, while having initially low levels of school poverty increases the likelihood that schools remain exclusively white or experience slowly increasing diversity through modest API/AI and Hispanic growth.

DISCUSSION

Identifying distinct paths of within-school racial change is a challenging and understudied area of school segregation. Although previous studies have documented aggregate trends in school segregation over the past several decades, less is known about the various paths of racial change and stability experienced by individual schools that ultimately create those overall patterns of segregation. Which schools have changing racial compositions, and how quickly are they changing? And conversely, which schools have not been affected by the dramatic demographic shifts in the overall U.S. student population? Answers to these questions can provide insight into whether stably diverse schoolssomething a large and growing literature suggests is positive for children from all backgroundsare likely, as well as point to specific policy options that can target schools in various trajectories to increase or maintain the number of diverse schools and identify potential resources to support schools undergoing demographic changes.

The analysis makes several methodological and substantive contributions to the literature on school diversity. I directly model the proportions of four racial groups, which provides a nuanced picture of racial dynamics over time without relying on arbitrary cutoffs or definitions for deciding whether a school is segregated or integrated. In addition, the use of finite mixture modeling allows for the identification of multiple trajectories of racial change, each with its own initial proportions and different rates of change for each racial group.

Substantively, the analysis finds that the trajectories of racial change among U.S. public elementary schools between 2000 and 2015 can be loosely grouped into three broad categories: stable racial isolation, minority isolating, and sustainable diversity. Nearly one half (45%) of all U.S. public elementary schools are racially isolated and another quarter is trending toward minority isolated (25%). Just 30% of all public elementary schools in the sample were experiencing demographic changes at a pace that would lead to sustainably diverse schools, defined here as having substantial and stable proportions of at least three of the four racial groups included in this analysis, for many decades to come.

In addition, the economic composition of the school in 2000 is strongly related to the type of change the school undergoes in the next 15 years, with initial economic disadvantage associated with minority-isolated or isolating schools. These results confirm prior findings on the association between minority-concentrated schools and poverty in cross-sectional studies (e.g., Logan et al., 2012; G. Orfield & Lee, 2005) and suggest a reinforcing relationship between poverty and school racial change, something found in studies of neighborhood change (M. Orfield, 2002). Schools with initially higher poverty levels may be situated in neighborhoods with lower housing costs, making them more accessible to minority families who, on average, have lower levels of wealth to draw upon when buying homes (Oliver & Shapiro, 2006). As minority students move in and the school begins to experience racial change, some studies have found that racial turnover can occur, particularly in inner-ring suburbs (Frankenberg, 2010; Frankenberg & Orfield, 2012).

STUDY LIMITATIONS

Despite this studys contributions, the analysis is not without limitations. Focusing broadly on all public elementary schools within the United States likely misses some of the local contexts that shape racial dynamics in schools, including school zoning approaches, choice policies, and housing values. District, metropolitan, or state-level analyses may allow for more detailed school and community characteristics that can better predict which schools are changing and why. Future research should test whether national results are replicated in smaller geographic scales. For instance, although research on districts released from court-ordered desegregation has found that schools tend to become increasingly white or increasingly minority (Billings et al., 2014; Reardon et al., 2012), the current analysis does not identify a trajectory with an increasing share of white students. These schools may be such a small fraction of schools in the country overall that they are incorporated into other trajectory classes, but more local analyses may detect them as distinct trajectories.

A second limitation is that analyses using mixture models are exploratory in the sense that one cannot definitively know the number of latent classes because they are by definition unobserved. Although the classification quality in this analysis was quite high (entropy=.98), there exists a nonzero probability that some schools fall into more than one class. Treating latent class membership as observed is misguided because misclassification is a concern with finite mixture modeling, as is the identification of an exact or definitive number of classes (Warren, Luo, Halpern-Manners, Raymo, & Palloni, 2015). Instead, the value of this analysis is in identifying broad patterns of stability and change within U.S. public elementary schools over the past 15 years. These allow for an examination of the extent of prolonged racial isolation and the likelihood of observed school diversity at a given point in time to be sustainable based on the pace of racial change.

POLICY IMPLICATIONS

School administrators, practitioners, and policymakers need a broad set of strategies to address the unique challenges posed by each trajectory category. Furthermore, within each category, specific policies must target individual trajectories.

Disrupting Stable Racial Isolation

Significant progress toward creating diverse schools could be made by disrupting the stable racial isolation that nearly half of public elementary schools experience. To do so, policy options need to target not only the stable white-isolated schools by (bringing in students of color) but also the isolated black and Hispanic schools (by bringing in white and Asian students). In highly fragmented areas common in most Northeastern and Midwestern states, many small suburban districts that are largely white surround a predominantly minority urban core. In these areas, counteracting the impact of segregating boundary lines can be accomplished through metropolitan or multidistrict solutions, including district consolidation (i.e., multiple districts merging together under a single larger district) or voluntary city-suburban district mergers. These policy solutions are rare and often face political resistance, but they have been tried in several areas, including recently in Memphis and Shelby County in Tennessee (Holme & Finnigan, 2013; Siegel-Hawley, 2014).

When changing district boundaries is not feasible, metropolitan strategies that increase student mobility across district lines can provide another way to bring together students from different racial backgrounds into one school. For instance, regional magnet programs with explicit diversity schools, similar to those in the Hartford, Connecticut region under the Sheff agreement (Rossell, 1996), provide students from suburban districts the opportunity to attend magnet schools within the city district and students from the city the opportunity to attend non-magnet schools in suburban districts. Whether these policies can be implemented on a sufficiently large scale to affect school racial trajectories likely depends on the level of support, both financially and politically.

Housing policies can also often provide effective means for diversifying stably racially isolated schools. Policies of exclusionary zoning prevent families with limited resources from moving into affluent neighborhoods that are often predominantly white. Inclusionary zoning policies, like those found in Montgomery County, Maryland, where specific percentages of newly built units are set aside as affordable housing (Schwartz, 2011), provide one solution that may bring more students of color into largely white schools.

Preventing Future Racial Isolation

Nearly one quarter of public elementary schools are trending toward becoming entirely minority isolated within the next several decades. These schools may result from education policies that have a segregating effect (e.g., choice policies without specific school diversity goals or the lifting of desegregation orders) or changing demographics in the school catchment area.

To prevent future racially isolation in these schools, policies can focus on redrawing school boundaries to improve student diversity and prevent schools from becoming minority isolated. Or, districts may opt to implement school choice polices that have explicit goals for school diversity. Several choice policy options exist, including controlled choice plans, magnet schools, and charter schools. Controlled choice plans have parents rank school preference but leave the ultimate school assignment decision to the district so that racial and/or socioeconomic balance across district schools can be maintained. Implementing controlled choice in a district with schools that were minority isolating would offer families school options while still allowing district officials to maximize school diversity and prevent schools from becoming racially isolated.

Magnet schools were originally designed to help districts reach desegregation goals and were sometimes mandated through court desegregation orders. Strategies to increase and maintain diversity within magnet schools include having explicit racial/ethnic enrollment goals and plans to reduce or prevent racial isolation, providing free transportation to school, conducting outreach to diverse sets of families, and locating schools in high-minority or high-poverty neighborhoods but having enticing school themes to draw a diverse student body (Frankenberg & Siegel-Hawley, 2009). Taken together, these strategies likely mitigate the trends experienced by schools in the minority isolating category.

Charter schools, on the other hand, do not have such diversity-maintaining provisions by design. Although some states have language that supports the idea of school diversity, there is weak regulation for enforcing diversity-related legislation (Siegel-Hawley & Frankenberg, 2010). Scholars have called for voluntary diversity goals within charter schools (Kahlenberg & Potter, 2012), but to date, broadening charter school access with the goal of preventing future racial isolation has not been widely accepted as a feasible policy solution for creating more diverse schools.

Sustaining Diverse Schools

Given the research evidence, sustainably diverse schools should be the goal for all public schools. And in fact, many schools are diverse at some point in time, even if they are experiencing rapid racial transition. The critical question is how policies or strategies can best be leveraged to keep schools diverse to maximize their benefit to all students.

Proactive efforts to build cross-racial relationships among administrators, principals, teachers, and students may improve the longevity of within-school diversity. Although there is a growing literature on how schools and districts react to demographic change (e.g., Cooper, 2009; Evans, 2007; Lowenhaupt, 2014; Tyler, Frankenberg, & Ayscue, 2016), researchers need to better understand the consequences of demographic change within public schools and provide evidence-based practices to practitioners to guide approaches to creating and maintaining welcoming and effective schools for students of diverse backgrounds. Reactions from school administrators, teachers, parents, students, and community members to demographic change within schools may vary, but responses taken together likely affect district and school resources, school climate, parent engagement, community support, students sense of belonging, and ultimately, student opportunity and achievement.

Schools that are undergoing demographic change may require a variety of different resources to effectively educate their students. Some resources may provide technical solutions, including funds to hire additional ESL teachers or Spanish-speaking administrative staff in schools with growing Hispanic student populations. But these solutions may be insufficient for engaging newcomers and their families in the school in meaningful ways that matter most for students educational success (Lowenhaupt, 2014). More holistic solutions may be necessary to prevent rapid demographic transitions and allow for stably diverse schools. School-wide initiatives that promote cultural inclusion ensure that not only are the immediate needs of students and their families met but also that the increasing diversity of the school is addressed positively and proactively (Cooper, 2009; Evans, 2007). This is undoubtedly a difficult task, in no small part because, historically, leaders have not all been trained, supported, or provided with resources to do this type of work (Miller & Martin, 2015). But it will be increasingly necessary to provide precisely this type of training, support, and resources to educational leaders in demographically changing schools, which account for 55% of all elementary schools and more than 26,000 schools. School leaders are in the position to build bridges among diverse groups of constituents, including parents, students, teachers, and community members, for the benefit of all students within their school buildings.

CONCLUSION

High levels of district and metropolitan segregation are concerning because they allow unequal access to resources across schools and negatively impact student educational outcomes. But tracking district or metropolitan segregation is not enough. This study provides a new lens through which policymakers, educators, and researchers can understand dynamic within-school racial composition. The ability to foster diverse communities and have students from different backgrounds learn together within the same classrooms is beneficial for students, but this can only happen if we understand student compositions in the countrys public schools and the rate at which they are changing. Despite the dramatic racial composition changes occurring within the overall student population, not all schools are becoming increasingly diverse. Of those that are, some are changing so quickly that they will not remain diverse for long absent intentional interventions. Providing the benefits of a non-racially isolated education for all children is possible, but we must first understand the school trajectories of change and stability, determine the most appropriate strategy for improving school diversity, and finally provide the resources and policies needed to foster and maintain diverse schools that are inclusive of all students.

Notes

1. Throughout the paper, racial is used instead of racial/ethnic to keep the language concise.

2. The proportion of each racial group in every year is transformed prior to including it in the model using the following transformation: . This transformation breaks the dependence of error variances on the mean and more normally distributes the data.

3. The result of the decision to use LCGA as opposed to GMM, specifically because it distinguished among additional classes, means that the results for various modeling strategies will likely yield different numbers of optimal latent classes. While LCGA models used in this analysis restrict the variance around the growth parameters to be zero, GMM relaxes the assumption that within-group variance is zero. This decision ensures that schools with similar initial racial compositions in addition to similar change over time will tend to be grouped in the same latent class, but it is not realistic to assume that there is no within-class variation on the intercept or slope, and the model fit may suffer as a result.

4. For the years between 2000 and 2008, the API/AI category includes Asian students and American Indian students. Beginning in 2009, the racial categories used in NCES reporting changed, and students who identified as Pacific Islander and two or more races were reported separately. For 2009 through 2015, Pacific Islander students were included in the API/AI category. Students reported as two or more races were not included in the analysis; and for 20092015, the denominator (i.e., the total number of students in the school used in calculating the proportion of each racial group) was recalculated to include only white, black, Hispanic, and API/AI students. It would be preferable to separate out Asian/Pacific Islander students from American Indian students, but this posed problems with the modeling strategy because so many schools had zero or near-zero proportions of American Indian students.

5. Results available from author.

6. Northeast states: Connecticut, Maine, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, Vermont. Midwest states: Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Nebraska, North Dakota, Ohio, South Dakota, Wisconsin. West states: Arizona, California, Colorado, Idaho, Montana, Nevada, New Mexico, Oregon, Utah, Washington, Wyoming. South states: Alabama, Arkansas, Florida, Georgia, Louisiana, Mississippi, North Carolina, South Carolina, Tennessee, Texas, Virginia. Border states: Delaware, District of Columbia, Kentucky, Maryland, Missouri, Oklahoma, West Virginia.

7. There is a growing body of literature that discusses the advantages and disadvantages of first identifying latent class membership using only latent class indicator variables and then using most likely latent class membership to regress class membership on predictor variables of interest (Asparouhov & Muthén, 2014; Schuler, Leoutsakos, & Stuart, 2014). The disadvantages of this approach largely center around not adequately accounting for the uncertainty of class membership. This concern is lessened in this particular study by the high level of entropy (i.e., there is very little uncertainty around classification), with values consistently higher than 0.95 for all models tested.

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Cite This Article as: Teachers College Record Volume 121 Number 9, 2019, p. 1-36 https://www.tcrecord.org ID Number: 22776, Date Accessed: 11/27/2021 8:52:52 PM Purchase Reprint Rights for this article or review