Abstract
We used the Stanford education data archive (SEDA) data to examine the heterogeneity among urban school districts in the United States. The SEDA 2.1 includes data sets on students’ mathematics (Math) and English language arts (ELA) achievement from 2008 to 2014 at the district level. Growth mixture modeling was used to uncover the underlying growth trajectories for urban student achievement from the third to the eighth grade. Two and three growth patterns were observed for ELA and Math achievement, respectively, over time. We used the critical theoretical framework QuantCrit to centralize race in the analysis of the data and shared implications for future research.
Keywords
Urban school districts are typically defined as communities with a high concentration of disenfranchized Black and Hispanic/Latinx (hereinafter will refer to as “Brown”) children who live in economically disadvantaged metropolitan communities and attend low performing schools (Gadsen & Dixon-Roman, 2016; Kucsera & Orfield, 2014). These schools usually have low student achievement, large numbers of students with below grade level performance in english language arts (ELA) and Math, and a majority of teachers who are inexperienced (Hanushek, 2014).
Variations in student achievement might be attributed to a multitude of factors in urban educational contexts. Shores et al. (2020) explained that racial disparities occur across educational outcomes such as disciplinary action, grade-level retention, special education and gifted and talented classification, and advanced placement course-taking, in addition to test scores on standardized assessments. They studied the extent to which Black students are disadvantaged in their school experience in comparison to White students and found that educational gaps for these outcomes are large and systematically correlated. Moreover, patterns of segregation and socioeconomic status differences are remarkably consistent predictors for each of the educational inequalities measured including achievement and discipline. Many of the districts (i.e., 1887 public school districts with 71% Black population) have large gaps in several outcomes and is an indication of the cumulative disadvantage facing Black students. Hanushek et al. (2020) estimated trends in SES-achievement gaps of long-run trends and found that performance disparities are large and highly persistent specifically stating that these gaps are large as in the mid-1960s when the Coleman report was written (i.e., Equality of educational opportunity). Further, results indicated that by eighth grade, students in the top quarter are about 3 years ahead of those in the bottom quarter.
Research explains that schools and neighborhoods are the two most contextual influences on students’ academic outcomes (Carlson & Cowen, 2014). In their analysis of the relationship between neighborhoods, schools, and student achievement gain in a large urban school district Carlson and Cowen (2014) indicate that these two contextual influences may interact to create conditions where students may be doubly disadvantaged with regard to educational outcomes. Relatedly, Owens et al. (2016) reported an increase in income segregation between schools and districts from 1990 to 2010 and that rising income inequality contribute to rising income segregation which might lead to increase resource disparities that impact student achievement. This is consistent with previous research that links income inequality and residential income segregation (Reardon & Bischoff, 2011). Further, Reardon et al. (2018) analysis indicates that segregation is a significant predictor of achievement gaps, and one consistent significant predictor is racial differences in exposure to school poverty. Moreover, family socioeconomic factors affect educational achievement and opportunity through residential and school segregation patterns.
In a recent intergenerational study focused on racial disparities and income, Chetty et al. (2018) concluded that mobility into and out of poverty is a central determinant of racial disparities, which leads to persistent gaps across generations, and subsequently influences the academic achievement of children within their local school districts. Therefore, differences in “urban context, resources, and conditions such as intergenerational legacies of unemployment, hardship, inadequate resources…” (Gadsen & Dixon-Roman, 2016, p. 442) restrict educational achievement and opportunities.
Shifts in urban districts (e.g., gentrification, school choice) affect the complexities of the issues for families and communities within them. An examination of enrollment and segregation within 97 urban districts from 1990 to 2010 determined that White enrollment has declined substantially in the past two decades; Black enrollment has fallen in the last decade; and Hispanic enrollment has increased tremendously in most urban districts in the past two decades (Billingham, 2015). Furthermore, this study concluded that within-district segregation, between Black and White and Hispanic and White students, is at high levels in many inner-city school districts, and “(i)n urban districts, a uniform pattern of desegregation has not taken hold” (p. 19). Orfield and Frankenberg (2014) found that low-income students are concentrated in schools with large numbers of Black and Brown students. Reardon et al. (2018) reported that there is not one school district in the United States that serves a moderately large number of Black or Brown students where achievement is even moderately high and where achievement gaps are near zero. The Black–White achievement gap tends to be larger in higher density schools (i.e., comprised of 60–100% Black students) usually located in cities in the South (Bohrnstedt et al., 2015). National reporting of White–Black achievement score gaps indicated ∼30 points higher for Reading and Math for fourth and eighth grade students; and White-Hispanic score gaps show about 20 points higher for the same subjects and grade levels (NCES, 2019). Additionally, racial minorities, particularly Black students have high school mobility rates compared to White students which detrimentally affects their academic achievement (Min, 2021). Findings from one of the largest school districts in the United States comprised predominantly of minority students indicate school mobility is harmful to students Math and Reading scores. Further, Asian students’ academic achievement was most impaired with within-year mobility more than other racial/ethnic groups (Min, 2021). Mobility effects on student academic achievement are another factor to consider in segregated schools and urban districts.
As the Spanish-speaking population increases in the United States, English learners (ELs) are the ones most likely to experience high levels of segregation (i.e., school and residential) because they often reside in segregated neighborhoods and consequently attend more segregated schools than their U.S. born counterparts (Fuller et al., 2019; Vasquez Heilig & Holme, 2013). Data indicate that the achievement score gaps of non-EL students and EL students for fourth grade Reading and Math were 33 and 23 points higher, and for eighth grade were 45 and 42 points higher. Though there is an increase of Brown students, many of whom are ELs, in urban districts (Gandara & Aldana, 2014), there is minimal quantitative research about their academic performance and the cultural and linguistic factors that shape their educational outcomes in this context (Rodriguez, 2009). Additionally, although patterns of racial disproportionality of children in special education increase for those who live in poverty (Bal et al., 2014; Oswald et al., 2001), limited information exists in urban education studies.
These aforementioned national-scale research on school districts and achievement have garnered important results relative to our use of the SEDA datasets for this study. The SEDA test score results are useful in the analysis of district-level academic achievement performance, third to eighth grade growth nationally, and in using district-level estimates to understand the distribution of learning opportunities in public school districts (Kuhfeld et al., 2019).
We employed growth mixture modeling (GMM), a data-driven person-centered approach to examining population heterogeneity in growth trajectories where different latent classes are uncovered, each with its unique growth pattern. School districts that belong to each latent class can be identified and their characteristics (e.g., race/ethnicity composition) can be further examined to see how they explain the various growth patterns. This approach is particularly useful in urban educational contexts because it can identify subpopulations that have distinct growth trajectories whereas conventional growth modeling, such as multilevel models or latent growth curve models, assumes that individuals come from a single population and share the same growth trajectory (Jung & Wickrama, 2008). Considering the numerous factors that impact student achievement in urban school districts, GMM can be an appropriate approach to fully capturing individual differences in change over time. In addition, conventional growth modeling assumes within-group homogeneity (i.e., when examining gender difference, females and males are treated as homogeneous subgroups), which often is not tenable given the interrelations among various factors in urban educational contexts. By contrast, GMM uncovers true differences in achievement based on data and does not rely on any one of the factors. Subsequently, distinct growth patterns can be linked with the various factors to examine how they would impact the longitudinal learning outcome of students.
The purpose of our study then was to use GMM to examine the SEDA 2.1 data sets on student Mathematics (Math) and English language arts (ELA) achievement over time, for urban school districts. We focused on two research questions:
What growth patterns exist for students in third to eightth grades in urban districts across the United States regarding their ELA and Math achievement from 2008 to 2014? What factors are related to the growth patterns (e.g., race/ethnicity composition, unemployment, free or reduced lunch, special education, ELs)?
GMM, the analytic approach used, is emerging in urban education research. Though quantitative studies have investigated aspects related to urban schools (Leana & Pil, 2006; Miller et al., 2008; Schwab-Stone et al., 1999), few studies have used structural equation modeling and longitudinal analysis to study urban education issues (Dixon-Roman, 2012; Drame, 2010; Eddy & Easton-Brooks, 2011; Munoz & Chang, 2007; Wang & Goldschmidt, 1999), and none was found that used GMM. We addressed this gap by using GMM to analyze student achievement data from 2008 to 2014 of urban school districts in the United States, and the impact of contextual factors on growth trajectories over time.
Moving forward, we reviewed the relevant literature on urban education. Then, we explained the utility of the QuantCrit framework as the analytical lens to centralize race/racism and related factors to understand achievement growth patterns in urban school districts. After which, we employed GMM to determine and subsequently explained the results. Finally, we discussed the insights garnered from the application of QuantCrit perspective to the growth patterns found in relation to urban school districts. We concluded with implications for further research.
Understanding Urban Education: Then and Now
In the following section, we provide a truncated explanation of the historical and current factors that contribute to our understanding of urban education in the United States. First, we define urban communities, then we discuss the inequities in segregated schools with an emphasis on urban schools which are mainly comprised of Black and Brown students. We end this section with an explanation of the importance of the opportunity gap framework and urbanicity to understand the realities of the urban school context.
Defining Urban Communities
According to the National Center for Education Statistics (NCES) (2019), urban is defined by the Census Bureau, to “represent densely developed territory, and encompass residential, commercial, and other non-residential urban land uses … To qualify as an urban area, the territory must encompass at least 2,500 people” (p. 2). Urbanized areas (UAs) are urban areas that contain 50,000 or more, and urban clusters (UCs) are urban areas that contain between 2,500 and 50,000 people. The NCES classifications of the city (i.e., large, midsize, small) is a territory inside UAs and in a Principal City with a population of 100,000 or more. Although these definitions of “urban” appear to simply describe population size and geographic location, urban communities have taken on a much deeper meaning over the past half-century.
After the passage of the Civil Rights Act of 1964, which officially ended racial discriminatory policies and practices and forced school desegregation, federal and local governments found other ways to separate people by race and social status, and housing is one of the prime examples. Sugrue (2005) explained, “…government housing programs perpetuated racial divisions by placing public housing in already poor urban areas and bankrolling white suburbanization through discriminatory housing subsidies” (p. 10). Furthermore, federal urban programs were dependent on the assistance of local community members (e.g., politicians, developers, real estate brokers) to restructure urban geography by class and race, through the enactment of housing policies.
Ghettoization seemed fated and a natural consequence of systemic racism where poverty, deteriorating neighborhoods, and overpopulation were depicted as, “signs of individual moral deficiencies, not manifestations of structural inequalities” (Sugrue, 2005, p. 9). These deficit-oriented perceptions and assumptions about racial identities constructed and perpetuated attitudes and actions that stigmatized Blacks living in urban communities. Race-based discriminatory policies and practices not only historically confined Blacks to urban communities, whereupon the distribution of resources was inequitable and consequently limited upward mobility but continues to this day specifically in relation to housing discrimination (Gooden & Thompson-Dorsey, 2014), as well as in health, employment, and educational disparities. Segregated schools became an inevitable conclusion (Bonilla-Silva, 2015).
To further conceptualize and define urban in relation to educational contexts, Milner (2012) described three conceptual frames that can be used to explain the situated realities of urban schools and communities. Urban intensive (UI) are schools located in large metropolitan cities with over a million people and social factors like housing, poverty, and transportation are directly connected to schooling. Urban emergent (UE) are schools in midsized cities with less than a million people where the challenges are not quite complex (e.g., limited resources) as in the UI category. Urban characteristic (UC) are schools beginning to experience challenges (e.g., increase in ELs) associated with UI and UE schools, located in small cities even rural and suburban areas. These frames are necessary to understand the nuances of the contextual realities students in urban schools encounter because racism is entwined within economics, property rights, and educational access (Gooden & Thompson-Dorsey, 2014). The interconnection of poverty, race, educational outcomes, and housing discrimination are reinforced through deeply entrenched mechanisms of oppression that result in generational inequities. One such example, is the impact of Brown and successive litigation and legislation of (de)segregation within the U.S. education system (Lomotey & Teddlie, 1996).
Inequities of Segregated Schools
The Brown v. Board of Education (1954) supreme court decision which ruled separate but equal racially segregated schooling as unconstitutional, was a reversal of the decision decreed in Plessy v. Ferguson (1896). Though, desegregation efforts which resulted from this decision was better enforced with the enactment of the Civil Rights Act of 1964 (Johnson, 2014), post-Jim Crow era, schools and communities were segregated and furthered the inequities based on race and class. White flight (Johnson, 2014), housing policies and residential segregation (Bonilla-Silva, 2015) were anti-civil rights efforts to impede racial integration in communities. Moreover, de facto segregation happened as a result of legal cases in the 1990s which solidified residential and school segregation (i.e., Board of Education of Oklahoma v. Dowell (1991), Freeman v. Pitts (1992)), and more recently, the Parents Involved in Community Schools v. Seattle School Dist. No. 1 (2007) contributed to re-segregation within districts. In addition, school re-segregation can be attributed to White private school enrollment, housing segregation, litigation, and school choice (Thompson-Dorsey, 2013).
According to Orfield and Frankenberg (2014) segregation has increased across the United States. for the past twenty-five years. The research explained the damaging effects of segregating Black and Brown children living in low-income communities from their white or middle-class peers in separate schools (Gandara & Aldana, 2014; Orfield & Frankenberg, 2014; Reardon & Owens, 2014; Vasquez Heilig & Holme, 2013). For instance, Orfield et al. (2016) explained that increased segregation by race and poverty for African American and Latino students clustered in schools barely meet outcomes of which are attained by their middle-class counterparts. These researchers further noted that for decades there has been a strong relationship between double segregation (i.e., racial and economic) and the lesser opportunities afforded to them. More recent research similarly reported triple segregation in schools by race, language proficiency, and poverty (Vasquez Heilig & Holme, 2013) and its harmful consequences.
Hanushek et al. (2009) and Guryan (2004) found that school segregation impacted the achievement of Black children negatively. Additionally, Fuller et al. (2019) described that the national growth of the Hispanic student population in segregated schools in large urban districts continues to increase. They found that “racial and economic segregation have been slow to move in recent decades for young Latino children … most face highly segregated settings, especially the offspring of immigrant parents” (p. 415). Furthermore, housing segregation in urban neighborhoods with EL students, who often are Hispanic, has damaging effects on English acquisition (Gandara & Aldana, 2014), because these students attend schools segregated by race, poverty, and language and have detrimental educational experiences (Milner & Lomotey, 2014).
Achievement Gap Versus Opportunity Gap
The focus on the achievement gap that exists between Black and Brown children and their white counterparts narrowly frames thinking, performance outcomes, and research about children and school systems. In urban communities, where residential and school segregation is commonplace (Moore & Lewis, 2014), there are struggling schools with unequal access to resources, experienced teachers, administrative and staff supports (Gagnon & Mattingly, 2012). “We have the schools we have because of the culture we have” (Ladson-Billings, 2004, p. 11); a broader society entrenched in systemic inequities because of racist structures that impact urban communities. Only with an understanding of the complicated and interwoven histories of race, residence, and work can the compounding issues get addressed (Sugrue, 1998).
The depiction of national performance of achievement between White and Black students and White and Hispanic students has been consistently reported as achievement gaps through the Nation's Report Card. According to NCES (2019), the most recent information reported that White–Black score gaps for Reading and Math for fourth and eighth grade students were 27, 25, 28, 32 points higher, respectively. The White-Hispanic score gaps for Reading and Math for fourth and eightth grade students were 21, 20, 18, 24, points higher, respectively. The Black–White achievement gap was reported to be larger in the highest density schools, where the highest density category were schools that were 60%–100% Black students and primarily located in the South, some in the Midwest, and in the cities (Bohrnstedt et al., 2015).
A deleterious structure that impacts the achievement of Black and Brown children is the residential location of families as it is related to the racial composition of schools (Hanushek & Yilmaz, 2011). In a study conducted by Hanushek et al. (2009), they found that the achievement gap is directly related to the racial makeup of schools. Furthermore, Reardon et al. (2018) argued, “achievement gaps should be understood as symptoms of underlying racial inequalities in the total set of children's educational opportunities resulting from differences in family resources, neighborhood conditions, and schooling experiences” (p. 41). Therefore, the achievement gap considerably impacts Black and Brown children and is only part and parcel of the overarching societal constrictions (i.e., political, cultural, legislative, social, economic, historical) which create inequitable structures and systems that have sustained and unfavorable consequences on Black and Brown communities. These longstanding racist and systemic injustices create the opportunity gap.
The opportunity gap framework “shifts our attention from outcomes to inputs – to the deficiencies in the foundational components of societies, schools, and communities that produce significant differences in educational outcomes” (Carter & Welner, 2013, p. 3). This framework focuses upon the systemic barriers and institutional structures that thwart opportunity and success (Milner, 2012) for Black and Brown students. There are five interrelated tenets: (1) Rejection of color blindness; (2) Ability and skill to work through cultural conflicts; (3) Ability to understand the myth of meritocracy; (4) Ability to recognize and shift low expectations and deficit mindsets; and (5) Rejection of context-neutral mindsets and practices (Milner, 2012). The systemic and institutional mechanisms, policies, and practices that impact students’ experiences are centered over their achievement outcomes. Opportunity gaps are worsened when a myopic view of excellence and success are instituted, and when “White performance is the gold standard to which all others should strive” (p. 10). The deficit assumptions associated with the achievement gap based on individual or family characteristics do not account for the historical and social contexts that shape student outcomes established through economic and racial inequities. The next section explains the utility of Critical Race Theory as the guiding perspective and QuantCrit as the framework for this study.
Theoretical Framework
Critical Race Theory
We apply a critical race perspective in the furtherance of critical racial justice in quantitative educational research. Critical race theory (CRT) challenges the status quo and the normality of racism in American society (Howard & Navarro, 2016; Ladson-Billings, 1998; Ladson-Billings & Tate, 1995). Highlighting the wider structural inequities, CRT scholars engender a commitment to “unveil, deconstruct, and transform the oppressive educational realities” of Black and Brown communities (Garcia et al., 2018, p. 152). Further, “(i)f we look at the way that public education is currently configured, it is possible to see the ways that CRT can be a powerful explanatory tool for the sustained inequity that people of color experience” (Ladson-Billings, 1998, p. 18). Thus, with CRT underpinnings, the value of analysis through the lens of QuantCrit framework (Gillborn et al., 2018) enabled us to understand urban educational achievement outcomes in nuanced and racialized ways.
Covarrubias and Velez (2013) explained how statistical data advanced deficit perceptions which influence policy, practice, and research. Quantitative approaches are canonically understood as impartial, as opposed to that all data are manufactured and analysis is driven by the human decision which are influenced by theories, beliefs, and biases (Gillborn et al., 2018). Therefore, we utilized QuantCrit principles which “embodies the need to apply CRT understandings and insights whenever quantitative data is used in research and/or encountered in policy and practice” (Gillborn et al., 2018, p. 169).
QuantCrit
Quantitative modes of inquiry are understood to be objective, scientific, and neutral. The privilege afforded to this insular research paradigm is evidenced in national policies and funding mechanisms as the valued, preferred, and responsible way to conduct and report research. Though quantitative research is traditionally understood in this way, critical quantitative researchers have critiqued this understanding and its utility of truth claims. Gillborn (2010) states, “statistical methods themselves encode particular assumptions which, in societies that are structured in racial domination, often carry biases that are likely to further discriminate against particular minoritized groups” (p. 254). The focus on race and racism in these contexts is to address the notion that quantitative data are also socially constructed (Carpentier, 2008) and to place emphasis on how socially constructed categorizations used in quantitative analytical approaches contribute to deficit orientations in research for particular children.
The tenets of QuantCrit (Gillborn et al., 2018, pp. 169–174) inform our thinking in this study. Each is described below.
The centrality of racism—QuantCrit recognizes that racism is a complex, fluid and changing the characteristic of a society that is neither automatically nor obviously amenable to statistical inquiry. In the absence of a critical race-conscious perspective, quantitative analysis will tend to remake and legitimate existing race inequities (p. 169). Numbers are not neutral—QuantCrit exposes how quantitative data are often gathered and analyzed in ways that reflect the interests, assumptions, and perceptions of White elites. …QuantCrit prompts researchers to examine behind the numbers in order to understand how findings have been generated and identify the racist logics that may have shaped conclusions (p. 170). Categories are neither natural nor given: for “race” read “racism”—QuantCrit interrogates the nature and consequences of the categories that are used within quantitative research … where complex, historically situated and contested terms (like race and dis/ability) are normalized and mobilized as labeling, organizing, and controlling devices in research and measurement (p. 171). Voice and insight: data cannot “speak for itself”—QuantCrit assigns particular importance to the experiential knowledge of people of color and other “outsider” groups (including those marginalized by assumptions around class, gender, sexuality, and dis/ability) and seeks to foreground their insights, knowledge, and understandings to inform research, analyses, and critique (p. 173). Using numbers for social justice—QuantCrit should work with/against numbers by engaging with statistics as a fully social aspect of how race/racism is constantly made and legitimated in society (p. 174).
Since educational disparities explained through quantitative analysis may construct racialized and deficit-infused narratives that marginalize Black and Brown children in low-income neighborhoods, we utilized the QuantCrit lens in our analysis as an alternative.
Methods
This study uses the SEDA version 2.1. The SEDA includes a set of publicly available district-level data sets on students’ Math and ELA achievement specifically from the 2008–2009 school year through to 2014–2015 (Fahle et al., 2018). In addition, district-level covariate data are available, which provide information regarding racial and socioeconomic composition. Using an indicator for whether the school was located in an urban area that was available in SEDA, this study included data from all urban school districts in the analysis. The number of urban school districts ranged from 0 to 174 across states (see Table 1). There was no urban school district in Hawaii. In Washington, D.C. and Delaware, there was one school district, respectively, included in the data set, while some states had over 30 urban districts (e.g., Arizona 36, California 174, Illinois 32, Michigan 38, and Texas 82).
The Number and Percentage of Urban School Districts by State.
Variables
For assessment data, Math and ELA achievement data on the grade (within Cohort) standardized (GCS) scale were used. Based on federal legislation, states are required to test students in Math and ELA every year on state-specific standardized assessments. Each state designs, administers the tests, and set their own standards to categorize students’ performance into various proficiency levels (Fahle et al., 2018). The raw data of SEDA included the number of students in each of the proficiency levels disaggregated by student subgroups (e.g., race/ethnicity, gender) for each grade, year, and subject. Data were then constructed and made comparable across grades, years, and states using the National Assessment of Educational Progress (NAEP). The GCS scale is one way of linking the data with NAEP. The score at the GCS scale represents students’ achievement in a certain school district relative to the national average achievement. For example, a score of 5 for 4th graders would indicate that students are one grade level above the national average achievement level.
For covariate data, we considered the racial composition in the school district, including the percentage of students of several racial backgrounds (Native American, Asian, Hispanic, Black, and White). We also considered the percentage of parents that were unemployed, the percentages of students that had free lunch or reduced lunch, as well as the percentages of English language learners and special education students.
Analytic Procedures
First, some descriptive statistics on the Math and ELA achievement data were presented by subject and grade level (i.e., third through eighth grade). Then, the potential heterogeneity in the growth trajectories of students in urban school districts was examined. Specifically, a series of growth mixture models with varying numbers of latent classes were fitted with the statistical software program Mplus 7.1 (Muthén & Muthén, 1998–2012). Note that latent classes were distinguished by the growth trajectories (i.e., baseline and growth rate). Given that school districts were nested within states, “type = complex” was specified in Mplus to take into account such nested data structure. Then the models were compared in terms of their fit and interpretability to decide the optimal number of latent classes. Model fit comparisons were made based on several information criteria, including Akaike's information criterion (AIC; Akaike, 1973, p. 1987), Bayesian information criterion (BIC; Schwarz, 1978), and sample-size-adjusted BIC (saBIC; Sclove, 1987). Small values of information criteria indicate better model fit. In addition, statistical tests were also used in model comparisons, including the Lo–Mendell–Rubin (LMR) likelihood ratio test (Lo et al., 2001), adjusted LMR, and the bootstrap likelihood ratio test (BLRT; McCutcheon, 1987; McLachlan & Peel, 2000). The standard likelihood ratio test cannot be used in this setting, because when comparing different numbers of latent classes, the test statistic does not follow a Chi-square sampling distribution (McLachlan & Peel, 2000). The LMR and adjusted LMR tests use the adjusted asymptotic distribution of the test statistic and the BLRT uses bootstrap samples to empirically derive the sampling distribution. All three tests compare the fit of a k-class model versus a (k-1)-class model and p-values that are below the employed alpha value (e.g., 0.05) indicate that the k-class model has a significantly better fit to the data. Subsequently, the composition of each latent class was examined with contextual factors to identify the relationship between the latent class membership and the contextual factors. Specifically, the probabilities of each school district belonging to different latent classes were estimated and the school district was assigned to the latent class that had the highest probability. Such latent class membership was retrieved from Mplus and used as the grouping variable in subsequent analysis. That is, t-tests (for two latent classes) or ANOVAs (for three or more latent classes) were conducted to compare the latent classes in terms of the race/ethnicity composition, the unemployment rate, the percentages of students that had free or reduced lunch, and the percentages of ELL students and students that received special education.
Results
Descriptive Statistics
Table 2 presents the descriptive statistics of students’ ELA and Math achievement by grade level. Overall students’ ELA and Math achievement in urban school districts were slightly below the national average achievement at each grade level. For example, the mean of students’ ELA achievement at Grade 5 was 4.72, whereas the national average achievement should be 5 at Grade 5. In addition, slightly greater variability was observed in math achievement at Grades 6, 7, and 8, as shown by larger standard deviations than those at other grade levels.
Descriptive Statistics of English Language Arts (ELA) and Math Achievement by Grade Level.
Determining the Number of Latent Classes for ELA and Math
The number of latent classes for ELA and Math achievements was determined by fitting and comparing a series of growth mixture models with different numbers of latent classes (see Table 3). For ELA, models with 1- to 3-class were fitted. LMR and adjusted LMR tests showed that increasing the number of latent classes from 2 to 3 did not improve the model fit significantly. Therefore, the 2-class growth mixture model for ELA was selected as the best-fitting model. Similarly, we first fitted 1- to 3-class to the math achievement data. All the information criteria and tests showed that the 3-class model had significantly better fit than the 2-class model. Therefore, we fitted a 4-class model. BIC and saBIC indicated that the 4-class model did not improve the fit much. In addition, the proportion of one latent class was below 1%, which was considered to be too small. Therefore, the 3-class model was selected as the best-fitting model for the math achievement data. To summarize, there were two growth patterns for ELA achievement data and three growth patterns for math achievement data.
Deciding the Number of Latent Classes for English Language Arts (ELA) and Math.
Note. AIC = Akaike’s information criterion; BIC = Bayesian information criterion; saBIC = sample-size-adjusted BIC. LMR = the Lo–Mendell–Rubin test; BLRT = the bootstrap likelihood ratio test. NA indicates that the test is not applicable when the number of classes is 1, because we cannot compare the fit of 1-class and 0-class model.
Examining the Growth Patterns for ELA and Math
These growth patterns were further examined for ELA and Math, where the growth patterns were defined by the initial achievement status (i.e., intercept) at Grade 3 and the growth rate (i.e., slope) over time. Figures 1 and 2 show the growth patterns for ELA and Math, respectively, where the X-axis is the grade level (from Grade 3 to Grade 8). For ELA (see Figure 1), it was observed that for the vast majority of school districts (99%), the initial status at Grade 3 was close to 3, indicating that they were at the national average level. The growth over time was steady and consistent (see Class 2 in Figure 1). Therefore, this latent class was named Increased Achievement Class. However, for a small number of school districts (8 districts or 1%; Class 1 in Figure 1), their initial status was about 2 grade levels above the national average level, but their achievement decreased over time when compared with the national average level. This latent class was thus referred to as Decreased Achievement Class.
Growth trajectories for each latent class for ELA achievement.
Growth trajectories for each latent class for Math achievement.
For math, two latent classes (Class 1 and Class 3) had steady growth over time. Class 1 (6%) had a lower initial achievement level at Grade 3 than Class 3 (93%) but had a faster growth rate. The achievement of students in these two latent classes was very comparable at Grade 8. Therefore, Classes 1 and 3 were named Catch-up Class and Increased Achievement Class, respectively. Class 2 (1%) had a similar initial achievement levels compared with Class 1, but their achievement slightly decreased over time. Class 2 was the Decreased Achievement Class.
Exploring the Relationship between Contextual Factors and Growth Patterns
Table 4 presents the race/ethnicity composition, the unemployment rate of the community, the percentages of students that had free or reduced lunch, as well as the percentages of ELL students and students that received special education by each latent class for ELA and Math. For ELA, results of t-tests showed that school districts that belonged to the Decreased Achievement Class had significantly lower percentage of White students and higher percentage of students that had reduced lunch, when compared with school districts that belonged to the Increased Achievement Class. Specifically, the percentages of White students were 46% and 26% for school districts in Increased and Decreased Achievement Classes, and the percentages of students that had reduced lunch were 8% and 7%. Although not statistically significant, school districts in the Decreased Achievement Class had higher percentages of Hispanic and Black students.
Contextual Factors by Latent Class for ELA and Math.
Note. *p < .05, **p < .01.
For Math, there were statistically significant differences across latent classes in the percentages of Hispanic and White students, the percentages of students that had free or reduced lunch, and the percentage of students that received special education. Specifically, on average, school districts in the Increased Achievement Class had significantly lower percentages of Hispanic students (26.65%) as compared with the other two classes (i.e., 45.34% and 57.76% for Catch-up and Decreased Achievement Classes, respectively). In addition, the Increased Achievement Class also had significantly higher percentage of White students (47.06%) on average than the Catch-up Class (30.21%) and the Decreased Achievement Class (12.96%). The Decreased Achievement Class had much higher percentage of students that need free lunch (75.16% as opposed to 47.33% and 48.99% for the Increased Achievement and Catch-up Classes). Interestingly, the percentage of students that had reduced lunch was the highest in the Catch-up Class (13.23%) and school districts that belonged to this class had higher percentage of students that received special education than the Increased Achievement Class.
Discussion
This study utilized a sophisticated statistical technique to examine factors that influence academic achievement in urban districts in the United States over time. This is useful information for researchers and practitioners in understanding the complexity of urban contexts.
The results indicate that achievement in Math and ELA are below the national average for each grade level, third to eighth grade, in urban districts. This is consistent with Lewis et al. (2008) finding that students in urban communities tend to score lower on standardized tests and below on national averages and show disparities in outcomes related to poor achievement in grades and high school dropout rates. Kwok (2017) explains that urban schools have larger class sizes, less experienced teachers, greater turnover rates, and students who are economically and racially diverse, which contribute to the detrimental impacts on student achievement. Further, Schwartz (2012) found that low-income students in low poverty schools scored significantly higher in Math and Reading than low-income students in high poverty schools which demonstrates that the economically advantaged schools affect academic performance.
This understanding of the opportunity gap in economically strapped and racially isolated urban school districts is not surprising. The well-studied achievement gap “can best be understood as a predictable result of systemic causes—a representation of the disparities in opportunities available to children of different racial, ethnic, socioeconomic, and cultural backgrounds” (Carter & Welner, 2013, p. 9). The linkage between opportunity gaps and achievement gaps is evident in that academic disparities for Black and Brown children who live in low-income urban communities are related to the deep-rooted systemic inequities that are found outside educational institutions. When these inequitable conditions are inherited and experienced generation after generation, the geographical and cultural places characterize and construct students and families and impact educational outcomes, economic mobility, and life trajectories.
By using GMM, we garnered information about achievement growth of time. Of importance, districts with decreased achievement in ELA had significantly lower percentage of white students and higher percentage of students on reduced lunch. This supports Reardon et al. (2018) discussion that the strongest correlates of achievement gaps are consistent with socioeconomic factors that affect educational opportunity through residential and school segregation patterns. Neighborhood conditions affect educational attainment and sustained exposure to disadvantaged neighborhoods and residential segregation may lead to inequalities in educational outcomes (Wodtke et al., 2016). Moreover, Moore and Lewis (2014) explains that African American students who experience residential and school segregation are concentrated in communities with high levels of poverty and difficulty in accessing opportunities. The inequalities and injustice that underlies the political, social, economic, and educational systems in urban districts create differentiated schooling experiences and detrimental outcomes.
The racialized effects of policies and structures of oppression in urban communities are reflective of the various established discriminatory practices (Gooden & Thompson-Dorsey, 2014; Scott & Quinn, 2014; Sugrue, 2005) that continue to disenfranchize Black and Brown children and families. Race and racism is, “a function of systems, institutions, and structures of oppression … ingrained in policies, practices, procedures, and systems of education” (Milner, 2020, p. 148). The constraints that reify urban boundaries that doubly or triply segregate based upon race/ethnicity, poverty, and/or language (Gandara & Aldana, 2014; Orfield & Frankenberg, 2014) mechanistically regulate and stigmatize groups through deficit-oriented racial assumptions, ideologies, and processes.
We additionally found that there were statistically significant differences in the percentage of Hispanic and White students, with the percentage of free or reduced lunch, and the percentage of children who receive special education services. There were significantly lower percentage of Hispanic students in the increased achievement class, of which there was a significantly higher percentage of White students. Further, a large percentage of students (i.e., 75%) were on free lunch in the decreased achievement class. Reardon et al. (2018), explained that “there is no school district in the United States that serves a moderately large number of Black or Hispanic students where achievement is even moderately high and where achievement gaps are near zero” (p. 35). They also specified that Black and Hispanic children live in poorer neighborhoods than White children. Hispanic students are increasingly becoming more segregated within urban districts (Fuller et al., 2019), where ELLs experience triple segregation (i.e., isolation by poverty, race, and language proficiency) (Vasquez Heilig & Holme, 2013).
Educational opportunities and equitable conditions are not possible to achieve in urban communities where racial and economic oppression and separation have been historically and structurally embedded. Dixon-Roman and Gordon (2012) explained that “space is both produced and producing, constituted and constituting, structured and structuring” (p. 7). This is how school and neighborhood segregation reproduces racial stratification (Johnson, 2014) and reinforces systemic processes that marginalize Black and Brown communities. Systems of power and repression underlie these injustices that maintain inequitable conditions in urban communities. These spaces are “filled with politics and privileges, ideologies and cultural collisions, utopian ideals and dystopian oppression, justice and injustice, oppressive power and the possibility for emancipation” (Soja, 2010, p. 103).
Conclusion
Overall, our findings show that educational disparities, reported through quantitative measures, need further interrogation of the underlying structures and oppressive mechanisms in society that creates differential access to resources and opportunity in urban communities. The neutrality of numbers is questioned since quantitative analysis may tend to normalize race inequity, and furthermore, data gathering can be shaped by theories and beliefs prone to racial bias (Gillborn et al., 2018). “Theoretical frameworks and methodological approaches grounded in place have great potential to unmask deep social, economic, and environmental inequities without the limitations inherent in some traditional approaches” (Butler & Sinclair, 2020, p. 68). Not only is race a social construction, it is also contextually, legally, geographically, and spatially constructed (Green, 2015; Milner, 2020; Milner & Lomotey, 2014; Pearman, 2020). Utilizing spatial justice theoretical perspective (Soja, 2010) and spatial analysis (Morrison et al., 2017) in conjunction with QuantCrit is important to understand more deeply the context of urban communities and racial inequities. The function of urban space and urban systems is mired by a historical and political geography/spatiality (Soja, 2010) which can “constrain opportunity, oppress, imprison, subjugate, disempower, close off possibilities” (Soja, 2010, p. 104). Critical Race Spatial Analysis (Morrison et al., 2017) integrates a critical spatial dimension to analysis to understand the complexity of racial oppression in educational, historical, and social spaces.
There are limitations of this research study that needs to be mentioned. First, no individual student-level data are publicly accessible, only district-level data sets are available to use. Consequently, this study also has the limitation that only secondary data analysis can be conducted. Further, specific attention to variability or variation of districts (i.e., in composition, and size) is not considered. In furtherance of this study, we would like to see future research focused on localized urban contexts and the use of various methodological approaches such as qualitative, mixed methods, and critical quantitative perspectives. For example, research that explores the lived experiences that guide and shape educational experiences and attainment in urban communities. There is a need to study the nuances of the contextual experiences for Black and Brown students in low-income communities through critical spatial perspectives which advance social justice in education (Soja, 2010). Moreover, research should focus on the spectrum of experiences, the opportunities (Green, 2015), and the negative impacts of racism and oppressive socio-spatial structures not only in urban contexts, but also in suburban and rural spaces.
Future research on the utility of the opportunity gap (Milner, 2012) theoretical framework should seek to understand the relationships between socially constructed markers of difference (as well as legally, spatially, historically constructed) (Milner, 2020) available resources, and educational outcomes to reveal inequality and forms of inherent oppressions. Not enough research studies are using critical quantitative approaches (Covarrubias & Velez, 2013; Garcia et al., 2018; Gillborn et al., 2018). We call on researchers to expand upon critical quantitative inquiries that include distinctive categorizations (e.g., disability, special education, language, gender, ethnicity, so on) and critical conceptual frameworks (e.g., intersectionality, DisCrit, etc.) (Tabron & Ramlackhan, 2018). Further, warranted is that researchers address the structural barriers and inequities that communities of color encounter and how accountability measures and neoliberalism are influencing policy and practice within these structures. Lastly, needed is research that explores how national policies and politics impact marginalized communities in relation to housing, healthcare, immigration, and the systems of power and inequitable conditions that contribute to disparate outcomes for children and families.
Footnotes
Acknowledgments
We appreciate and thank Dana Thompson Dorsey for offering feedback on the early draft of this article. We extend our gratitude to the anonymous reviewers for their helpful and insightful feedback.
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The authors received no financial support for the research, authorship and/or publication of this article.
