Queen Essays

Educational Researcher, Vol. 51 No. 4, pp. 245 –254 DOI: 10.3102/0013189X221081853

Article reuse guidelines: sagepub.com/journals-permissions © 2022 AERA. https://journals.sagepub.com/home/edr MAy 2022 245

Over the past three decades, children from low-income families have increasingly been attending different public schools than children from affluent families

(Owens et al., 2016). Importantly, segregation of students by income appears to be highly localized, growing fastest between schools within the same district.1 As we will review, economic, social, and demographic changes have shaped these patterns, but education policy has played a role, too. The processes through which students are mapped to traditional public schools have changed in ways that have contributed to growing income segre- gation of students at the school level. For example, segregation of students by income between schools has grown as school choice options grew due to the introduction of charter schools nearby (Marcotte & Dalane, 2019; Monarrez et al., 2019).2

Although recent work has documented trends in the segrega- tion of students by income between districts and schools, we know very little about such segregation of students as they expe- rience school—in the classroom. This is a potential oversight since the factors shaping income segregation between schools may not be barred by the school door. As neighborhoods change and school choice options grow, administrators at the district and school levels may seek to attract or retain students by chang- ing what is offered inside the school building. For example, administrators might expand ability tracking or offer targeted

school-within-a-school curricula to placate parents most likely to choose among multiple schools.

In this paper, we attempt to advance knowledge of trends in income segregation of students by examining changes within schools—at the classroom level. In our administrative data of all students attending public schools in North Carolina, the average public school has more than 110 students per grade, grouped into five or more classes. Our data include a measure of a stu- dent’s free/reduced-price lunch eligibility as well as information on classroom assignments. We refer to students who are eligible for free or reduced-price lunch as economically disadvantaged (ED) in accordance with our data-sharing agreement with the North Carolina Education Research Data Center (NCERDC).3 Using the ED status of each student in each classroom, we assess whether ED students are assigned to classes in the same pattern as other students or are clustered into different classrooms. That is, we measure within-school segregation at the classroom level of ED students from other students.4

Our main contribution is to model trends in income segrega- tion of students within schools as a function of school and dis- trict characteristics. We include school fixed effects in all of our models, so that we estimate changes in within school ED

1081853 EDRXXX10.3102/0013189X221081853EDUCATIONAL RESEARCHERMONTH XXXX research-article2022

1American University, Washington, DC

The Segregation of Students by Income in Public Schools Kari Dalane1 and Dave E. Marcotte1

Over the past three decades, children from low-income families have increasingly been attending different public schools than those from more affluent families. Though recent work has helped us understand patterns of income segregation between districts and schools within districts, we know little about segregation of students as they experience school: in the classroom. We attempt to advance knowledge of segregation of students by income at the classroom level. We use data from North Carolina that includes information on classroom assignments and students’ economically disadvantaged (ED) status. We assess whether ED students are clustered/segregated into different classrooms than other students. We find that within-school segregation rose by about 10% between 2007 and 2014 in elementary and middle schools we study.

Keywords: at-risk students; descriptive analysis; disparities; educational policy; regression analyses; secondary data

analysis

FEATuRE ARTIClES

246 EDuCATIONAl RESEARCHER

segregation that are due to patterns at the school level—rather than due to compositional changes in where students are attend- ing school. So, our estimates provide insight into how income segregation by classroom is changing at the typical school. Our paper is among the first to shed light on the magnitude of segre- gation within schools by economic disadvantage and whether such segregation has increased. We further consider whether ED segregation within a school is associated with the broader con- text of ED segregation in its district. This second question is vital for understanding whether any segregation between schools is offsetting or exacerbating broader trends in segregation of stu- dents by income within schools.

Background

Between-School Segregation

The topic of segregation in American public schools has long been a concern for researchers and policymakers. Much of that attention has focused on the between-school segregation of stu- dents by race. Though race and socioeconomic status (SES) are highly correlated, only recently have analysts employed data from various sources to study socioeconomic segregation specifically.5 For example, Owens et al. (2016) reported increasing levels of income segregation between districts in large metropolitan areas and between schools within the 100 largest districts. Marcotte and Dalane (2019) use more recent Common Core of Data data and report similar patterns of rising segregation of students by income in large districts but no substantial increase in small districts.

Rising socioeconomic segregation between schools and dis- tricts raises concerns for education policy by shaping the distribu- tion of economic opportunity. Schools with higher proportions of low-income students have fewer educational resources, so the concentration of poor students in poor schools could further exacerbate disparities of opportunity (Betts et al., 2000). Indeed, states with the highest levels of between-district segregation also have the highest level of variation in achievement between dis- tricts (Fahle & Reardon, 2018), and the income achievement gap is largest in U.S. metropolitan areas with the most residential seg- regation by income (Owens, 2018).

Within-School Segregation

Although researchers continue to sort out the possible drivers and consequences of socioeconomic segregation between school districts and between schools within districts, a question that has received almost no attention is whether socioeconomic seg- regation is changing within schools. This is surprising, since the changing neighborhoods and schooling options that may be driving system wide patterns may also be affecting the organiza- tion of schools themselves.

Previous work provides evidence that the assignment of stu- dents to different classes based on SES is driven by parent and teacher preferences (Kalogrides & Loeb, 2013). For example, Lareau (1987, 2000) has documented that parents (and espe- cially mothers) from families with higher incomes and educa- tion are more involved in their children’s schools, are more

likely to know the names and reputations of teachers within those schools, and more often intervene with principals in class- room assignment decisions on behalf of their children. Because wealthier, more educated families can vote with their feet, administrators can feel pressure to accede to their classroom assignment requests in order to retain them in their schools/ districts (Clotfelter et al., 2005). Principals may receive similar pressure from their teachers, who also have substantial interest in classroom assignment decisions as well as information about student performance. Students from low-income families have been found to have lower levels of classroom engagement because of poorer health or nutrition (Basch, 2011; Jansen, 2013) or expectations (Odéen et al., 2012) and are more likely to exhibit problems with attention and impulsive behavior (Liston et al., 2009). In an effort to retain their best teachers, principals may acquiesce to preferences for assigned students who present with fewer behavioral or academic challenges (Kalogrides & Loeb, 2013).6 Related, there is evidence that socioeconomic attributes of students affect assignment to hon- ors/gifted academic tracks (Gamoran, 1992; Grissom & Redding, 2016; Rosenbaum, 1976).7

Although this literature provides good evidence that parent SES shapes classroom assignment, we have little empirical evi- dence on levels and trends in within-school socioeconomic segre- gation of students. We are aware of five existing studies that examine within-school segregation, four of which focus on race. These studies find that most segregation takes place between schools, but within-school sorting adds to racial isolation, espe- cially at the high school level, where tracking is more prevalent (Clotfelter et al., 2002, 2021; Conger, 2005; Morgan & McPartland, 1981). Kalogrides and Loeb (2013) examine within- school segregation by both race and SES in elementary, middle, and high schools in three large urban school districts and find more segregation by race and SES than would be expected if stu- dents were placed into classes randomly at all levels. As in previous studies, segregation was highest at the high school level. Most, but not all, of the segregation could be explained by prior achievement levels, suggesting tracking plays an important role in how students are sorted into classes and contributes substantially to segregation. The authors further find that classes with higher proportions of minority and low-income students were more likely to be taught by novice teachers, which has clear equity implications.

Although no researchers have documented patterns of within- school segregation by income over time, Clotfelter et al. (2021) have done so for racial segregation using North Carolina adminis- trative data from 1995, 2006, and 2017. Specifically, the authors calculated within-school segregation as the difference in total district and between school segregation. Using this measure, they found that segregation within schools is “substantial” and is com- plementary to segregation between schools, meaning when one is higher, the other tends to be lower. Although their work is similar to ours, it is not directly comparable due to their focus on race (vs. economic disadvantage).8

Our objectives are to document levels and trends of within- school segregation of students by economic disadvantage. In pre- vious work on racial within-school segregation, researchers have found higher levels of segregation in middle grades than in

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elementary grades. Similarly, we anticipate higher levels of within-school segregation in middle school grades. One reason for this is that middle schools are generally larger than elemen- tary schools, so they are more likely to draw from larger, more diverse geographic zones. A more diverse student body could lead to higher levels of segregation than a highly homogenous student body. Second, achievement is correlated with SES, and tracking is more likely to take place in higher grades than in lower grades (Loveless, 2012).

Determinants of Segregation

With this context in mind, it is useful to recognize that trends in segregation within schools are affected by one (or both) of two potential mechanisms. First, segregation of ED students could increase or decrease as the composition of a school’s stu- dents changes over time. Any change in the level of educational disadvantage in a school would affect the mean against which all classrooms in the school are compared—compositionally changing within-school segregation even if there are no inten- tional changes in classroom assignment policies. Second, even if there is no change in the ED composition of students in a school, within-school segregation can change if the way stu- dents are assigned to classrooms changes. Evidence from previ- ous research along with changes in the broader educational context of public education suggests potential changes in within-school segregation via both the compositional and assignment mechanisms.

The rise in between-school segregation has meant that the student body within each school is becoming more homogenous over time. Clotfelter et al. (2021) find more homogenous stu- dent bodies are associated with lower levels of within-school seg- regation by race, and the same could be true for within-school socioeconomic segregation. However, the literature on assign- ment of students to classes described earlier suggests a different pattern should be expected for SES. Districts experiencing more growth in between-school segregation are necessarily undergoing substantial change that could include migration or economic and housing growth.9 High-income parents and experienced teachers have better capacity to change schools in response to these changes. Because of these preferences, school principals in districts experiencing changes in segregation between schools could face more pressure to employ within-school student group- ing to placate their most important constituencies: active parents and experienced teachers. Broader changes in the context of American education suggest that even without compositional changes, there may be upward pressure on within-school segre- gation by ED status through the assignment mechanism. Most relevant, the high-stakes-testing pressures associated with the accountability movement could lead to increased academic tracking, which would likely increase levels of within-school socioeconomic segregation.

In our empirical models we examine the net effect of district- level changes in ED segregation on within-school ED segrega- tion. As we describe later, we estimate a series of models of within-school segregation, adding in lagged measures of between-school ED segregation in a school’s district.

Analytic Plan and Methods

Data

To study segregation of students by classroom within schools, we use student-level administrative data from the NCERDC begin- ning in the 2006-2007 school year and ending in the 2013-2014 school year.10 These data provide information for every public school student in the state and provide measures of student demographic characteristics, school and district attributes, and whether a student was ED, as measured by eligibility for free/ reduced-price meals. Although this measure of a student’s SES is limited, Domina et al. (2018) find that ED status is a better predictor of educational disadvantage than family income obtained from IRS tax records. This suggests ED status measures SES and family background beyond income that are associated with student educational outcomes.

The NCERDC data enable us to identify the classrooms to which each student is assigned during the school day and thereby assess the socioeconomic and demographic attributes of students in each classroom and those of the schools overall. Because classes are grouped by grade, our unit of analysis is the grade-school level, by academic year. We limit our analysis to students in Grades 3 to 8 for both substantive and practical reasons. This is partly because these are the grades tested annu- ally for school and district accountability.11 Further, we cannot include lower grades because course enrollment data are reported only beginning in Grade 3. We exclude high school students from our analysis since high school classes are more likely to include students from multiple grades, which makes determining the appropriate reference grade for each course more difficult.

Measurement

For each year in our panel, we generate a district dissimilarity index measuring income segregation between schools for each grade within that district. This measure is generated by compar- ing the number of ED and non-ED students in each grade/ school with the total number of ED and non-ED students in the appropriate grade/district. If all schools serving the same grade in a district had an equal portion of ED students, the between- school dissimilarity index would be 0, regardless of the mean ED rate. If ED students and non-ED students in a particular grade and district were perfectly segregated into different schools, the between-school dissimilarity index would be 1.

We next generate measures of within-school segregation for each grade/school in our panel. Income segregation within a grade/school occurs when the characteristics of students in class- rooms deviate from the characteristics of students in the grade/ school overall, with some classrooms having more ED students than the grade/school mean and some fewer. The within-school dissimilarity index for school s, grade g, in year t is

Ds g t c g s t

g s t

c g s t

g s t c g s t, ,

, , ,

, ,

, , ,

, , , , ,

= −∑12 ED

ED

non-ED

non-ED ,

248 EDuCATIONAl RESEARCHER

where c indexes classrooms within the grade/school, EDc,g,s,t and non-EDc,g,s,t measure the number of ED and not-ED students within the classroom in each grade in a school in year t, and EDg.s,t and non-EDg,s,t are, respectively, the grade/school total number of ED and not-ED students enrolled in all classes.

The magnitude of the within-school dissimilarity index can be interpreted as the proportion of students that would need to be reallocated to equalize the proportion of low-income to higher-income students in each classroom. Zero means that no reallocation is needed, and 1 means all students would be affected by reallocation to equalize. An advantage of the dissimi- larity index is that it makes clear that the level of segregation in a school is a function of both the composition of students within a grade/school (i.e., the total number of ED and non-ED stu- dents enrolled) and how students are assigned to classrooms within schools (i.e., EDc,g,t and non-EDc,g,t for all c).

To calculate the within-school dissimilarity index, we aggre- gate our student-level data to the course level. We use a large set of variables to map students to courses, including school code, district code, course code, meeting code, section, cycle, period, teacher identification code, course title, and reported enroll- ment. We first generate the dissimilarity indexes for all courses in all periods within a grade. This includes all types of courses, including courses such as physical education and even home- room.12 In some elementary grades/schools, students can spend most/all of their day in one classroom. In middle school grades, students have more courses during a day. We next use course codes to isolate those courses identified as math courses and cal- culate the dissimilarity index within each grade/school/year using just these courses.13 We do the same for all English lan- guage arts (ELA) courses.14 We focus on math and ELA since they are the subjects to which students are nearly universally enrolled each grade. Just as importantly, math and ELA are most frequently tested on high-stakes tests. School administrators may feel more pressure to improve achievement in these subjects and may view tracking as a way to accomplish this goal. In all cases, an individual student can appear in more than one class in the same grade.15 This is easiest to see for middle school grades, when one student is assigned to different classrooms during vari- ous periods during the day. Courses may also appear more than once since some schools report the same course over different semesters. Rather than attempt to isolate one iteration of each course, we use the full set of unique course observations reported by each school. So, the dissimilarity index for a grade/school/ year measures unevenness in classroom ED characteristics across all classrooms during the academic year.

Once we have mapped students to classes, we then generate counts of the ED and non-ED students in each course. We cal- culate the total number of ED students in a grade as the sum of all ED students in relevant courses in that grade. We then do the same for non-ED students. In calculating each of the all-course, math, and reading dissimilarity indexes, we exclude any courses with just one student enrolled and those with more than 50 stu- dents enrolled since these are not typical courses. There are some instances in which courses consist of students from more than one grade.16 In those cases, we use the modal grade of enrolled students to assign courses to grades.

We generate grade-specific dissimilarity indexes for two main reasons. First, the composition of each grade within a school or district may differ. For example, if a school is becom- ing increasingly poor over time, lower grades in the school may have higher concentrations of ED students than higher grades. Since students typically take courses with students from their own grades, ED and non-ED enrollments in their own grades are the appropriate comparison group to generate dissimilarity indexes. Second, there may be different segregation patterns by grade. This may be especially true when comparing elementary grades with middle grades. Since we know from prior research that within-class ability grouping is more common in elemen- tary grades and academic tracking in separate classrooms is more likely to start in middle grades (Loveless, 2012), we expect there to be higher levels of within-school segregation in middle grades.

Empirical Models

To assess trends in segregation, we first generate time-series graphs of the enrollment weighted average district dissimilarity index, by grade. We create similar graphs to illustrate how within-school segregation is changing over time. Then, we esti- mate models of segregation at the grade-school level, over time, that take the following form:

D X tsgt sgt g

g g g s sgt= + + + + + +∑α β δ τ δ θ θ( ( * )) LEA 

where Dsgt is the segregation index within school s for grade g in year t. X measures the total enrollment and racial and ethnic composition of each school, grade, and year. Enrollment in the grade is an important predictor, since larger grades make student grouping more feasible. We control for race and ethnic composi- tion because they are related to segregation more generally and to limit the possibility that observed patterns of segregation by economic disadvantage are driven by racial segregation of stu- dents.17 We also include grade fixed effects and grade-specific linear trends.

We estimate this model separately for within-school segrega- tion in math, reading, and all classes. The coefficients of interests are the grade fixed effects (δg) and grade-specific time trends (τg). The grade fixed-effects measure differences in levels of segrega- tion by grade, and the time trends measure changes in within- school segregation by grade, net of what might have been expected due to changes in enrollments or racial composition. In all models, we control for district and school fixed effects (θLEA and θs). These models provide direct tests on whether there have been changes in the way schools allocate students into class- rooms over the panel.

To provide insight into how segregation between classrooms within schools is shaped by segregation between schools at the district level, we augment our empirical model of within-school segregation by adding in lagged measures of between-school ED segregation in a school’s district. Specifically, we add in grade- specific measures of the segregation of students by income between schools to our school, grade, and year panel models.

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Results

In Table 1 we provide descriptive statistics for our sample. Our unit of analysis is the grade/school/year.18 The average grade within a school in our panel enrolls about 114 students in a typical year and is 53% White, 27% Black, and 12% Hispanic. Approximately 55% of students in a typical grade are ED. The mean district dissimilarity index is 0.31, and the mean school dis- similarity indexes are 0.23 for all courses, 0.24 for math courses, and .025 for ELA courses. So, in the average grade/school, about 23% of students would be affected by reallocation to equalize the proportion of ED students in all classrooms. About 7% of our grade/school/year observations are charter schools.

Descriptive Analyses

To begin understanding how segregation is changing over time, in Figure 1 we show trends in the average level of ED segregation between and within schools in North Carolina, separately by grade, and weighted by district enrollment. In Panel A, for context we illustrate that between-school segregation rose substantially between 2007 and 2014 in North Carolina. This is consistent with prior research in other settings, discussed earlier. The mean district dissimilarity index increased by about 20% for all grades. Figure 1 also makes clear that elementary school grades have higher levels of between-school segregation than middle school grades, with an average 2007 district dissimilarity index of about 0.3 in elementary grades compared with 0.24 in middle grades. This is likely because elementary schools are typically smaller than middle schools and draw students from smaller geographic areas.

In Panel B of Figure 1 we focus on the outcome that has been less documented: trends in segregation between classrooms within schools. Middle school grades have higher levels of within-school segregation when compared with elementary grades. This is the opposite of what we observe in

between-school segregation. Elementary grades also have lower levels of within-school than between-school segregation, with a mean of 0.23 for the former and 0.34 for the latter. For middle school grades, within-school and between-school segregation both average about 0.27 over the period. Note that in absolute terms, within-school segregation grew more slowly than between-school segregation. Also note that these patterns are consistent with the patterns of racial segregation identified by Clotfelter et al. (2021): Between-school segregation is lower in middle school than in elementary school but offset by higher within-school segregation.

The trends in within-school ED segregation in Figure 1 include all courses offered in a school, including nonacademic subjects, such as physical education and band. Because within- school segregation might be higher in academic subjects that are more likely to be tracked, we plot the mean within-school dis- similarity index for only math courses by grade in Figure 2. Figure 2 makes clear that for middle school grades, within-school segregation is higher for math classes than overall levels for all courses in general (Figure 1, Panel B). This is to be expected, since tracking often intensifies in these grades. It is also notable that there is a more pronounced positive trend in segregation of students by ED status in math courses than in all courses overall. For example, in elementary grades, the dissimilarity index for math classes increased from about 0.22 to just over 0.25, whereas overall the increase was from approximately 0.22 to 0.24.

Multivariate Analyses

To further examine these trends, we next turn to our regression models of patterns of within-school segregation over our panel. Because the descriptive trends illustrate differences in segrega- tion by grade, we estimate separate trends for each grade. Our unit of analysis in these models is the grade/school/year, and the results are presented in Table 2. We include controls for

Table 1 Descriptive Statistics of Administrative Data of North Carolina Classrooms Grades 3 to 8 (N = 47,385)

Variable M SD Min. Max.

Grade 4.97 1.63 3 8 Total enrollment 114.07 85.65 10 674 Schools offering grades per district 27.76 31.93 1 119 % Black 27.44 25.20 0 100 % Hispanic 11.87 11.60 0 82.76 % Asian 2.17 4.21 0 78.57 % White 53.07 29.13 0 100 % ED 55.32 24.03 0 100 Percentage of grade with ED status 0.97 1.96 0 10 District dissimilarity index 0.31 0.13 0 0.85 Grade dissimilarity index (all courses) 0.23 0.13 0 1 Grade dissimilarity index (math courses)1 0.24 0.15 0 1 Grade dissimilarity index (ELA courses)1 0.25 0.15 0 1 Charter school 0.07 0.25 0 1

Note. Number of time periods: 8 (2007–2014); number of school districts: 115; number of schools: 2,097. ED = economically disadvantaged; ELA = English language arts. 1Because not all elementary school grades identify a unique math or ELA class, can measure math dissimilarity for 40,748 and ELA dissimilarity for 41,277 grade/school/ year observations. See text for details.

250 EDuCATIONAl RESEARCHER

enrollment, racial composition, and grade, school, and district fixed effects. We estimate trends in segregation by economic dis- advantage across all classes within schools, math classes, and then reading/ELA classes. We include both school and district fixed effects in all models, so the coefficients on the grade-spe- cific trends are net of school and district averages over the panel.

Enrollment is positively associated with segregation within schools. Schools with more students may have more flexibility in how they assign students to classes. The grade fixed effects con- firm what we saw in our graphs, with higher levels of within- school segregation in middle grades than in elementary grades. The proportion of students who are Hispanic is associated with meaningful differences in ED segregation. For example, a school/ grade that is 50% Hispanic has a math dissimilarity index that is 0.05 higher than a school/grade with no Hispanic enrollment. The coefficients on the linear time trends are positive and signifi- cant in all models for all grades, and there are no large differences in the trends between grades. The coefficients for the trends in math and ELA courses are larger than those for all courses.

To put the magnitudes of the coefficients on these trends in context, over the course of our panel, they imply that within- school ED segregation increased between 0.003 to 0.006 each year, depending on grade and type of course. This range is between 10% and 20% of the mean and about 0.18 to 0.32 standard deviations of the overall within school dissimilarity index values for the typical grade/school/year over the 8 years of the panel (Table 1).

In our final model, we estimate the impact of between-school segregation on within-school segregation. Here our unit of anal- ysis is the grade/school/year, and we use the math dissimilarity index as the outcome. Since we are interested in the relationship between segregation in the district and patterns within schools, we cluster standard errors at the district level. We include enroll- ment, racial composition controls, and grade, school, and dis- trict fixed effects. We also include a separate lag of the district dissimilarity index for each grade. The lag of the district dissimi- larity index captures the level of between-school income segrega- tion for a grade/district in the prior year. A positive coefficient on this lag would indicate that a growing dissimilarity between schools in a district is associated with higher dissimilarity indexes within school in math the following year. A negative coefficient would indicate the opposite relationship. We also include a lin- ear time trend that captures average growth in within-school seg- regation over time.

We present these results in Table 3. The coefficients on the grade indicators make clear the patterns described: Within- school segregation is higher in middle school grades. The coef- ficients of interest are those on the grade-specific lags of between-school segregation in the district. We find no real evi- dence that changes in segregation in the district are associated with changes in within-school segregation. The only exception is a significant coefficient on the lag of district-level segregation in Grade 3. That coefficient implies a unit increase in the between- school segregation index is associated with an increase in the within school segregation index of 0.064. To scale the coefficient, a one-standard-deviation increase in district level segregation (0.13) is associated with an increase in within-school segregation of 0.008. This is a bit less than a 10th of a standard deviation. On the whole, we find no evidence that changes in between- school segregation are associated with changes in within-school segregation in other grades. For ELA and all course measures, there is no significant relationship between district- and school- level segregation.

Panel A

Panel B

.1 5

.2 .2 5

.3 .3 5

M ea n G ra de D is si m ia rti y In de x*

2007 2008 2009 2010 2011 2012 2013 2014 Year

Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8

*weighted by enrollment

North Carolina Schools Serving Grades 3-8 Within School Segregation Over Time by Grade

FIGURE 1. Trends in between- and within-school segregation by economic disadvantage.

.1 5

.2 .2 5

.3 .3 5

M ea n G ra de M at h D is si m ia rti y In de x*

2007 2008 2009 2010 2011 2012 2013 2014 Year

Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8

*weighted by enrollment

North Carolina Schools Serving Grades 3-8 Within School Math Segregation Over Time by Grade

FIGURE 2. Within-school math segregation over time by grade.

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Discussion

In this paper, we illustrate that in North Carolina, segregation of students by income at the classroom level has increased in elementary and middle school grades. Our empirical models suggest that over the course of our panel, within-school segrega- tion increased between 10% and 20% (or approximately 0.18 to 0.32 standard deviations). The increases in within-school segregation tended to be larger in math and ELA than in overall courses. We also find that across grades, patterns of between- school and within-school segregation are very different. We find that between-school ED segregation is higher in elementary versus middle school grades, whereas within-school segregation is higher than between-school segregation for middle school grades.

This is the same pattern that Clotfelter et al. (2021) identify for racial segregation of students in North Carolina using the NCERDC data. They examine patterns of racial segregation between and within schools, rather than trends over time, and find that when one is low, the other tends to be high. Since race and SES are correlated, the parallels between our findings and those of Clotfelter et al. (2021) are unsurprising. In a series of auxiliary analyses not reported here to conserve space, we find smaller increases in segregation by race (between Black and White students) than by income, and these increases are limited to elementary school grades. It appears that even as racial segre- gation of students remains endemic, the segregation of students by economic disadvantage has been rising.

To interpret the magnitude of these increases in within-school segregation, consider that the mean math segregation index at the grade level in our panel was about 0.25.19 So, about 25% of stu- dents would have needed to change classroom assignments to equalize the proportion of disadvantaged students in each class- room within a school. In our models in Table 2, we estimate that the segregation index in Grades 3 through 8 rose by about 0.05 annually in math classes and by 0.04 in ELA classes. Over the full 8 years of our panel, this implies an increase of 0.04 and 0.032 in within-school segregation in math and ELA classrooms. So, by the end of our panel, about 28% to 29% of students (rather than 25%) would need to change classrooms to equalize the proportion of disadvantaged students across classrooms. This would mean that in a school with four classrooms of 25 students in a grade, by the end of the panel, two math classrooms would have one addi- tional ED student, and two would have one fewer.20 This is not a large change on average, but we view this as non-negligible.

Our findings help us to better understand the landscape of income segregation. The experience a student has in school is shaped by not just the district and school they attend but also the classrooms within a school where they receive instruction and interact with peers. These patterns are concerning in part because they challenge principles of egalitarianism in public edu- cation. Of course, if students are grouped based on ability, there may be pedagogical or other advantages that benefit all groups of students. If so, our concerns about segregation may be assuaged if SES is a valid proxy for ability. However, there are many rea- sons to doubt this supposition. Regardless of whether SES is a proxy for demonstrated achievement, we can assess whether and how ED students and their better-off peers are affected by segre- gation. To do this, we carry out supplementary analyses of changes in math achievement in state end-of-grade assessments between 2007 and 2014 by changes in ED segregation of math classrooms over the same period, summarized and described in the online appendix. We find suggestive evidence that within- school segregation had no beneficial effect for ED students but improved math achievement for higher-income students. As we illustrate in Appendix Figure A1, math achievement for ED stu- dents grew no faster or slower in schools experiencing the most growth in income segregation. However, math achievement grew more for higher-income students in schools where ED seg- regation grew. The different relationships between a school’s changing level of segregation and achievement for ED and other students illustrated in Figure A1 is merely descriptive and sug- gestive, not conclusive. It is clear that ED segregation may affect

Table 2 Regression Estimates of Trends in Within-School

Segregation

All Math ELA

Variable B (SE) B (SE) B (SE)

Enrollment (100s) 0.01097** (0.00270)

0.02070** (0.00324)

0.01683** (0.00321)

Grade 41 0.00103 (0.00276)

–0.00377 (0.00397)

0.00053 (0.00375)

Grade 5 –0.00964** (0.00278)

–0.00637 (0.00397)

–0.01135** (0.00377)

Grade 6 0.01169** (0.00395)

0.02040** (0.00484)

0.00061 (0.00468)

Grade 7 0.01894** (0.00407)

0.03056** (0.00496)

0.00893†

(0.00481) Grade 8 0.01299**

(0.00407) 0.03123**

(0.00496) 0.00297

(0.00481) Grade 3 trend 0.00336**

(0.00047) 0.00482**

(0.00063) 0.00394**

(0.00060) Grade 4 trend 0.00402**

(0.00047) 0.00614**

(0.00063) 0.00478**

(0.00060) Grade 5 trend 0.00346**

(0.00048) 0.00483**

(0.00063) 0.00445**

(0.00060) Grade 6 trend 0.00267**

(0.00067) 0.00306**

(0.00075) 0.00305**

(0.00073) Grade 7 trend 0.00361**

(0.00068) 0.00447**

(0.00076) 0.00315**

(0.00074) Grade 8 trend 0.00410**

(0.00068) 0.00539**

(0.00076) 0.00403**

(0.00074) % Black –0.00012

(0.00017) 0.00007

(0.00021) –0.00033 (0.00021)

% White 0.00013 (0.00017)

0.00025 (0.00021)

–0.00007 (0.00020)

% Hispanic 0.00071** (0.00019)

0.00100** (0.00024)

0.00059* (0.00023)

R 2 0.36966 0.39411 0.40648 Observations 47,385 40,748 41,277

Note. All models include district and school fixed effects. Standard errors clustered at the school level, in parentheses. 1Grade 3 is omitted/reference. †p < .10. *p < .05. **p < .01.

252 EDuCATIONAl RESEARCHER

achievement and achievement gaps. Assessing the implications of rising segregation at the classroom level is a topic that merits further attention.

Although we find evidence of upward trends in within-school segregation across Grades 3 through 8, we have not yet explored the factors shaping this trend. One possible mechanism is the introduction and growth of school-choice options within a stu- dent’s school district. Like many states, North Carolina saw growth in the charter school sector over the past two decades. The threat of losing students or staff to charters may lead tradi- tional public school administrators to make strategic decisions to retain students and teachers in public schools. Increased within- school segregation could be a by-product of efforts to make pub- lic school more appealing, such as specialized tracking or

school-within-a-school curricula. Although the goal of tracking is not to separate students by income, this could be an unin- tended consequence. Of course, academic tracking may be on the rise for reasons unrelated to school choice growth. Our panel falls during the No Child Left Behind (NCLB) era, which may also have shaped how students were sorted into classrooms within schools. It is possible that school leaders responded to the high-stakes-testing pressures of NCLB by reintroducing or ramping up academic tracking. Clearly, rising segregation of stu- dents by economic disadvantage raises many questions about origins and implications. What is clear from the current paper is that such segregation has occurred within school hallways as well as between school buildings.

NoTES

We have benefited from comments and suggestions by discussants and participants at the 2020 research conferences of the Association for Education Finance and Policy and the Association for Public Policy Analysis and Management. We acknowledge funding from the Smith Richardson Foundation. All interpretations and any errors are our own.

1Owens et al. (2016) estimate that segregation of students by income increased by 40% within school districts from 1990 to 2010, compared with an increase of about 15% between different districts within metropolitan areas over the same period.

2For example, Marcotte and Dalane (2019) find that a one-stan- dard-deviation increase in enrollments in charter schools in a district is associated with an increase in the segregation of students by economic disadvantage of 6% of a standard deviation.

3We discuss the limitations of economically disadvantaged (ED) status as a measure of socioeconomic status later.

4Unless otherwise specified, when we refer to segregation, we mean by income or economic disadvantage rather than race or ethnicity.

5Reardon and Owens (2014) discuss the evidence on segregation between schools and document patterns of segregation by race, ethnic- ity, and income.

6There is a long-standing literature on factors shaping how prin- cipals assign students to classrooms (e.g. Monk, 1987). In a study of 22 elementary schools and how principals in these schools assigned stu- dents to more than 200 classrooms, Burns and Mason (1998) describe a multistep process that includes principals asking teachers for assignment preferences; principals’ assessment of student achievement, motivation, needs, and behavior; and principals’ desires to create balanced class- rooms. Burns and Mason report a final step after rosters were drawn up in which principals adjusted class assignments based on possible student conflict, parent requests, and attrition. Osborne-Lampkin and Cohen- Vogel (2014) further report that principals heavily weight classroom heterogeneity and a sense of “fairness” to teachers.

7Mickelson (2001) provides a relevant example in North Carolina, finding that decades after a court-ordered racial desegregation order, academic tracks within schools in the Charlotte-Mecklenburg school district remained racially segregated.

8Further, unlike Clotfelter et al. (2021), we calculate changes in within-school segregation directly rather than as the difference in total district and between school segregation. More importantly, we estimate segregation at the classroom relative to the school mean rather than the district mean. That is, we focus on changes in each grade/school over time as the relevant unit of analysis. This means we directly assess whether the typical school is becoming more segregated over time rather than whether all classrooms in a district are diverging from overall dis- trict characteristics. Finally, Clotfelter et al. (2021) do not examine asso- ciations in between- and within-school segregation over time.

Table 3 Impact of Between-School Segregation on Within-

School Segregation

Variable B (SE)

Total enrollment (100s) 0.01694** (0.00423)

Grade 41 0.01090 (0.00768)

Grade 5 0.01251 (0.00801)

Grade 6 0.03131** (0.01140)

Grade 7 0.05299** (0.01196)

Grade 8 0.06789** (0.01326)

% Black –0.00030 (0.00030)

% White –0.00006 (0.00028)

% Hispanic 0.00072* (0.00032)

Lag of district dissimilarity index Grade 3 0.06383*

(0.02999) Grade 4 0.03627

(0.02585) Grade 5 0.00701

(0.02665) Grade 6 0.02145

(0.02865) Grade 7 0.00198

(0.02916) Grade 8 –0.03248

(0.03775) Time trend 0.00524**

(0.00052) R2 0.40140 Observations 34,971

Note. Models include school and district fixed effects (not shown). Standard errors clustered at the school level, in parentheses. 1Grade 3 is omitted/reference Unit of analysis is the grade-school-year. †p < .10. *p < .05. **p < .01.

MAy 2022 253

9For example, in the Wake County Public School System (North Carolina), total enrollment increased from 99,000 to 143,000 during first decade of the century, driven by large increases in enrollment from Hispanic and Asian families (Domina et al., 2021). In an attempt to prevent and address socioeconomic concentration of students at the school level, the district implemented a school reassignment policy as it built new schools, with the aim of ensuring the socioeconomic charac- teristics of all schools matched the overall district characteristics.

10We do not include data after the 2013-2014 school year because a new school meals program, the Community Eligibility Provision, became available in North Carolina in 2014-2015. This program changed the way participating schools in the state reported students as ED.

11The schools in our sample include 1,275 elementary schools, 558 middle schools, and 264 schools that enroll students in elementary and middle school grades. In North Carolina, most elementary schools enroll students in Grades K through 5, and most middle schools enroll students in Grades 6 through 8. Of the 1,275 elementary schools, 1,152 have the highest grade of 5; 43 enroll students until fourth grade and 80 until sixth grade. Of the 558 middle schools, 470 enroll students begin- ning in sixth grade; 38 enroll students beginning in fifth grade and 50 beginning in seventh grade.

12We focus on all classes rather than in a given period since schools vary in how they arrange schedules. The resultant measure assesses within school segregation over the course of a day—which can happen between classes in a given period or between periods. In cases where students are in more than one math/English language arts (ELA) class, it is not obvious how to assign the student to only one course. A com- plete list of all courses for recent years can be found on North Carolina Department of Public Instruction’s website (https://www.dpi.nc.gov/ educators/home-base/powerschool-sis/nc-sis-resources#courses). In the most recent year available, there are over 3,600 unique course codes. Many of these courses are available only to high school students, so they are not relevant for our analysis. A typical elementary student in our data set might have either an elementary course code reported along with separate course codes for all specials or course codes for all aca- demic courses along with all specials. Middle school students usually have course codes for all academic subjects and specials or electives. Some schools also report “homeroom”-type courses, which we also include for all students. If special education students take courses with non–special education students, special education and general edu- cation students have similar sets of course codes within each school. Special education students who are in self-contained classrooms typi- cally have fewer course codes reported than other students if they spend their entire days in those rooms.

13We also check course names for words like “technology” and “computer” to eliminate courses classified as math courses that are focused on computer skills.

14We calculate math and ELA dissimilarity indexes only if 90% or more of the students in a grade/school/year have at least one math or ELA course, respectively. Since some schools report general “elemen- tary” courses rather than subject-specific courses, especially in Grades 3 to 5 early on in the panel, we calculate a math dissimilarity index for approximately 86% of our grade/school/year observations and an ELA dissimilarity index for approximately 87% of our grade/school/ year observations.

15In our sample, 94.8% of students are enrolled in only one math course and 74% of students are enrolled in only one ELA course. Elementary grade students are more likely to have two ELA courses since these students sometimes have separate courses for reading and language arts, both of which are classified as ELA.

16Students from more than one grade are included in 5.9% of course observations.

17In separate analyses not reported here, we find that increases in

within-school segregation by race were smaller and more limited than increases in within-school segregation by ED status.

18Our sample consists of 2,097 unique schools. Most elementary schools end in Grade 5 (1,152), and most middle schools begin in Grade 6 (470). There are 191 schools that serve all Grades 3 through 8.

19The mean was between 0.23 and 0.25 for Grades 3 through 5 and between 0.26 and 0.28 for Grades 6 through 8.

20In a 100 student grade, the reallocation of one ED student affects the dissimilarity index by 0.01.

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AuThoRS

KARI DALANE is a PhD candidate in the School of Public Affairs, American University, 4400 Massachusetts Ave. NW, Washington, DC 20016; [email protected]. Her research focuses on equity issues in K–12 education.

DAVE E. MARCOTTE, PhD, is a professor in the School of Public Affairs, American University, 4400 Massachusetts Ave. NW, Washington, DC 20016; [email protected]. His research interests include education policy, equity, and achievement.

Manuscript received December 16, 2020 Revisions received July 20, 2021;

October 7, 2021; January 13, 2022 Accepted February 1, 2022