key: cord-0794129-4448f782
authors: Vinopal, Katie; Morrissey, Taryn W.
title: Neighborhood Disadvantage and Children’s Cognitive Skill Trajectories
date: 2020-07-09
journal: Child Youth Serv Rev
DOI: 10.1016/j.childyouth.2020.105231
sha: 4e355e2242129a0ac481e7a9a2290b509e1fbe19
doc_id: 794129
cord_uid: 4448f782

This study examined how neighborhood poverty is associated with children’s trajectories of growth in math and reading skills in early elementary school, and how these associations vary by student characteristics, using multilevel growth models with nationally representative data from the 2011 Early Childhood Longitudinal Study-Kindergarten Cohort. About one-quarter (25.6%) of children lived in communities of concentrated poverty. Findings suggest that achievement gaps by neighborhood disadvantage are large and present before Kindergarten, shrink during the Kindergarten year, but then widen the year following, and remain relatively consistent in the first years of elementary school. Growth in math skills appeared to vary more with neighborhood poverty than growth in reading skills. There was limited evidence that the relationship between neighborhood poverty and test score trajectories varied by child race, ethnicity, early education and Kindergarten experience, and parents’ immigration status, but growth differences across student characteristics were small. Policy and research implications are discussed.

Poverty in the United States has become increasingly concentrated (Bishaw, 2014) , raising concerns about the implications of the growing proportions of today's children who are growing up in disadvantaged communities. .4 percent -14 million Americanslived in communities of concentrated poverty, defined as census tracts in which 40 percent or more residents were poor, more than twice as many people as in 2000 (Kneebone, 2014; Kneebone & Holmes, 2016) . A growing body of research indicates that neighborhood poverty has negative effects on children's short-and long-term outcomes (e.g., Morrissey & Vinopal, 2018b) . One policy-relevant research question is how neighborhood disadvantage relates to children's trajectories of growth in cognitive scores in elementary school, and how children's individual circumstances relate to these trajectories.

This study uses recent, nationally representative data from the 2010-2011 Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K:2011) to examine associations between neighborhood disadvantage and children's trajectories of cognitive growth in Kindergarten through third grade to better understand how the communities in which children live relate to their patterns of academic success at different points in their development, and how these associations vary by child and family characteristics.

Bio-social ecological theory asserts that children grow and develop via bidirectional interactions with the contexts within which they are embedded (Bronfenbrenner & Morris, 1998) . As the most proximal context for most children, the family or household typically has a primary influence on development, but other contexts regularly and directly experienced, including the neighborhoods in which children live and learn, also have considerable influence.

The negative effects of family poverty for children's outcomes are well-documented (Duncan, Magnuson, Kalil, & Ziol-Guest, 2011; Duncan, Ziol-Guest, & Kalil, 2010; Shonkoff & Garner, 2012) . A growing body of research demonstrates that in addition to family resources, the resources of the neighborhoods in which children learn and grow affect their short-and longterm health, academic, and economic success (Chetty, Hendren, & Katz, 2016; Chetty, Stepner, et al., 2016; Tama Leventhal & Brooks-Gunn, 2000; Minh, Muhajarine, Janus, Brownell, & Guhn, 2017; Morrissey & Vinopal, 2018b; Wolf, Magnuson, & Kimbro, 2017) . Likewise, recent studies suggest that, within a few months of entering Kindergarten, children from high-poverty neighborhoods have poorer health behaviors, lower cognitive scores, and higher rates of food insecurity (but not necessarily poorer behavior) compared to those from lower-poverty neighborhoods (Kimbro & Denney, 2013; Morrissey, Oellerich, Meade, Simms, & Stock, 2016; Morrissey & Vinopal, 2018b; Wolf et al., 2017) . There is also evidence that one's neighborhood during childhood has intergenerational effects on their own children's cognitive performance (Sharkey & Elwert, 2011) . Associations between neighborhood resources and children's development are also found in other countries. For example, research in Canada suggests that neighborhood vulnerability (an index of variables including economic and social factors) is associated with poorer measures of children's developmental health in Kindergarten (Webb et al., 2017) , and studies in Australia show similar associations between spatial neighborhood characteristics and children's health behaviors (Villanueva, Badland, Giles-Corti, & Goldfeld, 2015) .

Although the causal effects of neighborhoods are difficult to identify given that neighborhood sorting is associated with other factors that affect children's outcomes (e.g., family income), evaluations of Moving to Opportunity (MTO), for which families were randomly assigned housing vouchers, some of which could only be used in low-poverty areas, found relatively few short-term effects of low-poverty neighborhoods but strong longer-term effects on health, educational attainment, and earnings (Chetty, Hendren, et al., 2016; Ludwig et al., 2011 Ludwig et al., , 2012 . Further, research examining historical data suggests that observational estimates are predictive of neighborhood effects (Chetty, Friedman, Hendren, Jones, & Porter, 2018) .

One of the hypothesized mechanisms via which neighborhoods may affect children's development -for better or worse -is the K-12 education system (Leventhal & Brooks-Gunn, 2000) . Indeed, for many, the quality of schools is a driver of housing decisions and neighborhood housing prices (Kane, Staiger, & Reigg, 2006) , though on average, parents judge schools based on the achievement and characteristics of enrolled students, rather than the effectiveness of the instruction (Abdulkadiroǧlu, Pathak, Schellenberg, & Walters, 2020) . And, in any case, families may be constrained in these decisions by their income and oftentimes by their race, as Black families face discrimination from landlords, realtors, and white neighbors (Wodtke, Harding, & Elwert, 2011) . Schools in lower-income areas average higher teacher turnover (Boyd, Lankford, Loeb, & Wykoff, 2005) and poorer curricula (Darling-Hammond, 1998) . Historically, schools in lower-income communities have spent less per child on education than those in higher-income areas, although this varies considerably by state (Chingos & Blagg, 2017) , particularly since school finance reforms in the 1990s directed more funds toward low-income schools, which had large effects on student achievement (Lafortune, Rothstein, & Schanzenbach, 2018) .

However, recent research suggests that school quality per se may not be a main driver of neighborhood disparities in educational outcomes, as achievement gaps by family and neighborhood resources appear well before Kindergarten (Chetty & Hendren, 2017; Leventhal, 2018 ). An analysis of the MTO Study found that the neighborhood in which one lived as a very young child was more predictive of college attendance and income in young adulthood than the neighborhood experienced as an adolescent (Chetty, Hendren, et al., 2016) . Likewise, although achievement gaps between children from high-and low-socioeconomic status (SES) families widen somewhat during the elementary school years, the majority of the gap appears well before children begin Kindergarten (Halle et al., 2009; Reardon, 2011) , highlighting the developmental sensitivity of the early childhood period.

This suggests achievement gaps may be due to a number of social and environmental factors other than school quality. For example, racist policies and preferences have led to highly segregated neighborhoods, under-resourced schools, and the devaluation of homes in majority Black neighborhoods in many metropolitan areas-even controlling for neighborhood amenities and home quality-which has contributed to the Black-white wealth gap and led to less upward mobility by Black children in those neighborhoods (Hannah-Jones, 2014; Perry, Rothwell, & Harshbarger, 2018) . And environmental factors such as pollution from nearby factories, which are more commonly located in low-income areas, show substantial and sustained effects on children's academic achievement (Persico & Venator, 2019) .

Most research on the effects of neighborhoods or K-12 education on children's outcomes has focused on measures at a point in time (i.e., absolute differences between children from different backgrounds). Research on absolute score tests is important, given gaps presumably reflect meaningful differences in skills or preparedness for higher education or the workforce, which educational policies should seek to narrow. However, the growth of or change in cognitive outcomes have been less frequently studied, but has important implications for education and policy. For example, an analysis of trajectories over the early years of schooling may indicate a particular developmental period best suited for an intervention to narrow or close achievement gaps. Further, although absolute test scores are often used by policymakers and parents alike to compare, rank, and reward or penalize schools, test score differences may more accurately reflect children's experiences prior to Kindergarten entry, whereas growth in test scores may be a more meaningful proxy for the quality of teaching and education provided by the school (Abdulkadiroǧlu et al., 2020; Reardon, 2019) .

Research on growth in test scores has increased in recent years. For example, the valueadded approach to assessing teacher or school quality focuses on growth in student test scores that can be attributed to their teacher or school (Deming, 2014) . Reardon (2019) examined academic growth using national data from over 45 million students in 11,000 school districts, finding a weak and negative correlation (-0.13) between average third grade test scores and the change or growth in test scores between third and eighth grades. Tellingly, school district SES was more strongly associated with average test scores than growth (0.68 vs. 0.32). These results imply that there is considerable heterogeneity between school districts in children's learning within categories of initial performance (as assessed in third grade), and by school SES. Reardon concluded that a neighborhood's early educational opportunities, in his study defined as prior to third grade (early elementary school, preschool, and child care), are largely uncorrelated with educational opportunities in middle childhood (later elementary and middle school, and out-ofschool opportunities). He also identified some differential patterns of growth by race, ethnicity, and gender. However, the use of district-level averages precluded an examination of how individual characteristics such as child sex, race/ethnicity, or family income may influence individual patterns of growth.

An emerging body of work uses individual-level data from the 1998 or 2010-2011 Early Childhood Longitudinal Study-Kindergarten Cohorts (ECLS-K) to examine growth in cognitive skills (Mccoach, O'connell, Reis, & Levitt, 2006) and by specific child characteristics, such as measures of English proficiency or approaches to learning at kindergarten (Li-Grining, Votruba-Drzal, Maldonado-Carreño, & Haas, 2010; Roberts & Bryant, 2011) . von Hippel and colleagues found that achievement gaps by family SES shrink during the academic year (from fall to spring), and grow during the summer months (from spring to fall) (Downey, Hippel, & Broh, 2004; von Hippel, Workman, & Downey, 2018 ). An earlier study of children in preschool through first grade found that SES differences in cognitive measures at the end of one or two years of school were similar to those at the beginning of the year, indicating roughly equal gains by SES (Stipek & Ryan, 1997) . While these studies provide suggestive evidence that schools can narrow or at least not widen gaps between students at various individual SES levels, we lack an understanding of the patterns of inequality across neighborhoods with different SES and resource contexts.

To date, few studies have examined trajectories of children's outcomes by neighborhood characteristics using individual data. In one exception, Root and Humphrey (2014) examined measures of parent-reported health in the ECLS-K, finding that initial health assessments and growth in this measure were strongly associated with child race, household income, and parental marital status, but not with neighborhood racial composition. Arguably, however, health and cognitive development are affected by different neighborhood characteristics and via different pathways. Indeed, neighborhood characteristics appear to be less strongly associated with children's health, food security, or behavioral measures than cognitive outcomes (Morrissey et al., 2016; Morrissey & Vinopal, 2018b; Root & Humphrey, 2014; Wolf et al., 2017) . In another paper, Pearman (2017) used nationally representative data from the Panel Study of Income Dynamics (PSID) to examine how neighborhood poverty related to growth in math achievement.

Controlling for children's initial scores, he found that children in high-poverty neighborhoods experienced poorer growth, and estimated that they would need an additional 1.5 months of schooling to have math scores on par with children in low-poverty neighborhoods (Pearman, 2017) . However, this study did not examine how the age or developmental period during which neighborhood poverty exposure occurred is associated with growth, how reading and math achievement measures differed from each other, or how growth in relation to neighborhood poverty varies with individual child characteristics. Despite growing research, there is a lack of clarity on how trajectories of growth in individual-level measures of cognitive development relate to neighborhood disadvantage.

Given recent growth in economic segregation (Bishaw, 2014; Kneebone, 2014; Kneebone & Holmes, 2016) , better understanding how where one lives affects his or her educational success is vital to inform policies that support future generations. However, how neighborhood disadvantage relates to children's trajectories of growth in cognitive scores in elementary school, or how children's individual circumstances, including their demographic characteristics and experiences prior to Kindergarten, relate to these trajectories, is not well understood. This study uses nationally representative, longitudinal, child-level data merged with neighborhood-level contextual data to examine the associations between residential neighborhood disadvantage and children's trajectories of cognitive growth, independent of children's household and family circumstances, to better understand how where children live affects their academic success, and how these associations vary by student characteristics. Specifically, we use data from 2. How do student characteristics (race/ethnicity, sex, immigrant status, household poverty, urbanicity, early care and education experience, and full-or part-day Kindergarten attendance) influence the relationships between neighborhood disadvantage and children's trajectories of cognitive scores in elementary school?

The Using children's residential census tracts, we merged child-level data from the ECLS-K dataset with tract-level poverty rate from the 2010-2015 Five-year American Community Survey (ACS) estimates, to match the years in which child-level data were collected. The 2010-2015 period largely matches the period during which children attended elementary school. The multiyear data offer the advantage of increased statistical reliability for less populated areas and small population subgroups, and it is the only source for poverty rates at the census tract level.

Although census tracts may not map on to neighborhoods as defined by residents, they represent small, relatively permanent subdivisions of a county or city containing a population size of 1,200 to 8,000 people (with an optimum size of 4,000) and are updated prior to each decennial census. 2 Census data are generally accepted as the only comprehensive source of detailed information at the tract level, and using the percent of households or residents below the federal poverty line is a common approach to assessing neighborhood disadvantage (Bishaw, 2011; Morrissey & Vinopal, 2018b; Wolf et al., 2017) .

Because census tracts are relatively small geographic areas, most children attend schools in census tracts different from their residential census tracts (approximately 33% of children attended Kindergarten in a school located within their own residential census tract), but, given growing rates of economic segregation, most children attend schools in neighborhoods very similar to those in which they live. 3 We replicated this analysis with the poverty rate of the census tract in which children's elementary schools were located, described in the sensitivity analysis section below.

Our sample is comprised of children in the ECLS-K with nonmissing data on measures of math and reading scores at the fall and spring of Kindergarten, the spring of first grade, the spring of second grade, the spring of third grade and on their residential census tracts, as well as all covariates described below (N 43,000 child-year observations; or about 9,000 children out ≈ of a possible 18,170 in fall of Kindergarten). Most observations excluded from the sample were missing information on test scores, neighborhood poverty, or family poverty, all crucial to the current analysis. Fewer observations were excluded because respondents did not provide information regarding parental education, immigrant status, whether English was spoken at home, parents' marital status, urbanicity, and whether the child attended full or part day Kindergarten, and whether the child attended center-based care before entering Kindergarten. 4

The ECLS-K was a voluntary survey, and it is likely that those who left the study differed from those who continued with data collection. We used IES-recommended weights to help address this problem. To the extent that the families who left the study differ substantially in how neighborhood poverty relates to their cognitive growth, our results may be biased.

Dependent variables. Dependent variable construction relied on the ECLS-Kadministered direct child assessments that track respondents' academic growth in math and reading over time. These assessments were adapted from national and state standards and 4 There are several small but statistically significant differences between our analysis sample and the ECLS-K sample overall. Compared to our analysis sample, excluded observations were slightly more likely to live in higher poverty neighborhoods, move between waves, be a twin, live in a household with more members, speak a language other than English, have parents who are not married, live in an urban or suburban area, have household income below 200 percent of the poverty line, be Black, Hispanic, American Indian, or Asian, have parents born in the United States, attend full-time Kindergarten, and have parents who do not have a college degree. There are not statistically significant differences in math or reading scores, child sex, or use of center-based child care. accommodate children who speak a language other than English at home. A theta score is provided in the ECLS-K:2011 data file for each child who participated in the direct cognitive assessment for each cognitive domain assessed and for each administration. We used the reading and math theta scores in this analysis. The theta score is an estimate of a child's ability in a particular domain (e.g., reading) based on his or her performance on the items he or she was actually administered. Theta scores for reading and mathematics are provided in for the fall and spring kindergarten, and spring of first, second, and third grade data collection rounds. Theta is iteratively estimated and re-estimated; therefore, the theta score is derived from the means of the posterior distribution of the theta estimate. The theta scores are reported on a metric ranging from -6 to 6, with lower scores indicating lower ability and higher scores indicating higher ability. Theta scores tend to be normally distributed because they represent a child's latent ability and are not dependent on the difficulty of the items included within a specific test, 5 and have been used in previous research to examine children's cognitive growth by household income (von Hippel et al., 2018) . Thus, theta scores are useful in assessing growth in skills over time.

Independent variables. Neighborhood disadvantage was measured using the poverty level of the census tract in which children lived. The census tracts of children's homes at the fall of Kindergarten were merged with information from the ACS on the average value of the percent of residents living below the federal poverty line (FPL) from 2010-2015. Following previous work (Bishaw, 2011) , we classified tracts into one of four categories: low poverty neighborhoods, census tracts with less than 14 percent of residents living below the FPL (i.e., representing a neighborhood with a poverty rate below the national average); moderate-low poverty neighborhoods, tracts in which 14-19 percent of residents live below the FPL; moderate-high poverty neighborhoods, in which 20-39 percent of residents live below the FPL; and high poverty neighborhoods, in which 40 percent or more residents live below the FPL. Previous research suggests that the 20 and 40 percent poverty thresholds are particularly meaningful, finding that poor individual outcomes like crime, school drop-out, and longer spells of poverty duration increase with neighborhood poverty between 20 to 40 percent levels (Galster, 2010) . In our analysis sample, in the fall of Kindergarten, about 62 percent of children lived in lowpoverty neighborhoods, 13 percent in moderate-low poverty neighborhoods, 22 percent in moderate-high poverty neighborhoods, and 4 percent in high-poverty neighborhoods. These proportions are similar to those found from other work that examines children's residential census tracts in the ECLS-K:2011 (Morrissey & Vinopal, 2018a , 2018b Wolf et al., 2017) . For children who moved schools between waves 6 , we use the poverty level of the tract that their new home was in, and add a dummy variable indicating the move.

Covariates. Covariates included parent-reported child sex, grade in school, age (in continuous months at assessment), race/ethnicity (non-Hispanic Black, Hispanic, non-Hispanic White, American Indian, Asian, Other), whether the child was a twin, whether the child speaks a language other than English in the household, household size (centered to the mean), household poverty level (calculated using respondents' reports of household size and income; under 100% FPL, or over 200% FPL) , whether the child's parents were married, the highest level of parental education (neither parent graduated high school, at least one parent has a high school degree, at least one parent had some college, and at least one parent graduated from college), the urbanicity (urban, rural, or suburban) of the child's residential census tract, whether the child has at least one parent born outside the United States (immigrant), whether the 6 7.2% of children in our analytical sample move at some point during the analyzed waves. child attended full or part day Kindergarten, and whether the child attended center-based care before entering Kindergarten.

To address Research Question (RQ) 1, individual growth models were used to predict children's test score levels and trajectories from measures of neighborhood disadvantage.

Growth models simultaneously examine within-and between-person change over time to assess how both levels and growth in levels vary across children (Rabe-Hesketh & Skrondal, 2008; Singer & Willett, 2003) . We treat time as a dummy variable, which offers greater flexibility and easier interpretation (Mccoach et al., 2006) and enables understanding of whether neighborhood poverty rates predict cognitive growth rates unique to particular periods of students' lives. We estimated a three-level (grade-child-school) mixed model of student cognitive growth-treating time as a categorical variable-to estimate four separate growth slopes (from fall to spring of kindergarten, from spring of Kindergarten to spring of first grade, from spring of first grade to spring of second grade, and from spring of second grade to spring of third grade) interacted with each category of neighborhood poverty, described above. The low-poverty census tract (less than 14% poverty) served as the reference group for neighborhood poverty. We allowed for random intercepts at both the child and school levels.

Our main model is displayed in Equation 1:

where Y ijk represents the math or reading theta score for child j in neighborhood k at time i.

GRADE is a series of dummy variables representing the child's grade in school (fall of K

[reference], spring of K, spring of first, spring of second, and spring of third grades).

NEIGH_POV represents the key independent predictor of interest, the poverty level of the census tract in which the child's residence is located (i.e., our measure of neighborhood disadvantage), also a series of dummy variables (low poverty [reference], moderate-low poverty, moderate-high poverty, and high poverty). X ij represents background characteristics for child j at time i. V 00k represents the random intercept for the school, and U 0j0 represents the random intercept for the child within schools. These represent the level-2 residuals that permit the level-1

individual growth parameters to vary stochastically across children; both are assumed to have bivariate normal distributions with means of zero and unstructured covariance matrices. The interaction terms between GRADE and NEIGH_POV (producing a total of 12 interaction terms, as each is represented by a series of dummy variables) serve as our main parameters of interest, representing how the linear rate of growth in math or reading scores varies with neighborhood poverty between each data wave. The residual R ijk represents the portion of unexplained child j's cognitive scores (Singer & Willett, 2003) . Models also include state fixed effects (S).

It is important to note that the main objective of our paper was to illustrate trajectories of cognitive growth over the first years of elementary school and importantly, to include growth during the Kindergarten year. However, we also ran models that controlled for children's baseline test scores (at the fall of Kindergarten) to predict levels of and growth in test scores between the spring of Kindergarten, first, second, and third grades. Results indicate that test score growth, especially in Kindergarten, is partially contingent on skills upon Kindergarten entry, which vary by neighborhood poverty, as expected.

For RQ2, we added triple interaction terms to Equation 1, interacting our grade dummy variables, our neighborhood poverty dummy variables, and, separately, key student characteristics. These student characteristics are: race (Black or non-Black); ethnicity (Hispanic or non-Hispanic); sex; whether the child's parents were immigrants; whether the school is located in a rural area (versus urban/suburban); and household poverty status (poor versus non-poor households). We also tested two characteristics regarding children's educational experiences: early care and education experience (the child attended any center-based care prior to Kindergarten vs. no experience in center care); and part-or full-day Kindergarten attendance. 7

Weighted average math and reading scores by neighborhood poverty category are provided in Table 1 as well as Appendix Figure A1 . Table 1 . Children living in low-poverty communities were more likely to be White or Asian, to live in households above 200 percent of the FPL, and to have parents who had graduated college, whereas children living in high poverty areas were more likely to be Black or Hispanic, to live under the poverty level, to have parents who were immigrants, and to have parents with a high school degree or less. Children in higher-poverty neighborhoods were more likely to attend full versus part day Kindergarten and less likely to have attended center-based ECE before Kindergarten. Speaking a language other than English did not follow a stepwise pattern with neighborhood poverty.

Insert Table 1 here.

Results from the main regression models without control variables (unconditional models) are shown in columns 1 and 3 of Table 2 for math and reading scores, respectively, and our full models are shown in columns 2 and 4. Like the descriptives, the unconditional models show a stepwise relationship between neighborhood poverty and test scores at Kindergarten entry, such that as neighborhood poverty increases, test scores decrease.

The full models (columns 2 and 4 in Table 2 ) show much smaller coefficients when control variables are included. As expected, neighborhood poverty category has a main effect of lowering average scores at school entry. From fall to spring of Kindergarten, children in high poverty neighborhoods averaged lower average scores in math and reading (-0.226 and -0.138), compared to those in low-poverty neighborhoods. The relationship between neighborhood poverty and test scores at Kindergarten entry showed a stepwise pattern for math, but not for reading, for which living in a neighborhood with any level of poverty higher than low poverty (14% or more) was consistently associated with lower scores (about -0.1). Children's scores grew as they progressed through elementary school, shown in the coefficients for grades.

Insert Table 2 here.

The main parameters of interest for the first research question in this study are the interactions between neighborhood poverty and grade, which reflect the rates of growth in children's scores. In Table 2 , these interactions represent the rates of growth in children's scores relative to Kindergarten entry. Appendix Figure A2 contains a Slope Estimates table that provides the growth rates for math and reading scores between each grade. Statistical significance is calculated based on the difference between the slope for low poverty, and each of moderate-low, moderate-high, and high poverty.

The interactions between neighborhood poverty and grade are shown in Table 2 (columns 2 and 4, with full controls). The reference category consists of children in low-poverty neighborhoods in the fall of Kindergarten. The Slope Estimates table in Appendix Figure A2 show that children in low poverty neighborhoods grew an average of 0.64 in math and 0.78 points in reading from fall to spring of Kindergarten, whereas children in moderate-low and moderate-high poverty neighborhoods grew an average of 0.73 and 0.79 points in math, and 0.84 and 0.85 points in reading (translating to 14-23% higher growth rates in math, and 8-9% higher growth rates in reading).

Because children in higher poverty neighborhoods scored lower than their peers at Kindergarten entry, these higher growth rates suggest some degree of "catch-up" during the Kindergarten year. Children in high poverty neighborhoods grew at faster rates in math (but not reading) than those in low poverty neighborhoods (0.85 points, 33% higher growth rate) compared to their peers in low poverty communities. Between the spring of Kindergarten and first grade, however, this pattern reversed such that children in higher poverty neighborhoods grew at slower rates than their peers in low poverty neighborhoods in math and reading (children in moderate-high poverty neighborhoods grew 13% slower in math and 4% slower in reading, and children in high poverty neighborhoods grew 11% slower in reading scores). Between the spring of first and second grades (waves 2 and 3), children grew at roughly the same rates, maintaining but not widening or narrowing gaps. Between second and third grade, however, there was evidence for additional "catch-up" in math (not reading), as children in the highest poverty communities grew at higher rates in math relative to those in low poverty neighborhoods (an 80% higher growth rate).

While the background characteristics we controlled were not our main variables of interest, it is notable that in Appendix Table A1 (showing full controls), the main associations between the poverty of children's residential census tracts and math or reading test scores were similar to or larger than those between test scores and children's own household poverty.

Relative to children in households above 200 percent of poverty, poor children scored 0.083 points lower in math and reading across Kindergarten through third grade. These differences were smaller than those of living even in moderate-low poverty neighborhoods, in fall of Kindergarten (-0.163 and -0.135 for math and reading), after controlling for other factors.

Importantly, however, this may be an artifact of a child's household poverty correlating highly with neighborhood poverty. 8 Further, in Appendix Table A1 , the coefficient for household poverty represents the average effect across grades, whereas the neighborhood poverty coefficient represents the effect at the fall of Kindergarten. In low poverty neighborhoods at Kindergarten entry, 69.4 percent of children had incomes above 200 percent FPL, compared to only 12.6 percent of those in high poverty neighborhoods (see Table 1 ). It is likely that children in poorer communities were on average more disadvantaged, and thus the coefficients for the broad measure of household poverty status underestimate the true associations between family income and test scores.

Our second research question relates to whether student characteristics moderate relationships between neighborhood poverty and growth in cognitive scores. In our regressions for RQ2, the main parameters of interest are the triple interactions between grade, neighborhood poverty, and the student characteristic. Results from these models predicting math and reading scores are shown in Appendix Tables A2 and A3, Sex. In general, as shown in the first columns of Appendix Tables A2 and A3, the triple interaction terms for female, neighborhood poverty, and grade were small and not statistically significant, indicating that males and females exhibit similar associations between neighborhood poverty and rates of growth in math and reading scores during early elementary school (see Appendix Figure A3 ). Indeed, few significant differences in slopes by neighborhood poverty category are found (see Slope Estimates).

Appendix Figure A4 ), Black children showed similar patterns of growth by neighborhood poverty as non-Black students with some notable exceptions. In Kindergarten, the gap between non-Black students in moderate-low poverty neighborhoods and non-Black students in low poverty neighborhoods shrunk more compared to that same gap for black students. Similarly, between first and second grade in moderate-high poverty neighborhoods, and between second and third grade in high poverty neighborhoods, non-Black students gained ground compared to their non-Black peers in low-poverty neighborhood, but Black students in higher-poverty neighborhoods lost ground. However, the reading scores of Black children in high poverty grew faster than the scores of Black children in low poverty neighborhoods during Kindergarten, whereas the opposite was true for non-Black children.

Hispanic Ethnicity. Results for testing whether rates of growth by neighborhood poverty vary between Hispanic and non-Hispanic students are shown in the third columns of Appendix Tables A2 and A3 (and Appendix Figure A5 ). From Kindergarten to first grade, non-Hispanic children in moderate-low poverty neighborhood lost ground compared to their non-Hispanic, low poverty peers, whereas Hispanic in moderate-low poverty neighborhood kept pace with their Hispanic peers in low poverty neighborhoods. Between second and third grade, Hispanic students in high poverty neighborhoods gained a great deal of ground compared to children in low poverty neighborhoods, whereas non-Hispanic students lost ground that year. In reading, however, non-Hispanic students in the highest poverty neighborhoods showed higher growth rates relate to low-poverty, non-Hispanic students during Kindergarten, but this was not true for Hispanic students, who lost ground that year.

Household poverty. Results testing whether rates of cognitive growth by neighborhood poverty varied between children growing up in poor and non-poor households are shown in the fourth columns of Appendix Tables A2 and A3 and Appendix Figure A6 . There was little evidence that poor children's growth rates were differentially affected by their neighborhood disadvantage, compared to non-poor children.

Urbanicity. Results testing whether cognitive growth by neighborhood poverty differ in rural vs. urban or suburban areas are shown in the fifth column of Appendix Tables A2 and A3 and Appendix Figure A7 . Children in higher-poverty rural and non-rural areas both showed catch-up patterns in math during Kindergarten, and the magnitude of this growth difference was stronger for children in rural, moderate-low poverty neighborhoods than for their counterparts in non-rural communities. Across the later grades, differences in growth rates between neighborhood poverty was associated with growth rates similarly for both rural and non-rural students; where statistically significant differences emerged, they were in the direction of stronger growth (or smaller losses) for rural students. In reading, however, results indicate stronger growth for non-rural students in higher-poverty neighborhoods with the exception of rural students in high-poverty neighborhoods between first and second grade, who demonstrated stronger growth relative to their low poverty rural peers. Tables A2 and A3 and Appendix Figure A8 show results from models testing the moderating effect of having immigrant parents.

In general, the math and reading test scores gap by neighborhood poverty shrank more so for the children of immigrants than those gaps for the children of non-immigrants. However, the initial gaps by neighborhood poverty status at fall of Kindergarten were wider for the children of immigrants. Appendix Tables A2 and   A3 and Appendix Figure A9 display the results from differences in the associations between school poverty and cognitive growth by whether the child attended full-day Kindergarten compared to part-day. Gaps by neighborhood poverty in both math and reading scores at

Kindergarten entry for part-day students were much wider than for full-day students. In moderate-high poverty neighborhoods, the relative growth rates in math were stronger for those in part-day programs during Kindergarten. From Kindergarten to first grade, those who attended part-day Kindergarten and lived in moderate-low poverty neighborhoods continued to catch up in math, whereas those in other neighborhood poverty categories, in both full-and part-time Kindergarten, lost ground. These losses were larger for full-time Kindergarten students in moderate-high poverty neighborhoods compared to their part-time Kindergarten counterparts. In reading, the patterns between neighborhood poverty and growth rates were similar across children attending part-and full-day Kindergarten, except that those in part-day Kindergarten in moderate-low poverty communities grew at slower rates from spring of Kindergarten to spring of first grade, then showed more catch-up between the first and second grades. These differences may reflect selection regarding the types of communities that implement full-day Kindergarten, and the general lack of variation in full-day Kindergarten attendance (94% of children in moderate-high poverty neighborhoods and 98% in high poverty neighborhoods attended full-day Kindergarten vs. 74% of children in low poverty neighborhoods; see Table 1 ).

and A3 and Appendix Figure A10 display the results for testing whether cognitive growth by school neighborhood poverty differs by children's experiences in center-based ECE prior to Kindergarten entry, finding no differences in neighborhood gaps in math and reading growth by ECE history during Kindergarten. Between Kindergarten and first grade in math, however, both center ECE attendees and non-attendees in higher-poverty communities lost ground relative to their peers in low poverty communities, but those who had attended center-based ECE lost more ground.

We re-ran our models using census tract-level poverty rates merged onto the census tracts in which children's elementary schools, instead of their homes, were located (33% of children had matching school and residential tracts; relevant correlations can be found in Appendix Table   A5 ). Results suggest that children attending schools in moderate-low and moderate-high poverty communities exhibit higher rates of growth in math scores, but not in reading, through third grade compared to their peers in schools in low poverty neighborhoods. However, those in schools in high poverty neighborhoods (only 4% of the sample) showed similar or lower growth rates in math compared to their peers at low poverty schools. Results are presented in Appendix Table A4 . Findings showed a stepwise pattern in which children living in high poverty tracts scored lower than those in moderate-high poverty tracts.

This study examined how neighborhood disadvantage, as measured by the poverty level of the census tracts in which children live, relates to both the levels of and growth in children's cognitive skills during the first three years of elementary school. Previous research indicates that children growing up in low-resourced communities score lower, on average, than those in more advantaged communities (Chetty, Hendren, et al., 2016; Reardon, 2019) , but their skill growth during early elementary school -arguably a better measure of learning than absolute scores -is less-often studied (Reardon, 2019) . Our results highlight learning patterns by neighborhood poverty, with implications for the timing and targeting of policy interventions.

Consistent with previous research (Morrissey & Vinopal, 2018b; Reardon, 2019; Wolf et al., 2017) , this study finds that children exhibit, on average, large gaps in test scores by their residential neighborhood poverty level, with children in high poverty neighborhoods (poverty rates of 40% or more) scoring one-seventh and one-quarter of a point lower in reading and math in early elementary school compared to their peers in low poverty neighborhoods (less than 14% poverty), after controlling for a range of background characteristics. This association is approximately 18 percent and 35 percent of the average differences in reading and math scores between fall and spring of Kindergarten, or what can be considered what children in low poverty neighborhoods learn in their first year of K-12 schooling. This is approximately one-third of the main effect of having neither parent graduate high school (compared to a college degree or more).

Importantly, the patterns of association between neighborhood poverty and growth in math and reading test scores were different than those of average test scores. Children from higher-poverty communities showed faster rates of cognitive growth -presumably a measure of learning -during Kindergarten compared to their counterparts in lower-poverty communities.

These higher growth rates were particularly strong for math, with children in moderate-low, moderate-high, and high poverty neighborhoods showing 14 to 33 percent faster growth rates from fall to the spring of Kindergarten than their peers in low poverty communities. However, from the spring of Kindergarten to the spring of first grade, growth rates in math for children in more disadvantaged communities slowed relative to their peers in low poverty communities, but grew faster again between the second and third grades. In reading, the slow-down in growth for children in higher-poverty neighborhoods during first grade was smaller compared to that in math. These differential findings by cognitive domain underscore the importance of separating math and reading scores in research. Together, these findings provide some evidence for "catchup," or a narrowing of gaps by neighborhood poverty, particularly during the first year of formal schooling, but also point to first grade as an important year for intervention in high poverty neighborhoods to maintain upward trajectories.

In general, the "catch-up" phenomenon in our results is consistent with previous research finding that elementary schools may narrow SES inequalities in achievement (Downey et al., 2004; Raudenbush & Eschmann, 2015; von Hippel et al., 2018) . Notably, the Kindergarten year showed this pattern more strongly, and was the only period of growth in this study that lacked a summer (growth was measured from fall to spring of Kindergarten, the next from the spring of Kindergarten to the spring of first grade, etc.). Higher relative growth rates for children in high poverty neighborhoods during Kindergarten may be an artefact of SES gaps in summer experiences and learning loss, which has been identified in previous research (Downey et al., 2004; Gershenson, 2013; von Hippel et al., 2018) ; that is, that children in low poverty neighborhoods learn more/experience more cognitive growth in the summer relative to their peers, perhaps because of access to more educational opportunities.

Alternatively, this higher relative growth during Kindergarten may derive from children's experiences prior to Kindergarten entry. Children in low-resourced communities have different early experiences than those in higher-income communities, including lower access to highquality early care and education (ECE), which promotes school readiness (Chaudry, Morrissey, Weiland, & Yoshikawa, 2017; Gordon & Chase-Lansdale, 2001; McCoy, Connors, Morris, Yoshikawa, & Friedman-Krauss, 2015; Morris et al., 2018) . Recent research finds that attending center-based ECE is associated with improved cognitive outcomes across neighborhoods with different poverty levels (Morrissey & Vinopal, 2018a) . However, despite increased rates of preschool and center care attendance, particularly among low-income children (Bassok, Finch, Lee, Reardon, & Waldfogel, 2016; Magnuson & Waldfogel, 2016) , research suggests that Kindergarten teaches much of the same content as preschool (Engel, Claessens, & Finch, 2013) , which may serve to help children lacking in ECE experience to catch up with their peers. For example, research suggests that specific types of instruction, particularly math, may have differential effects for children based on their initial skill levels (Chiatovich & Stipek, 2016 Results also have implications for the debate surrounding the long-term "fade-out" of the effects of preschool on children's test scores (Yoshikawa et al., 2013) . Research has documented that preschool and other types of early education produce short-term increases in cognitive skills, but the test score gaps between children who attended preschool and those that did not attend narrows, or converges, over time (Ansari, 2018; Yoshikawa et al., 2013) . Our findings add to this literature by identifying some "catch-up" of children in higher-poverty communities, and slower rates of cognitive skill growth among children in low poverty communities.

The patterns identified between neighborhood poverty and growth in cognitive skills did not meaningfully vary by child sex, household poverty, or urbanicity. Our results regarding child sex differ from recent research in Canada, which found that the neighborhood SES gradient for early childhood developmental measures (as assessed by the Early Developmental Index [EDI]) was steeper for males compared to females (Webb et al., 2020) . These differential findings may result from the different measures of neighborhood disadvantage (for which we used poverty only) or of children's outcomes, as our study included test scores from direct math and reading assessments, whereas the EDI involves teachers' reports across health, cognitive, and other domains. Children in rural high poverty communities gained more ground on their peers in low poverty areas in reading during Kindergarten, relative to their counterparts in urban and suburban high poverty neighborhoods, but otherwise showed similar patterns of growth; however, children in rural communities showed lower initial test scores at Kindergarten entry.

To varying degrees, however, patterns of cognitive growth differed somewhat by children's experience in center-based ECE (discussed above), enrollment in part-versus full-day Kindergarten, child race, Hispanic ethnicity, and parents' immigrant status. Specifically, Black children appeared particularly vulnerable to the negative effects of living in higher poverty communities in terms of absolute levels of and growth in math, which is consistent with earlier work on neighborhood poverty (Wodtke et al., 2011) , and may reflect the fact that historical and current discriminatory policies and patterns have resulted in the higher-poverty neighborhoods that Black children live in being relatively more disadvantaged compared to their non-Black peers. Conversely, the neighborhood poverty gap in math closed more so during the

Kindergarten year for the children of immigrants in moderate-low or moderate-high poverty neighborhoods than for children with non-immigrant parents. These patterns did not continue in later grades, however. Similar to recent research (Reardon, 2019) , the patterns between neighborhood poverty, test scores, and growth were somewhat different among Hispanic children compared to non-Hispanic White or Black children. Again, it may be that the higherpoverty neighborhoods that Black children live in are more disadvantaged than those of Hispanic children.

Surprisingly, the main association between living in a high poverty neighborhood and test scores was larger than the main association between growing up in a poor household relative to growing up in a household with income 200 percent of the federal poverty line. It is important to note that this represents the association between being poor and test scores after controlling for a host of background characteristics, including parent education, which is correlated with poverty but appears to drive math and reading scores more so than income alone. Our findings are consistent with recent research showing that children growing up in very similar household conditions in different neighborhoods can have vastly different outcomes later in life, with school measures accounting for less than half of the variation in social mobility across neighborhoods .

Together, these neighborhood poverty differences in average absolute test scores and growth in test scores suggest that gaps emerge before school entry, and these gaps narrow during

Kindergarten, widen again in first grade, and then generally follow parallel patterns through third grade, with the magnitude of differences somewhat dependent on student characteristics. These findings have relevance for children short-and long-term socioeconomic outcomes. For example, Kindergarten test scores are strongly related to outcomes in adulthood, including earnings, college attendance, and retirement savings, despite fade-out effects in the years following Kindergarten (Chetty et al., 2011) .

Findings have implications for policy and practice. Our findings add to the literature suggesting that the use of average test scores as a measure of school quality is likely not accurately assessing how well a school promotes learning among its students, and may simply measure gaps in children's skills that are present at school entry or earlier (Reardon, 2019; Reardon & Portilla, 2016) . Second, research demonstrates that several policy interventions are effective in promoting both overall growth across children's SES, neighborhood, and other characteristics, while narrowing gaps -that is, "lifting all boats" but promoting greater growth among the most disadvantaged. For example, high-quality ECE has been found to do this (e.g., Yoshikawa et al., 2013) , and can prevent or mitigate inequalities by family and neighborhood SES before children enter Kindergarten (Chaudry et al., 2017) . Other policies such as K-12 resource redistribution or higher per-child spending, which research demonstrates can narrow gaps (Kreisman & Steinberg, 2019; Lafortune et al., 2018) , may also help accomplish these goals. Indeed, research demonstrates the power of cognitive performance to be nurtured and strengthened in K-12 education and other interventions (Carnevale, Fasules, Quinn, & Campbell, 2019) . Our finding that the neighborhood poverty gap widens during first grade, in particular,

suggests that the early grades may serve as a point of intervention. Given the decades of growth in economic inequality, and the ongoing COVID-19 public health crisis and its economic fallout that is likely to widen the disparities between schools in low and high poverty communities (Barnum, 2020) , policies that prevent children at risk from falling behind are all the more important.

Results must be interpreted within the context of the study's limitations. First, the associations between neighborhood poverty, cognitive scores, and growth in scores identified in this study cannot be interpreted as causal, given selection of families into specific neighborhoods and schools. Second, although we use a large, nationally representative, longitudinal dataset, attrition and missing data may bias our results. Third, census tracts are a typically used, but imperfect, measure of neighborhoods. Further, our data lack measures of cognitive growth before Kindergarten or after third grade, preventing us from examining how these gaps emerge before entering the K-12 education system, or how growth progresses after early elementary school.

Fourth, our analysis includes only a U.S. sample, a country with uniquely high levels of child poverty and concentrated poverty. Finally, our analyses focused on associations between neighborhood poverty rates and children's test scores and growth. Other measures of neighborhood disadvantage may generate different relationships with children's cognitive growth.

This study found that the level of disadvantage of children's neighborhoods is associated with both average math and reading test scores and growth in test scores. There was largely a stepwise pattern between neighborhood disadvantage and children's average test scores, but students living in higher-poverty communities displayed some higher growth rates -or "catchup" -compared to their peers in schools in more advantaged communities during their

Kindergarten year in particular, but then fall behind again in first grade. Given the importance of early math scores for longer-term academic success (Claessens, Duncan, & Engel, 2009; Duncan et al., 2007) and the growing phenomenon of concentrated poverty (Bishaw, 2014) , results

suggest that the unraveling of neighborhood economic segregation is key for narrowing SES achievement gaps.

Parent education some college 31.95% 42.06%*** 33.38% 27.35%

Parent education college or more 53.82% 24.90%*** 23.38%*** 8.76%*** Observations (Fall K) 5,570 1,130 1,980 320 Statistical significance tested differences between low poverty neighborhood compared to each of the other neighborhood poverty categories; *** p<0.01, ** p<0.05, * p<0.1 

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Table 1. Analytic Sample Descriptive Statistics by Neighborhood Poverty

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