Doctor of Philosophy

Understanding Educational Achievement Gaps: A Summer Learning Perspective by Jie Min Educational achievement gaps change by season. While students from different class backgrounds learn at similar rates when school is in session, over the summer classbased achievement gaps grow the fastest. The story is different for race-based achievement gaps. Black/white achievement gaps tend to widen more during the school year than over the summer. However, researchers have largely overlooked English learners (ELs), who are likely to be highly sensitive to summer break, a time when they are away from school and may not have enough exposure to an English language environment. In addition, summer learning scholars have long demonstrated that family socioeconomic status is the main driver of summer learning, but they fail to account for potential neighborhood effects on summer learning. Using administrative and assessment data from the Houston Independent School District (HISD), this dissertation addresses these gaps with three empirical studies. The first compares learning trajectories of three groups—Els whose home language is other than English, English proficient students whose home language is other than English, and English proficient students who speak English at home. I found reading learning gaps between English proficient students whose home language is other than English and the other two groups widen further during the academic year, but not during the summer. The second study assesses neighborhood effects on students’ reading learning rates, using 3-level piecewise linear models with neighborhood characteristics incorporated. Results indicate that concentrated disadvantage and violent crime have stronger effects on students’ reading outcomes during the academic year than in the summer. The third empirical piece examines the causal effects of a remedial summer program with two regression discontinuity designs. Results demonstrate that students who were at the margin of summer school eligibility did not benefit significantly from summer school. Taken together, these findings suggest that educational achievement gaps increase faster during the academic year than during the summer break.


Acknowledgments
First, I need to thank my advisor, Dr. Ruth Lopéz Turley, for being an amazing person and an amazing advisor, for really helping me get here today. Her enthusiasm for narrowing educational achievement gaps has solidified my interests in educational research. Her expertise in education of sociology has steered me through the rocks and reefs in research. I thank her for always remembering to introduce me to people in conferences and other similar occasions. I appreciate her for always supporting my decisions and speaking up for me in many circumstances. I sincerely feel lucky to be her mentee over the past five years.
I am also indebted to my other committee members for guiding this dissertation from the very beginning to the end. Dr. James Elliott has served on both my master's thesis committee and doctoral dissertation committee. I cannot thank him enough for helping me hone each chapter of the dissertation and pushing me to think out of the box.
Dr. Anna Rhodes's expertise in qualitative research was instrumental to my dissertation.
She guided me to delve into possible mechanisms behind the statistics and to provide a comprehensive picture of the dissertation. I also appreciate Dr. Yinghua He, who served as my external committee member, for talking me through the methodological details and sharing his insights from a different field.
I would like to thank the sociology department at Rice University for providing me with stipends and support when necessary. Special thanks go to Dr. Michael Emerson,  Table 2-

Background
This dissertation was sparked by Downey et al.'s (2004) Great Equalizer study, which highlights the importance of summertime by arguing that American children spend much more of their waking hours at non-school environments (e.g. family, neighborhood, etc.) than school environment. They claim that teasing out students' educational achievement when school is in session versus out may have substantive implications for understanding the sources of educational achievement gaps, because students spend time in both school and non-school environments during the academic year, whereas they spend time in non-school environments only during the summer (Downey et al. 2004;Heyns 1978). Comparison of students' relative achievement during the academic year versus the summer also bears on a key question in educational research: Do schools reduce, reproduce, or exacerbate educational disparities? This comparison can lead to different answers.
Answer 1: If educational achievement gaps grow faster during the academic year than during the summer, schools exacerbate existing educational disparities.
Answer 2: If educational achievement gaps grow faster during the summer than during the academic year, schools play a role of reducing educational inequality.
Answer 3: If there is no substantive difference between summer learning and academic-year learning, schools serve as a reproducing engine of educational inequality.
In existing educational research, there are both empirical and theoretical evidence supporting each one of these claims. The argument that-schools reproduce or even exacerbate educational achievement gaps through structural and cultural mechanisms-is quite prevalent in educational literature. The structural explanation refers to students from advantaged backgrounds tend to attend schools with better educational resources and more experienced teachers (Bowles and Gintis 2011). Even within the same school, advantaged students are more likely to be placed in higher ability groups or advanced curriculum tracks (Gamoran 1986;Tach and Farkas 2006). In terms of cultural mechanisms, educational system favors cultural capital (habits, attitudes, and demeanor) from elite families than that from non-elite families (Bourdieu 1977;Bourdieu and Passeron 1990). A related explanation is that teachers tend to hold higher expectations for advantaged students than disadvantaged students (Jennings and DiPrete 2010). As a result, advantages transmit through structural and cultural mechanisms and thereby have positive effects on student academic performance. These studies come down on the side of viewing that schools reproduce or exacerbate educational inequalities.
Another line of research suggests that schools reduce educational achievement gaps. There are two main perspectives that illustrate this argument. First, the variation of students' non-school environment tends to be much larger than school environments (Entwisle and Alexander 1992;Downey et al. 2004). Specifically, the variance in family income has been growing substantially over the last few decades, while the variance in school funding has shrunk (Reardon and Bischoff 2011;Western et al. 2008). Second, many empirical evidence suggests that policies and teachers often play an active role in promoting disadvantaged students' academic performance. For instance, a wide array of policies/programs targets students with disadvantages, such as special education, free/reduced-price lunch, bilingual services, and full day kindergarten or pre-K programs.
Furthermore, many teachers report higher willingness to help low-performing students than high-performing students in a national survey (Loveless et al. 2008). These research offer support to the assertation that educational inequalities primarily originate from contexts outside of schools and schools can actually diminish educational disparities.
As demonstrated above, various studies might lead to different answers to the question about school's role in educational outcomes. To examine these answers, a seasonal comparison approach provides an innovative perspective to investigate the extent to which schools contribute to educational inequality. Previous research typically focuses on the effects of a specific mechanism on students' academic outcomes and thus fails to consider how all the school-based or non-school-based mechanisms affect academic performance as a whole. The seasonal design tests students twice annually-the beginning and end of each academic year, which enables the comparison between academic-year learning and summer learning. An appealing feature of the seasonal comparison design is that it allows an assessment of the relative importance of different contexts in shaping students' academic outcomes when a comprehensive set of family, school, and other mechanisms are not available or not really needed (von Hippel et al. 2018).
There has been a long tradition of summer learning research and several findings are widely accepted by both academics and non-academics (Entwisle and Alexander 1992;Heyns 1978;Downey et al. 2004;von Hippel et al. 2018). First, class-based achievement gaps tend to grow faster when school is out of session than during the academic year (Entwisle and Alexander 1992;Downey et al. 2004). Second, race-based achievement gaps primarily grow when school is in session than during the summer (Entwisle and Alexander 1992). Third, summer learning losses can accumulate across school years and may result in severe long-term academic consequences (Alexander et al. 2007). Overall, previous summer learning studies generally agree upon the compensatory role of schooling in narrowing class-based educational disparities.

Research Approach
In this dissertation, I revisit the conventional wisdom about summer learning literature for two main reasons. First, recent research concerns how the test forms and scaling methods used in previous studies might yield misleading conclusions about summer learning and educational achievement gaps (von Hippel et al. 2018;von Hippel and Hamrock 2019), but the traditional arguments are not easy to be challenged. Thus, more summer learning research is needed to re-examine the summer learning patterns by using more scientific test forms and interval vertical scaled tests. Second, despite the conventional theories, there are mechanisms that potentially matter to students' academic achievement but have been overlooked by previous summer learning studies. For example, students spend a significant portion of their summertime under non-school environments, we know little about the factors outside family contexts that contribute to students' summer learning. In addition, English language learners make up a sizable population in U.S. public schools, but their summer learning experiences have been largely ignored.
Therefore, this dissertation seeks to fill these gaps by providing empirical evidence on how neighborhood mechanisms and language proficiency status shape students' summer learning. I believe this investigation will allow me to develop a better understanding of the causes of summer learning disparities, as well as mechanisms associated with educational achievement gaps. This dissertation primarily relies on administrative and assessment data provided by Houston Independent School District (HISD). The sample includes students who entered the first to the seventh grade in 2015-2016 and stayed in the school district for two consecutive years. The remaining chapters consist of three distinct studies. Each addresses a different aspect related to summer learning and educational achievement gaps.
The second chapter, "Summer Learning for English Learners," examines the role of English language proficiency and students' home language in students' summer reading achievement. In particular, this chapter compares learning trajectories of three groups-ELs whose home language is other than English, English proficient students whose home language is other than English, and English proficient students who speak English at home. The findings suggest that for students at early grades, reading learning gaps between English proficient students whose home language is other than English and the other two groups widen further during the academic year, but not during the summer.
For students at upper grades, however, reading learning gaps remain constant and change little either when school is in session or not.
Summer learning scholars have long demonstrated that family socioeconomic status is the main driver of summer learning, but they fail to account for potential neighborhood effects on summer learning. The third chapter fills this gap by assessing neighborhood effects on elementary and middle school students' learning rates in the summer and in the academic year, using 3-level piecewise linear models with neighborhood characteristics incorporated. Relying on data from the American Community Survey (ACS), Houston police records, Infogroup's U.S. business database, and the Risk-Screening Environmental Indicators Geographic Microdata (RSEI-GM), I constructed four neighborhood factors-concentrated disadvantage, violent crime rate, neighborhood learning resources, and physical environment (air quality). Results indicate that concentrated disadvantage and violent crime have stronger effects on students' reading outcomes during the academic year than in the summer.
The fourth chapter examines the causal effects of a remedial summer program offered by the school district to students who are at risk of being retained. Students who were initially retained at the end of academic year have the chance to be promoted by the end of summer if they make up deficiency in certain subjects during the summer school.
This chapter leverages the fact that students at the border of promotion standards can be considered as being randomly assigned to summer school. By assuming that there are no observable and unobservable differences between students who attend summer school and those who do not, I present two regression discontinuity designs to estimate the effect of being assigned to summer school and the effect of actually attending summer school.
Results suggest that students who were at the margin of summer school eligibility did not benefit significantly from summer school. This study extends our understanding of the remedial summer school effects for elementary and middle school students. It suggests that both program duration and specific subject of instruction are crucial for summer school effectiveness.
Building off these findings, the final chapter summarizes the most consistent patterns across the three studies. It shows how the three separate analyses can be considered together to better understand sources of educational achievement gaps. This chapter also discusses specific implications for future research and policy.

Summer Learning for English Learners
Although summer learning research has explored extensively learning gaps by socioeconomic status and race/ethnicity, English learners (ELs) largely have been overlooked. In this chapter, I compared learning trajectories of ELs and English learners during the summer as well as during the academic year. Students' home language was also considered to account for the interactive relationships between English proficiency and home language for reading achievement. I found that English proficient students whose home language is other than English score higher in reading than English proficient students who speak English at home and ELs. Reading learning gaps between English proficient students whose home language is other than English and the other two groups widen further during the academic year, but not during the summer. In addition, these results only pertain to students during the early grades. For later grades, no significant differences in reading were observed between English proficient students who speak English at home versus their counterparts who do not speak English at home, both during the academic year and during the summer.

Introduction
The existing summer learning literature provides a mixed picture regarding racial/ethnic achievement differences. Some have found that race-based achievement gaps only grow during the school year and do not widen during the summer (Downey et al. 2004), while others suggest that racial/ethnic disparities in academic achievement not only rise when school is in session but continue to do so during the summer months (Atteberry et al. 2016;von Hippel et al. 2018). The differences across studies are in part a result of the changing population of racial/ethnic groups (von Hippel et al. 2018), and in part about different studies that often answer slightly different questions (Quinn 2015).
For this reason, comparisons between studies on racial/ethnic differences in summer learning must be made with caution.
What is lost in the summer learning studies on racial/ethnic disparities, is an understanding of variation across ethnoracial minority groups. This has particularly strong implications for Latino and Asian students-not only do they currently comprise the largest and fastest-growing immigrant groups in the United States, respectively, but they also represent the burgeoning population of English learners (ELs) in the U.S. school system (National Center for Education Statistics 2019). It has been found that the persistent achievement gaps between Latino and white students are largely driven by the growth of the Latino EL population (Hemphill et al. 2011). Since summer is a critical time for academic achievement gaps to enlarge, it is imperative for summer learning research to pay more attention to the new immigrant groups, especially these EL students.
This chapter delineates the summer learning patterns for ELs based on the administrative and assessment data from Houston Independent School District (HISD).
The data contain both spring and fall reading tests for elementary and middle school students in the 2015-16 through 2016-17 academic years. A set of piecewise linear models (PLMs) were applied to examine the academic learning trajectories of ELs and non-ELs during the academic year versus during the summer. Students' home language is also considered to distinguish reading learning rates of three groups: English proficient students whose home language is English, English proficient students whose home language is other than English, and EL students whose home language is other than English. Thus, I aim to examine how ELs' and non-ELs' reading achievement changes over time and how home language might play a role in this process.

Social Class Disparities in Summer Learning
The relationship between students' social class background and their academic achievement during the summer has been well documented in the literature (Entwisle and Alexander 1992;Heyns 1978). Specifically, there has been consensus among scholars that class-based achievement gaps grow faster over the summer than during the school year. While students from different class backgrounds can learn at roughly the same rates when school is in session, lower-income students tend to fall behind their higher-income counterparts during the summer (Alexander et al. 2007;Entwisle and Alexander 1992;Heyns 1978). This phenomenon has largely been explained by the "faucet theory," which suggests that the school calendar controls the on and off of the faucet of school resources (Alexander et al. 2007;Entwisle and Alexander 1992). While school is in session, the faucet is turned on and allows all students to enjoy school resources. When summer comes, however, the faucet is switched off. As a result, while higher-income students are able to draw on family resources to advance their academic achievement during the summer, such learning support is not available for lower-income students.

Ethnoracial Disparities in Summer Learning
Although scholars largely agree upon the association between class-based achievement gaps and summer break, whether summer contributes to race-based achievement gaps has been contested (Benson and Borman 2010;Burkam et al. 2004;Cheadle 2008;Downey et al. 2004;Quinn 2015). Early studies of summer learning suggest that black students are more vulnerable to a summer setback than their white counterparts (Burkam et al. 2004;Entwisle and Alexander 1992;Heyns 1978), but recent evidence is conflicting on black-white differences in summer learning. Some research demonstrates that summer learning does not significantly differ for black and white students (Downey et al. 2004;Fryer and Levitt 2004), while other studies argue black students lose more ground during the summer (Atteberry et al. 2016). Despite the inconsistent findings, scholars have been reluctant to explore the reasons behind the inconsistency or to tap into the mechanisms that lead to black-white achievement disparities during the summer, with just a few exceptions (Cheadle 2008;Quinn 2015).
Besides different modeling strategies across studies, researchers often make different assumptions about test scales, handle measurement errors differently, or even answer different research questions (Quinn 2015). All these differences would result in mixed findings on black-white differences in summer learning.
In addition, a large body of summer learning scholarship on racial/ethnic disparities focuses on black-white comparisons (Entwisle and Alexander 1992;Heyns 1978). Only a handful of studies have examined Hispanic-white or Asian-white differences in summer learning. Similar to the black-white achievement disparities in summer learning, findings on Hispanic-white summer learning differences are inconsistent. Some research shows that Hispanic-white gaps do not grow during the summer (Downey et al. 2004), whereas other studies demonstrate Hispanic students fall steadily behind white students in summers (Atteberry et al. 2016). One study even finds that Hispanic-white summer learning gaps display an unstable pattern that might change across summers and cohorts (von Hippel et al. 2018). One possible reason for the inconsistency is that race explains at most 11 percent of the variance in summer learning rates (Atteberry et al. 2016) and students from the same race group could vary substantially in both observed and unobserved characteristics. Because different studies often rely on data from different cohorts, the inconsistent summer learning gaps can partly be attributed to different characteristics of the changing cohorts over time.
Summer learning studies on Asian-white comparisons are even scarcer, and the limited information on Asian-white achievement differences in summer learning is also inconsistent across studies. Earlier work has documented that white students could learn more during the academic year than Asian American students, but lose more ground over the summer than Asian children (Downey et al. 2004). In contrast, later research finds evidence supporting the belief that white students learn faster than Asian American students in math during the summer, at least for students in the early grades (von Hippel et al. 2018). Another possible reason for the inconsistency of Hispanic-white and Asianwhite summer learning gaps is that Hispanic and Asian American populations have continued to grow over the past few decades and English learners were not tested in the old cohort for some data such as Early Childhood Longitudinal Survey (von Hippel et al. 2018). Therefore, early evidence on Hispanic-white or Asian-white achievement differences may not reflect the actual patterns.

Summer Learning for English Learners
In addition, the existing summer learning literature on Latino and Asian students leaves unaddressed the potential language barrier for these students. Prior research notes little effort has been made to understand the summer learning patterns for English learners (Alexander et al. 2016), which are disproportionally composed of Latino and Asian immigrant students. Over the past forty years, Latino and Asian immigrants have been the largest and fastest growing immigrant population in the United States (Radford and Noe-Bustamante 2019). Between 1980 and 2015, the Hispanic immigrant population increased by about 280 percent in the United States, from just 6.5 percent of the total U.S. population to 17.6 percent (Flores 2017). During the same period, the U.S. Asian immigrant population increased by over 400 percent, from 1.1 percent of the total U.S. population in 1980 to 4 percent in 2015 (Zong and Batalova 2016). Also noteworthy is that, since 2010, more Asian immigrants have arrived in the United States than Hispanic immigrants annually (Radford and Noe-Bustamante 2019).
The dramatic increase of immigrant population also brings notable changes to the U.S. classrooms. One of the most crucial changes is the rising number of English learners in the U.S. education system, especially public schools (National Center for Education Statistics 2019). The term "English learner," or "student of limited English proficiency," refers to a student whose primary language is other than English and whose English language skills are such that the student has difficulty performing ordinary classwork in English (Texas Education Agency 2019). Thus, the concept of the English learner (EL) emphasizes two dimensions. On the one hand, an English learner has to be someone whose native language is not English. On the other hand, an English learner's difficulty in speaking, listening to, reading, or writing English suffices to deter his/her academic advancement in school (Artiles et al. 2005).
In U.S. public schools, the percentage of EL students had reached 10 percent in 2016 at the national level (National Center for Education Statistics 2019). The percentage of ELs is 10 percent or more in nine states, including California (20.2%), Texas (17.2%), Nevada (15.9%), New Mexico (13.4%), Colorado (11.7%), Washington (11.1%), Kansas (11.1%), Alaska (11.0%), and Florida (10.3%). Among all EL students in U.S. public schools, Hispanic students make up over three-quarters and Asian American students constitute over 10 percent of the total EL population. Additionally, EL students are unevenly distributed across grade levels, with a higher proportion of ELs in early grades and a lower percentage in later grades. This pattern is likely driven by the propensity to reclassify ELs as fluent English proficient within a certain number of years in the U.S. K-12 education system (Saunders and MarcELetti 2013). In terms of home language for EL students, Spanish is the most common primary language (76.6% of all EL students), followed by Arabic, Chinese, and Vietnamese (National Center for Education Statistics 2019). Yet interestingly, English is the fifth most common home language reported by ELs. This is partly because some ELs reside in multilingual families, and partly because some are adoptees from foreign countries whose first language is other than English but who currently live in English-speaking families (National Center for Education Statistics 2019).
Previous research indicates that the primary language spoken at home interferes with an EL student's acquisition of English proficiency at school (Suárez-Orozco and Suárez-Orozco 2001). However, evidence on the relationship between home language and academic achievement seems to be contradictory. Some have found that speaking a language other than English at home is beneficial for a variety of academic outcomes, such as academic expectations (Zhou and Bankston 1994) and high school completion (Feliciano 2001). Other studies have found either no association or negative association between speaking non-English at home and academic outcomes (Fuligni 1997;Carpenter and Ramirez 2007). One possible reason for the inconsistency is that home language use is not static, but rather changes over time (Zarate and Pineda 2014). Since home language use is deeply entwined with parental language proficiency and acculturation, which are also dynamic, it is possible that home language has different effects at different points over the K-12 school trajectory.
Given that the overwhelming majority of EL students live in households where English is not spoken, ELs are likely to be highly sensitive to summer break, a time when they are away from school and may not have enough exposure to an English language environment (Alexander et al. 2016). As Cooper et al. (1996) predict, "Children who speak a language at home other than English may have their acquisition of English language skills set back by an extended period without its usage" (p.229). Limited evidence suggests that students whose primary home language is not English obtain a lower literacy score after summer than those who speak English at home, with baseline academic achievement and background characteristics controlled (Kim 2004;Lawrence 2012). Moreover, low-income Latino students whose home language is other than English do not benefit as much from summer reading intervention as their counterparts who speak English at home (Kim and Guryan 2010).
These studies highlight the influence of home language environment on students' literacy performance in general, but they by no means provide a complete picture of summer learning patterns for English learners. Although it is quite possible that English learners live in families that speak a language other than English, students who come from non-English speaking families are not necessarily going to be English learners. In fact, substantial numbers of students from non-English speaking families are English proficient and even academically outperform students who live in families whose primary language is English (Stiefel et al. 2003). Because a home language other than English is not equivalent to English learners, it is important not to conflate the two by differentiating the effects of home language and English language proficiency in summer learning studies.

Summer Learning Across Grade Levels
A large body of summer learning research tends to focus on a specific grade level and ignores the accumulation of summer learning gains/losses over the course of the school trajectory. For example, Heyns (1978) follows two cohorts of middle school students-the sixth and seventh graders-for two academic years and the summer in between. Studies using the ECLS-K dataset examine the summer between kindergarten and first grade (Burkam et al. 2004;Downey et al. 2004;von Hippel et al. 2018). One exception is the Beginning School Study (BSS), in which Alexander and his colleagues follow the first graders to the start of their high school and find two-thirds of the classbased academic achievement gaps in the ninth grade can be traced to students' summer learning differences in the elementary school years (Alexander et al. 2007). Still, it is unclear at which specific grade levels summer learning gaps would widen the most.
Therefore, this chapter also investigates whether the summer learning trends are the same for lower-grade versus higher-grade students.

The Context of Houston
This study focuses on the Houston Independent School District (HISD), which is the seventh largest school district in the United States and enrolls more than 214,000 students in 8 early childhood centers, 159 elementary schools, 38 middle schools, 38 high schools, and 41 combined/other schools (Houston Independent School District 2019).
Several features make HISD an opportune place to study the summer learning patterns of English learners. HISD comprises predominantly racial minority students (61.8% Hispanics, 24% blacks, 8.7% whites, 4% Asians, and <1.5% other race/ethnicity). For all K-12 students in HISD, around 31.5% are identified as having limited English proficiency (LEP); in comparison, the proportion of EL students at the national level is around 10 percent and that in the state of Texas is 17.2 percent (National Center for Education Statistics 2019). Analyses based upon a school district with such a high percentage of EL students will afford a unique opportunity to understand EL students' academic achievement. In this chapter, I attempted to answer the following research questions: 1) How do average learning rates of ELs compare to English proficient students during the summer?
2) How do average learning rates of ELs compare to English proficient students during the academic year?
3) How does home language alter the learning rates, both during the summer and during the academic year? 4) Are the above patterns the same for students at lower grades and those at upper grades?

Dependent Variables
Data for this study were compiled from the following HISD administrative and assessment files for the academic years 2015-16 through 2016-17: Istation's Indicators of Progress (ISIP) test scores in reading, and the Public Education Information Management System (PEIMS) data on student demographic characteristics. The outcome of interest is students' reading achievement, which comes from the ISIP data. The ISIP is a reading assessment administered to students from Pre-K through Grade 8 at three points during the academic year: beginning (September), middle (January), and end (April). The ISIP assessment is an adaptive testing in which test scores are vertically scaled to better describe student academic growth over time. Although math is an essential component of academic achievement as well, lack of math tests at the beginning of the academic year prevented a parallel test of math performance. Reading scores at the four time points enable me to capture both academic year and summer learning rates. Note that students were not tested exactly on the first day of school nor on the last day of school, and test dates varied by school. In fact, students were tested several weeks after the start of the school year and several weeks before the end of the school year, and the testing window was about two weeks long, both in the fall and in the spring. This means that the amount of time between the spring test date and the fall test date of the following academic year was about five months, significantly longer than the actual summer break of three months. To obtain a more accurate estimate of summer learning, the reading scores were extrapolated to what students would have obtained at the beginning and at the end of the summer. The dependent variables were students' extrapolated ISIP overall reading scores at the four time points.

Explanatory Variables
The key independent variables include Limited English Proficiency (LEP) status and student's home language. LEP status was coded as a dummy variable (0 = Non-LEP, 1 = LEP). The home language variable is a record of the language spoken at each student's household. Because HISD is a district where more than 100 languages are spoken, home language was coded as a dummy variable for the purpose of this analysis.
Students who speak English at home were classified as 0, and those who speak a language other than English at home were assigned to 1.
Other student-level predictors included race/ethnicity, gender, economic disadvantage status, and special education status. Race/ethnicity was documented based on the racial/ethnic identity that the student reported (1 = white, 2 = Hispanic, 3 = black, 4 = Asian). Gender is coded as a dummy variable (0 = male, 1 = female). Economic disadvantage status was also a dummy variable (0 = non-disadvantaged; 1 = economically disadvantaged, including being eligible for free/reduced-price lunch or in poverty status 1 ). Special education information was available for students who had a cognitive disability (1 = receive special education, 0 = do not receive special education).
Magnet program was also a dummy variable (1 = in a magnet program, 0 = not in a magnet program). Grade level was determined by the grade that the student attended in the 2015-16 academic year, which included grades 1, 2, 4, 5, and 6. The ISIP tests adopt different grading scales for grades 1-3 (under 300 points) and grades 4-8 (above 1,500 points). As such, students in grade 3 during the 2015-16 academic year were eliminated due to the difficulty in assessing their progress toward grade 4 because of inconsistent grading scales.

Sample and Descriptive Statistics
As mentioned earlier, I limited my analytical sample to students in grades 1 through 6 (except grade 3) during the 2015-16 academic year and assessed them through their subsequent grades. I also dropped students without complete testing scores at the four points. That is, every student in the sample had no missing values in the four ISIP reading scores. Furthermore, I dropped students who self-identified as Native Indians, Pacific Islanders, and multiracial, which constituted less than two percent of the total student population. The final analytical sample for analysis includes 140,080 observations of 35,020 students during the two-year period. In the analytical sample, the student population was predominantly Hispanics (61%) and blacks (22.9%), with the remaining 16 percent consisting of whites and Asians. The sample included almost equal numbers of female and male students. About 77.8 percent were identified as economically disadvantaged, 36.8 percent were enrolled in magnet programs and 6.8 percent were entitled to special education. In general, there are more students in the lower grades than in the upper grades. Approximately one in five students had limited English proficiency, and almost one in two students lives in households where English is not the primary language spoken.
To better understand how home language is associated with students' English proficiency, Figure 2-1 shows the percentage of students in English proficiency and home language groups. Students who are English proficient and live in English-speaking homes constitute more than half of the sample. Approximately 21.4 percent of students come from homes where English is not primarily spoken but are English proficient. A similar proportion of the students has limited English proficiency and lives in homes where a language other than English is primarily spoken. Note that a very small percentage of students comes from English-speaking households but has limited English proficiency, which aligns with the literature (National Center for Education Statistics 2019).    As noted previously, HISD is a school district where more than 100 languages are spoken. Among all home languages other English, Spanish is the most common language, followed by Chinese (including Mandarin, Cantonese, and other dialects), Vietnamese, and Arabic. Figure 2-2 presents the distribution of English proficiency status across the four language groups. Spanish-speaking students have the highest EL rate (54.81%), and Chinese-speaking students have the lowest EL rate (12.54%).
Vietnamese-speaking students also have a relatively low percentage (23.86%) of EL students, and the Arabic-speaking students have a relatively high rate of EL students.

Figure 2-2 -Percentage of English Proficiency for Top Four Non-English Home
Languages.

Method
The main research questions focus on how EL and non-EL students' reading outcomes change over time. Taking advantage of the multiple observations of reading scores for each student, a Piecewise Linear Model (PLM) was specified to fit an individual learning trajectory as each student progressed through two sequential school years and the summer in-between. The ISIP reading scores were modeled as repeated observations (level one) nested within students (level two). Instead of assuming students had a steady trajectory across time, a PLM allowed the trajectories to differ in each phase in terms of learning rates (Raudenbush and Bryk 2002 In the PLM analysis, reading score growth was divided into three separate parameters. Time 1 was coded as 0 prior to entry into grade 1, and coded as 9 at the end of grade 1 (9 represents 9 months in the first academic year). The parameter of Time 1 was held constant (at 9) when this student entered into the summer. Again, Time 2 was coded as 0 prior to the summer and coded as 3 after the summer (3 indicates 3 months in the summer). The parameters of Time 1 (at 9) and Time 2 (at 3) were both held constant when the student entered grade 2. In other words, the parameters for each time variable change only when the student enters into a different time period.
The analyses were conducted in five steps. First, I ran a model to map the overall gains of reading ability during the summer without the timing variables and students' demographic and background variables (except for EL status and home language) controlled. Second, I included EL status as a predictor of students' reading achievement.
Next, I estimated the effects of home language on reading outcomes by adding home language into the analysis. Finally, I manually created a new variable consisting of the three interactions between home language and EL status (1 = non-EL & English home, 2 = non-EL & non-English home, 3 = EL & non-English home) 2 , and then added interaction terms between the constructed variable and timing variables into the analyses.
As can be seen from Table 2-2, lower grades and upper grades display quite different distributions of ELs and non-ELs. Additionally, ISIP testing adopts different grading scales for lower grades and upper grades. Thus, all PLM analyses were run separately for students at lower grades (grades 1 and 2) and those at higher grades (grades 4, 5, and 6). 3 The notation can be written as: Where = (==1, 2, …, X) represents the student population; . (. =1, 2, 3) indicates three phases. !"#$% &' is the measured reading score for student = at phase ., ) ** is the average initial reading score for the entire population. ) ,* , ) 3* , and ) 6* are the learning rates of reading per month in the first grade, summer, and second grade, respectively. 9 ' are student-level predictors, and ) *, is the coefficient for 9 ' . : *' is the variability of the initial reading ability between students that is left unexplained by time, : ,' is the between-person variation around the population-averaged monthly learning rate, and ; &' is the within-person variability of reading scores left unexplained by time.

Results
As stated previously, PLMs were estimated separately for lower grades (grades 1-2) and upper grades (grades 4-6). Results for lower grades are displayed in Table 2-3, and those for upper grades are shown in Table 2-4. Model 1 in Table 2 Since the test grading scales are different for lower and upper grades, I am more interested in the substantive meaning of coefficients within each model and less concerned with the differences in magnitudes of coefficients between Models 1 and 6.
Overall, Models 1 and 6 suggest that students' reading learning rates change faster while they are in school compared to during the summer. Moreover, the covariance between variability in the initial status and the variability in rate of change was positive and significant, indicating that students with higher average initial reading scores tended to experience higher average learning growth. The measures of individual explanatory variables are consistent across Models 1 and 6. Female students had slightly higher reading scores than males. Black students scored lower than white students, and Hispanic students scored even lower. Economic disadvantage, limited English proficiency, and special education were all adversely associated with reading performance; being in a magnet program was positively associated with reading achievement.
Models 2 and 7 added EL status into analyses to see whether EL status affects reading scores and whether previous estimates would change. Controlling for EL status, reading learning rates while school was in session still showed more rapid growth than during the summer. Not surprisingly, EL status is statistically significant and negative, suggesting that ELs enjoyed less gain in reading than non-ELs, both for lower grades and upper grades. After including EL, the relative magnitudes of coefficients reversed between Hispanic and black students. The coefficients of Hispanics in Models 2 and 7 shrank slightly in magnitude compared to Models 1 and 6, and black students now scored the lowest among four racial/ethnic groups. EL status is thus an important contributor to the reading achievement gaps between whites and Hispanics.
Models 3 and 8 examine how home language influences the estimated effects of EL status. Model 3 shows a significant and positive coefficient of home language, suggesting that students at lower grades could benefit somewhat from their home language being other than English. The coefficient of EL status remained its negative sign but increased in magnitude, implying that EL students at lower grades would have lower reading achievement if they lived in English-speaking homes than EL students whose home language is other than English. By contrast, Model 8 presents a nonsignificant coefficient of home language, suggesting that students at higher grades do not benefit from living in a non-English speaking household in terms of their reading achievement.  13.375*** 12.317*** 12.291*** 12.29*** 12.294*** Level-2: correlation between random parts 0.305*** 0.357*** 0.346*** 0.348*** 0.353*** Level-1: within-person 9.725*** 9.725*** 9.729*** 9.729*** 9.719*** Note: † p< .1 * p< .05, ** p< .01, *** p< .001 (two-tailed tests)  Note: † p< .1 * p< .05, ** p< .01, *** p< .001 (two-tailed tests) The difference in estimates of home language in Models 3 and 8 calls for a more nuanced understanding of the intersection of EL status with home language. As already mentioned, I constructed a three-category variable such that EL status is combined with home language (1 = non-EL & English home, 2 = non-EL & non-English home, 3 = EL & non-English home). Note that EL students who live in English-speaking households are excluded from analysis due to the small sample size. Models 4 and 9 replaced the separate EL status and home language variable with this newly constructed variable. As shown in Model 4, English proficient students whose home language was other than English scored significantly higher than the other two groups. EL students who were exposed to non-English home languages scored the lowest among the three groups. In Model 9, English proficient students who were exposed to non-English home languages enjoyed no significant advantages in reading relative to English proficient students who lived in English-speaking homes. EL students who lived in non-English speaking households still scored the lowest compared to the other two groups. Taken together, home language does not matter for reading outcomes of upper grade students as much as that for lower grade students.
To discern how home language combined with EL status to influence students' reading scores over time, interactions between the constructed variable and timing variables were incorporated into Models 5 and 10. Figure 2-3 displays the estimates of interaction effects from Model 5. There is no significant difference in reading learning rates during the academic year between English proficient students living in Englishspeaking homes and EL students who were exposed to non-English home languages.
English proficient students whose primary home language is other than English learned at a markedly higher rate in reading during the academic year than the other two groups.
The interaction during the summer reveals a different pattern. The slightly negative slope of the upper line indicates that English proficient students whose primary home language is other than English experienced a small decline in reading scores during the summer. In addition, EL students in non-English speaking homes tended to catch up a little with their peers over the summer.  two lines are nearly parallel, indicating that English proficient students who live in non-English households do not enjoy an advantage in reading scores, neither during the academic year nor during the summer, compared with their counterparts whose home language is English. Moreover, large gaps in initial reading scores already exist between English proficient students and EL students for upper grades and seemed to change little after that. Even the tiny narrowing gaps during the summer would not make any difference because the gaps persisted as soon as the school year started.

Conclusion and Discussion
The summer learning research has extensively documented the relationship between summertime and class-based and race-based academic achievement gaps. This current study builds on that knowledge and incorporates additional components to summer learning research-specifically, the role of English language proficiency and home language in influencing students' reading achievement over time. The analyses yield three main findings. First, for students at early grades, English proficient students whose home language is other than English score higher in reading than English proficient students who speak English at home and ELs. Thus, speaking English at home does not seem to be harmful and actually benefits lower grade students' reading achievement.
Prior research has demonstrated that obtaining or maintaining English proficiency does not require parental use of English at home (Duursma et al. 2007), and there is a positive relationship between fluency in bilingualism and intellectual development (Zhou and Bankston 1998). This might explain why English proficient students who live in non-English-speaking households do not fall behind their English-home peers in reading. As previous descriptive statistics ( Table 2-2) have shown, the three groups vary in their demographic characteristics such as economic disadvantage status and race/ethnicity.
Although the data available do not allow me to make further investigation, the observed statistics signal that there are substantial social differences between these groups.
A crucial difference could be immigrant generation status. EL students are likely to be first-or 1.5-generation immigrants whose initial language is other than English and have only recently moved to the United States (Duursma et al. 2007), or 1.5-generation immigrants who are raised in non-English-speaking households. Students who live in non-English-speaking families but who have acquired English proficiency might be 1.5or second-generation immigrant children whose parents choose to maintain their bilingual fluency by speaking the second language at home. Students who are both English proficient and live in English-speaking households could either be native speakers or second-generation immigrant children whose parents believe that speaking only English would help them to attain greater social mobility (Grosjean 1982), although this is less likely to be the second case in the recent periods. Another important difference is social class difference. Higher-income immigrant parents may believe bilingualism is a valuable asset and thus make a conscious effort to retain their children's native language, preferring not to speak English at home. For lower-income immigrant parents, it is perhaps that they have arrived in the new country only recently and are not able to speak fluent English themselves.
The second finding that stands out is that, for students at early grades, reading learning gaps between English proficient students whose home language is other than English and the other two groups widen further during the academic year, but not during the summer. Specifically, I find an advantage of home language other than English for English proficient students, who surpass their English-home counterparts in reading learning rates when school is in session. Although English proficient students living in non-English speaking homes might fall slightly behind their English-home peers in reading during the summer, they would quickly catch up as the semester starts.
A third finding derived from the analyses is that the aforementioned results only pertain to students during the early grades. For later grades, no significant differences in reading were observed between English proficient students who speak English at home versus their counterparts who do not speak English at home, both during the academic year and during the summer. The positive effect of non-English home language does not apply to upper grades, possibly because older children tend to have more freedom to hang out outside home. If older children were not exposed to the home environment as much as their younger counterparts, they might not have enjoyed a comparable benefit from non-English home language.
According to previous literature, English learners are expected to experience a summer slide to some extent (Alexander et al. 2016;Cooper et al. 1996). The summer learning patterns for EL students that I found, however, differed from this hypothesis by showing slight learning growth over the summer months. Moreover, despite their overall academic excellence, English proficient students do not enjoy an advantage in reading learning growth over the summer. Thus, there is possibly a tendency for regression to the mean when school is out of session, with high-achieving students declining and lowachieving students improving. Nonetheless, since the amount of growth for EL students is quite limited during the summer, the achievement gaps between EL and non-EL students fail to converge at the end of the summer. In addition, the tiny growth in reading for EL students during the summer cannot obscure the fact that the reading achievement gaps always persist or widen further as students enter into the academic years.
The current study also points to the importance of early childhood education for later educational outcomes (Duncan et al. 2007). My investigation of students' academic trajectories at a younger age (grades 1 and 2) shows that the differences in initial reading achievement are already formed before they start elementary school. The reading achievement disparities widen faster when school is in session than over the summer during the first two years of elementary school. Furthermore, reading learning gaps for students at an older age (grades 4 through 6) remain quite stable over time. If the gaps already emerge at a very young age and grow faster primarily in the first two years of school, then we should direct more attention to differences in early childhood education and formal schooling for early grade children.

Seasonal Change of Neighborhood Effects on Educational Achievement
This chapter addresses two gaps in the literature. First, summer learning scholars have long demonstrated that family socioeconomic status is the main driver of summer learning, but they fail to account for potential neighborhood effects on summer learning.
Second, urban scholars consistently have shown that neighborhood context plays a crucial role in children's cognitive development and students' academic performance, but they have rarely considered seasonal changes in neighborhood effects. I fill these gaps by assessing neighborhood effects on elementary and middle school students' learning rates in the summer and in the academic year, using 3-level piecewise linear models with neighborhood characteristics incorporated. Results indicated that concentrated disadvantage and violent crime have stronger effects on students' reading outcomes during the academic year than in the summer.

Introduction
Students from poor families often experience more summer learning loss than those from more advantaged backgrounds because school resources are cut off when school is out of session (Entwisle and Alexander 2007;Heyns 1978). Compared to highincome parents, low-income parents are not able to provide the same amount of learning support to their children (Entwisle and Alexander 1992). When summer ends, children from low-income families fall behind their peers in educational outcomes, due to their discontinuous study and unstructured summer leisure activities. Despite the increased attention on this issue and unremitting efforts to mitigate summer learning loss, scholars have not recognized the importance of neighborhood context in predicting summer learning differences.
In this chapter, I argue that to understand why students' educational achievement changes by season, scholars should consider how neighborhood characteristics operate above and beyond how family backgrounds are associated with educational achievement.
Although families are extremely important in student educational achievement, residential context is a nonnegligible factor in shaping students' summer learning activities. Drawing on a variety of data sources, I examined how mechanisms of the neighborhood context-the residential location in which students reside-played a role in student academic outcomes not only during the academic year, but also over the summer.
The findings have strong implications for how we understand summer learning and neighborhood effects as a whole. Summer learning scholars typically focus on summer learning disparities stemming from family class differences, but there is reason to expect that neighborhood differences may also contribute to unequal summer learning.
In addition, much of the urban scholarship focuses on the temporal or cumulative effects of neighborhood disadvantage but has yet considered seasonal changes in neighborhood effects on student achievement. This chapter provides an avenue to connect the two literatures by investigating whether neighborhoods influence students' reading performance differently during the summer compared to the academic year.

Family Background and Summer Learning
Prior research suggests that summer learning gaps should be largely a function of family's social class position (Alexander et al. 2007;Entwisle and Alexander 1992;Gershenson 2013;Heyns 1978). The famous metaphor-"faucet theory"-has been used to illustrate that school calendar controls the "on and off" of school resources (Alexander et al. 2007;Entwisle and Alexander 1992). When the faucet is on, a family's social class position is less salient in shaping students' academic performance, because school resources are available to all students. When summer comes, however, the faucet is switched off and family class background becomes more important. Without school resources, children from middle-class families draw on family resources to continue and advance their study during the summer, while working-class children lose ground due to lack of family resources.
High-socioeconomic status (SES) family means more than extra learning resources. Many mechanisms underlie the association between family social class position and students' summer learning, such as investment models, parenting practices, parental psychological resources, stress in the home, and summer school (Borman et al. 2005). First, the investment model suggests that parents' material wealth and time use are associated with their ability to invest in child development (Becker and Tomes 1986).
Second, high-SES parents may employ age-specific parenting strategies that promote children's cognitive development (Entwisle et al. 1997;Heyns 1978). Third, the parental psychological resources mechanism suggests that high-SES parents tend to have higher expectations for their children's educational attainment, and hence are more likely to engage their children in summer learning activities. These higher expectations are positively related to students' educational expectations and academic performance (Entwisle et al. 1997). Fourth, low-income children are exposed more to the stress and other negative experiences at home during summer, a time when schools are not able to buffer or compensate for such jeopardies arising from home (DuBois et al. 1992(DuBois et al. , 1994Entwisle et al. 1997). Finally, high-SES children are likely to benefit more from summer school (Cooper et al. 2000), perhaps because students from different backgrounds are offered different types of summer programs or because parents' attitudes toward summer school vary, which in turn affects student achievement (Harrington-Lueker 2000). These mechanisms may operate simultaneously to produce students' learning inequalities during the summer.

Neighborhood Effects and Summer Learning
Although family influences are paramount for student achievement and summer learning in particular, the neighborhood environment also is likely to be significant and vary by season. Neighborhoods are an important lens through which to investigate causal processes and social mechanisms (Sampson 2011a(Sampson , 2011b. Neighborhood effects, however, have always been understood in the narrow sense that a neighborhood can only exercise its influence through "face-to-face" daily interaction (Sampson 2011b: 229). As a result, many scholars typically ignore neighborhood effects when they believe their research subjects rarely engage in neighborhood activities or have few ties with their neighbors. However, Sampson (2011b) suggests we understand neighborhood effects in a broader sense and treat neighborhoods not only as a physical entity but also the site upon which a variety of social processes take place.
In the urban literature, scholars have identified several mechanisms through which neighborhoods influence students' academic performance, including concentrated disadvantage, social (dis)organization, neighborhood learning resources, and physical environment (Ainsworth 2002;Massey and Denton 1993;Sampson 2011b;Wilson 1987Wilson , 1996Wodtke et al. 2011). Concentrated disadvantage is a primary mechanism of neighborhood effects and affects academic achievement in several ways. First, neighborhood poverty is associated with parental mental health such that moving from a high-poverty neighborhood to a relatively low-poverty neighborhood significantly improves caregivers' mental health, especially among mothers (Sampson 1997). Positive mental health contributes to better parenting practices, and this in turn, could benefit children's cognitive development. Second, social isolation theory suggests that poor, racial-minority neighborhoods are often disconnected from the mainstream society (Jencks et al. 1990;Wilson 1987). Due to the disconnectedness, children and adolescents living in these neighborhoods tend to lack "role models," someone who plays a central role in encouraging them to engage in school work and reminding them of the link between school success and future career development. A related theory considers linguistic isolation (Massey and Denton 1993;Ogbu 1999). Living in a segregated immigrant or racial/ethnic neighborhood may limit children's access to English or academic English, which is directly connected to their literacy performance in school.
Social organization theory highlights the importance of social cohesion in regulating deviant behaviors (Sampson 2011b). In neighborhoods with high levels of social cohesion, resident adults usually have strong intention to supervise delinquency and exercise informal social control of crime. By contrast, in neighborhoods with low levels of social cohesion, youngsters or adolescents are likely to engage in deviant behaviors that are highly correlated with grade retention, high school dropouts, or other negative school outcomes (Wodtke et al. 2011). Even if youths do not engage in delinquency or crime, they might be indirectly impaired by a lack of collective efficacy.
In violent neighborhood environments, the fear and stress of parents may cause them to shield their children's direct interaction with neighbors; this could jeopardize children's opportunities for language and social skill development (Morenoff 2003;Sampson et al. 2008).
The third mechanism-neighborhood learning resources-emphasizes the institutional support for learning that a neighborhood provides to residents ( Directly, proximity to freeways and chemical plants or residing in deteriorated housing increases residents' exposure to toxicities, especially air pollutants. Long-term exposure to toxicities is likely to negatively impact children's health and consequently disrupt progression through school (Wodtke et al. 2011). Indirectly, physical environments, such as proximity to parks, shape and enable children's recreational activities (Kaczynski and Henderson 2008).

Seasonality of Neighborhood Effects
Urban scholars have extensively investigated neighborhood effects-both temporary and cumulative effects-on student academic achievement (Ainsworth 2002;Sampson 2011b;Wilson 1987;Wodtake et al. 2011). However, they have yet to recognize the seasonal changes of neighborhood effects on academic achievement (Pallas 2016). Neighborhood effects on students' academic achievement might differ when school is in session versus over the summer because summertime increases students' exposure to neighborhood environments, and neighborhood environments are likely to change during the summer months. Specifically, there are two possible ways through which neighborhood effects change with the seasons (Pallas 2016). One is that students' access to non-profit services might differ by season, in part because non-profit services such as after-school programs may only be available when school is in session (Pallas 2016). Because underprivileged students often rely more on non-profit services compared to middle-class students, they are more likely to be impacted when such resources are cut off during the summer. This view echoes the faucet theory (Alexander et al. 2007;Entwisle and Alexander 1992) by arguing that school calendars not only regulate the on and off switch of school resources but also non-school resources.
An alternative explanation for the seasonality of neighborhood effects is related to social organization theory. Because violent crime often peaks during the warmer months (Ceccato 2005;Quetelet 2013) and summer increases children's time spent at home, parents in crime-ridden neighborhoods tend to reduce their children's exposure to their neighborhoods and "regulate their behavior more rigorously" over the summer than during the school year (Pallas 2016). The isolation from potential violence, however, might also lead to isolation from supporting social networks embedded in the neighborhood community (Pallas 2016) or perhaps influence children's normal social interactions with peers and hence limit their vocabulary development (Sampson et al. 2008).
To date, what Pallas (2016) has offered are simply hypotheses, and no empirical study has examined how neighborhood effects on academic achievement differ by seasons. As such, there is an urgent need to incorporate neighborhood effects into summer learning studies, as well as to consider seasonal change of neighborhood effects.
In this chapter, I attempt to bridge the summer learning and neighborhood effects literature to address the respective gaps in both subfields. I examined the seasonal effects of neighborhood environment on students' reading learning rates. The analysis elucidates the mechanisms mediating neighborhood effects and student academic outcomes by addressing the following research questions: (1) With neighborhood characteristics controlled, how do students' reading scores change when they are in schools versus out (summer)?
(2) How is the predictive utility of neighborhood-level factors different from when school is in session?

Reading Learning Rate
In this study, the outcome of interest is students' reading learning trajectory. I used the Istation's Indicators of Progress (ISIP) data provided by the Houston Independent School District (HISD), which is the seventh largest school district in the United States and enrolls more than 210,000 students in 10 early childhood schools, 153 elementary schools, 37 middle schools, 40 high schools, and 43 combined/other schools.
HISD is comprised of predominantly racial minority students who likely reside in neighborhoods with disadvantaged conditions compared to school districts predominantly comprised of white students. Analyses based upon this particular school district will provide unique insights into neighborhood effects on summer learning. The ISIP data include students' (from Pre-K to Grade 8) reading scores at three points during the academic year: beginning (September), middle (January), and end (April). Information on reading scores at the beginning and end of academic years (for two years) allowed me to

Demographic Characteristics
Student-level predictors included race/ethnicity, gender, economic disadvantage status, limited English proficiency, and special education status. Race/ethnicity was documented based on the racial/ethnic identity that the student reported (1 = white, 2 = Hispanic, 3 = black, 4 = Asian). Gender is coded as a dummy variable (0 = male, 1 = female). Economic disadvantage status was also a dummy variable (0 = nondisadvantaged; 1 = economically disadvantaged, including being eligible for free/reduced-price lunch or in poverty status 4 ). Limited English Proficiency (LEP) status was coded as a dummy variable (0 = Non-LEP, 1 = LEP). Special education information was available for students who had a cognitive disability (1 = receive special education, 0 = do not receive special education). Magnet program was also a dummy variable (1 = in a magnet program, 0 = not in a magnet program). Grade level was counted by the grade that the student attended in the 2015-16 academic year, which included grades 1, 2, 4, 5, 6, and 7. The ISIP tests adopt different grading scales for grades 1-3 (under 300 points) and grades 4-8 (above 1,500 points). As such, students in grade 3 during the 2015-16 academic year were eliminated due to the difficulty in assessing their progress toward grade 4 because of inconsistent grading scales.

Neighborhood Characteristics
To obtain students' residential neighborhood information (e.g., racial composition, neighborhood poverty status), students' home addresses were geocoded and The four mechanisms through which neighborhoods influence students' academic achievement-concentrated disadvantage, social (dis)organization, neighborhood resources, and physical environment-are measured in the following ways. Concentrated disadvantage is comprised of six elements: percentage of households living in poverty, percentage of adults (25 years old or above) without a high school degree, percentage of households headed by a single female, reverse-scored percentage of employed residents (16 years old or above) holding a professional or managerial job, percentage of Hispanic households, and percentage of households not speaking English at home. A single concentrated disadvantage index was constructed from the six elements using principal component analysis-a data reduction technique to capture the variance among variables (Sampson et al. 2008). Higher values of the concentrated disadvantage index indicate higher levels of disadvantage embedded in a neighborhood.
Social organization is conceptualized as a neighborhood having a lower violent crime rate. Following Peterson and Krivo's (2010) definition of crime, I estimated violent crime by aggregating aggravated assault, murder, rape, and robbery for 3-year periods (2015)(2016)(2017) in each block group and calculating the violent crime rate (i.e., the total number of violent crime incidences per 1,000 residents). The resulting violent crime rate was highly right skewed, partly because some block groups had only a few residents. To reduce the right skewness and non-normality, I took the natural log of the violent crime rate (Graif 2015, Burdick-Will 2017. It is worth noting that log transformations of zero value result in "missing" values in the log transformed crime rate. This would cause a reduction of sample size and bias of estimation when taking neighborhood factors into account. Therefore, I added 1 to the number of violent crime incidences in each block group and then did a natural log transformation. For neighborhood resources, I drew neighborhood learning resources data from 2016 Infogroup's U.S. business database. Infogroup is a for-profit organization that provides geocoded business information. The Infogroup database is organized based upon the U.S. government's standard industrial classification coding system, and every business has been verified via phone call to confirm its operation status (Liesch et al. 2015). Such information allows for a more accurate measure of neighborhood learning resources. I aggregated the following amenities/facilities: libraries, museums, youth facilities, bookstores, and religious organizations. As with violent crime rates, a value of 1 was added to the raw number of learning resources before doing the natural log transformation to reduce its skewness.
Physical environment of a neighborhood was measured using 2016 Risk-Screening Environmental Indicators (RSEI) Block Group Microdata. RSEI offers healthrelated risks from air toxic releases that have been reported by certain industrial facilities to Toxics Release Inventory (TRI). 5 It incorporates estimates from the TRI on "the amount of toxic chemicals released, along with factors such as the chemical's fate and 5 A facility needs to report to TRI if it is (a) in a covered industry sector based on the North American Industry Classification System (NAICS) codes; and (b) exceeds the established employee and chemical thresholds. The covered industries include mining, utilities, manufacturing, all other miscellaneous manufacturing, merchant wholesalers, non-durable goods, wholesale electronic markets and agents brokers, publishing, hazardous waste, and federal facilities. transport through the environment, each chemical's relative toxicity, and potential human exposure" (Documentation for RSEI Geographic Microdata 2017). However, RSEI is subject to limitations from the original data sources-TRI data. For example, TRI data only provide releases from certain industrial facilities and thus do not capture toxic releases from other sources, such as small industrial facilities and Superfund sites (Documentation for RSEI Geographic Microdata 2017).

Sample Restriction and Missing Data
As mentioned earlier, I limited my sample to students in grades 1 through 7 (except grade 3) during the 2015-16 academic year and assessed them through their subsequent grades. I also dropped students without complete testing scores at the four points. That is, every student in the sample had no missing values in the four ISIP reading scores. Furthermore, I dropped students who self-identified as Native Indians, Pacific Islanders, and multiracial, which constituted less than two percent of the total student population. This left me with a sample size of 40,040 students. Among the 40,040 students, less than 1.5 percent lacked of a valid geocode and thus could not be matched to neighborhood files. Less than 1.5 percent had missing information on crime even if they had a valid geocode. The analyses excluded students with missing data on any neighborhood characteristics. The final sample size was 38,923 students nested within 1,096 block groups.

Method
A Piecewise Linear Model (PLM) was specified to fit an individual learning trajectory for each student as he/she progressed through two sequential school years and the summer in-between. A three-level PLM allowed the trajectories to differ in each phase in terms of learning rates, while taking account of both neighborhood-level and student-level predictors. The ISIP reading scores were modeled as repeated observations (level one) nested within students (level two), and students were nested within neighborhoods (level three). Average summer learning rates were estimated using the difference between the test score at the beginning of the 2016-17 fall semester and the score at the end of the previous 2015-16 spring semester, divided by the number of summer months.
The analyses were conducted in four steps. First, I ran a baseline model to map the overall gains of reading ability during the summer without any predictors. Second, I included all the student-level variables as predictors of reading ability. These studentlevel variables were included to examine how much of the variation in reading ability could be attributed to between-student differences in these characteristics. Next, I estimated the neighborhood effects on reading ability by adding neighborhood-level variables into the analysis. Finally, interaction terms between neighborhood predictors and time of assessment were added into analyses separately. The notation can be written as:

Figure 3-1 -Average Monthly Learning Rates of Reading
The findings from piecewise linear models are presented in Table 3-2. Model 1 depicts the unconditional growth model with three phases as the only predictor. On average, students' reading scores increased 6.853 points each month in the 2015-16 academic year compared to 0.557 points per month during the summer and 4.376 points per month in the 2016-17 academic year. This suggests that students' reading learning rates change faster when they are in school compared to not in school (i.e., during the summer). Moreover, the covariance between between-neighborhood variability in the initial status and the variability in rate of change was positive and significant, indicating that students who reside in neighborhoods with higher average initial reading scores also tended to have higher learning rates. The significant positive covariance between withinneighborhood between-person variability in the initial status and the variation in rate of change suggests that, even in the same neighborhood, students with higher initial reading achievement experience faster learning growth. Figure 3-1 plots the predicted learning rates of reading in three phases, derived from the estimates in Model 1.
Model 2 specified a piecewise linear model with all the individual variables taken into account. Controlling for student-level factors, reading learning rates while school was in session still showed more rapid growth than during the summer. The magnitude of change in reading learning rates was slightly smaller compared to that in Model 1, indicating that some of the educational differences found in Model 1 can be attributed to individual background differences. All individual covariates were statistically significant at the .05 level. Female students had slightly higher reading scores than male students.
Compared to white students, Hispanic and black students had lower reading scores.
Consistent with prior literature, economic disadvantage, limited English proficiency, and special education were all negatively associated with reading performance; being in a magnet program was positively associated with reading achievement. Also worth noting is the reduction of random estimates. Compared to the between-neighborhood variation in initial reading ability in Model 2, accounting for student-level covariates explain the bulk (80.57%) of the between-neighborhood variation in reading ability. In addition, 24.6% of the within-neighborhood between-person variation was explained by individual background. all significantly associated with reading learning rates. The coefficients suggest that students who resided in a worse-off neighborhood were likely to have lower reading achievement. The coefficient of average toxicity-weighted concentration is negative but not statistically significant, suggesting higher toxicity concentration at the block group does not significantly predict lower reading scores. As indicated by the reductions in the magnitudes of learning rates, between-neighborhood variation, and within-neighborhood between-person variation, a significant portion of the reading achievement differences were explained by accounting for neighborhood contexts.
To determine whether neighborhood effects varied by season, Models 4 through 6 incorporated interactions between the timing variable and the three significant neighborhood covariates-concentrated disadvantage, neighborhood learning resources, and violent crime rate-separately, because estimating the three interactions simultaneously would dramatically complicate the analyses. In Model 4, the main effect of concentrated disadvantage persisted when interaction terms were added into the model.
The interaction terms between concentrated disadvantage and the three timing variables were all significant, providing evidence that concentrated disadvantage yielded different effects across time. Specifically, the interaction between concentrated disadvantage and academic year was negative, and the interaction between concentrated disadvantage and summer was positive. This suggests that concentrated disadvantage was a larger predictor of reading learning rates while school was in session than during the summer months. To see the patterns more clearly, Figure 3-2 compares the predicted reading learning rates by different concentrated disadvantage levels based on estimates from Model 4 separately for students residing in neighborhoods with concentrated disadvantage at the 25th and 75th percentile. In Model 6, the interactions between neighborhood learning resources and timing were not significant, suggesting that the effects of learning resources on students' reading outcomes do not vary by season.

Figure 3-3 -Interaction Effects Between Timing and Violent Crime Rate.
In summary, findings lend strong support to the hypothesis that neighborhood effects on reading ability change across seasons. Among the four neighborhood predictors, the seasonal changes of neighborhood effects were more prominent with respect to concentrated disadvantage and violent crime rate. Furthermore, results indicated that concentrated disadvantage and high crime rate were more harmful during the academic year than over the summer. Although neighborhood learning resources were significantly associated with higher students' reading achievement, their effects did not vary by season. Finally, air quality made little difference on reading achievement for the students under study. Results provide clear evidence that neighborhood contexts matter for student achievement gaps, and the academic year is the key time when neighborhood characteristics generate unequal reading outcomes for students. Fourth, the school calendar might control the faucet of course-related resources and services provided by neighborhoods. Pallas (2016) hypothesized that non-profit services might be more available during the academic year, and lower-class students are more vulnerable from the cutoff of these resources during the summer as they rely more heavily on these resources than middle-class students. Although this hypothesis makes sense, my findings point to an alternative explanation. Namely, not only would non-profit services be more available during the academic year, for-profit services might also be more available while school is in session. Middle-class students' dependence on forprofit school-related services might explain their faster reading learning rates during the academic year. In this case, it is not the existence of neighborhood resources/services per se that generate achievement gaps, but unequal distribution of course-oriented services across neighborhoods while school in session. If students, no matter of their class status, are more likely to engage in neighborhood-based activities during the academic year, greater neighborhood effects on educational achievement will be observed.

Conclusion and Discussions
Last, the testing form of the reading test used in the current study might also explain why neighborhood effects are stronger during the academic school year. von Hippel and Hamrock (2019) note that a common measurement artifact is present in many previous studies on summer learning, including some of the most foundational work in the field. For example, in the Baltimore study, students were administered the same test form in the fall and spring of an academic year. After the summer, however, students were switched to a more difficult test form. Therefore, it is not surprising to observe a substantial summer slide given the two different forms used before and after summer.
Modern testing solves this problem by adopting adaptive techniques (Gershon 2005 . "Summer stagnation" is so extreme that even neighborhood contexts would not make a difference. This being the case, the seasonal changes of neighborhood effects is a reflection of seasonal changes of students' learning rates.
There are several limitations and caveats of the study that need to be acknowledged when interpreting the findings. First, students without any of the four reading test scores were eliminated from the analyses. Missing a test score likely occurred because students moved out of the school district under study or were absent due to student illness and health-related matters. If it was the former, eliminating mobile students would possibly over-or under-estimate the neighborhood effects on reading achievement, as mobility could either be driven by high-achieving or low-achieving students. If it was the latter, missingness for health-related reasons is less likely to cause systematic measurement errors in test scores.
Second, measures of neighborhood mechanisms can be proxies for individual characteristics, and the identified neighborhood effects might actually be attributable to unmeasured individual attributes (Owens 2010 A related issue is selection effects, which refers to the idea that individuals might self-select into neighborhoods (Owens 2010;Sampson 2011a). If this is the case, the observed neighborhood effect may be biased, as it could at least partially be attributed to unobserved individual attributes such as parents' expectations. Because it is difficult to rule out the possibility of selection effects, caution is advised when inferring causal effects or generalizing the findings of the current study to other cases. Further inquiries into this issue should consider using causal techniques to validate or invalidate these findings.
Ultimately, the current study speaks to two bodies of research: the summer learning and neighborhood effects literatures. I attempted to expand upon both literatures by simultaneously examining neighborhood mechanisms and students' learning trajectories across seasons. The findings reveal that family background is not enough to explain summer learning patterns, and neighborhood contexts matter differently for students' reading outcomes depending on whether or not school is in session. To my knowledge, this is the first attempt to gauge the seasonal change of neighborhood effects empirically, which could be a promising direction for future research.

Effect of Summer School on Reading: A Binding-Score Regression Discontinuity Analysis
Summer school is a way to supplement the lack of educational resources over the summer break, aiming to reduce the summer setback and decrease the academic achievement gaps between groups. In this chapter, I first discuss previous studies on the effects of summer school and the methodological challenges that might distort the identification of causal effects. Next, I present two regression discontinuity designs to estimate the effect of being assigned to summer school and the effect of actually attending summer school. Results suggest that students who were at the margin of summer school eligibility did not benefit significantly from summer school. This study extends our understanding of the remedial summer school effects for elementary and middle school students. It demonstrates that both program duration and specific subject of instruction are crucial for summer school effectiveness.

Introduction
Educational achievement gaps change by season. Although students from different class backgrounds learn at similar rates while school is in session, they learn at very different rates over the summer (Entwisle et al. 1997;Downey et al. 2004).
Recognizing the importance of summertime for students' academic achievement, schools have widely adopted various kinds of summer programs throughout the United States (Cooper 2000;Matsudaira 2008). For instance, Summerbridge is a voluntary enrichment summer program founded in San Francisco and has gradually expanded to 16 states (Laird and Feldman 2004). Since the first mandatory summer school was adopted by Chicago Public School System in 1996, school districts in many other cities have followed in its footsteps (Matsudaira 2008).
In spite of the wide range of summer programs, scholars have attempted to capture the general effects of summer programs. Meta-analyses find that summer programs geared to remove learning deficiencies or accelerate learning have positive effects on students' learning (Cooper et al. 2000;McEachin et al. 2016). Overall, the positive effects range from one seventh to one quarter of a standard deviation.
Nonetheless, the causal link between summer programs and improved educational attainment has been only weakly supported: most studies simply compare pre-versus post-program outcomes without enough controls for pre-program differences (Cooper et al. 2000).
This study aims to provide a thorough evaluation of the causal effects of remedial summer school in the Houston Independent School District (HISD) by answering the following research questions. How does being assigned to HISD summer school influence students' reading outcomes? How does actually participating in HISD summer school influence students' reading outcomes? Using data from HISD, two regression discontinuity designs will be conducted to compare the effects of HISD summer school for students who are just above the cutoff point for summer school eligibility to those who are just below.

Summer Setback in the United States
Summer setback has been documented as early as the 1970s, when the family background of students was found to have more to do with summer learning than learning during the academic year (Heyns 1978). Moreover, summer learning loss accumulates throughout the school years rather than gradually disappearing (Entwisle and Alexander 2007;Alexander et al. 2016). For instance, students' academic disadvantages in the first year of high school could probably be traced back to their learning losses over the elementary school years (Alexander et al. 2016).

Socioeconomic and Ethnoracial Disparities in Summer Learning
Educational scholars have long been interested in the association between students' socioeconomic background and their academic achievement. In similar fashion, summer learning researchers are also concerned with whether summer break plays a role in shaping students' socioeconomic-based achievement gaps (Heyns 1978;Entwisle and Alexander 1992;Burkam et al. 2004;Downey et al. 2004;Quinn 2014). There has been consensus among scholars that socioeconomic status has a disproportionate influence on children's learning opportunities and outcomes during the summer, and socioeconomicbased achievement gaps grow faster over the summer than during the school year (Entwisle and Alexander 1992;Burkam et al. 2004;Downey et al. 2004). While lowerincome and higher-income students learn roughly at the same rates when school is in session, lower-income students tend to fall behind their higher-income counterparts when summer comes.
Although scholars largely agree upon the association between SES-based achievement gaps and summer break, whether summer contributes to race-based achievement gaps has been contested (Burkam et al. 2004;Downey et al. 2004;Cheadle 2008;Benson and Borman 2010;Quinn 2014). The findings have been split into two camps, one which suggests that white/black achievement gaps mainly widen during the school year (Downey et al. 2004;Cheadle 2008;Benson and Borman 2010), and another that suggests white/black achievement gaps not only grow during the school year, but also enlarge over the summer (Burkam et al. 2004). Researchers who study white/black summer learning gaps, however, have only mapped the general patterns without providing plausible explanations (Condron 2009).

Summer Programs as Support for Summer Learning
As summer learning research develops, educators and policymakers have gradually recognized the importance of summertime in students' cognitive development and academic achievement (Borman et al. 2016). Various kinds of summer interventions have been implemented throughout the country, especially geared toward students from disadvantaged backgrounds (Cooper et al. 2000;McEachin et al. 2016). At the national level, summer interventions can be grouped into three categories: remedial summer programs, voluntary summer programs, and at-home summer interventions . Remedial summer programs are generally classroom based and mandatory for low-performing students to avoid getting retained. Voluntary summer programs are also classroom based, but students are free to choose whether to attend considering nonparticipation is not associated with their promotion statuses. At-home interventions usually encourage students to maintain reading or self-learning at home by equipping them with books, tools or incentives over the summer (Guryan et al. 2016).
Researchers have presented three ways to measure whether a summer program is successful (Cooper et al. 2000;Stein and Fonseca 2016). The first one is "percentagemastery criterion," which simply assesses the percentage of students completing a course that is either specific or failed during the summer program. If the assessed percentage exceeds the goal set by program designers or evaluators, the program is considered to be effective. This criterion is rarely used by researchers because the percentage goal usually involves substantial subjective judgment, and it may be the case that the student simply completing the course during the summer may be no more likely to obtain higher academic performance than similar students who do to take the course during the summer.
Two other measures are more commonly used by scholars, both of which use comparison techniques (Kim 2006;Borman and Dowling 2006;Matsudaira 2008;Kim and Quinn 2013;Mariano and Martorell 2013). The first of these two measures compares a student's academic achievement prior to the summer program with one's academic achievement after summer intervention, while the second one compares the academic achievements of students who have attended summer programs with those who have not.
These designs are more reasonable than the "percentage-mastery criterion," but each of these two measures has its own constraints, and caution is warranted when interpreting the results (Cooper et al. 2000;Stein and Fonseca 2016).
Because of the wide range of summer programs and different evaluation techniques, scholars have attempted to identify the general effects of summer programs.
Meta-analyses find that summer programs (including both mandatory and voluntary summer programs) geared to remove learning deficiencies or accelerate learning have positive effects on students' learning (Cooper et al. 2000;McEachin et al. 2016).
Additionally, middle-class students tend to benefit more from summer programs compared to those from lower social class backgrounds (Cooper et al. 2000;. Nonetheless, the causal link between summer program and improved educational attainment is weakly supported: most studies simply compare pre-versus post-program outcomes without enough control for pre-program differences (Cooper et al. 2000). Therefore, this study aims to examine the causal effects of summer school in the Houston Independent School District (HISD) by carefully taking pre-program differences into account.

Data and Context
Each year, the HISD offers a summer education program to assist students with a variety of instructional needs. The 2016 summer education program provided students the opportunity to repeat required courses needed for promotion, to get ahead by taking required courses before the next school year, or to receive specialized instruction based In addition, students at all grade levels must have sufficient attendance (a student's total number of unexcused absences cannot exceed 10% of class meetings) to avoid retention.
It should be noted that three committees-the Grade Placement Committee (GPC), 8 the Admission, Review, and Dismissal (ARD) Committee, 9 and the Attendance Committee 10 -have the authority to promote a student who has not met the above standards. At the end of a regular school year, any student who has neither met all the promotion criteria nor been promoted by the three committees shall be retained unless they make up their deficiencies in summer programs offered by the school district.
Although HISD summer school is geared towards retained students, promoted students could voluntarily attend summer school for enrichment purposes. It should be noted that promoted students who marginally fail are more likely to attend summer school than other promoted students, because their schools/teachers tend to strongly recommend they do so.
The ISIP data include students' (from Pre-K to Grade 8) reading abilities at three points during the academic year: beginning (September), middle (January), and end (April). Information on reading scores at the beginning of the academic year allows me to focus on students' achievement during the summer specifically. I will restrict my sample to students of grades 1 through 7 during the 2015-16 academic year and follow them through their subsequent grades in the next academic year. The ISIP tests use different 8 The function of the GPC is to make decisions on an individual student basis to ensure the most effective way to support the student's academic achievement for those students who have not satisfied all promotion standards and to address parents' appeals of retainment decisions. The GPC is composed of the principal or principal's designee, the student's parent or guardian, and the student's teacher(s) of the subject of the grade advancement test(s) on which the student has failed to demonstrate proficiency. 9 The ARD Committee determines appropriate assessment and acceleration options for each eligible student with disabilities. 10 The responsibility of the school's Attendance Committee is to address any appeals related to a student's retention brought about by excessive unexcused absences under the district's current attendance policy.
grading scales for grades 1-3 (under 300 points) and grades 4-8 (above 1500 points). To make the comparison across grade levels possible, the ISIP reading scores will be standardized by grade level.
Students are not tested exactly on the first day of school nor on the last day of school, and test dates vary by school. Students are tested several weeks after the start of the school year and several weeks before the end of the school year, and the testing window is about two weeks long, both in the fall and in the spring. This means that the amount of time between the spring test date and the fall test date of the following academic year is about five months, significantly longer than the actual summer break which is only three months long. That is to say, the estimated amount of summer time does not only contain students' learning during the summer, but also includes at least one month's learning at school. This means that estimates of summer learning are usually overestimated because students have had the chance to review a little before being tested.
Previous scholars are prone to address this issue by extrapolating the scores that would have been obtained at the first and last day of the academic year, based on students' learning rates during the school years (Downey et al. 2004). To get a more realistic estimate of summer learning, I will follow the same strategy to extrapolate students' reading scores at the first and last day of the school year. The dependent variables will be students' extrapolated ISIP overall reading scores at the beginning of the 2016-17 academic year. Note that for some students an extrapolated fall score is not available due to lack of a spring score (because of changing schools or dropping out) and thus they lack of a learning rate to serve as the basis of extrapolation. For these students, raw reading scores rather than extrapolated ones will be used as dependent variables. My key independent variable is summer school attendance, which is a dummy variable (1=attend, 0=not attend). Whether a student has attended summer school was identified by using variables from the 2015-16 Promotion Standards data. Students with non-missing information on either summer campus ID, present days, or absent days were categorized as program attendees; otherwise, they were categorized as ones who did not attend. The other independent variables include race/ethnicity, gender, economic disadvantage status, limited English proficiency, and special education status.
Race/ethnicity is documented based on the racial/ethnic identity that the student reported (1=white,2=Hispanic,3=black,4=other). Gender is coded as a dummy variable (0=male, 1=female). Economic disadvantage status is also a dummy variable (0=nondisadvantaged, 1=economically disadvantaged, including being eligible for free/reduced-price lunch or in poverty status 11 ). Limited English Proficiency (LEP) status is a dummy variable (1=LEP, 2=Non-LEP). Special education is for students who have cognitive disabilities (1=receive special education, 0=do not receive). Grade level is counted by the grade that the student attended in the 2015-16 academic year, which includes grades 1 through 7.
The base sample includes 79,526 students who were in grades 1 to 7 in the 2015-16 academic year. students, whereas 37.6% were promoted students who did so for enrichment purposes. To be categorized as "in poverty" on the disadvantaged status variable students have to be in a family that receives some form of in-kind or cash transfers from federal and/or state governments and fails to complete the National School Lunch Program (NSLP) application form or in schools do not participate in the NFLP. The naming of the category as "poverty" stems from the fact that these students tend to have poorer outcomes than the other two categories of disadvantaged students (e.g., free and reduced-price lunch eligible). The district tends to group all three disadvantaged categories together.

Regression Discontinuity Design
In this study, the effects of HISD summer school on students' reading achievement are measured using the regression discontinuity (RD) design. The RD design relies upon the fact that eligibility for many programs or policies in the social world is often determined by arbitrary cutoff points (Angrist and Pischke 2008;Imbens and Lemieux 2008;Morgan and Winship 2014). Since the cutoff points are somewhat arbitrary, individuals on either side of the cutoff points are likely to be roughly identical in all but the eligibility criterion. In this case, the treatment of attending HISD summer school can be considered as a discontinuous function of a primary aspect of the promotion standards-students' overall yearly average course scores, as well as their course scores in separate subjects. 12 Students who were just below the criteria were mandated to attend summer program, while those who were just above the criteria were not required to. Given the assumption that students who fall just below or above the cutoff point is random, the different outcomes among students who fall just above the threshold and those who fall just below are therefore caused by summer school. Graph 1 is a graphical illustration of the basic idea of the RD design. Two RD analyses will be conducted, and each is based on slightly different assumptions and model specifications. 12 Polychoric tests have been conducted to assess the association between students' promotion status and available promotion standard variables. The results indicate both average course scores and individual course scores are highly correlated with promotion status (mostly greater than 0.5), while attendance rate is not (mostly around 0.2). Therefore, I focus on the discontinuity of course scores alone because 1) the attendance rate is weakly associated with promotion status, and 2) the decisions made by committees are subjective and not continuous.

Binding-Score Sharp Regression Discontinuity
The first RD analysis estimates the causal effects among students who barely pass the promotion criteria and those who barely fail based on their course scores. The latter are required to attend HISD summer school, whereas the former are not. This analysis has the advantage of comparing a group of students who are assigned to summer school to students with identical characteristics who are not assigned to summer school.
Compliance rates with the summer school assignment are relatively high: for instance, 83.24% of students at the .5 standard deviation (SD) margin above and below the threshold comply with their assignment-attend summer school when they are required to, and do not attend summer school when they are not. The equation for the analysis is: !"#$%&'()*+" , = . / + . 1 233%'& , + . 4 5*67*3%8"()*+" , + . 9 !#)" , + . : ;"6#<" , +. = >)*&$%3 , + . ? @"7 , + . A (7"$ , + . B + C , Conventional RD analysis usually relies on a single rating score variable, which therefore cannot be applied directly to this case since the assignment of summer school are based on more than one rating score variable. To deal with the multiple rating score case, binding-score RD-one type of multiple rating score regression discontinuity (MRSRD) design-will be utilized (Robinson 2011;Reardon and Robinson 2012;Umansky 2016b). The idea of binding-score RD is to construct a new single rating score variable that can perfectly predict treatment assignment (Reardon and Robinson 2012).
Students are assigned to summer school if they score below 70 points on any of these five components 13 : average course score, reading score, other language arts score, math score, and science/social studies score. In other words, students are not assigned to summer school unless they score at 70 points or below for all of the five components. Thus, it is the minimum of the five scores, rather than any of the five scores alone, that determines the assignment to summer school. The composite rating score variable for each student can be constructed as (Reardon and Robinson 2012): 5*67*3%8"()*+" , = min (2I"+#'"5*J+3"()*+" , + !"#$%&' , + K8ℎ"+@#&'J#'"2+83 , +M#8ℎ , + ()%"&)"/(*)%#<(8J$%"3 , ) Each score has been standardized and centered at the cutoff score first, then the lowest standardized score of each student will be taken as the value for the composite rating score variable. A student should be assigned to summer school if his/her lowest standardized score is below zero. 233%'& , is a dummy variable indicating whether a student should be assigned to summer school on the basis of the composite rating score variable (1=assigned, 2=not assigned). . 1 is the primary coefficient of interest in this model, which estimates the effect of assignment to summer school on reading performance for students close to the cutoff points. Therefore, this analysis is an "intentto-treat" (ITT) model (Umansky 2016a).
As mentioned previously, the scales of ISIP scores are not consistent across grade levels. To control the inconsistency of ISIP grading scales, the dependent variable 13 Seven components for students in grade 5 only because STAAR reading and math scores are not promotion standards for other grade levels in the 2015-16 academic year. Since for most students in the study there are five promotion standards, I focus on the five components while presenting the binding-score RD strategy.
!"#$%&'()*+" , has been standardized at each grade level. The five control variables include race, gender, economic disadvantage status, limited English proficiency status, and special education. In addition, . B represents grade-level fixed effects (six dummy variables for the seven grade levels), which control for unobserved characteristics associated with each grade level.
To restrict the sample within appropriate bandwidths around the cutoff point, I employed the optimal bandwidth selection analysis recommended by Imbens and Kalyanaraman (2012). Based on the analyses, optimal bandwidths range from .6 SD to .8 SD for most grade levels. In the holistic model with students of all grade levels from the sample, consequently, four bandwidths-.5 SD, .6 SD, .7 SD, and .8 SD above and below the cutoff points-were used to construct the analytical sample. Different models were run with the selected bandwidths, and the results will be discussed and compared.

Binding-Score Fuzzy Regression Discontinuity
As noted earlier, the assignment of attending HISD summer school was obeyed quite well but not without exceptions, since there are students who were mandated to attend summer school but did not actually attend, and vice versa. To address the noncompliance issue, the second RD analysis will implement a fuzzy RD design (also called RD with instrumental variables). Although only a small proportion of students did not comply with the assignment they received, there might be unobserved student attributes that not only cause the nonincompliance but also affect the outcome to be measured. To account for the potential endogeneity associated with participation in summer school, instrumental variables will be utilized.
For all the regression discontinuity analyses in this study, students from the Promotion Standards data (including promotion status and summer school information)

Findings From Sharp Regression Discontinuity
As discussed in the methodology section, the first regression discontinuity model investigates the impact of summer school assignment on reading outcomes, among students at the margin of summer school assignment from grades 1 through 7. The results are displayed in Table 4-3. From left to right, the analytic sample is restricted based on increasingly loose bandwidths around the cutoff points. After adjusting for control variables, the effect of the key variable of interest-assigned to summer schoolmaintains its statistical nonsignificance at the p<.05 level across all four models. These results suggest that summer school assignment does not lead to increased reading scores among students who are close to the threshold for summer school assignment.   Just as I did in the prior RD analysis, I also conducted a robustness check by using smaller bandwidths around the thresholds. The results are displayed in Table 4-6 in the Appendix. As expected, the sample sizes become smaller and the standard errors become larger as the bandwidths shrink. For the two smaller bandwidths, the estimated LATEs of attending summer school are consistent with the estimates presented in Table   4-4.

Conclusion and Discussion
The primary goal of this chapter is to examine the causal effects of HISD summer school. To answer this research question, this study has taken a binding-score RD approach. Both sharp and fuzzy binding-score RD analyses have been considered. The sharp RD approach estimates the ITT effect of being assigned to summer school, while the fuzzy RD analysis examines the LATE of attending summer school by only including compliers in the analytical sample. In addition, several bandwidths around the threshold at each grade level were used to confirm the consistency and robustness of the findings.
Overall, the findings suggest that HISD summer school attendance makes little difference to students' reading achievement for students who are just above or below the cutoff point for being required to summer school.
My study contributes to previous work on summer school and, in the broader literature, on program/policy evaluation in several ways. First, a binding-score RD design, which is under-utilized by prior research, has been fully leveraged in this study.
The binding-score RD approach carefully considers the fact that in the real world, there may not always be a single criterion for program/policy eligibility. Hence, traditional regression discontinuity analyses that rely on a single rating score variable is likely to imperfectly predict treatment assignment eligibility. A major strength of the bindingscore RD approach is to create a composite score that captures all the criteria for program eligibility. The estimated effects from the binding-score RD analyses are therefore deemed to be less biased than RD measures with a single rating score variable (Robinson 2011;Reardon and Robinson 2012;Umansky 2016b).
Second, the two different RD approaches employed in this study fully exploit the discontinuity feature of the assignment of summer school. Additionally, the fuzzy RD design accounts for the non-compliance issue involved in the actual treatment. By implementing a 2SLS analysis, this approach allowed me to estimate the causal effects of attending HISD summer school on students' reading attainment. Last but not least, I used data collected by the seventh largest urban school district (out of more than 14,000) in the United States, whose summer school has rarely been studied by scholars. Unlike districts with predominantly white students, this school district is dominated by racial minorities and economically disadvantaged students, and therefore might exhibit different patterns in the relationship between summer school and reading achievement. This research provides unique insights into the goals and effectiveness of remedial summer programs in minority-majority school districts.
One important caveat to keep in mind when interpreting the RD results is that the analytic sample only includes students who scored closely around the cutoff points in each grade level. Neither the ITT effects nor the LATEs identified in this study can speak to students who did not score around the threshold-either high-performing or extremely low-performing students. Despite its non-generalizability to the broader student population, the identified effect is of substantive interest and is most relevant to the central research inquiry in this study, since we might not expect remedial summer school to offer much to the already high-achieving group and it is also not enough of an intervention to make a significant impact on extremely low-achieving students. Rather, it is for the students who are on the borderline of the thresholds and who are also the targets of HISD summer school that we anticipate potential effects.
On the surface, the results provide little evidence of a positive effect of remedial summer school on reading achievement, which is unexpected but not unprecedented (Heyns 1978;Downey et al. 2004). There are two possible explanations that might account for the ineffectiveness of HISD summer school. One potential explanation relates to the duration of summer school-the HISD summer program only consists of 22 days of instruction, which might not be long enough for the program to take effect. Hazelton et al. (1992) note that 35 days of instruction are needed to bring significant changes to students' academic achievement, while meta-analyses provide compelling evidence that summer programs that offer 20 to 40 days of instruction would be most beneficial to students (Cooper et al. 2000).
An alternative explanation has to do with the specific subject of instruction (e.g., reading, math, social studies, etc.) provided by HISD summer school. According to the administrator who is in charge of HISD summer school, it is likely that elementary and middle school students received accelerated instruction in the area for which they were retained and at least one additional core subject area. For example, a third-grade student may have been retained for reading. However, the student would not be expected to engage in reading instruction for the 6.5 instructional hours each day. Typically, schools engage students in rotations that consist of reading, math and enrichment courses based on campus needs. Since the available data do not include such information, it is unclear whether students receive any type of reading instruction in summer school, as is the length of reading instruction students receive, if any. It is possible that students who failed math tests only were not offered reading instruction in summer school; therefore, the effectiveness of summer school would not be reflected in the outcome measured in this study-students' reading performance after summer break.
In this chapter, my findings provide little evidence of positive effects of HISD summer school. To better understand how the summer program operates and what might contribute to the ineffectiveness, I propose future data collection should include more information on the features of summer school, such as subject of instruction (e.g., reading, math, social studies, etc.), length (hours) of instruction per day, test scores during summer school, class size, teacher qualifications, quality of instruction, etc.
Availability of this information will help researchers discern the possible causes of summer school ineffectiveness.  Chapter 5

Conclusion
The preceding empirical analyses do not intend to provide a comprehensive investigation of the mechanisms related to summer learning; rather, I focus on important issues that tend to be overlooked by previous summer learning research. Besides the social class or race-related causes of summer learning disparities, there are many other factors that can affect the magnitude of academic achievement gaps during the summer.
The large amount of time spent at home and neighborhood environment over the summer break shapes the extent to which non-school factors play a role in students' academic performance. When formal schooling is temporarily unavailable, would less exposure to English-speaking environment lead to slower learning rates for ELs? With more waking hours spent at one's neighborhoods, would neighborhoods make a larger impact on students' reading achievement? Would providing remedial summer programs to lowperforming students produce a meaningful difference on the growth of their reading achievement? Although all three empirical pieces appear to answer separate questions, there are several findings they share in common. In the section below, I will discuss how the three studies fit together to reveal a cohesive pattern of summer learning and educational achievement gaps more broadly.

Summary of Findings
First of all, academic achievement gaps are already formed before the start of formal schooling. Evidence for this conclusion comes from both Chapter 2 and Chapter 3. In Chapter 2, I found that the reading achievement gaps between ELs and English proficient students emerge at the beginning of first grade and remain quite stable over the course of elementary school years. Chapter 3 shows that achievement gaps in reading between students from relatively advantaged neighborhoods and those from disadvantaged neighborhoods occur at the onset of formal schooling and change little in later years. This is in agreement with some research on the patterns of educational achievement gaps. For instance, reading gaps between students from the top 10 percentile families and those from the bottom percentile families only grow 12 percent over the course elementary school and middle school; the achievement gaps in math even narrow a bit (Reardon 2011). Furthermore, there is evidence suggesting that test score gaps between disadvantaged and advantaged groups grow little after the age of five (von Hippel and Hamrock 2019). Regarding the question raised in the introduction chapter "Do schools reduce, reproduce, or exacerbate educational disparities?" findings from this dissertation lend support to the argument that schooling does not exacerbate educational inequality.
Despite educational achievement gaps are present before students start formal schooling and change little afterwards, it does not mean there is no difference between summer learning and academic-year learning. Chapters 2 and 3 demonstrate that advantaged students are likely to learn faster in reading than disadvantaged students when school is in session, and both groups' learning rates slow down during the summer. In some cases, disadvantaged students' summer learning rates even exceed their advantaged counterparts. This appears to lead to the conclusion that summertime does not hurt all students equally and advantaged students are more susceptible to summer break.
Nonetheless, the extent to which reading learning gaps shrink during the summer is not comparable to the amount of growth in reading learning gaps during the academic year and thus is less substantively meaningful. Even if the slight shrink in reading learning gaps is meaningful, there are at least two explanations for that. First, this issue raises the possibility of a "ceiling effect," wherein high-performing students often have more room to lose than do low-performing students. In a similar vein, a regional student mobility study produced by HERC indicates that student mobility yields more detrimental effects for advantaged students. Second, this could be because advantaged families tend to consider the summer months as an opportunity for their kids to learn new things that are not taught in school (Boulay 2015). For these students, they are able to get away from the regular coursework and pursue their interests. As a result, what they have learned during the summer may not be reflected in the formal test scores.
Finally, it turns out that the mechanisms/practices that might affect summer learning do not operate the way as once hypothesized. Chapter 2 finds that home language other than English does not hurt students' reading achievement, particularly for older kids. Chapter 3 proves that living in a concentrated disadvantaged neighborhood may have less of an effect on students' summer learning than expected. Chapter 4 suggests attending a short, remedial summer program does not produce a positive effect for low-performing students. Taken together, these findings hint at least two messages.
First, the "summer stagnation" or "summer slowdown" pattern is quite stable, regardless of students' home language, neighborhood contexts, and summer school attendance.
Second, there could be other unobserved or unmeasured factors that protect disadvantaged students against falling further behind during the summer. For example, although children's family schedules, summer camps or other activities are not captured in this study, one might expect that practices or activities targeted at low-performing students may buffer them from negative influence that comes from a non-English speaking home environment or a disadvantaged neighborhood.

Research Implications
I believe this dissertation has a number of implications, some of which relate to our understanding of educational achievement gaps and some of which are relevant to educational policies. The very fact that achievement gaps (at least reading) form primarily before the start of formal schooling, prompt us to rethink conventional explanations for educational disparities. Indeed, it needs to be acknowledged that school plays a critical role in shaping students' academic performance and widening educational achievement gaps through processes such as school segregation (Owens 2017), curriculum tracking (Gamoran 1986;Tach and Farkas 2006), and teacher with different experiences (Phillips and Chin 2004). Yet the magnitude of achievement gaps due to these school factors has not been compared to academic gaps formed before the onset of formal schooling. The majority of empirical educational research focuses on a specific school mechanism or practice. While these studies demonstrate powerful effects of this single process, we know little about how various factors work together to shape student academic achievement.
Considering other educational research, the findings in this dissertation are not altogether surprising. Literature on early childhood education indicates strong association between high-quality preschool education and higher levels of school readiness as well as lower rates of grade retention in later school years (Reynolds et al. 2011). There are also some studies arguing that schools do not exert much of an effect on school performance.
For instance, teacher expectations do predict students' academic performance to some extent, but the effects tend to dissipate rather than accumulate over time (Jussim and Harber 2005). In addition, the difference between more qualified and less qualified teacher only contributes two percentile points to educational achievement gaps (Isenberg et al. 2013). Using appropriate interval vertical scaled test scores, future research could study whether the patterns hold for other subjects or contexts. For example, given the accumulative nature of math learning (Ready 2010), it is possible that school instruction is more closely tied to math scores and math achievement gaps may exhibit more variation over time.
This dissertation is reliant on administrative data. A strength of district administrative data is that it contains the entire student population and rarely has missing values for test scores and basic demographic characteristics. Such data allow me to examine how summer learning varies from academic-year learning. In administrative data, however, most of the variation in family characteristics is not captured. As a result, some scholars analyzing administrative records choose to rely on neighborhood characteristics as proxies for family characteristics (Burdick-Will 2013). Therefore, one crucial concern is that neighborhood effects observed in Chapter 3 might be confound with unobserved family factors. It is likely the magnitudes of neighborhood effects are subject to change with access to a wider array of family characteristics. One way to address this issue for future research is to supplement administrative data with survey data. Once more detailed survey data were collected, sensitivity analysis can be conducted to check whether the results are robust to more accurate variable specification.

Policy Implications
The findings should also prompt policymakers to rethink their efforts to promote students' academic achievement during the summer. While the remedial summer program has successfully avoid retaining a significant number of students, the study indicates weak links between attending summer school and improving reading scores.
This reinforces the notion that remedial summer school alone cannot account for differences in summer learning. Given the potential of summertime as a chance for lowperforming students to catch up, more strategic and targeted efforts are needed to make sure investments in summer programs are particularly beneficial to the most disadvantaged students. At the very least, as argued in Chapter 4, district-level summer programs can improve their services in two ways: (1) by making summer curriculum more aligned with the content to be tested, and (2) by extending the length of instruction.
As far as I know, HISD has made changes in summer programs since the summer of 2017, the new schedule may lead to more positive effects to student academic achievement.
Furthermore, it may not be appropriate to pose the majority of the burden to schools for educational achievement gaps so that they were punished for accountability purposes. It appears that some schools make great efforts to serve their students, while others not. From a longitudinal perspective, the achievement gaps due to school differences are not comparable to the gaps prior to formal schooling. Evidence supporting this argument note that children are highly sensitive to the environmental stimuli in early childhood and their brain develop the fastest during that stage (Johnson et al. 2016). It is the family, rather than school, where infants and toddlers spend the most time.
Particularly, students with high-educated mothers and non-poverty status are exposed to richer vocabulary and have better readiness for formal schooling (Cooper et al. 2011).
Research shows that early childhood educational programs have been effective in reducing special education rates and grade retention (Reynolds et al. 2011). Given that, preschool programs aimed at promoting kids' cognitive development and school readiness might be more cost-effective compared to interventions implemented after formal schooling.