The Impacts of Social-Emotional Competence and Other Student, Parent, and School Influences on Kindergarten Achievement

THE IMPACTS OF SOCIAL-EMOTIONAL COMPETENCE AND OTHER STUDENT, PARENT, AND SCHOOL INFLUENCES ON KINDERGARTEN ACHIEVEMENT

A dissertation submitted to the Kent State University College of Education, Health, and Human Services in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Vincent Schiavone

December 2018

A dissertation written by

Vincent Schiavone

B.A., University of Toledo, 2010

M.Ed., University of Toledo, 2013

Ph.D., Kent State University, 2018

Approved by

______, Director, Doctoral Dissertation Committee Jason Schenker

______, Member, Doctoral Dissertation Committee Tricia Niesz

______, Member, Doctoral Dissertation Committee Caven McLoughlin

Accepted by

______, Director, School of Foundations, Leadership, and Administration Kimberly Schimmel

______, Dean, College of Education, Health and Human Services James Hannon

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SCHIAVONE, VINCENT, December 2018 Evaluation and Measurement

THE IMPACTS OF SOCIAL-EMOTIONAL COMPETENCE AND OTHER STUDENT, PARENT, AND SCHOOL INFLUENCES ON KINDERGARTEN ACHIEVEMENT (157 pp.) Director of Dissertation: Jason Schenker, Ph.D.

The purpose of this quantitative study was to examine the influence of social-emotional competence (SEC) and various other student- and school-level variables on the academic achievement of kindergarteners. Data were collected on a nationally representative cohort of kindergarteners as part of the United States Department of Education’s Early Childhood

Longitudinal Study (ECLS-K: 2011) beginning in fall 2010 (n = 18,174). As part of the ECLS-

K: 2011, students were assessed via a wide range of sources of information about the children’s development, early learning, and school progress. The obtained data were analyzed via

Hierarchical Linear Modeling to investigate the influence of student- and teacher-level factors on student achievement.

The study found the following: 1) that there was a significant amount of variability in children’s mathematics and reading achievement in spring of kindergarten that is explained by school-level variables, as opposed to student-level variables; 2) that children’s membership in particular racial groups, gender categories, and socioeconomic statuses all resulted in significant within-school mathematics and reading achievement gaps in spring of kindergarten, controlling for various student background characteristics; 3) that various school-level variables significantly contributed to models predicting children’s spring kindergarten mathematics and reading achievement; and 4) children’s poverty interacted with their school membership to affect spring kindergarten mathematics and reading achievement.

TABLE OF CONTENTS

Page

LIST OF TABLES …...... vii

CHAPTER

I. INTRODUCTION………………………….…………………………………………………1 Overview…………..………………………………………………………...………………...1 Rationale and Purpose…..…………………………………………………...………………...3 Statement of the Problem…………..………………………………………...…………….….7 Research Questions………………..……..…………………………………..……………….8 Significance of the Study………………..………………………….………….……………..8 Research Paradigm………………………..……………………..…….……….……………..9 Variables in the Study…………..……..…………………………………………..………...10

II. LITERATURE REVIEW………………………....…………………………………..…….16 First-Level Variables: Within-Child Factors..………………………...…………..………....16 Second-Level Variables: The Impacts of the Student’s School…….………….…………....37

III. METHODS………………..………………………………………………….………..….45 Procedure………………………………………………………………………………….…..45 Participants……………………………………………………………………….…………....46 Measures……………………….…………………………………………...…….…………....48 Statistical Analyses………………………………………………………………...………….58

IV. RESULTS………………………………………………………………………………..…71 Mathematics Achievement…………………...……………………………………………….72 Reading Achievement…………………………………………………………………...….…83

V. DISCUSSION…………………….……………………………………………………..…95 Comparisons of the Findings with Extant Literature………….…………………………..…..95 Comparing the Models……………………………………………………………………….102 Limitations………………………………………………….…………………………...……107

APPENDICES………………………………………………………………………………….115 APPENDIX A: KENT STATE INSTITUTIONAL REVIEW BOARD APPROVAL……..…116 APPENDIX B: PROPERTIES OF COMPUTED VARIABLES…………………….………..118

REFERENCES………………...…………………………………………………………….…124

LIST OF TABLES

Table Page

Table 1: Independent Variables at each Level that Influence Student Achievement…..…..…....10

Table 2: Descriptive Statistics and Reliability Coefficients for each SSRS Subscale………..….50

Table 3: Descriptive Statistics and Reliability Coefficients for Cognitive Assessments…….....56

Table 4: Mean Subgroup Scores of First-Time Kindergarteners………………….………….….57

Table 5: Estimates of Fixed Effects and Covariance Parameters for Null Model:

Mathematics…………………………………………………………………………………...…73

Table 6: Estimates of Fixed Effects for Random Intercepts Model with Only Child-Level

Predictors: Mathematics……………………………………………………………………….…74

Table 7: Estimates of Covariance Parameters for Random Intercepts Model with Only Child-

Level Predictors: Mathematics……………………………………….……………………….…75

Table 8: Estimates of Fixed Effects: Random Intercepts Model with Child-Level and School-

Level Predictors: Mathematics……………………………………………………….………….77

Table 9: Estimates of Covariance Parameters: Random Intercepts Model with Child-Level and

School-Level Predictors: Mathematics…………………………………………………….….…78

Table 10: Estimates of Fixed Effects: Random Intercepts and Slopes Model with Poverty used to Examine Cross-Level Interactions: Mathematics……………………………………….…….81

Table 11: Estimates of Covariance Parameters: Random Intercepts and Slopes Model with

Poverty used to Examine Cross-Level Interactions: Mathematics………………………………82

Table 12: Fixed Effects and Variance Components for Null Model for Reading………………84

Table 13: Estimates of Fixed Effects: Random Intercepts Model with Only Child-Level

Predictors: Reading………………………………………………………………………………86

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Table 14: Estimates of Covariance Parameters: Random Intercepts Model with Only Child-

Level Predictors: Reading……………………………………………………………………..…86

Table 15: Estimates of Fixed Effects: Random Intercepts Model with Child-Level and School-

Level Predictors: Reading……………………………………………………………………..…89

Table 16: Estimates of Covariance Parameters: Random Intercepts Model with Child-Level and

School-Level Predictors: Reading……………………………………………………………….90

Table 17: Estimates of Fixed Effects: Random Intercepts and Slopes Model, with Poverty used to Examine Cross-Level Interactions: Reading………………………………………………….92

Table 18: Estimates of Covariance Parameters: Random Intercepts and Slopes Model, with

Poverty used to Examine Cross-Level Interactions: Reading……………………………………94

Table 19: Summary of Models’ Random Residuals, Intercepts, and Intra-Class Correlation

Coefficients………………………………………………………………………..……………103

Table 20: Outcome of Each Model to Predict Achievement of Child……………………..…...106

Table 21: Descriptive Statistics: Social-Emotional Competence (SEC)……………………...119

Table 22: Inter-Item Correlation Matrix: Social Emotional Competence (SEC)………..……120

Table 23: Item-Total Statistics: Social-Emotional Competence (SEC)……………………….120

Table 24: Scale Statistics: Social-Emotional Competence (SEC)……………………………..120

Table 25: Recoded Binary Poverty – Student-Level…………………………………………..121

Table 26: School Sector in Fall of Kindergarten (public vs private)…………………………..122

Table 27: School Size in Spring of Kindergarten………………………………….…………..122

Table 28: School Urbanicity in Fall of Kindergarten………………………………………….123

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CHAPTER I

INTRODUCTION

The present study examined the multilevel variables that influence mathematics and reading performance among kindergartners participating in the Early Childhood Longitudinal

Study beginning in the 2010-2011 school year (ECLS-K:2011). This study utilized student- and teacher-level variables to examine their impact on students’ academic performance. In this chapter, a brief overview is offered to provide background on the rationale and purpose of the research. The unique contribution of the project and its significance are also discussed. The chapter concludes with a discussion of the goals of the research and a presentation of the research questions, which served to guide the investigation.

Overview

Over last two decades, elementary and secondary education in the United States has become less focused on the holistic and social-emotional development of students (National

Research Council and Institute of Medicine, 2009) and, likely due in part to the 2002 enactment of the No Child Left Behind (NCLB) Act, more focused on academic learning, achievement, and test scores (Zins, Weissberg, Wang, & Walberg, 2004). This development has come in spite of established evidence that factors that are not primarily academic, such as social-emotional competence (SEC), can be extremely important for children’s adjustment into adulthood (Merrell

& Gueldner, 2010). Moreover, there has been an increasing recognition of SEC promotion as a credible strategy for the prevention of mental, emotional, and behavioral disorders in children and youth (O’Connell, Boat, & Warner, 2009), as well as the promotion of academic success

(Payton et al., 2008).

Social-emotional competence (SEC) has been studied in a variety of contexts. For example, some researchers have examined individual social-emotional competencies, such as peer relations (Rubin, Bukowski, & Parker, 2006) or self-regulation (Eisenberg et al., 1997).

However, there is increasing consideration of these individual competencies in the literature as a broader construct, SEC (sometimes referred to as social-emotional learning, or SEL), which helps promote resilience. The psychological framework known as resilience has garnered rapidly increasing attention in both academic and popular literature in recent years, and there has been a subsequent practice and policy emphasis on resilience as an organizing framework for the provision of mental health services (New Freedom Commission on Mental Health, 2003).

Resilience has been defined as “the process of adapting well in the face of adversity, trauma, tragedy, threats, or significant sources of stress” (American Psychological Association, 2016).

Put another way, resilience might best be thought of as the process of “bouncing back” from difficult experiences. A search of the Social Sciences Citation Index conducted by LeBuffe,

Ross, Fleming, and Naglieri (2013) revealed that published articles containing the word

“resilience” or its variants in the title or topic fields jumped from less than 20 citations in 1990 to over 1,200 citations in 2010. It should come as no surprise, then, that a variety of child-serving professions now consider finding ways to increase clients’ capacity for resilience to be critical for promoting children’s abilities to overcome life’s challenges (LeBuffe et al., 2013).

As Epstein and Sharma (1998) asserted, strength-based psychological assessments can provide information about the emotional and behavioral skills and characteristics that create a sense of accomplishment, contribute to satisfying relationships with family members, peers, and adults, enhance the ability to cope with stress, and promote social and academic development.

Data on children’s social and emotional strengths were collected as part of the Early Childhood

Longitudinal Study (ECLS-K: 2011); such data can be used to target the within-child protective factors each child possesses to promote early intervention and prevention practices both in school and at home.

Because resilience connotes the maintenance of positive adaptation by individuals despite experiences of significant adversity, it is of particular interest to study SEC in populations facing systemic oppression, such as that of race, ethnicity, and socioeconomic status. One of the research questions of the present dissertation, therefore, sought to examine the role of poverty in moderating the relationship between school-level predictor variables and academic achievement

(Elias & Haynes, 2008; Klebanov, Brooks-Gunn, & Duncan, 1994; Haveman & Wolfe, 1995;

Smith, Brooks-Gunn, & Klebanov, 1997). As numerous studies have found, even academically gifted children from certain historically marginalized groups are vulnerable to social and emotional difficulties, and this is particularly true of those students from low-income, single- parent, and Black families (Ford, 1996; Moon, Zentall, Grskovic, Hall, & Stormont-Spurgin,

2001).

Rationale and Purpose

The rationale for the present study is derived from the increasing availability of large- scale educational datasets for public use. As Doolan, Winters, and Nouredini (2017) have argued, technological breakthroughs, especially over the last twenty years, have made sharing and analyzing large data sets much easier, and research studies are increasingly being conducted using existing large data sets instead of relying on data collected by the study authors themselves. Using secondary data sets, especially those collected at the population level, increases statistical power and external validity as a result of a larger sample size and greater diversity of respondents (with regards to race, ethnicity, and socioeconomic status). Using an

4 existing data set can help a researcher obtain results much more quickly, at a lower cost, and without exposing new research subjects to many of the potential harms and burdens associated with research participation—and this is particularly true of multi-year, longitudinal studies, which can have the benefit of examining children’s development over time but can impose substantial burdens on participants. The avoidance of new research participants being subjected to risks is a major ethical benefit. Moreover, the availability of large-scale datasets makes it easier to answer research questions such as the ones addressed by the present dissertation. For this reason, making data sets available to researchers is increasingly seen as an ethical mandate by organizations conducting the original large-scale studies. For example, in the field of education, using existing large-scale datasets can potentially reduce disparities among schools by avoiding the process of recruiting new subjects for every study, and therefore demonstrating best practices more quickly. The existing data from ECLS-K: 2011 is a good fit for present dissertation because the ECLS-K: 2011 is a high-quality, national study and the dataset has all the variables required to answer the present dissertation’s research questions, and a large enough sample size to develop a complex, multilevel model designed to predict student achievement with high degree of statistical power.

There is an increasing need for governments and educational institutions to predict student achievement from both student-level and school-level variables. As Jerald (2006) has argued, the prediction of which students will drop out of high school, for example, requires more than simply knowing which personal and educational characteristics dropouts are most likely to exhibit. Researchers who have followed single-district cohorts of students such as Roderick

(1993), Neild and Balfanz (2006), and Balfanz, Herzog, and Mac Iver (2007), have identified highly predictive academic, behavioral, and attendance-related risk factors for student

5 withdrawal from middle school or high school as early as kindergarten (particularly noteworthy is Roderick’s finding from an urban district in Massachusetts that being retained in any grade, even kindergarten, was highly predictive of a student’s eventual dropping out of school).

Advances in computing technology have made the use of advanced statistical modeling techniques more feasible at the individual school or district level, and changes in educational policy at the local, state, and national levels (including the introduction of performance-based funding mechanisms) have made the development of such predictive analyses perhaps more of a necessity than ever (Ekowo & Palmer, 2016; Mesecar & Soifer, 2016). Such models can equip school leaders with clues regarding, among other things, the appropriate times to provide student-level interventions in order to prevent students’ withdrawal from school or promote college readiness (Stuit et al., 2016).

In addition to the research already discussed, there is a growing body of literature that attempts to find characteristics by which students can be identified as being at risk of exhibiting subpar academic achievement several semesters or even years into the future, in order that such students can then be matched with interventions to help them improve their chances of succeeding in school (Heppen & Therriault, 2008; Jerald, 2006; Kennelly & Monrad, 2007;

Neild, Balfanz, & Herzog, 2007; Pinkus, 2008). The present dissertation improves upon the extant literature in three ways. First, as West, Denton, and Germino-Hausken (2000) have argued, most literature on the academic achievement of children is focused on elementary (e.g., fourth-graders in the National Assessment of Educational Progress) and secondary school students (e.g., twelfth-graders in the National Assessment of Educational Progress and eighth-, tenth- and twelfth-graders in the National Education Longitudinal Study of 1988). By contrast, relatively little data is available on kindergarten programs. Information concerning

6 kindergartners can inform educational policy and practice, and especially those policies and practices that are targeted to meeting the needs of a diverse population of children entering kindergarten for the first time.

Second, a limited number of studies attempting to predict academic achievement among children incorporate the independent variable of social-emotional competence—most studies adopt a deficit approach, rather than the strengths-based paradigm intrinsic to SEC (Chain,

Shapiro, LeBuffe, & Bryson, 2017). Even Chatterji (2005), who developed a multilevel model predicting first-grade reading achievement using the original ECLS-K from 1998, excluded direct measures of social-emotional competence from her model development process—despite the fact that such data was collected and available to her. Unlike macrosystemic causes of the achievement gap (e.g., racism, poverty, etc.) that are likely impossible to change through the actions of a single agent in the timeframe of the education of a single child, improving a child’s social-emotional competence is potentially within a teacher’s sphere of influence (Civic

Enterprises, Bridgeland, Bruce, & Hariharan, 2013; Durlak, Weissberg, Dymnicki, Taylor, &

Schellinger, 2011).

Third, the findings of the available literature discussing the relationships between student achievement and school-level variables, are not entirely conclusive. Several such school-level variables collected in the ECLS-K: 2011 due to literature suggesting they have a bearing on academic achievement include the following: frequency of individualized educational plans

(IEPs; Lee, Shin, & Amo, 2013); student attendance rate (Dekalb, 1999; Rothman, 2001; Ziegler,

1972); school size (Ayers, Bracey, & Smith, 2000; Lee & Smith, 1993; Lee & Smith, 1995;

Lindsay, 1982; Pittman & Haughwout, 1987; Williams, 1990); public versus private school status (Braun, Jenkins, & Grigg, 2006); parent involvement at the school (Boggess, 2009;

Bricheno & Thornton, 2007; Little-Harrison, 2012; Liu & Wang, 2008; Westerlund, Gustafsson,

Theorell, Janlert, & Hammarstrom, 2013); and aggregate poverty within the school (Garmezy,

1993; Garmezy & Masten, 1986; Hansen et al., 2011; Werner, 1993; Zill & West, 2001).

Despite findings indicating that these variables could be predictive of student achievement, much of the extant research on these topics is inconclusive or dated (e.g., Darling-Hammond, 2000).

Therefore, further study on the impacts of these types of school variables on student achievement is warranted.

Statement of the Problem

As will be discussed in further detail in the literature review, a substantial body of research supports the premise that social and emotional variables are integral to learning (Wang,

Haertel, and Walberg, 1997). Moreover, literature dating back at least to the 1960s supports the premise that various other student- and school-level variables could be predictive of students’ academic achievement. However, the precise nature and predictive strength of the relationships among social-emotional competence (SEC), other student-level variables, school-level variables, and academic achievement vary depending on how SEC and academic achievement are operationalized, what other student- and teacher-level variables are included in the model, and what student population is examined. The extant literature is lacking in studies that incorporate

SEC, other student-level variables, and school-level variables to predict the academic achievement of kindergarteners in both reading and mathematics (e.g., Chatterji, 2005).

As discussed previously, the present dissertation utilizes a strength-based approach. A strength-based approach, as opposed to a deficit-based approach, leverages students’ existing strengths to overcome barriers and achieve both student and community goals (Simmons,

Shapiro, Accomozzo, & Manthey, 2015). Given the dearth of literature that focuses on social-

8 emotional strengths rather than deficits, further strength-based research on students’ social- emotional development is warranted. Fortunately, data on various social-emotional strengths were collected as part of the Early Childhood Longitudinal Study (ECLS-K: 2011).

Research Questions

The purpose of the present study is to examine: 1) the extent to which variability in children’s mathematics and reading achievement in spring of kindergarten is explained by school-level variables (as opposed to student-level variables) collected in fall of kindergarten; 2) whether children’s membership in a specific subgroup resulted in significant within-school mathematics and reading achievement gaps in spring of kindergarten, controlling for various student background characteristics; 3) the degree to which various school-level variables significantly contribute to models predicting children’s kindergarten spring mathematics and reading achievement; and 4) whether children’s poverty interacted with their school membership to affect spring kindergarten mathematics and reading achievement, and school factors accounting for the variance in school slopes.

Significance of the Study

The findings of the present study both contribute to the body of academic literature and provide educational practitioners with what amounts to an early warning system for identifying students who are at risk of exhibiting poor academic achievement later in the school year.

The present study contributes to the academic literature by testing the relationships that have been found in some previous work between academic achievement and the following: student gender (Barrow, Boyle, Ginsburg, Leu, Pier & Price-Rom, 2007; Ganimian, 2009;

Marks, 2008; Michaelowa, 2004; Mullis, 2007); student race (Elias & Haynes, 2008); student socioeconomic status (Klebanov, Brooks-Gunn, & Duncan, 1994; Haveman & Wolfe, 1995;

Smith, Brooks-Gunn, & Klebanov, 1997); student social-emotional competence (Blair, 2002;

Diamond and Lee, 2011; Kong, 2013); frequency of individualized educational plans (IEPs; Lee,

Shin, & Amo, 2013); student attendance rate (Dekalb, 1999; Rothman, 2001; Ziegler, 1972);; public versus private school status (Braun, Jenkins, & Grigg, 2006); parent involvement at the school (Boggess, 2009; Bricheno & Thornton, 2007; Little-Harrison, 2012; Liu & Wang, 2008;

Westerlund, Gustafsson, Theorell, Janlert, & Hammarstrom, 2013); and aggregate poverty within the school (Garmezy, 1993; Garmezy & Masten, 1986; Hansen et al., 2011; Werner, 1993; Zill &

West, 2001).

Research Paradigm

As stated earlier, the purpose of this study is to examine the extent to which various student- and school-level factors are predictive of kindergarteners’ mathematics and reading performance. The present study adopted a quantitative research design and strategy of inquiry grounded in a post-positivist philosophical worldview (Creswell, 2009). In keeping with the post-positivist assumption that research is the process of making claims and then refining or abandoning those claims when others are more strongly warranted, the present study tested claims that are supported by the extant literature. However, in keeping with the post-positivist assumption that evidence established in research is always imperfect and fallible, it is worth acknowledging that the instruments used in the present study likely provide an incomplete understanding of the students’ academic proficiencies and various social-emotional competencies; indeed, this is why such instruments are periodically refined and revised. Other post-positivist assumptions include the notion that data, evidence, and other rational considerations (on which the present study relies) shape knowledge; and that researchers must examine their methods and conclusions for bias (which the present study did by, among other

10 things, discussing literature that has examined the psychometric properties of the instruments used).

Variables in the Study

The student- and school-level variables included in the present study are summarized in

Table 1 below (the properties of the instruments by which the variables were measured are discussed in greater detail in Chapter 3):

Table 1

Independent Variables at each Level that Influence Student Achievement Level Variables Frequency of individualized educational plans (IEPs); student attendance rate; School school size; public versus private school status; parent involvement at the school; aggregate poverty within the school Socioeconomic Status, Gender; Race; Fall 2010 SEC measures; Fall 2010 scores Student on the two-stage reading and mathematics assessments Note. The Dependent Variable for all levels is spring 2011 student achievement in the two- stage reading and mathematics assessments.

1. Student achievement on the two-stage mathematics and reading assessments: The

variables of mathematics and reading achievement were used as continuous dependent

variables. Scores were calculated using Item Response Theory (IRT) procedures;

therefore, children were administered a set of items appropriate for their demonstrated

ability level, rather than all the items in the assessment.

2. Socioeconomic Status: The variable of socioeconomic status as recorded by the parent

was used as a first-level continuous independent variable. Socioeconomic status was

hypothesized to be important in explaining variability in academic achievement due to

the literature finding that various components of socioeconomic status, including parent

education and household income, are important in predicting children’s achievement

(Klebanov, Brooks-Gunn, & Duncan, 1994; Haveman & Wolfe, 1995; Smith, Brooks-

Gunn, & Klebanov, 1997). The ECLS-K: 2011 data provide a continuous measure of

children’s socioeconomic status, which is a composite of parents’ income, education, and

occupational prestige (z scored, M = 0, SD = 1). More specifically, the components used

to create the SES variable are father/male guardian’s education, mother/female

guardian’s education, father/male guardian’s occupational prestige, mother/female

guardian’s occupational prestige, and household income. In households with two mothers

or two fathers, education and occupational prestige for both mothers/fathers was used.

Each parent’s occupation was scored using the average of the 1989 General Social

Survey (GSS) prestige scores for the 1980 census occupational category codes that

correspond to the ECLS-K occupation code.

3. Gender: The variable of gender of a student (i.e., male or female) as recorded by the

parent was used as first-level categorical independent variable. Gender was hypothesized

to be important in explaining variability in academic achievement due to the literature

finding that girls tend to outscore boys in tests of verbal ability, while boys tend to

outscore girls in tests of mathematics ability (Barrow, Boyle, Ginsburg, Leu, Pier &

Price-Rom, 2007; Ganimian, 2009; Marks, 2008; Michaelowa, 2004; Mullis, 2007). In

the ECLS-K: 2011 data, the child-level analyses incorporate a dummy-coded gender

measure (girls = 1, boys = 0).

4. Race: The variable of race of a student as recorded by the parent was used as first-level

categorical independent variable. Race was hypothesized to be an important in explaining

the relationship between social-emotional competence and academic achievement due to

the literature finding that this relationship is stronger for Black students than for students

of other racial categories (Elias & Haynes, 2008). In the ECLS-K: 2011, a respondent

could select one or more of five dichotomous race categories when reporting their own

race or that of their child. Each respondent additionally had to identify whether he or she

was Hispanic. There are six dichotomous race variables indicating whether a respondent

or study child was of a certain race (White, Black, Asian, Native Hawaiian or Other

Pacific Islander, American Indian or Alaska Native, and more than one race) as well as

one dichotomous ethnicity variable indicating whether a respondent or study child was

Hispanic. These variables were used to create one race/ethnicity composite variable with

mutually exclusive categories: White, not Hispanic; Black, not Hispanic; Hispanic of any

race; Asian, not Hispanic; Native Hawaiian or Other Pacific Islander, not Hispanic;

American Indian or Alaska Native, not Hispanic; and Two or more races, not Hispanic.

5. Prior Mathematics and Reading Achievement: The variables of students’ prior

mathematics and reading achievement were used as continuous IVs that serve as

covariates. The scores reflecting prior achievement are generated from the fall 2010

administration of the two-stage mathematics and reading assessments (with the DV

coming from the spring 2011 administration of the same tests). This variable controls for

students’ prior mathematics and reading proficiency.

6. Prior performance on measure of SEC: The teachers reported how often their students

exhibited certain social skills and behaviors using a modified version of the Social Skills

Rating System (SSRS; Gresham & Elliott, 1990). The four subscales included in the data

are Self-Control, Interpersonal Skills, Externalizing Problem Behaviors, and Internalizing

Problem Behaviors. As Blair (2002) and Diamond and Lee (2011) have found, early

social-emotional competencies, including behavioral regulation, attention skills, and

problem solving, are critical to academic achievement in young children.

7. Frequency of individualized educational plans (IEPs): Each school’s total IEPs was

computed to serve as an index of the special education services provided by each school.

Frequency of IEPs was hypothesized to be important in explaining variability among

students in academic achievement due to the literature finding that schools identified as

being in need of improvement (i.e., schools in accountability treatment, as opposed to

schools in good standing) have significantly greater portions of students with IEPs than

those schools identified as being in good standing (Lee, Shin, & Amo, 2013).

8. Student attendance rate: Student attendance was computed as a percentage of total days

attended in the school year, based on the number of absences reported for each child in

the ECLS-K: 2011 database. This was then aggregated across children within each

school. Student attendance rate was hypothesized to be important in explaining variability

among students in academic achievement due to the literature finding a direct correlation

between student attendance and student achievement, and linking poor attendance to poor

academic achievement (Dekalb, 1999; Rothman, 2001; Ziegler, 1972).

9. School size: School size was dummy-coded (greater than or equal to 500=1, less than

500=0). School size was hypothesized to be important in explaining variability among

students in academic achievement due to the literature finding that the ideal school size

for younger children is approximately 300-400 students, and that schools with more than

500 students are less effective at promoting student achievement, student attendance,

teacher satisfaction, and parent and community involvement (Ayers, Bracey, & Smith,

2000; Lee & Smith, 1993; Lee & Smith, 1995; Lindsay, 1982; Pittman & Haughwout,

1987; Williams, 1990).

10. Public versus private school status: School sector was dummy coded as 1=public,

0=other. Public versus private school status was hypothesized to be important in

explaining variability among students in academic achievement due to the literature

finding that the adjusted average score for public schools was significantly higher than

the average for private schools in grade 4 mathematics, while the average for private

schools was significantly higher than the average for public schools in grade 8 reading.

(Braun, Jenkins, & Grigg, 2006).

11. Parent involvement at the school: This index showed the degree to which parents

reported involvement in school, based on attending events and functions, volunteering,

fundraising, etc. Parent involvement at the school was hypothesized to be important in

explaining variability among students in academic achievement due to the literature

finding that parental involvement does a great deal to moderate the established

relationship between socioeconomic status and academic achievement (Boggess, 2009;

Bricheno & Thornton, 2007; Little-Harrison, 2012; Liu & Wang, 2008; Westerlund,

Gustafsson, Theorell, Janlert, & Hammarstrom, 2013).

12. Aggregate poverty within the school: Aggregate poverty within the school was

hypothesized to be important in explaining variability among students in academic

achievement due to the fact that the impact of the students’ socioeconomic background

on academic achievement, while largely outside of school influence, is not likely to be

entirely independent of school arrangements. Rather, schools themselves may be

influenced in a variety of ways by the background of their students. Schools located in

high-poverty neighborhoods tend, for example, to be bigger; such schools also have less

control over their recruitment, and, thus, end up with a teaching staff that is less

15 normatively coherent. Moreover, high-poverty schools tend to be located in neighborhoods with fewer academic role models for students to mimic (Garmezy, 1993;

Garmezy & Masten, 1986; Hansen et al., 2011; Werner, 1993; Zill & West, 2001).

CHAPTER II

LITERATURE REVIEW

The following review of the literature is not intended to be a comprehensive meta- analysis; instead, it is a review of select research to provide evidence of relationships among the variables of interest in the present study. In accordance with the procedures of hierarchical linear modeling, separate sets of predictor variables were selected for analyses at the child level and at the school level. Where appropriate, relationships among the predictor variables are examined in the present literature review. All of these theoretically relevant variables were incorporated into the models.

First-Level Variables: Within-Child Factors

At the child level, predictor variables included child development factors (e.g., the child’s gender), socio-demographic factors (e.g., the child’s ethnicity and family socioeconomic status), and cognitive measures taken prior to formal schooling (i.e., mathematics and reading achievement scores in the beginning of the kindergarten year). The ethnic minority sub-samples of interest in this study consist of children coded as African-American, Asian, and Hispanic (any race) students in the ECLS-K: 2011 database. The term “poverty” refers to students falling at or below the second quintile on the continuous measure of family socioeconomic status used in the

ECLS-K: 2011.

Social-Emotional Competence and Academic Achievement across Demographic Categories

It is well established in the literature that students with an emotional/behavioral disability, male students, and students of minority ethnicity are disproportionately represented in disciplinary referrals (e.g., Zhang, Katsiyannis, & Herbst, 2004), and several researchers (e.g.,

Hemmeler, 2011) have surmised that this may be due at least in part to a larger societal problem

17 of discrimination. Given the evidence that demographic variables play a role in the relationships among components of social-emotional competence and academic achievement, gender and race served as moderators in the model examined in the present study. While disability has been found to be related to both SEC and academic achievement and is therefore discussed briefly here, there is insufficient variability on that variable in fall of kindergarten to incorporate it into the model; moreover, it is presumed that the presence of an emotional or behavioral disability would negatively correlate so strongly with SEC as to add only trivial predictive power to the model.

Gender. Among children and adolescents, girls have been found to adjust better to social situations and display more prosocial behavior than their male peers (Masten, Juvonen, &

Spatziere, 2009). Overall, girls also tend to exhibit greater ability in self-regulation than boys

(Raffaelli, Crocket, & Shen, 2005). Studies examining gender differences from a deficit perspective (though not the focus of the present study, which emphasizes a strengths-based resiliency framework) have found additional behavioral disparities among male children and adolescents as compared to females in rates of behavioral diagnoses such as Attention Deficit

Hyperactivity Disorder (ADHD; Reid et al., 2000). In addition, Hartman, Turner, Daigle, Exum, and Cullen (2009) found that self-esteem has been shown to be a significant factor in protecting girls from delinquency, but not boys. Moreover, girls have been found to be more likely than boys to be sensitive to the distress of others, seek support, and express emotions (Rose &

Rudolph, 2006). These behaviors constitute a portion of the social-emotional competencies believed to promote resiliency. These findings suggest that girls develop SEC at greater levels, and therefore may have a greater capacity for resiliency, than do boys.

Although existing studies on gender-based differences in SEC generally favor girls over boys, the evidence on gender-based differences in academic achievement is more complicated.

For example, Eccles (1984) found that while boys tend to have greater self-efficacy (i.e., confidence in their ability to succeed) in mathematics, girls tend to have greater self-efficacy in reading. However, Marsh and Yeung (1998) found that despite this, girls’ scores on standardized reading assessments were only slightly higher than those of their male peers, and their scores on standardized mathematics assessments were only slightly lower than those of their male peers. This suggests that the differences in achievement found between boys and girls may be reinforced by culture, rather than merely innate ability.

More recent research has explored the role of cultural understandings of intelligence and academic proficiency in gender-based differences in achievement. For example, Dweck (2000) found that girls are more likely than boys to believe their intelligence is fixed and therefore adopt a learned helplessness in their studies—that is, they are more likely to think, “I’m just not a math person.” Neihart and colleagues (2002) found that even though girls perform more poorly than boys on some standardized assessments, their classroom grades in some of those areas are higher than their male peers; here, then, that learned helplessness manifests itself in girls believing they are “bad test-takers.” Further findings, including those of Lummis and Stevenson (1990) and of

Meece and Daniels (2008), have revealed that although boys and girls may differ slightly in some areas of cognitive ability, this does not translate into many differences in academic achievement.

Race and ethnicity. As Brunsma (2005) argued, the contemporary United States is a society “where race and racism is denounced and supposedly diminished [but] where, in the end, race still matters as an axis through which goods, services, opportunities and life chances are

19 distributed unequally to members of the same society” (p. 1132). However, as Zakrzewski

(2016) has asserted, programs designed to promote social-emotional learning may be able to help create safe classroom environments “in which students and educators can have open, honest, and validating conversations about the [racism] students face every day, [and] provide students with emotional tools to counter negative messages and stand up against racism in their communities”

(para. 22). Therefore, it is perhaps unsurprising that there is emerging evidence in the literature on the racial achievement gap in education (e.g., Lee, 2002) suggesting that the relationship that exists between SEC and academic achievement can depend, at least to some extent, on racial and ethnic variables. For example, Elias and Haynes’s (2008) finding that third-graders’ SEC and perceived teacher support were predictive of end-of-year academic outcomes was much stronger for Black students than for students of other racial groups. In addition, in a recent study focusing on the relationship between SEC and academic achievement among American Indian/Alaska

Native (AI/AN) students, Chain, Shapiro, LeBuffe, and Bryson (2017) found not only that identification as AI/AN or Other Students of Color (i.e., visible minorities) were each significantly associated with lower academic achievement (even while holding student poverty and school-level factors constant), but also that the correlations between several components of

SEC (including Personal Responsibility and Decision Making) and academic achievement were significantly stronger for AI/AN students than for White students.

Socioeconomic status. Children living in poverty face a higher risk than children with more financial resources of developing a variety of social-emotional problems, including internalizing and externalizing symptoms (Duncan, Brooks-Gunn, & Klebanov, 1994), lower levels of sociability and initiative (Hanson, McLanahan, & Thomson, 1997), problematic peer relations, and disruptive classroom behaviors (Patterson, Kupersmidt, & Vaden, 1990).

Thompson and Winer (2012) have found that parents’ education levels and household incomes have short-term impacts on preschoolers’ understanding of emotions, and lasting effects on children’s SEC throughout early childhood; moreover, the researchers found mother’s educational attainment to be a stronger predictor than household income. Moreover, as might be expected, the literature on academic achievement consistently has demonstrated that various components of socioeconomic status, including parent education and household income, are important in predicting children’s achievement (Klebanov, Brooks-Gunn, & Duncan, 1994;

Haveman & Wolfe, 1995; Smith, Brooks-Gunn, & Klebanov, 1997).

In the Early Childhood Longitudinal Study (ECLS-K: 2011), data was collected on several components of socioeconomic status, including parent employment (in fall 2010), parent income and assets (in spring 2011) and parent education (in both fall 2010 and spring 2011).

Because there are numerous findings in the literature suggesting that these components of socioeconomic status are predictive of both SEC and academic achievement, children’s poverty is included as a dichotomous variable in the model.

Disability. Whisman and Hammer (2014) have found that students with disabilities experience a greater likelihood for multiple in-school suspensions, for single and multiple out-of- school suspensions, and expulsion-related actions than their peers without diagnosed disabilities.

Moreover, the authors found that while having a single disciplinary referral had no impact on the academic achievement of students with disabilities, disabled students who received 2 to 4 referrals were 3.7 times more likely to score below proficiency on a standardized achievement test, and disabled students with 5 or more disciplinary referrals they were 12 times more likely to score below proficiency. Furthermore, Zhang and colleagues (2004) found that students whose disabilities are classified as behavioral/emotional were twice as likely as all other students with

21 disabilities to be excluded from instruction through disciplinary procedures such as suspensions.

As Hemmeler (2011) asserted, “The behavior of these students is more likely to be connected to their disability than any other student with a disability; therefore, questions remain about the frequency of seemingly punishing students for having a disability” (p. 7).

Given Zhang and colleagues’ (2004) findings that emotional and/or behavioral disorders impact dropout rates, absenteeism rates, grade point averages, standardized achievement test scores, rates of incarceration, and even adult outcomes, students with emotional and behavioral disabilities are in particular need of social emotional competency (SEC) skills training. However, there is insufficient variability on the variable of disability in the ECLS-K: 2011 fall kindergarten data to incorporate disability into the model; moreover, it is presumed that the presence of an emotional or behavioral disability would negatively correlate so strongly with SEC as to add only trivial predictive power to the model.

Social-Emotional Competence and Disciplinary Practices

The most recent data available indicates disciplinary practices in schools, including detentions, suspensions, and expulsions, are widely used even at the preschool and elementary levels (United States Department of Education, 2016). As early as preschool, gender and racial disparities begin to emerge among the children receiving suspensions, with Black children much more likely to be suspended than White children and boys much more likely to be suspended than girls. Negative short- and long-term consequences of expulsion and suspension practices revealed in the literature include academic failure, negative attitudes about school, and rates of incarceration (Lamont et al., 2013; Petras, Masyn, Buckley, Ialongo, & Kellam, 2011).

Consequently, the U.S. Departments of Education and Health and Human Services have issued a joint statement (2014) recommending that early learning programs should use evidence-based

22 practices and approaches to promote social-emotional competence in young children in order to severely limit expulsions and suspensions.

Disciplinary Practices and Academic Achievement

A growing body of research suggests there is a relationship between school discipline practices—particularly the use of suspensions—and lower academic achievement. The level of disciplinary involvement also has a strong negative relationship with the ability of students to achieve at grade level or graduate from high school. In a large-scale study following three cohorts of Texas seventh graders, Fabelo and colleagues (2011) found that students with one disciplinary action during were twice as likely to repeat a grade or to drop out of school as students with no disciplinary contacts; moreover, as the number of disciplinary contacts increased, so did the odds of grade retention or dropping out.

Although there are certain illegal or violent behaviors that warrant exclusionary consequences in order to maintain a safe school environment, students’ ability to do well academically is generally further impeded when disciplinary involvement leads to removal from the instructional environment. Several mechanisms contribute to that problem. Most prominent in the literature is the simple loss of instructional time that comes with suspensions. Students’ academic achievement tends to improve with increases in instructional time (Brophy, 1988;

Fisher et al., 1981; Greenwood, Horton, & Utley, 2002; Gregory, Skiba, & Noguera, 2010); therefore, reducing instructional time can be counterproductive. Second, students who are excluded from school “may become less bonded to school, less invested in school rules and course work, and subsequently, less motivated to achieve academic success” (Gregory, Skiba, &

Noguera, 2010, p. 60). As a result of those weakened bonds to the school, students are also more likely to repeat the misbehaviors for which they were previously reprimanded and even turn to

23 law-breaking outside school (Fabelo, et al., 2011; Hemphill, Toumbourou, Herrenkohl,

McMorris, & Catalano, 2006).

Social-Emotional Competence and Academic Achievement

The present study examines the relationship between SEC and academic achievement. A substantial body of research supports the premise that social and emotional variables are integral, rather than incidental, to learning (Wang, Haertel, and Walberg, 1997). As Blair (2002) and

Diamond and Lee (2011) have found, early social-emotional competencies, including behavioral regulation, attention skills, and problem solving, are critical to academic achievement in young children. The instrument used to measure SEC in the present study consists of self-control, interpersonal skills, externalizing problem behaviors, and internalizing problem behaviors. The subsections below discuss the impact of the domains measured by each subscale on academic achievement:

Self-control. LeBuffe, Shapiro, and Naglieri (2009) assert that self-control (often characterized as consisting of self-management, self-regulation, self-awareness, personal responsibility, goal-directed behavior, and/or emotion regulation in the literature) is “a child’s success in controlling his or her emotions and behaviors, to complete a task or succeed in a new or challenging situation” (p. 4). For example, behavior exhibiting self-control might be when a child waits his/her turn, stays calm when faced with a challenge, or adjusts well to changes in plans. As Schrunk and Zimmerman (2003) pointed out, students with emotional and behavioral disorders (EBD) often do not manage their own behavior; therefore, programs that provide systematic instruction for developing self-control skills have become increasingly common in schools. Such programs consist of interventions such as self-monitoring, self-evaluation, self- instruction, goal-setting, and strategy instruction. As Elias and colleagues (1997) have asserted,

24 such programs may build greater cognitive-affect regulation in the brain’s prefrontal cortex, indicated by improvements in planning, inhibitory control, and set-shifting (the ability to disengage from an irrelevant task set and switch engagement to a relevant task set).

Self-control has been found to be related to children’s academic achievement, school/classroom adjustment, and even kindergarten readiness (Bierman, Nix, Greenberg, Blair,

& Domitrovich, 2008; Bodrova, & Leong, 2006; Howse, Calkins, Anastopoulos, Keane, &

Shelton, 2003; McClelland et al., 2007). Merrell and Gueldner (2010) found that when students have poor emotion regulation, they are less able to engage in the cognitive processes needed to attend to instruction, remember concepts, and plan to complete homework. Zins and colleagues

(2004) also found that emotion regulation can affect the development of children’s intrinsic motivation to face challenges, and this may influence long-term academic engagement.

Moreover, Casillas and colleagues (2012) found that “self-regulation, as measured by orderly conduct, has a relatively high association with GPA (r = .37) and standardized achievement (r =

.28), respectively” (p. 410).

To date, three meta-analyses have examined the relationship between self-control and academic achievement. First, Hughes, Ruhl, and Misra (1989) reviewed six studies conducted on school-aged populations and indicated that all six studies reported positive findings regarding academic performance in the settings in which self-management treatment variables were manipulated. Somewhat concurrently, Nelson, Smith, Young, and Dodd (1991) concluded from a review of three studies of self-management intervention programs for students with EBD that self-management procedures were viable tools to promote the academic behaviors of such students. Most recently, Mooney, Ryan, Uhing, Reid, and Epstein (2005) reviewed 22 studies of self-management interventions targeting academic outcomes and found that overall, the studies

25 revealed that students with EBD demonstrated improvements in discrete academic skills when self-management interventions were introduced when compared to baseline conditions.

Specifically, Mooney and colleagues found that the mean effect size across all self-management intervention types and academic domains was 1.80; in other words, average student gains were nearly two standard deviations. Furthermore, there is an evidence base reporting favorable effects of self-control on academic achievement for both students with disabilities and students without disabilities (e.g., Fantuzzo, Polite, Cook, & Quinn, 1988; Graham, Harris, & Reid, 1992;

Reid, 1996; Shapiro, Durnan, Post, & Levinson, 2002; Skinner & Smith, 1992; Swanson &

Sachse-Lee, 2000).

Another component of self-control is personal responsibility. LeBuffe, Shapiro, and

Naglieri (2009) define personal responsibility as “a child’s tendency to be careful and reliable in her/his actions and in contributing to group efforts” (p. 4). Examples of behavior exhibiting personal responsibility include a child remembering important information, serving an important role at home or in school, and handling personal belongings with care. As Dweck and Reppucci

(1973) found, students who exhibit weaker academic achievement tend to be those who take less personal responsibility for the outcomes of their actions and who, when they do accept responsibility, attribute success and failure to presence or absence of ability rather than to expenditure of effort; by contrast, those students who persist in the face of prolonged failure tend to place more emphasis on the role of effort in determining the outcome of their behavior.

Dweck and Reppucci’s findings are largely consistent with both prior and subsequent literature on the relationship between personal responsibility and achievement. Weiner and

Kukla (1970), for example, found that individuals high in achievement motivation are more likely to take personal responsibility for success than individuals low in achievement motivation;

26 however, the authors did not find clear differences in perceived responsibility for failure between the two motive groups. In addition, Crandall, Katkovsky, and Crandall (1965) found in a study of students in grades 3 through 12 that children’s sense of personal responsibility

(operationalized as scores on a scale measuring children’s beliefs that they, rather than other people, are responsible for their intellectual and academic successes and failures) was already established by third grade, that older girls gave more self-responsible answers than older boys, and that responsibility scores were moderately related to intelligence and family size.

More recent literature has supported previous findings on the impact personal responsibility has on academic achievement. As Benham (1995) summarized in her review of 80 studies spanning several decades of research on the subject, “students’ perceptions about the amount of control they have over academic successes and failures contribute significantly to school performance” (p. 3). Although all students are responsive to some extent during instruction, those students who display initiative, intrinsic motivation, and personal responsibility have been found to achieve particular academic success (Zimmerman, 1990).

Another component of self-control is goal-directed behavior. LeBuffe, Shapiro, and

Naglieri (2009) define goal-directed behavior as “a child’s initiation of, and persistence in completing, tasks of varying difficulty” (p. 4). A child would exemplify goal-directed behavior when he/she seeks out additional information, takes steps to achieve goals, or keeps trying when unsuccessful. As Locke and Latham (2002) have argued, goal-directed behavior is predictive of academic outcomes in student populations ranging from elementary school to graduate school.

Dweck and her colleagues (Dweck, 1986; Dweck & Leggett, 1988; Elliott & Dweck,

1988) found that two personality traits characterized children in the classroom. The authors described the first trait as learning goal orientation (LGO); LGO is a desire to acquire knowledge

27 and skills. LGO stands in contrast with performance goal orientation (PGO), which is a desire to attain a performance outcome such as a grade or a score. The authors found that students primarily motivated by an LGO performed better on school-related subjects than those students primarily motivated by a PGO. In other words, students who wish to “learn for learning’s own sake,” so to speak, likely exhibit stronger academic achievement than those students who wish to simply earn an A on a test. This suggests that the relationship between goal-directed behavior and academic achievement is influenced by how goal-directed behavior is operationalized.

Another component of self-control is self-awareness. LeBuffe, Shapiro, and Naglieri

(2009) describe self-awareness as “a child’s realistic understanding of her/his strengths and limitations and consistent desire for self-improvement” (p. 4). Examples of behavior exhibiting self-awareness include a child giving an opinion when asked, describing how he/she is feeling, and asking for feedback. As Aronson (2002) proposed, programs designed to promote social- emotional learning are successful because self-awareness leads students to demonstrate greater effort and persistence in the face of challenges.

As Goleman (1995) asserted, “Self-awareness—recognizing a feeling as it happens—is the keystone of emotional intelligence…The ability to monitor feelings from moment to moment is crucial to psychological insight and self-understanding” (p. 43). This sort of self- understanding, in which students gain greater awareness of how they acquire knowledge and obtain an insight into their strengths and weaknesses, allows students to improve their own academic performance. As Weil and colleagues (2013) found, for example, increases in students’ metacognitive abilities were accompanied by greater achievement. Programs designed to promote social-emotional competencies therefore typically encourage children to discuss

28 feelings and experiences that are personally meaningful in the context of a supportive classroom environment.

Interpersonal skills. LeBuffe, Shapiro, and Naglieri (2009) describe interpersonal skills as “a child’s consistent performance of socially acceptable actions that promote and maintain positive interactions with others” (p. 4). A child would exhibit strong interpersonal skills when he/she compliments or congratulates someone, offers to help someone, or expresses concern for someone. Reviewing five decades of resilience research in child development, Luthar (2006, p.

780) concluded, “Resilience rests, fundamentally, on relationships.” Children with poor peer relations tend to experience a wide range of academic difficulties, including weak school engagement (Kuperminc, Leadbeater, & Blatt, 2001), poor academic achievement (Guay,

Boivin, & Hodges, 1999), high absenteeism (DeRosier, Kupersmidt, & Patterson, 1994), and dropping out of school (Cairns, Cairns, & Neckerman, 1999).

In the literature, interpersonal skills are typically described as consisting of prosocial behaviors such as cooperating, sharing, and helping, and are measured through peer and teacher ratings on instruments such as the Social Skills Rating System (Gresham & Elliott, 1990). Such skills have been found to be predictive of third-graders’ end-of-year grades in reading and mathematics (Elias and Haynes, 2008), and when such skills are measured in third grade, they form a coherent latent variable that can predict academic grades as late as eighth grade (Caprara,

Barbaranelli, Pastorelli, Bandura, & Zimbardo, 2000; Malecki & Elliott, 2002). Importantly, these studies often took negative variables such as aggression into consideration and found that it was only the interpersonal skills, and not those skills in combination with aggression, that impacted academic achievement.

Interpersonal skills are also related to (and sometimes treated as synonymous with, or consisting of) empathy, prosocial behavior, altruistic behavior, and emotion knowledge (Caprara,

Barbaranelli, Pastorelli, Bandura, & Zimbardo, 2000; Goleman, 1995; Wentzel, 1993). LeBuffe,

Shapiro, and Naglieri (2009) use the term “social-awareness,” which is “a child’s capacity to interact with others in a way that shows respect for their ideas and behaviors, recognizes her/his impact on them, and uses cooperation and tolerance in social situations” (p. 4). A child who can get along with different types of people, cooperate with peers or siblings, or forgive someone who has hurt or upset him/her would likely be perceived as possessing strong social-awareness.

Several studies have found links between interpersonal skills, academic achievement, and classroom adjustment in preschoolers (Garner & Waajid, 2008; Leerkes, Paradise, O’Brien,

Calkins, & Lange, 2008). Izard and colleagues (2001) even found that 5-year-old children’s emotion knowledge was predictive of their age 9 social and academic competences

(operationalized as scores on the Social Skills Rating System; Gresham & Elliott, 1990).

A well-established body of literature has revealed a relationship between students’ empathetic understanding (often considered one component of interpersonal skills) and their academic performance. For example, Bonner and Aspy (1984) identified significant correlations between student scores on measures of empathetic understanding and their grade point averages.

In addition, Feshbach and Feshbach (1987) found that empathy was a significant predictor of later reading and spelling achievement, but only in girls. Moreover, a review of the literature pertaining to empathy training and instruction programs concluded that such interventions enhanced both critical thinking skills and creative thinking skills (Gallo, 1989). More recently,

Wentzel (1993) found a significant positive relationship between sixth- and seventh-graders’ prosocial behavior and grade point average, as well as a significant negative relationship between

30 the students’ antisocial behavior and grade point average. Finally, Caprara and colleagues

(2000) found that prosocial relations in elementary school years have a strong and positive impact on later academic achievement during middle school; however, the authors did not find evidence supporting Wentzel’s previous conclusion pertaining to the relationship between antisocial behavior and academic achievement.

Despite previous findings, some more recent literature calls into question the causal direction of the relationship between interpersonal skills (or empathy) and academic achievement. Kidd and Castano (2013), for example, found that reading classic works of literary fiction, as opposed to more accessible works of popular fiction, engages the “psychological processes needed to gain access to characters’ subjective experiences…Readers of literary fiction must draw on more flexible interpretive resources to infer the feelings and thoughts of characters. That is, they must engage [Theory of Mind] processes” (p. 1). In other words, by forcing students engage in the more difficult academic endeavor of thinking, empathizing, and assuming, rather than simply interpreting the tropes commonly employed in popular literature, reading classic works of literary fiction enhances students’ emotional intelligence, and therefore their interpersonal skills.

Theory of Mind, as discussed in the previously mentioned findings, is a concept related to empathy (and, by extension, to interpersonal skills); while empathy is the recognition and understanding of other people’s beliefs, desires, and emotions, Theory of Mind is the ability to understand that those beliefs, desires, and emotions are different from one’s own (Premack &

Woodruff, 1978). Theory of Mind has similarly been found to enhance academic performance.

One recent study of kindergarten students, for example, found that Theory of Mind correlated

31 strongly with academic performance over the course of a school year (Lecce, Caputi, & Pagnin,

2013).

Externalizing problem behaviors. According to Liu (2004), externalizing behaviors are negative behaviors that are focused outward onto an individual’s external environment.

Externalizing behaviors consist of aggression, delinquency, and hyperactivity; other examples of such behaviors include disobeying rules, cheating, stealing, and destruction of property.

Program designed to reduce externalizing problem behaviors in young children often focus on promoting decision-making skills, encouraging children to find an “approach to problem solving that involves learning from others and from her/his own previous experiences, using her/his values to guide her/his action, and accepting responsibility for her/his decisions” (LeBuffe,

Shapiro, & Naglieri, 2009, p. 4). A child would display strong decision making when he/she follows the example of a positive role model, accepts responsibility for misbehavior, and learns from experiences. In the measure of externalizing problem behaviors used in the present study, a higher score (i.e., fewer incidences of externalizing behaviors) would suggest that the child has stronger decision-making skills.

Researchers have often used the choices children make in response to hypothetical peer dilemmas (such as peer provocation) as a measure of responsible decision-making. As Zins and

Elias (2006) asserted, students who use problem-solving skills to overcome obstacles and make responsible decisions about studying and completing homework perform better academically.

More specifically, responsible decision-making has been linked to classroom adjustment and early academic functioning (Bierman, Domitrovich, et al., 2008; Denham, Bouril, & Belouad,

1994), as well as grade-point average (Dubow, Tisak, Causey, Hryshko, & Reid, 1991;

Rotheram, 1987). Moreover, Ryan, Gheen, and Midgley (1998) have found that students’

32 avoidance of help seeking is negatively related to students’ academic efficacy—particularly in classrooms where teachers do not believe they should attend to students’ social and emotional needs.

Internalizing Problem Behaviors. According to Rooney and colleagues (2013), internalizing behaviors are negative behaviors that are focused inward. Examples of internalizing problem behaviors include fearfulness, depression, loneliness, social withdrawal, and somatic complaints. Programs designed to prevent or reduce internalizing problem behaviors in school-age children are generally focused on promoting optimistic or positive thinking. Therefore, in the instrument used to assess internalizing problem behaviors in the present study, a higher score would indicate greater levels of optimistic thinking.

LeBuffe, Shapiro, and Naglieri (2009) conceptualize the construct of optimistic thinking as “a child’s attitude of confidence, hopefulness, and positive thinking regarding herself/himself and her/his life situations in the past, present, and future” (p. 4). Although there is no consistent definition for optimism in the extant literature, the definition perhaps best fitting to the present study’s resilience framework was identified by Seligman (1991), who asserted that optimistic thinking is exemplified when an individual interprets negative events in his/her life as temporary, rather than permanent or stable. Individuals who are able to give the negative event a temporary status are more likely to develop resilience, which is associated with more effective coping.

Conversely, pessimistic thinkers interpret positive life events as being temporary, while optimistic thinkers assign positive life events a permanent status.

Much of the literature on the relationship between optimistic thinking and academic achievement is in regard to adolescents, rather than the early childhood population that served as the subject of the present study. For example, Maata, Stattin, and Nurmi (2002) found that

33 adolescent students who used an optimistic achievement strategy exhibited less depression, better teacher relations, improved academic achievement, less norm-breaking behavior, and greater self-esteem than students who did not use an optimistic achievement strategy. Similarly, Hall,

Spruill, and Webster (2002) found higher Grade Point Averages (GPAs) in students who felt they had a greater sense of control over their future than in students who felt they had no control over their future. In other words, the belief that success was under the students’ personal control resulted in greater effort applied towards goal achievement, which in turn led to greater achievement.

In contrast to the aforementioned findings, Harju and Bolen (1998) found that optimism was only slightly related to academic achievement (again, operationalized as GPA). In addition,

Chang, D’Zurilla, and Maydeu-Olivares (1994) found no significant relationship between optimism indices and academic performance; however, the sample for their study was 400 college students. The inconclusive nature of the relationship between optimistic thinking and academic achievement in the literature begs further investigation.

Interrelations among SEC components. Each of the components of SEC discussed here have been found to interact with one another in a variety of ways. For example, Denham and colleagues (2003) and Miller and colleagues (2006) have argued that emotion regulation and emotional expressiveness are likely to be related; moreover, Leerkes, Paradise, O’Brien, Calkins, and Lange (2008) have found that emotion regulation and emotional knowledge are related; after all, children’s ability to identify their own emotions and others’ emotions helps them formulate and choose fruitful strategies for regulating those emotions.

Both Blair (2002) and the team of Howse, Calkins, Anastapoulos, Keane, and Shelton

(2003) have also found relationships among various types of self-regulation, such as emotional

34 regulation and behavioral regulation. Rimm-Kaufman, Curby, Grimm, Brock, and Nathanson

(2009) even found that among kindergarteners, direct assessments of self-regulation taken at the beginning of the school year were predictive of students’ teacher-reported behavioral regulation and work habits in the spring; in other words, a student who could walk on a balance beam, sort toys, or wait for a gift to be wrapped in the fall would be likely to be rated by his/her teacher as having the ability to stick to a task, anticipate consequences, work toward goals, follow classroom procedures, work well independently, and use time wisely in the spring.

Similarly, authors have found relationships among SEC’s self-awareness and responsibility components. For example, Rotheram (1987) found that self-esteem was related to social problem-solving. Moreover, Zahn-Waxler and colleagues (1994) found relationships between emotion knowledge and teacher ratings of classroom social behavior. Therefore, there is evidence that the components of SEC do not exist in isolation; they are intrinsically associated with one another.

Several researchers have gone further, examining the relationships among multiple components of SEC and academic achievement. Eisenberg, Sadovsky, and Spinrad (2005), for example, proposed that verbal ability and emotion knowledge are predictive of emotion regulation, which, in turn, is predictive of academic motivation and skills. However, Schultz,

Izard, Ackerman, and Youngstrom (2001) found a conflicting structure, wherein attentional and behavioral regulation are predictive of emotion knowledge. Denham and Brown (2010) have suggested that the discrepancy between the two studies may be due to the measurement of SEC variables taking place at different time intervals, or due to the possibility of differing factor structures for different student subpopulations. However, given the lack of consensus in the

35 literature regarding the dynamics among academic achievement and various SEC components

(other than that some relationship exists), further research in this area is warranted.

SEC programs and curricula. Given the abundant evidence that there is a relationship between SEC and academic achievement, a growing number of jurisdictions are establishing

SEC standards that must be met alongside their academic standards. Such standards have been introduced or proposed in at least eleven U. S. states and one Canadian province (LeBuffe &

Fleming, 2014). The jurisdictions cited by LeBuffe and Fleming include the U. S. states of

Illinois, Ohio, New York, Washington, New Jersey, Pennsylvania, Kansas, Oklahoma,

Tennessee, and Vermont, as well as the city of Anchorage, Alaska, and the Canadian province of

British Columbia. This suggests that there is no geographic or political pattern by which the introduction of SEC standards might be predicted; this is not a “red state” or “blue state” phenomenon, but rather a nonpartisan translation of empirical evidence into policy—and, therefore, a trend that is likely to continue. Due to this growing awareness among education practitioners and policymakers across the political spectrum that SEC influences academic achievement, various programs and curricula have been developed specifically for the purpose of helping to improve students’ SEC skills.

A growing body of literature has focused on the academic benefits of programs designed to improve students’ SEC skills. Several such programs have been found to be effective, including the Incredible Years series (Webster-Stratton, Reid, & Stoolmiller, 2008) the

Promoting Alternative Thinking Strategies (PATHS) curriculum (Domitrovich, Cortes, &

Greenberg, 2007), and many others. It should come as no surprise, given the vast body of research, that several such interventions can influence students’ SEC skills. Hawkins (1997), for example, found that children are generally more engaged in their learning when their teachers

36 offer students frequent opportunities to use SEC skills in meaningful ways. Wilson, Gottfredson, and Najaka (2001) found in a meta-analysis examining 165 studies of programs designed to improve students’ SEC skills that such programs resulted in increased attendance and decreased dropout rates. Zins and colleagues (2004) found that programs designed to improve students’

SEC skills improved student attitudes, behaviors, and academic performance. Payton and colleagues (2008) found that interventions designed to improve students’ SEC skills were accompanied by increases in achievement test scores of up to 17 percentile points.

Subsequent evaluations on the impacts of SEC interventions have supported existing evidence on the relationship between SEC and academic achievement across a variety of student populations. A more recent meta-analysis of over 200 studies conducted by Durlak, Weissberg,

Dymnicki, Taylor, and Schellinger (2011) revealed that such interventions resulted not only in increases in students’ SEC, but also in reductions in student conduct problems and emotional distress, as well as improvements in prosocial behaviors, attitudes toward school, and scores on standardized reading and mathematics assessments. In a study of gifted students, Kong (2013) found that even when first controlling for intelligence (operationalized as scores on the Cognitive

Abilities Test), SEC (operationalized as scores on the Devereux Student Strengths Assessment, or DESSA) added value when predicting students’ achievement (operationalized as scores on the

Stanford Achievement Test). Most recently, LeBuffe and Fleming (2014) found that students in grades 3 through 5 in a majority-Hispanic Pennsylvania school district who had typical or exceptionally strong DESSA scores were nearly three times as likely to perform in the proficient or advanced level on a statewide achievement assessment as students who had exceptionally weak DESSA scores. The findings suggest, then, that rather than diverting schools from their

37 primary academic mission, developing programs designed to improve students’ SEC skills advances that academic mission.

Achievement in Subject Areas

As the studies described here indicate, researchers vary in how they have chosen to operationalize academic achievement, with some using narrow measures such as standardized assessment scores and others adopting broader, more holistic sub-constructs such as school attitude (e.g., motivation or attachment to school), school behavior (e.g., attendance, engagement, or study habits), and school performance (e.g., academic grades or test scores; Zins et al., 2004). Even among those studies that use only standardized assessment scores to measure achievement, the instruments used vary. Scholars have found relationships between SEC and scores on the TerraNova group achievement test (LeBuffe, Shapiro, & Naglieri, 2009), the

Stanford Achievement Test (Kong, 2013), the Pennsylvania System of School Assessment

(LeBuffe & Fleming, 2014), and many other state-level and nationwide standardized tests.

Nonetheless, the fact remains that regardless of how academic achievement is defined, there has been found to be evidence of relationship between it and SEC.

Standardized achievement tests typically have at least two sections: one dedicated to verbal skills (e.g., reading, writing, etc.) and one dedicated to quantitative skills (e.g., arithmetic, measurement, geometry, algebra, etc.). Other assessments may have sections on other academic disciplines, but the measure used in the present study examines only reading and mathematics proficiency.

Second-Level Variables: The Impacts of the Student’s School

The present study utilized multilevel modeling, wherein student-level variables such as social-emotional competence, race, socioeconomic status, and gender were examined at the first

38 level of the model, and school-level variables collected in the ECLS-K: 2011 were examined at the second level of the model. These second-level variables included aggregated context factors

(e.g., poverty rate and school size), organizational practice factors (e.g., student attendance rate and incidence of individualized educational plans), and parent involvement factors (e.g., parental attendance at school functions).

Throughout the 1970s and 1980s, there emerged a body of literature discussing how to improve the efficacy of K-12 institutions. This so-called “effective schools” literature found that improved student achievement was associated with strong school leadership, a focus on students’ academic outcomes, a positive and orderly school climate, and teachers’ positive expectations for students (Brookover, Beady, Flood, Schweitzer, & Wisenbaker, 1979; Clark, Lotto, &

McCarthy, 1980; Edmonds, 1979; Rowan, Bossert, & Dwyer, 1983). Although critics such as

Purkey and Smith (1983) and Rosenholtz (1985) argued that these “effective schools” studies often failed to arrive at common factors supported by robust statistical evidence, some factors identified in those studies have resurfaced in the recent literature on standards-based reforms, and merit further empirical testing.

More recent research has revealed that improvements in academic achievement are associated with several family-, classroom-, school-, and district-level factors, including the allocation of resources to support the infusion of technology, smaller school sizes (Ayers,

Bracey, & Smith, 2000; Williams, 1990), alignment of classroom instructional practices with new content standards, longer blocks of time dedicated to subject-specific instruction, development of practices designed specifically to serve multicultural student populations, and increased parent involvement in children’s education. Moreover, there is substantial evidence that school context factors, such as overall poverty levels among the students in a school, can

39 influence leadership behaviors, schooling practices, and organizational culture (Hannaway &

Talbert, 1993; Hannaway & Kimball, 1998), and therefore, academic outcomes. These hypothesized predictors of academic achievements were incorporated into the model.

Frequency of Individualized Educational Plans

An individualized educational plan (IEP) is a special programmatic accommodation put into place for students with some kind of academic difficulty, learning disability, or psychosocial disorder. There is some research indicating that the percentage of students with an IEP within a school is predictive of the school’s academic achievement. For example, Lee, Shin, and Amo

(2013) found that schools identified by New York State as being in need of improvement (i.e., schools in accountability treatment, as opposed to schools in good standing) had significantly greater portions of students with IEPs than those schools identified as being in good standing.

Therefore, in the ECLS-K: 2011, the “special education” service variable refers to the incidence of IEPs, aggregated by school (i.e., the portion of children in the study sample identified by their schools as having IEPs on file).

Student Attendance Rate

A substantial body of research has found that class attendance is a useful predictor of subsequent academic achievement. Regular school attendance is an important factor in school success (Rothman, 2001). Research has shown a direct correlation between good attendance and student achievement (Dekalb, 1999). Conversely, poor attendance has been linked to poor academic achievement (Ziegler, 1972). Therefore, the ECLS-K: 2011 included an item on students’ attendance. Student attendance was computed as a percentage of total days attended in the school year. This index was based on the number of absences reported for each child in the

ECLS-K: 2011 database, and aggregated across children within each school.

Parental Involvement in the School

A substantial body of literature has found that parenting and family factors are major predictors of children’s cognitive and social development because families play a central role in children’s lives and both genetic and environmental influences are known to have a combined effect on their scholastic success (Collins, Maccoby, Steinberg, Hetherington & Bornstein,

2000). As Bricheno and Thornton (2007) have asserted, the absence of role models and mentors from the families and social environments of children who live in disadvantaged neighborhoods is often proposed as an explanation for those children’s diminished educational and professional outcomes later in life.

Parental involvement in children’s studies, particularly in terms of academic socialization, has consistently been found to improve students’ academic achievement and promote children’s overall health and cumulative wellbeing (Westerlund, Gustafsson, Theorell,

Janlert, & Hammarstrom, 2013). As Boggess (2009) concluded, parental involvement has the long-term potential to break the multigenerational cycle of poverty. Moreover, as Little-Harrison

(2012) and Liu and Wang (2008) have observed, parental involvement does a great deal to moderate the established relationship between socioeconomic status and academic achievement.

Similarly, Parker (2013) and Dowey (2013) have observed that verbally persuasive, encouraging, supportive, and involved parents can help ameliorate the lack of school-age minority girls interested in science and, subsequently, the underrepresentation of minority women enrolled in undergraduate STEM programs. Families living in high-poverty neighborhoods are also known to employ fewer education-oriented practices with their children. Large scale studies using nationally representative databases have revealed that such education-oriented parental practices have an extremely positive effect on children’s mathematics achievement, especially for children

41 living in disadvantaged neighborhoods (Greenman, Bodovski, & Reed, 2011). Children with high parental expectations for education and maternal years of education are better able to learn basic mathematics skills (Wang, Shen, & Byrnes, 2013).

Parental interest in their children’s education may in fact have shielding effects on academic achievement brought about by deprivation. An explanation offered for this is perhaps it camouflages the effect of a range of risk involving factors, including low socioeconomic position, psychological and physiological stress, and negative emotions. In particular, parental interest in their children’s studies during the final year of high school has been found to better predict adult allostatic load, which is the physiological outcome of chronic stress. Parental academic involvement has also been found to predict children’s lifetime academic and occupational achievement more accurately than do parent’s social class or availability of practical academic support (Westerlund, Gustafsson, Theorell, Janlert, & Hammarstrom, 2013).

The supportive but firm parenting style described in the educational psychology literature as authoritative parenting (i.e., neither permissive nor authoritarian) has been shown to be a significant predictor of children’s self-efficacy, resilience, and academic achievement (Speight,

2010), as well as at-risk status, academic performance, hopelessness, and depression (Bryant,

2007). Speight (2010) suggested that this finding is due to supportive, authoritative parents acting as role models, thereby adding a shield against deprivation by mitigating risk factors.

Families’ perceptions of, and interactions with, schools and teachers can also play an essential role in young people’s educational outcomes. For example, Hampden-Thompson and

Galindo (2016) found, positive school-family relationships are a predictor of achievement, and this association is mediated by the degree of parents’ satisfaction with their child’s school.

School Size

The extant literature suggests that the ideal school size for younger children is roughly

300–400 students (Williams, 1990); in other words, schools with more than 500 students are less effective at promoting student achievement, especially among minority and low-income students.

Smaller schools have also been found to increase attendance rates, teacher satisfaction, and parent and community involvement (Williams, 1990; Ayers, Bracey, & Smith, 2000). However, as Lee and Smith (1993) note, there are some positive consequences of increased school size found in the literature; this more optimistic perspective draws on the economics of scale to focus on the greater diversity of program offerings and on resource issues. Nonetheless, most literature on school size centers on the more formal and impersonal social interactions as impeding success. Recently, research evidence is accumulating to support the argument that student achievement is weaker in larger schools. Greater school size is shown to be associated with reduced academic engagement among eighth-grade students (Lee and Smith 1993), and at the high school level with lower student participation in school activities (Lee and Smith 1995), less satisfaction with school experiences and lower school attendance (Lindsay 1982), and higher dropout rates (Pittman and Haughwout 1987). Based on these research findings, many reforms call for dividing large schools into smaller subunits (e.g., Oxley 1994, Boyer 1995), in order to provide students with a more stable and supportive educational experience.

School Sector

There is some literature suggesting the students enrolled in private schools perform better in reading and mathematics than their peers enrolled in public schools. For example, Braun,

Jenkins, and Grigg (2006) found that in grades 4 and 8 for both reading and mathematics, students in private schools achieved at significantly higher levels than students in public schools; however, adjusting the comparisons for student characteristics (such as family background)

43 resulted in reductions in all four average differences. Based on adjusted school means, the average for public schools was significantly higher than the average for private schools for grade

4 mathematics, while the average for private schools was significantly higher than the average for public schools for grade 8 reading. The average differences in adjusted school means for both grade 4 reading and grade 8 mathematics were not significantly different from zero. Moreover, within the private school category, there were significant differences in achievement among

Catholic, Lutheran, and Conservative Christian schools, with Conservative Christian schools performing about the same as public schools (and significantly worse than Catholic and Lutheran schools) in grade 8 reading and performing significantly worse than public schools (and other types of private schools) in grade 8 mathematics.

Aggregate Poverty within the School

Aggregate poverty within the school was operationalized as the percentage of students within the school who are of a low socioeconomic status. Poverty is frequently cited as an academic risk factor in the clinical and childhood development literature (Garmezy, 1993;

Garmezy & Masten, 1986; Werner, 1993). Consistent with literature in clinical and child development fields, Zill and West (2001) found in their analyses of the ECLS-K 1998 data that variations in kindergarten academic achievement were partially related to family risk factors; one such family risk factor was welfare dependency or poverty status. Children’s health and behaviors were, in turn, found to be dependent on family risk factors. These family risk factors were more common among kindergartners from ethnic minorities than among those from White families in the ECLS-K 1998 sample, and these at-risk children started with lower scores on cognitive assessments in the beginning of the kindergarten year.

Even the level of poverty within a student’s school can serve as a predictor of a student’s academic performance (Hansen et al., 2011). The impact of the students’ socioeconomic background on academic achievement, while largely outside of school influence, is not likely to be entirely independent of school arrangements. Rather, schools themselves may be influenced in a variety of ways by the background of their students. Schools located in high-poverty neighborhoods tend, for example, to be bigger; such schools also have less control over their recruitment, and, thus, end up with a teaching staff that is less normatively coherent. Moreover, high-poverty schools tend to be located in neighborhoods with fewer academic role models for students to mimic (Hansen et al., 2011). Hence, any valid model of relations between school- based organizational factors and achievement must take the effects of background factors such as aggregate poverty on both a school’s organization and its average achievement into account.

CHAPTER III

METHODS

Procedure

The present study utilized existing data from the Early Childhood Longitudinal Study,

Kindergarten Class of 2010-11 (ECLS-K: 2011). The National Center for Education Statistics

(NCES) within the Institute of Education Sciences (IES) of the U.S. Department of Education sponsored collection of the data between fall of 2010 and spring of 2016 as part of a national program examining a variety of early childhood variables that could be related to academic achievement (Mulligan, Hastedt, & McCarroll, 2012). Information regarding child development, early learning, and school progress was drawn together from multiple sources to provide data on children's early school experiences beginning with kindergarten and following children through fifth grade. The purpose of the ECLS-K: 2011 was to provide information on children's status at entry to school, their transition into school, and their progression through the elementary grades.

Some of the data collected as part of the ECLS-K: 2011 is publicly available on the NCES website, although data from the later years of the study has not yet been released. Therefore, the present dissertation examined only data from prior to 2012.

Data collected for the ECLS-K: 2011 came from various instruments administered to children, their families, teachers, schools, and care providers; these data provided information on the children’s cognitive, social, emotional, and physical development (Mulligan, Hastedt, &

McCarroll, 2012). Surveys administered to caregivers, teachers, and administrators also provided information on children's home environments, home educational activities, school environments, classroom environments, classroom curricula, teacher qualifications, and before- and after-school care. The data of interest to the present dissertation include: the survey administered to

46 administrators in fall 2010 and spring 2011 (i.e., the Administrator Questionnaire), which provided data on school-level variables; the survey administered to teachers in fall 2010 and spring 2011 (i.e., the Teacher Questionnaire); the interview administered to caregivers in fall

2010 and spring 2011 (i.e., the Parent Interview), which provided data on caregivers’ income, education, and employment, as well as children’s race and gender; the two-stage measure of social-emotional competence, which included items measuring students’ self-control, interpersonal skills, externalizing problem behaviors, and internalizing problem behaviors; and the measure of academic achievement, which assessed students’ proficiency in mathematics and reading.

On February 3, 2017, the Kent State University Institutional Review Board reviewed and approved the principal researcher’s Application for Approval to Use Human Research

Participants as Level I/Exempt from Annual review research. The Institutional Review Board found that the research project involves minimal risk to human subjects and meets the criteria for the following category of exemption under federal regulations: Existing Documents, Data, and

Specimens (Exemption 4). The letter from the Institutional Review Board can be found in

Appendix A.

Participants

The 18,174 children in the ECLS-K: 2011 consist of a nationally representative sample selected from both public and private schools attending both full-day and part-day kindergarten in 2010-11 (Mulligan, Hastedt, & McCarroll, 2012). The children were enrolled in 970 schools throughout the United States at the beginning of the study. The children came from diverse socioeconomic and racial/ethnic backgrounds, and the sample includes both children in kindergarten for the first time and kindergarten repeaters. Also participating in the study were the

47 children's parents, teachers, schools, and before- and after-school care providers; however, the individual students themselves are considered the primary unit of observation and analysis. The

ECLS-K: 2011 is a voluntary study; no one was required to respond to surveys or complete any instruments. In addition, all data provided by respondents that relate to or describe identifiable characteristics of individuals are maintained anonymously and are used only for statistical purposes.

The sample was nationally representative in terms of student age, race/ethnicity, socioeconomic status, and household language. As reported by Mulligan, Hastedt, and

McCarroll (2012), 95 percent of kindergarten students in fall 2010 were first-time kindergarteners, as opposed to kindergarten-repeaters. Of these first-time kindergarteners, most were born prior to September 2005 (7 percent of the cohort was born in September 2005 or later), meaning that most of these kindergartners were 5 years of age or older at the start of the school year. 53 percent of these first-time kindergartners were White, 24 percent were Hispanic,

13 percent were Black, 4 percent were Asian, 4 percent were two or more races, 1 percent was

American Indian or Alaska Native, and less than 0.5 percent was Native Hawaiian or other

Pacific Islander. Students living in households with incomes below the federal poverty level made up 25 percent of these first-time kindergartners. 38 percent had parents whose highest level of education was a bachelor’s degree or higher and 76 percent started kindergarten living in a two-parent household. 84 percent of first-time kindergartners lived in a home with English as the primary language.

The ECLS-K: 2011 cohort was sampled using a multistage sampling design. The first- stage sampling frame was a list of the 3,141 counties in the United States. The county-level frame was used to form a list of primary sampling units (PSUs) from which a subset of PSUs

48 was sampled. Ten PSUs with a large measure of size (defined as the number of 5-year-old children in the PSU) were included in the ECLS-K: 2011 sample with certainty. The remaining

PSUs were sampled using a stratified sampling procedure. They were grouped into 40 strata defined by region, size, per capita income, and the racial/ethnic distribution of 5-year-old children residing in the PSU. Two PSUs were selected without replacement in each stratum, with probability proportional to size and with known joint probability of inclusion of the pair.

The second stage of sampling involved selecting samples of schools that have kindergarten programs from within the sampled PSUs. In order to achieve the base-year target of 180 private and 720 public schools, approximately 280 private schools and 1,030 public schools were sampled. Schools were selected with probability proportional to kindergarten enrollment. In the third stage of sampling, approximately 23 kindergartners were selected from a list of all enrolled kindergartners or students of kindergarten age being educated in an ungraded classroom in each of the sampled schools. Asian/Pacific Islander students were oversampled to assure that the sample included enough students of this race/ethnicity to be able to make accurate estimates for these students as a group.

Measures

In addition to demographic data obtained from the administrator questionnaires and parent interviews, the present dissertation considered two measures compiled from other assessment instruments as part of the ECLS-K: 2011. These instruments include a measure of

SEC and a measure of academic achievement. Below are descriptions of those two instruments.

Socioemotional Development Assessments

The measure of social-emotional competence used in the ECLS-K: 2011 was adapted from the Social Skills Rating System (SSRS; Gresham & Elliott, 1990), and was included in the

49 child-level teacher questionnaire. In fall of 2010, teachers reported how often students exhibited certain social skills and behaviors using a four-option frequency scale ranging from “never” to

“very often.” The battery includes some items taken verbatim from the Social Skills Rating

System, some items that are modifications of original Social Skills Rating Systems items, and some items that measure the same kinds of skills and behaviors captured in the Social Skills

Rating System but use wording developed specifically for the ECLS studies.

Four social skill subscales were developed based on teachers’ responses to various SSRS items. The score on each subscale is the mean rating on the items included in the scale. The four teacher-assessed scales are as follows: self-control (4 items), interpersonal skills (5 items), externalizing problem behaviors (6 items), and internalizing problem behaviors (4 items). A score was computed when the respondent provided a rating on at least a minimum number of the items that composed the scale. The minimum numbers of items that were required to compute a score were as follows: self-control (3 out of 4 items), interpersonal skills (4 out of 5 items), externalizing problem behaviors (4 out of 6 items), and internalizing problem behaviors (3 out of

4 items). Higher scores indicate that the child exhibited the behavior represented by the scale more often (e.g., higher self-control scores indicate that the child exhibited behaviors indicative of self-control more often; higher interpersonal skills scores indicate that the child interacted with others in a positive way more often). The table below reflects the descriptive statistics and reliability coefficients (Cronbach, 1951) for each of those four subscales, as measured in fall of

2010 (Tourangeau et al., 2017, p. 3-35). As the data indicate, each subscale’s reliability coefficient was strong enough to suggest that the items within each subscale measure the same underlying concept. Note: “X1” refers to fall of 2010 (i.e., the first round of measurements).

Table 2

Descriptive Statistics and Reliability Coefficients for Each SSRS Subscale

Note: Reprinted from Tourangeau, K., Nord, C., Lê, T., Wallner-Allen, K., Vaden-Kiernan, N., Blaker, L., & Najarian, M. (2017). Early Childhood Longitudinal Study, Kindergarten Class of 2010–11 (ECLS-K: 2011) User’s Manual for the ECLS-K:2011 Kindergarten–Second Grade Data File and Electronic Codebook, Public Version (NCES 2017-285). U.S. Department of Education. Washington, DC: National Center for Education Statistics.

In addition, several items assessing the frequency of various positive learning behaviors were included in the ECLS-K: 2011. These items are called the Approaches to Learning subscale, and were assessed by teachers in fall of 2010. For these items, teachers used the same four-option response scale to indicate how frequently children exhibited various behaviors or characteristics, such as: “keep working at something until he/she is finished”; “show interest in a variety of things”; and “concentrate on a task and ignore distractions” (Tourangeau et al., 2017, p. 3-34). Higher scale scores indicate that the child exhibited positive learning behaviors more often. The Approaches to Learning subscale was created only if there were valid data on at least

4 of the 6 items. The subscale score is computed as the mean of the items comprising the score.

The Approaches to Learning scale was completed for a total of 14,770 students, had a weighted mean of 2.93, had a standard deviation of 0.680, and was found to have a reliability estimate

(Cronbach, 1951) of .91 in the fall 2010 round of data collection, indicating strong internal consistency.

Importantly, the Social Skills Rating System (SSRS), which formed the basis for many of socioemotional items used in the ECLS-K: 2011, is a strengths-based assessment, and therefore stands in stark contrast with the historic focus in the counseling and mental health fields on identifying only symptoms and deficits associated with diagnoses. A growing body of research

51 indicates that child protective factors associated with resiliency more accurately predict social, emotional, and behavioral outcomes than traditional deficit and pathology-based approaches

(Garmezy, 1993). As Endrulat, Tom, and Merrell (2009) have asserted, strengths‐based assessment provides information that has been lacking in traditional deficit‐based approaches by assessing positive characteristics associated with resilience. This is particularly relevant in in the presence of findings that have indicated subjective well‐being and psychopathology can contribute to predictions of children’s functioning (Greenspoon & Saklofske, 2001; Suldo &

Schaffer, 2008). In addition, the goal of a positive approach to evaluation is not only to reduce symptoms, but also to promote well‐being (Beaver, 2008). Based in positive psychology

(Seligman & Csikszentmihalyi, 2000), strengths‐based assessment focuses on assets, not deficits, and aims to prevent problems, rather than simply identifying existing problems. As a strengths‐ based assessment, the SSRS targets a child’s overall well‐being by placing a focus on students’ skills, knowledge, and competence, as well as the link between assessment and intervention.

Each of the socioemotional items used in the ECLS-K: 20112 were completed by children’s parents and teachers. However, in the present dissertation, only teacher ratings were utilized, due to Brown and colleagues’ (2007) findings of weak inter-rater correlation between parent ratings and teacher ratings of child behavioral functioning and mental health; in that study, parents failed to detect over half of school-aged children considered to be seriously disturbed by their teachers. Scores on each teacher-assessed subscale were summed for a total social-emotional competence (SEC) score (except for Internalizing Problems, which was considered as a separate predictor variable in the models, due to it failing to correlate strongly with the other subscales).

The Social Skills Rating System (SSRS), on which the socioemotional items in the

ECLS-K: 2011 were based, is frequently used in many externally funded research studies and school districts across the country (Gresham, Elliott, Vance, & Cook, 2011). The SSRS has been validated in studies on a variety of populations, including children with attention deficit hyperactivity disorder (Van der Oord et al., 2005), low-income children (Fantuzzo, Manz, &

McDermott, 1998), children in an urban Head Start program (Fagan & Fantuzzo, 1999), children with autism (Ozonoff & Miller, 1995), children with learning disabilities and other cognitive impairments (Bramlett, Smith, & Edmonds, 1994), as well as the broader preschool population

(Walthall & Konold, 2005). In the present study, teacher ratings were completed concurrently with the assessment of academic achievement. Although SSRS parent rating and student self- report forms exist, and teacher, parent, and student scores are often assessed simultaneously and compared or aggregated in order to establish inter-rater reliability, only teacher ratings were incorporated into the model in the present dissertation. However, as several authors have argued

(Loeber, Green, & Lahey, 1990; Routh, 1990), teachers’ reports are generally more accurate than student self-ratings in providing information about externally visible behaviors, such as disruptiveness.

The SSRS has been shown to accurately discriminate between students with social skills deficits and those with appropriate social skills, as well as between students who have learning, intellectual, behavioral, and/or emotional problems and students who do not have such problems.

Content, construct, and concurrent validity have been supported by extensive research (Bramlett,

Smith, & Edmonds, 1994; Diperna & Volpe, 2005; Fagan & Fantuzzo, 1999; Fantuzzo, Manz, &

McDermott, 1998; Flanagan et al., 1996; Gresham, Elliott, Vance, & Cook, 2011). While the instrument used in the ECLS-K: 2011 is only partially derived from the SSRS, and therefore has

53 its own internal subscale reliability coefficients, the extant literature on the SSRS has revealed moderate-to-strong convergent validity with the Behavioral Assessment System for Children

(BASC; Flanagan et al., 1996), as well as with the Social Skills Improvement System-Rating

Scales (SSIS-RS; Gresham, Elliott, Vance, & Cook, 2011). Both the BASC and the SSIS-RS are measures of child socioemotional skills and behaviors that are frequently used in educational settings; this suggests that the items used in the ECLS-K: 2011, which are derived largely from the SSRS, measures SEC reasonably well.

Direct Cognitive Assessments

The second standardized measure used in this study is the direct cognitive assessment of mathematics and reading proficiency. The direct cognitive assessment was completed by students in fall 2010 and spring 2011. Assessors spent 50 to 70 minutes asking children questions related to images (such as pictures, letters of the alphabet, words, or short sentences for reading or numbers and number problems for mathematics) that were presented on a small easel; children responded by pointing or telling the assessor their answers. The direct cognitive assessments measured knowledge and skills that are typically taught and developmentally important. The assessment frameworks were derived from national and state standards, including those of the National Assessment of Educational Progress (NAEP), the ECLS-K frameworks, and selected states' curriculum standards. The ECLS-K: 2011 assessments include items that were specifically created for the ECLS studies, items adapted from commercial assessments with copyright permission, and items from other NCES studies.

The direct cognitive assessments were adaptive, two-stage measures. The first stage in each subject test was a routing section; the items covered a broad range of item difficulty. The second stage, reflecting the adaptive nature of the test, was targeted toward students’ level of

54 ability; a child's performance on the routing section determined which one of three second-stage tests (low, middle, or high difficulty) the child was administered. The purpose of this adaptive assessment design is to maximize accuracy of measurement and minimize both administration time and the potential for floor and ceiling effects. As numerous authors have asserted (Lord,

1977; Kingsbury & Weiss, 1983; Way, 2006; Way, Twing, Camara, Sweeney, Lazer, & Mazzeo,

2010), adaptive testing is a particularly effective method of measuring an individual student’s status and growth over time in K-12 assessment due to time and cost savings, improved reliability and validity, and multiple testing opportunities for formative and interim assessments.

The mathematics assessment measures conceptual knowledge, procedural knowledge, and problem solving, and includes items pertaining to number sense, properties, and operations; measurement; geometry and spatial sense; data analysis, statistics, and probability; and patterns, algebra, and functions. The reading assessment, on the other hand, measures basic skills such as print familiarity, letter recognition, beginning and ending sounds, recognition of common words

(sight vocabulary), and decoding multisyllabic words; vocabulary knowledge such as receptive vocabulary and vocabulary-in-context; and reading comprehension. Reading tasks included identifying information specifically stated in text, making complex inferences within and across texts, and objectively judging the appropriateness and quality of various passages in the genres of poetry, letters, fiction, and nonfiction.

Because not all children received all items, the assessment scores in the ECLS-K: 2011 are modeled using Item Response Theory (IRT). Based on children’s performance on the items they received, an ability estimate (theta) is derived for each domain. The theta is used to derive other scores, such as scale scores and T-scores. The IRT scale scores represent estimates of the number of items children would have answered correctly if they had received all of the scored

55 questions in a given content domain. They are useful in identifying cross-sectional differences among subgroups in overall achievement levels and provide a summary measure of achievement useful for correlational analysis with status variables. The IRT scale scores are also used as longitudinal measures of overall growth.

The psychometric properties of the direct cognitive assessments were calculated as part of the ECLS-K: 2011. Tables 3 and 4 (Mulligan, Hastedt, & McCarroll, 2012) reflect the descriptive statistics for the instrument at both kindergarten data collections (fall 2010 and spring

2011), both for the entire sample and for various subgroups (note: discrepancies between Table 3 and the “Total” row in Table 4 are due to differences in weighting methods and the exclusion of kindergarten-repeaters in Table 4).

Table 4 reflects the mean IRT scale scores for various subgroups of first-time kindergarteners (as opposed to kindergarten-repeaters) in fall 2010 and spring 2011. As the data indicate, students’ performance differed by age and race/ethnicity, as well as household-level inputs such as socioeconomic variables and language spoken at home. Students born from

January 2004 through August 2004 tended to score higher on the math assessment than all other age groups; they also tended to score higher on the reading assessment than did all but one of the other age groups (the group born from September through December 2004). In addition, the two groups of students born from September 2004 through April 2005 both scored higher in reading and math than did kindergartners in any of the three groups born in May 2005 or later.

Asian students had higher mean reading and math scores than students of other race/ethnicities. White students had higher mean reading and math scores than Black, Hispanic,

Native Hawaiian/ Pacific Islander, and American Indian/Alaska Native students. Black students scored higher, on average, than Hispanic students in reading. Students of two or more races

56 scored higher, on average, than Black, Hispanic, and American Indian/Alaska Native students on both assessments and higher, on average, than Native Hawaiian/Pacific Islander students in reading. Native Hawaiian/ Pacific Islanders had higher mean math scores than Hispanics.

In terms of differences among types of households, students in households with two parents had higher reading and math scores, on average, than those in households of different structures. Students whose primary home language was English scored higher, on average, in reading and math than those coming from homes with a primary home language that was not

English. Scores on reading and math were lowest, on average, for students in households with incomes below the federal poverty level and highest, on average, for those in households with incomes at or above 200 percent of the federal poverty level. For both reading and math, mean scores increased with parental education level. Students attending private school had higher reading and math scores, on average, than those in public school.

Table 3

Descriptive Statistics and Reliability Coefficients for Cognitive Assessments

Range of Weighted Standard Number Reliability Description n Possible Values Mean Deviation of items Coefficient X1 Reading IRT Scale Score 15,669 0.0-120.0 46.7 11.284 120 0.95 X2 Reading IRT Scale Score 17,185 0.0-120.0 61.02 13.276 120 0.95 X1 Math IRT Scale Score 15,595 0.0-113.0 31.32 11.243 113 0.92 X2 Math IRT Scale Score 17,143 0.0-113.0 44.86 12.217 113 0.94 Note: Reprinted from Mulligan, G.M., Hastedt, S., and McCarroll, J.C. (2012). First-Time Kindergartners in 2010-11: First Findings From the Kindergarten Rounds of the Early Childhood Longitudinal Study, Kindergarten Class of 2010-11 (ECLS-K:2011) (NCES 2012-049). U.S. Department of Education. Washington, DC: National Center for Education Statistics. Retrieved 3 Feb 2018 from http://nces.ed.gov/pubsearch.

Table 4

Mean Subgroup Scores of First-Time Kindergarteners

The reliability coefficients of each subscale were calculated at both the fall 2010 and spring 2011 test intervals. As indicated in Table 3, both the mathematics and reading assessments demonstrated strong internal consistency at both test intervals. In addition, evidence for the validity of the direct cognitive assessments was derived a review of national and state

58 performance standards (specifically, Texas, California, New Jersey, Florida, and Virginia), comparison with state and commercial assessments (U.S. Department of Education, 1996; U.S.

Department of Education, 2009), and the judgments of curriculum experts.

Pools of potential items were developed for each domain based on the framework or standards pertinent to the domain. An expert panel of school educators, including curriculum specialists in the subject areas, then examined the pool of items for content and framework strand design, accuracy, non-ambiguity of response options, and appropriate formatting. The items were included in a field test and the best performing items were selected for the final assessment.

Statistical Analyses

The present study utilized multilevel modeling as the method of analysis. Because multilevel modeling was developed simultaneously across several fields, multilevel modeling is known by several names, including hierarchical linear-, mixed level-, mixed linear-, mixed effects-, random effects-, random coefficient (regression)-, and (complex) covariance components-modeling (Raudenbush & Bryk, 2002). Multilevel modeling is a complex form of ordinary least squares (OLS) regression that is designed for developing statistical models of parameters that vary at more than one level. Because the goal of the present study is to develop predictive models of academic achievement that contain measures for individual students (i.e., the first level) as well as measures for schools within which the students are grouped (i.e., the second level), multilevel modeling is an appropriate approach. A multilevel model allows for different regression coefficients for each predictor in each school.

Advantages of Multilevel Modeling

As Woltman, Feldstain, MacKay, and Rocchi (2012) articulated, the ability of multilevel modeling to simultaneously examine relationships within and between hierarchical levels of

59 grouped data makes it more efficient than other existing analyses at accounting for variance among variables at different levels. The authors point out that the analysis of hierarchical data using fixed parameter simple linear regression techniques, as was often done prior to the development of multilevel modeling and the advanced computing power necessarily to make multilevel modeling feasible, is insufficient because such techniques neglect the shared variance in hierarchically structured data. Moreover, as Hox (2002) has argued, the use of traditional statistical techniques in lieu of multilevel modeling, such as treating school-level variables as individual-level variables (a practice known as “disaggregation”), would bias findings by violating the statistical assumption of independence of observations; this issue is known as atomistic fallacy. Another traditional approach used prior to multilevel modeling, wherein individual-level variables are treated as school-level variables (known as “aggregation”), poses perhaps even greater threats to findings, as the practice discards all within-group information

(because it uses the means of the individual-level variables), thereby wasting as much as 80-90% of the variance, inflating the relationships among variables, and decreasing power (Bryk &

Raudenbush, 1988; Fidell & Tabachnick, 2007). Multiple authors have found that although the historical use of disaggregation and aggregation made analysis of multilevel data technically possible, the consequences of these flawed approaches included the incorrect partitioning of variance to variables, dependencies in the data, and increased risk of making a Type I error

(Beaubien, Hamman, Holt, & Boehm-Davis, 2001; Gill, 2003; Osborne, 2000).

Multilevel modeling is also advantageous compared to other statistical techniques due to its resistance to violations of statistical assumptions. As Raudenbush and Bryk (2002) have argued, multilevel modeling requires fewer assumptions to be met than other statistical methods, and can accommodate violations of independence of observations, sphericity, and homogeneity

60 of variance, as well as missing data and small or discrepant group sample sizes. These violations have been found to have little impact on effect size estimates, standard errors, and variance

(Beaubien, Hamman, Holt & Boehm-Davis, 2001; Gill, 2003; Osborne, 2000).

Potential Concerns with Multilevel Modeling

Although multilevel modeling has been found to have several advantages over traditional statistical techniques, Dedrick and colleagues (2009) identified four broad areas of concern regarding the potential pitfalls of multilevel modeling. These methodological issues fall into the realms of model development and specification, data considerations, estimation procedures, and hypothesis testing. Issues associated with model development and specification in multilevel modeling, for example, include: questions regarding how to select predictor variables (e.g., based on dataset, based on theory, etc.); how to center data to make regression equations more understandable in cases when predictor variables are not able to have zero-points; which fit indices are most appropriate for determining the fit of a given covariance structure; and how to determine the degree to which the findings of an analysis are generalizable, as well as how sensitive those findings are to characteristics of the data.

Dedrick and colleagues (2009) also outlined data considerations that can influence the findings of a multilevel model. For multilevel models, distributional assumptions regarding independence and normality are made about the errors (i.e., residuals) at each level in the model; although multilevel modeling is resistant to violations of most statistical assumptions, violation of the assumption of normality of errors can lead to biases in the standard errors at all levels, thus raising questions regarding the validity of statistical tests and the accuracy of reported confidence intervals (however, Dedrick and colleagues suggested that transforming the outcome variable, such as by using the natural logarithm, can help overcome non-normality). In addition,

61 considerations of outliers, measurement error, power, and missing values are more complex in multilevel models than in single-level models. For example, considerations of power are complicated by the fact that multilevel designs typically have multiple purposes (e.g., detecting main and interaction effects within and across levels of analysis, testing variance components, etc.) and the fact that there are more components that contribute to power in multilevel designs than in single-level designs (i.e., number of units per level, strength of intra-class correlation coefficient, presence of covariates at each level, effect size, and alpha level used in inferential tests).

Another methodological issue inherent in multilevel modeling that was outlined by

Dedrick and colleagues (2009) is estimation. There is no single, agreed-upon approach to estimating the parameters in multilevel modeling, and previous researchers have used maximum likelihood (ML), restricted maximum likelihood (REML), and Bayesian estimation (Kreft & de

Leeuw, 1998; Raudenbush & Bryk, 2002). Moreover, each estimation method can be carried out using multiple possible algorithms. Factors such as sample size and normality can help researchers determine which estimation method is right for a particular study; however, no estimation method is entirely satisfactory across all data conditions.

A final methodological issue associated with multilevel modeling highlighted by Dedrick and colleagues (2009) is in regard to hypothesis testing and statistical inference. In multilevel modeling, hypothesis testing can be used to make inferences about variance parameters, fixed effects, and random Level 1 coefficients. When attempting to make inferences about a variance parameter, a researcher could calculate the confidence interval by adding and subtracting 1.96 times the standard error of the parameter estimate, although several authors (Littell, Milliken,

Stroup, & Wolfinger, 1996; Raudenbush & Bryk, 2002) have cautioned against this approach in

62 cases when sample sizes or variance parameters are small. Examples of options for overcoming such limitations when calculating confidence intervals for a variance parameter include the

Satterthwaite approach (Littell et al., 1996) and bootstrapping (Carpenter Goldstein, & Rasbash,

1999; Meijer, van der Leeden, & Busing, 1995). Similarly, researchers attempting to make inferences about fixed effects can calculate the confidence interval or conduct statistical tests, keeping in mind that degrees of freedom should be adjusted when normality is violated (Zucker,

Lieberman, & Manor, 2000). When making inferences about random Level 1 coefficients,

Dedrick and colleagues (2009) suggest two approaches: either estimating the Level 1 model separately for each Level 2 group (e.g., school) using ordinary least squares (OLS) estimation, which has the drawback of basing each estimate on relatively few observations; or obtaining empirical Bayes estimates, which consider all available information and, despite biasing the estimates, tend to produce values that are closer to the parameter values (i.e., a smaller expected mean square error) than those based on OLS estimation (Bingenheimer & Raudenbush, 2004;

Raudenbush & Bryk, 2002).

An additional disadvantage of multilevel modeling, as Woltman and colleagues (2012) point out, is that it requires large sample sizes at each level for adequate power. Snijders (2005) has asserted that for testing the effect of a Level 1 variable, the Level 1 sample size is of primary importance; for testing the effect of a Level 2 variable it is the level-two sample size. The average cluster size, on the other hand, is not very important for the power of tests of regression coefficients, but is important for the power for testing random slope variances at the second level, i.e., between-school variances of effects of student-level variables. As Maas and Hox

(2005) found, having groups of fewer than 50 could lead to biased estimates of the second level standard errors.

Analysis

The purpose of the present study was to examine: 1) the extent to which variability in children’s mathematics and reading achievement in spring of kindergarten was explained by school-level variables (as opposed to student-level variables) collected in fall of kindergarten; 2) whether children’s membership in a specific subgroup resulted in significant within-school mathematics and reading achievement gaps in spring of kindergarten, controlling for various student background characteristics; 3) the degree to which various school-level variables significantly contributed to models predicting children’s kindergarten spring mathematics and reading achievement; and 4) whether children’s poverty interacted with their school membership to affect spring kindergarten mathematics and reading achievement, and school factors accounting for the variance in school slopes.

Prior to the study, I expected the following results: that there would be a significant amount of variability in children’s mathematics and reading achievement in spring of kindergarten that was explained by school-level variables, as opposed to student-level variables

(Hypothesis 1); that children’s membership in particular racial groups, gender categories, and socioeconomic statuses would all result in significant within-school mathematics and reading achievement gaps in spring of kindergarten, controlling for various student background characteristics (Hypothesis 2); that various school-level variables would significantly contribute to models predicting children’s spring kindergarten mathematics and reading achievement

(Hypothesis 3); and children’s poverty would interact with their school membership to affect spring kindergarten mathematics and reading achievement (Hypothesis 4).

Analyses were conducted using SPSS 24 (IBM, 2017). First, descriptive statistics and patterns of missingness for all variables were examined, and assumptions of normality were

64 checked. Missing data was handled using weights provided in the ECLS-K: 2011 dataset, which were created to account for patterns of non-response among students, parents, teachers, and administrators. Percentages were computed for categorical predictor variables. Alpha for all statistical analyses was set to .05. The intent was to define the characteristics of the sample and examine data patterns relevant to the next step of the analysis.

Next, multilevel modeling was conducted to assess the effects of various student- and school-level variables on student reading and mathematics achievement. Multilevel analysis is a methodology for the analysis of data with complex nested patterns of variability; for example, students nested in classroom, classroom nested in school. A multilevel model analysis approach would handle the complexity of the variations between different participants nested in various levels of the schools, the relationships between the outcome variables with the predictors at different levels, and the possible interactions between the predictors coming from different levels. Given the cluster sampling of students nested in schools, a two-level multilevel model

(student level and school level) was needed to disentangle the contextual and participant factors in this study. The dependent variables are the students’ end of year mathematics and reading achievement scores. Independent variables at the individual or student level (level 1) included student beginning of year reading and mathematics scores, beginning of year social-emotional competence scores, race, socioeconomic status, and gender. Predictors at the cluster or school level (level 2) included the school aggregates for race, socioeconomic status, parent involvement, and various organizational context variables.

A series of two-level models, with children’s achievement modeled at the child-level, nested under schools at the second level, were run with SPSS 24 (IBM, 2017). The research rationale for each HLM is as follows. These models build somewhat on the work of Chatterji

(2005), who used multilevel modeling of student- and school-level variables from the original

ECLS-K (kindergarten class of 1998-99) to predict first-grade mathematics achievement.

However, Chatterji notably excluded social-emotional competence from her model, which is likely significantly predictive of kindergarten academic achievement.

Unconditional (null) model. The first step in multilevel model analysis is to conduct a one-way random effects ANOVA, which is called the unconditional model (also known as a null, basic, or empty model). This first unconditional model characterizes only random variation between groups and random variation within groups. Therefore, the null model explains the variance in academic achievement within and between schools; in other words, each student’s end-of-year reading and mathematics achievement scores were modeled as a function of the mean achievement of their schools and random error at the student level, and each school’s mean achievement as a function of the grand mean and random error at school-level. This analysis was motivated by the need to partition the total variance in achievement into within- and between-school components. The variance estimates were obtained by fitting an HLM where each child’s end-of-kindergarten achievement score, yij, was explained by the estimated school mean, β0j, and unique error associated with that child, rij. School means were explained by the grand mean, G00, and unique error for each school, uj.

yij= β0j+ rij.

β0j = G00+ uj.

No predictor variables at either the school level or the student level were included in this null model. The purpose of this null model was to distinguish the estimations of the variances at two different levels and determine the justification of further multilevel analysis. The analysis with the null model also yielded answers to three basic questions: How much do individual

66 students vary around their school means? How much of total variance in academic achievement is attributable to schools? and How precise an estimate of the population mean is the school mean, β0j? These questions were answered by examining the variance estimates within schools

(σ2) and between schools (τ), and the size of the intra-class correlation coefficient (ICC; the proportion of total variance that is between schools). ICC values greater than .10 indicate that there are sufficient within-school dependencies to justify multilevel modeling (Chatterji, 2005).

A reliability estimate for school mean estimates (intercepts, β0j) is reported in the output. A criterion of .60 was set for the reliability of the intercepts, indicating moderately strong reliability

(Chatterji, 2005). Subsequent models incorporating predictors at both levels were evaluated against these initial variance estimates.

Random intercepts model with only child-level predictors. Based on the unconditional model, a series of models with different random components were built to determine which random effect had the best fit for the data. At each stage of model building process, slopes were fixed to increase model fit if the random effects were not significant.

Multilevel models are typically built up in a series of stages (Raudenbush & Bryk, 2002). This allows for an increasing number of parameters to be compared with the overall fit of the empty

(also known as null or basic) model. In this way, single predictor variables can be tested to determine if they significantly improve upon the existing background variables.

In these models, restricted maximum likelihood was the estimation method used to estimate the parameters and to evaluate the overall model fit, because this method is more useful for estimating random components than the full maximum likelihood estimation method

(Raudenbush & Bryk, 2002). This series of HLMs was specified to answer two main questions:

Given the estimated within-school variance, what proportion of that variance in achievement can

67 be accounted for by child background characteristics, such as their prior academic achievement, social-emotional competence, gender, socioeconomic status, and race? Compared to school mean estimates and controlling for other child background characteristics, how large are the achievement gaps in selected racial, socioeconomic, and gender groups? The school-level model remained as in the null model; predictors will all be entered in the child-level equation.

All predictors were centered around their school means; thus, the estimated coefficients for each risk group showed the within-school achievement differential, controlling for the other child background characteristics serving as predictors in the models but allowing variability between schools.

Achievement푖푗 = 훽0푗 + 훽1푗ChildisAsian풊풋 + 훽2푗ChildisBlack풊풋 + 훽3푗ChildisHispanic풊풋 +

훽4푗ChildisWhite풊풋 + 훽5푗ChildPoverty풊풋 + 훽6푗ChildisMale풊풋 + 훽7푗InternalizingProblems풊풋 +

훽8푗SocialEmotionalCompetence풊풋 + 훽9푗PriorAchievement풊풋 + 푒푖푗

훽0푗 = 훾00 + 푢0푗

훽1푗 = 훾10 + 푢1푗

훽2푗 = 훾20 + 푢2푗

훽3푗 = 훾30 + 푢3푗

훽4푗 = 훾40 + 푢4푗

훽5푗 = 훾50 + 푢5푗

훽6푗 = 훾60 + 푢6푗

훽7푗 = 훾70 + 푢7푗

훽8푗 = 훾80 + 푢8푗

훽9푗 = 훾90 + 푢9푗

Achievement gaps among levels of the various child background characteristics were estimated at the end of kindergarten, using the measures taken at kindergarten entry as prior achievement indicators in separate models for reading and mathematics. Findings were compared. The models were evaluated against the null model by examining the proportion of unexplained within-school variance that was accounted for after all the child-level predictors were included in the model.

Random intercepts model with child-level covariates and school-level predictors. In the third series of HLMs, theoretically-supported school variables were modeled to explain between-school variability in academic achievement, with child-level predictors also entered.

Effects of child-level predictors that were main focus of the study, including SEC, race/ethnicity, gender, and socioeconomic status were again allowed to vary randomly between schools—that is, they were group (school) mean-centered. School aggregates on socioeconomic status, SEC and prior academic achievement were re-entered in second level equations as context controls to study effects of school factors, adjusted for these average effects. Again, the kindergarten entry academic achievement measures were used as covariates at the child-level to examine reading and mathematics separately in different runs.

Achievement푖푗 = 훽0푗 + 훽1푗ChildisAsian풊풋 + 훽2푗ChildisBlack풊풋 + 훽3푗ChildisHispanic풊풋 +

훽4푗ChildisWhite풊풋 + 훽5푗ChildPoverty풊풋 + 훽6푗ChildisMale풊풋 + 훽7푗InternalizingProblems풊풋 +

훽8푗SocialEmotionalCompetence풊풋 + 훽9푗PriorAchievement풊풋 + 푒푖푗

β0j = G00+ G01AverageDailyAttendancePct + G02FreeReducedLunchPct +

G03ParentInvolvement + G04PercentNonWhiteinSchool+ G05PercentSpecialEd +

G06SchoolPublic + G07SchoolSize + G08SchoolUrbanicity + uj, where

β1j = G01

β2j through β8j (all slopes fixed as in β1j).

This series of HLMs revealed the degree to which the selected school factors significantly and positively influenced academic achievement in school, as main, additive effects. The reduction in the variance estimate of uj enabled a calculation of the proportion of originally estimated between-school variance (from the Null Model) that could be explained by the school factors chosen, and an evaluation of the usefulness of models. Slope parameters for predictors at the child level were again fixed; that is, the influence of individual child-level characteristics were not set to vary by school.

Random intercepts and slopes models with child poverty explaining cross-level interactions. In the final step, the relationships between the predictor variables and student reading and mathematics achievement were investigated by employing all of the predictor variables and the interactions at both levels into the model. The restricted maximum likelihood estimation method was again used to estimate the parameters and model fit. To answer questions as to whether academic achievement varied due to interaction of a child’s risk group membership modeled in the child-level equation and schools in which they are enrolled, modeled at the second-level, slopes for these predictors would typically be allowed to vary randomly. If statistically significant slope variance were found, the equation for that slope parameter would be modeled with school-level predictors to identify significant explanatory variables. For the present dissertation, the interaction of poverty and school-level variables in predicting academic achievement was of particular interest, due to prior literature indicating that the interactions between student poverty and the following school-level variables all had significant effects on the slope variability of academic achievement outcomes: total time teachers gave per day to

70 mathematics and reading instruction; IEPs in school; and public versus private sector (Chatterji,

2005). Therefore, the research questions were: Does academic achievement vary significantly in poverty-affected versus non-poor children who belong in different schools? If so, what school variables significantly explain the achievement variance in the slopes? The equations were:

β6j (Poverty) = G60+ u6

The above equation examined if the poverty slope, β6j, had significant variance when modeled as a random variable. To identify significant explanatory variables, a subsequent equation was built as follows:

β6j = G60+ + G61AverageDailyAttendancePct + G62FreeReducedLunchPct +

G63ParentInvolvement + G64PercentNonWhiteinSchool+ G65PercentSpecialEd +

G66SchoolPublic + G67SchoolSize + G68SchoolUrbanicity + u6

These analyses were pursued with one slope modeled at a time. The number of schools with necessary data at the school level were reported in tables with results. The reliability of the slopes and intercepts were checked at each stage of the analysis and were also reported.

CHAPTER IV

RESULTS

Data were weighted to account for the complex sampling design of the ECLS-K:2011— for example, the deliberate oversampling of Asian/Pacific Islander students. There were two purposes for using full sample weights. The first was to weight the sample up to the population total of interest, thereby producing national-level estimates. In addition, the full sample weight was designed to adjust for differential nonresponse patterns that may lead to bias in estimates due to people with certain characteristics systematically being less likely than others to respond to a survey. Although a sample weight could not be produced for use with data from every combination of assessments, interviews, and surveys used in the study (due to impracticality and budgetary reasons), the weight “W1_2P0” (Child based weight adjusted for nonresponse associated with either fall or spring kindergarten parent interviews) was chosen because it maximized the number of sources of data included in the analyses for which nonresponse adjustments were made, thus minimizing bias in estimates. The results of the final models are presented in the tables below. (Note: Full SPSS output can be found in the appendices.)

In addition, the intraclass correlation coefficient (ICC), ρ, was calculated for each model below. The ICC is the proportion of variance in the outcome variable that is explained by the grouping structure of the hierarchical model. It is calculated as a ratio of group-level error variance over the total error variance:

where is the variance of the level-2 residuals and is the variance of the level-1 residuals.

In other words, the ICC reports on the amount of variation unexplained by any predictors in the

72 model that can be attributed to the grouping variable, as compared to the overall unexplained variance (within and between variance).

Mathematics Achievement

In the first set of models, the dependent variable was mathematics achievement measured in the spring of the kindergarten year. The data below reflect the findings of those models.

Null Model for Mathematics

The tables below reflect the null model, specified in mixed format as:

X2MTHETK2푖푗 = 훾00 + 푢0푗 + 푒푖푗

The unconditional mixed model specification resembles a one-factor analysis of variance

(ANOVA) with 훾00 as the overall mean and 푢0푗 as the school effect. However, in the present model, 푢0푗 is being considered as a random effect (a normally distributed variable with a mean of zero), not a fixed factor effect as in ANOVA. Therefore, the estimate for 푢0푗 is interpreted as the variance of the mean for each school around the overall mean spring mathematics score.

The estimate for 훾00 is the mean of the means of spring mathematics achievement for each school, instead of the mean of all students in the study. If the data were completely balanced (i.e., the same number of students in every school), then the results of the unconditional model would equal those from an ANOVA procedure.

The null model shows the amount of variability in kindergarten spring mathematics achievement that can be attributed to which school each student is enrolled in. Children were found to vary significantly around their school means, as evidenced by the statistically significant t-value. The overall mean achievement (across schools) is estimated as 0.424. The mean for school j is estimated as 0.424 + û0j, where û0j is the school residual.

Table 5

Estimates of Fixed Effects and Covariance Parameters for Null Model: Mathematics

Fixed Effects Estimate St. Error t p

Intercept (훾00) 0.424 0.0140 30.249 <0.001

Variance Components Estimate St. Error z p Residual (eij) 0.446 0.0003 1386.806 <0.001 Intercept (u0j) 0.233 0.0096 24.255 <0.001

Based on these findings, the intraclass coefficient (ICC) for the null model can be calculated by dividing the between-schools variability in achievement by the sum of the within- and between-schools variability in achievement, like so:

휌 = = 0.233 / (0.233 + 0.446) = 0.343

This means that about one-third of the total variation in students’ mathematics achievement in the spring of their kindergarten year can be attributed to the school in which they were enrolled. As Chatterji (2005) asserted, ICC values greater than .10 indicate that there are sufficient within-school dependencies to justify multilevel analysis.

Random Intercepts Model with Only Child-Level Predictors: Mathematics

The next series of models was specified to determine what proportion of within-school variance in mathematics achievement was attributable to child background characteristics, such as prior achievement in mathematics, gender, socioeconomic status, and ethnicity. All non- binary predictors in this school-level model were centered around school means (i.e., group- mean centering); therefore, the estimated coefficients for each risk group showed the within- school achievement differential, controlling for the other child background characteristics serving as predictors in the models but allowing variability between schools.

The table below provides the estimates on the size and significance of mathematics achievement gaps and child-level predictors, adjusting for kindergarten-entry versus

74 kindergarten-end variability in children’s mathematics achievement. The model is specified in hierarchical format as:

X2MTHETK2푖푗 = 훽0푗 + 훽1푗ChildisAsian풊풋 + 훽2푗ChildisBlack풊풋 + 훽3푗ChildisHispanic풊풋 +

훽4푗ChildisWhite풊풋 + 훽5푗ChildPoverty풊풋 + 훽6푗ChildisMale풊풋 + 훽7푗InternalizingProblems풊풋 +

훽8푗SocialEmotionalCompetence풊풋 + 훽9푗X1MTHETK2풊풋 + 푒푖푗

훽0푗 = 훾00 + 푢0푗

훽1푗 = 훾10 + 푢1푗

훽2푗 = 훾20 + 푢2푗

훽3푗 = 훾30 + 푢3푗

훽4푗 = 훾40 + 푢4푗

훽5푗 = 훾50 + 푢5푗

훽6푗 = 훾60 + 푢6푗

훽7푗 = 훾70 + 푢7푗

훽8푗 = 훾80 + 푢8푗

훽9푗 = 훾90 + 푢9푗

Table 6

Estimates of Fixed Effectsa for Random Intercepts Model with Only Child-Level Predictors: Mathematics

95% Confidence Interval

Parameter Estimate Std. Error df t Sig. Lower Bound Upper Bound

Intercept .424221 .014440 948.835 29.377 .000 .395882 .452560

ChildisAsian .035006 .001519 2359420.029 23.044 .000 .032029 .037984

ChildisBlack -.081236 .001236 2359367.696 -65.709 .000 -.083659 -.078813

ChildisHispanic -.016949 .000832 2359614.794 -20.363 .000 -.018580 -.015318

ChildisWhite .049606 .001200 2359311.048 41.350 .000 .047254 .051957

ChildPoverty -.059875 .000690 2359372.196 -86.762 .000 -.061228 -.058522

ChildisMale .016360 .000520 2359069.825 31.467 .000 .015341 .017379

GroupMeanCentered_ChildPret .009891 .000576 2358793.725 17.157 .000 .008761 .011020

estInternalizingProbsReverseCo

ded

GroupMeanCentered_ChildSoci .054394 .000303 2358811.397 179.364 .000 .053799 .054988 alEmotionalCompetence

GroupMeanCentered_X1MTH .659505 .000344 2358899.207 1919.882 .000 .658832 .660178

ETK2 a. Dependent Variable: X2 MATH THETA-K2 DATA FILE.

Table 7 Estimates of Covariance Parametersa for Random Intercepts Model with Only Child-Level Predictors: Mathematics 95% Confidence Interval

Parameter Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound

Residual .132956 .000122 1085.983 .000 .132716 .133196 Intercept [subject = S2_ID] Variance .194080 .008980 21.612 .000 .177254 .212503 a. Dependent Variable: X2 MATH THETA-K2 DATA FILE.

The equation of the average fitted regression line (across schools) is:

X2MTHÊTK2ij = .424221 + .035006 ChildisAsianij + -.081236 ChildisBlackij + -.016949

ChildisHispanicij + .049606 ChildisWhiteij + -.059875 ChildPovertyij + .016360 ChildisMaleij +

.009891 GroupMeanCentered_ChildPretestInternalizingProbsReverseCoded ij + .054394

GroupMeanCentered_ChildSocialEmotionalCompetence ij + .659505

GroupMeanCentered_X1MTHETK2ij.

The equation indicates that, as expected, the strongest predictor of end-of-year kindergarten achievement, by far, is beginning-of-year kindergarten achievement. For every one-unit increase in beginning-of-year achievement scores, there is a 0.66 increase in end-of-year achievement scores. All of the other predictor variables entered into the model were found to be significant (p < .001). The fitted line for a given school will differ from this average line in its intercept, by an amount û for school j. However, the slope of the school lines is assumed to be fixed; the effect of each predictor variable is assumed to be the same for all schools. Therefore, a plot of the predicted school lines would show a set of parallel lines.

The intra-class coefficient (ICC) for this model is larger than for the null model; this is to be expected, since the model controls for some student-level variation by adding several fixed factors.

0.19408 휌 = = 0.593451 0.19408 + .132956

With this model, almost 60 percent of the total variation in end-of-year kindergarten mathematics achievement can be accounted for by both the school in which the student was enrolled and the various student-level variables entered.

Comparing the results with the null model, the addition of all the student-level predictor variables has reduced the amount of variance at both the school and student levels. The between-school variance has reduced from 0.233 to 0.194, and the within-school variance has reduced from 0.446 to 0.133. The decrease in the within-school variance is expected because of the addition of all the student-level predictor variables; the reduction in the between-school variance suggests that the distribution of students by each predictor variable differs from school to school.

Random Intercepts Model with Child-Level and School-Level Predictors: Mathematics

In the next model, level-2 (school-level) predictor variables were entered. All non- dichotomous school-level variables were grand-mean centered, which is the only centering option for top-level variables because group-mean centering them would result in their original values. As with the previous model, dichotomous predictor variables were left as their original values for ease of interpretation. The model is presented in hierarchical format as:

X2MTHETK2푖푗 = 훽0푗 + 훽1푗ChildisAsian풊풋 + 훽2푗ChildisBlack풊풋 + 훽3푗ChildisHispanic풊풋 +

훽4푗ChildisWhite풊풋 + 훽5푗ChildPoverty풊풋 + 훽6푗ChildisMale풊풋 + 훽7푗InternalizingProblems풊풋 +

훽8푗SocialEmotionalCompetence풊풋 + 훽9푗X1MTHETK2풊풋 + 푒푖푗

훽0j = G00+ G01AverageDailyAttendancePct + G02FreeReducedLunchPct +

G03ParentInvolvement + G04PercentNonWhiteinSchool+ G05PercentSpecialEd +

G06SchoolPublic + G07SchoolSize + G08SchoolUrbanicity + uj, where

β1j = G01

β2j through β8j (all slopes fixed as in β1j).

The model has a fixed slope coefficient with no interaction between school-level predictor variables and student-level predictor variables, meaning that the slopes for student- level predictor variables are the same regardless of the properties of the school in which the student is enrolled.

Table 8

Estimates of Fixed Effectsa: Random Intercepts Model with Child-Level and School-Level Predictors: Mathematics

95% Confidence Interval

Parameter Estimate Std. Error df t Sig. Lower Bound Upper Bound

Intercept .685532 .024603 902.060 27.864 .000 .637247 .733817 ChildisAsian .037660 .001813 1655008.495 20.777 .000 .034107 .041212 ChildisBlack -.079010 .001504 1655008.632 -52.529 .000 -.081958 -.076062

ChildisHispanic -.026258 .001018 1655049.314 -25.782 .000 -.028254 -.024262 ChildisWhite .068970 .001434 1654927.457 48.109 .000 .066161 .071780 ChildPoverty -.057447 .000842 1654862.781 -68.187 .000 -.059098 -.055796

ChildisMale .012548 .000635 1654900.328 19.757 .000 .011303 .013792 GroupMeanCentered_Child .006633 .000695 1654603.504 9.538 .000 .005270 .007996 PretestInternalizingProbsRe verseCoded

GroupMeanCentered_Child .058671 .000370 1654600.927 158.576 .000 .057946 .059396 SocialEmotionalCompetenc e GrandMeanCentered_Scho .019411 .006757 609.720 2.873 .004 .006142 .032680 olAverageDailyAttendance

Pct GrandMeanCentered_Scho -.001330 .000654 627.554 -2.035 .042 -.002614 -4.625495E-5 olFreeReducedLunchPct

GrandMeanCentered_schoo .014839 .018315 610.286 .810 .418 -.021129 .050807 lparentinvolvement GrandMeanCentered_schoo -.003507 .000577 623.089 -6.081 .000 -.004640 -.002374 lPercentNonWhiteinSchool GrandMeanCentered_schoo -.001324 .002412 613.330 -.549 .583 -.006060 .003412 lPercentSpecialEd

SchoolPublic -.407552 .012382 260766.424 -32.916 .000 -.431819 -.383284 SchoolSize .060636 .031212 613.335 1.943 .053 -.000659 .121930 SchoolUrbanicity .181667 .009986 97007.004 18.191 .000 .162094 .201241

GroupMeanCentered_X1M .661766 .000420 1654666.557 1575.918 .000 .660943 .662589 THETK2 a. Dependent Variable: X2 MATH THETA-K2 DATA FILE.

Table 9 Estimates of Covariance Parameters:a Random Intercepts Model with Child-Level and School-Level Predictors: Mathematics 95% Confidence Interval

Parameter Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound

Residual .139146 .000153 909.537 .000 .138846 .139446 Intercept [subject = S2_ID] Variance .145380 .008336 17.440 .000 .129926 .162671 a. Dependent Variable: X2 MATH THETA-K2 DATA FILE.

As the data in the tables indicate, most of the predictor variables were strongly statistically significant (with the exceptions of the average level of parent involvement in the school, the percentage of students in the school receiving special education services, and the size of the school, which were all non-significant). For example, a child in a public school would be expected to have a score that is .408 points lower than a child in a private school (adjusted for all other school- and student-level predictor variables). Interestingly, the sector of the school

(public versus private) was by far the strongest predictor variable (other than prior achievement).

Comparing this model to the previous one, there is a reduction in between-school variance. After accounting for the various school-level predictor variables, the between-school variance reduces from 0.194 to 0.145. The intra-class coefficient (ICC) for this model is smaller than for the previous model. This is to be expected, since ICC is a measure of how much of the unexplained variation can be accounted for by which school a student is in; by adding school- level predictors, the model is accounting for a larger portion of the variation among the different schools. Therefore, less variation exists in the random intercept, 푢0푗, for this model than those without any level-2 predictors, and thus the ICC is also smaller.

0.145380 휌 = = 0.510955 0.145380 + 0.139146

With this model, about half of the total variation in end-of-year kindergarten mathematics achievement can be accounted for by both the school in which the student was enrolled and the various predictor variables entered.

Random Intercepts and Slopes Model, with Poverty used to Examine Cross-Level

Interactions: Mathematics

The analysis thus far has revealed that mathematics achievement in the spring of kindergarten is significantly related to the child’s prior achievement, race, ethnicity, socioeconomic status, gender, internalizing problems, and social-emotional competence, as well as the school’s average daily attendance, portion of students with free or reduced lunch, portion of non-White students, sector, and urbanicity. However, only the main effects of these variables have been considered. In practice, the relationship between an outcome variable and a predictor variable may depend on the interaction effect between the predictor variable and a second

80 predictor variable. Of particular interest to the present study are cross-level interactions between student poverty (level 1) and various school-level variables (level 2).

As with the previous model, dichotomous predictor variables were left as their original values for ease of interpretation, while non-dichotomous student-level variables were group- mean centered and non-dichotomous school-level variables were grand-mean centered. The model is presented in hierarchical format as:

β6j = G60+ + G61AverageDailyAttendancePct + G62FreeReducedLunchPct +

G63ParentInvolvement + G64PercentNonWhiteinSchool+ G65PercentSpecialEd +

G66SchoolPublic + G67SchoolSize + G68SchoolUrbanicity + u6

For every interaction except for that of child poverty with school urbanicity, the effect was significant (and the estimate was several times greater than the standard error). This means there is evidence that the effect of a child’s poverty on that child’s academic achievement is greater for students enrolled in public schools than for students enrolled in private schools; is greater for students enrolled in schools with more than 500 students than for students enrolled in schools with fewer than 500 students; is greater for students in schools that have more students served by free/reduced lunch programs; and is weaker for students in schools that have higher average daily attendance percentages, more parent involvement, more non-White students, and more students receiving special education.

Interestingly, a school’s size, level of parent involvement, and portion of students receiving special education were themselves not significant predictors of achievement in this model, even though their interactions with student poverty were indeed significant predictors of achievement. It is a possible that a variable with a non-significant main effect could be involved

81 in a significant interaction effect. This is one reason that several apparently non-significant predictors were left in the models used throughout this dissertation.

Table 10 Estimates of Fixed Effectsa: Random Intercepts and Slopes Model with Poverty used to Examine Cross-Level Interactions: Mathematics 95% Confidence Interval Parameter Estimate Std. Error df t Sig. Lower Bound Upper Bound Intercept .701932 .024623 904.286 28.507 .000 .653607 .750257 ChildisAsian .037956 .001813 1655004.87 20.937 .000 .034403 .041509 ChildisBlack -.079153 .001504 1655002.63 -52.630 .000 -.082101 -.076205 ChildisHispanic -.026108 .001018 1655038.17 -25.638 .000 -.028104 -.024112 ChildisWhite .068587 .001434 1654924.91 47.833 .000 .065776 .071397 ChildPoverty -.145429 .004908 1655122.05 -29.634 .000 -.155048 -.135811 ChildSex .012884 .000635 1654891.97 20.288 .000 .011639 .014129 GroupMeanCentered_C .006358 .000697 1654594.17 9.124 .000 .004992 .007724 hildPretestInternalizing ProbsReverseCoded GroupMeanCentered_C .058854 .000370 1654596.75 159.092 .000 .058129 .059579 hildSocialEmotionalCo mpetence GrandMeanCentered_S .020299 .006759 610.042 3.003 .003 .007026 .033572 choolAverageDailyAtte ndancePct GrandMeanCentered_S -.001427 .000654 628.018 -2.182 .029 -.002711 -.000143 choolFreeReducedLunc hPct GrandMeanCentered_sc .018444 .018321 610.684 1.007 .314 -.017537 .054424 hoolparentinvolvement GrandMeanCentered_sc -.003189 .000577 623.586 -5.527 .000 -.004322 -.002056 hoolPercentNonWhitein School GrandMeanCentered_sc -.000992 .002412 613.683 -.411 .681 -.005729 .003746 hoolPercentSpecialEd SchoolSector -.414319 .012430 261024.077 -33.333 .000 -.438681 -.389958 SchoolSize .047974 .031223 613.747 1.537 .125 -.013342 .109291 SchoolUrbanicity .172713 .010030 97334.571 17.220 .000 .153055 .192372 GroupMeanCentered_X .661534 .000420 1654657.04 1575.162 .000 .660711 .662357 1MTHETK2

ChildPoverty * -.003000 .000354 1655097.88 -8.480 .000 -.003693 -.002307 GrandMeanCentered_S choolAverageDailyAtte ndancePct ChildPoverty * .000773 4.52197E-5 1655075.01 17.103 .000 .000685 .000862 GrandMeanCentered_S choolFreeReducedLunc hPct ChildPoverty * -.014202 .000980 1655080.41 -14.488 .000 -.016123 -.012281 GrandMeanCentered_sc hoolparentinvolvement ChildPoverty * -.001136 3.46435E-5 1655100.86 -32.804 .000 -.001204 -.001069 GrandMeanCentered_sc hoolPercentNonWhitein School ChildPoverty * -.000829 .000126 1655030.28 -6.579 .000 -.001076 -.000582 GrandMeanCentered_sc hoolPercentSpecialEd ChildPoverty * .057983 .005179 1655107.16 11.196 .000 .047832 .068134 SchoolSector ChildPoverty * .048889 .001692 1655104.42 28.899 .000 .045574 .052205 SchoolSize ChildPoverty * .000818 .001881 1655125.95 .435 .664 -.002869 .004506 SchoolUrbanicity a. Dependent Variable: X2 MATH THETA-K2 DATA FILE.

Table 11 Estimates of Covariance Parametersa: Random Intercepts and Slopes Model with Poverty used to Examine Cross-Level Interactions: Mathematics 95% Confidence Interval Parameter Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound Residual .138913 .000153 909.535 .000 .138614 .139212 Intercept [subject = Variance .145447 .008339 17.442 .000 .129987 .162745 S2_ID] a. Dependent Variable: X2 MATH THETA-K2 DATA FILE.

Comparing this model to the previous one, there is a slight increase in between-school variance. After accounting for the interaction of poverty with the various school-level predictor variables, the between-school variance increases only slightly, remaining at about 0.145. The

83 intra-class coefficient (ICC) for this model is only slightly larger than for the previous model.

This suggests that the addition of cross-level interaction effects did not substantially change the amount of unexplained variation that could be accounted for by which school a student is in.

About the same amount of variation exists in the random intercept, 푢0푗, for this model as there is in the random intercept of previous model where there were student-level and school-level predictors but no cross-level interactions, and thus the ICC is also about the same.

0.145447 휌 = = 0.511489 0.145447 + 0.138913

Reading Achievement

In the second set of models, the dependent variable was reading achievement measured in the spring of the kindergarten year. The data below reflect the findings of those models.

Null Model for Reading

. The tables below reflect the null model, specified in mixed format as:

X2RTHETK2푖푗 = 훾00 + 푢0푗 + 푒푖푗

The unconditional mixed model specification resembles a one-factor analysis of variance

(ANOVA) with 훾00 as the overall mean and 푢0푗 as the school effect. However, in the present model, 푢0푗 is being considered as a random effect (a normally distributed variable with a mean of zero), not a fixed factor effect as in ANOVA. Therefore, the estimate for 푢0푗 is interpreted as the variance of the means for all schools around the overall mean spring reading score.

The estimate for 훾00 is the mean of the means of spring reading achievement for each school, instead of the mean of all students in the study. If the data were completely balanced (i.e., the same number of students in every school), then the results of the unconditional model would equal those from an ANOVA procedure.

The null model shows the amount of variability in kindergarten spring reading achievement that can be attributed to which school each student is enrolled in. Children were found to vary significantly around their school means, as evidenced by the significant t-value.

The mean for school j is estimated as 0.432 + û0j, where û0j is the school residual.

Table 12

Fixed Effects and Variance Components for Null Model for Reading

Fixed Effects Estimate St. Error t p

Intercept (훾00) 0.432 0.0140 30.835 <0.001

Variance Components Estimate St. Error z p Residual (eij) 0.456 0.0003 1388.104 <0.001 Intercept (u0j) 0.232 0.0096 24.252 <0.001

휌 = = 0.232 / (0.232 + 0.456) = 0.3372

This means that about one-third of the total variation in students’ reading achievement in the spring of their kindergarten year can be attributed to the school in which they were enrolled.

As Chatterji (2005) asserted, ICC values greater than .10 indicate that there are sufficient within- school dependencies to justify multilevel analysis.

Random Intercepts Model with Only Child-Level Predictors: Reading

The next series of models was specified to determine what proportion of within-school variance in reading achievement was attributable to child background characteristics, such as prior achievement in reading, gender, socioeconomic status, and ethnicity. All non-binary predictors in this school-level model were centered around school means (i.e., group-mean centering); therefore, the estimated coefficients for each risk group showed the within-school achievement differential, controlling for the other child background characteristics serving as predictors in the models but allowing variability between schools.

The table below provides the estimates on the size and significance of reading achievement gaps and child-level predictors, adjusting for kindergarten-entry versus kindergarten-end variability in children’s reading achievement. The model is specified in mixed format as:

X2RTHETK2푖푗 = 훽0푗 + 훽1푗ChildisAsian풊풋 + 훽2푗ChildisBlack풊풋 + 훽3푗ChildisHispanic풊풋 +

훽4푗ChildisWhite풊풋 + 훽5푗ChildPoverty풊풋 + 훽6푗ChildisMale풊풋 + 훽7푗InternalizingProblems풊풋 +

훽8푗SocialEmotionalCompetence풊풋 + 훽9푗X1RTHETK2풊풋 + 푒푖푗

훽0푗 = 훾00 + 푢0푗

훽1푗 = 훾10 + 푢1푗

훽2푗 = 훾20 + 푢2푗

훽3푗 = 훾30 + 푢3푗

훽4푗 = 훾40 + 푢4푗

훽5푗 = 훾50 + 푢5푗

훽6푗 = 훾60 + 푢6푗

훽7푗 = 훾70 + 푢7푗

훽8푗 = 훾80 + 푢8푗

훽9푗 = 훾90 + 푢9푗

Table 13

Estimates of Fixed Effectsa: Random Intercepts Model with Only Child-Level Predictors: Reading

95% Confidence Interval

Parameter Estimate Std. Error df t Sig. Lower Bound Upper Bound

Intercept .454004 .014850 950.040 30.573 .000 .424862 .483146 ChildisAsian .075408 .001572 2364017.503 47.983 .000 .072328 .078488

ChildisBlack -.013250 .001281 2363964.231 -10.345 .000 -.015760 -.010740 ChildisHispanic -.017136 .000860 2364205.962 -19.917 .000 -.018822 -.015450 ChildisWhite .022378 .001243 2363907.824 18.006 .000 .019942 .024814

ChildPoverty -.070708 .000716 2363976.633 -98.726 .000 -.072112 -.069304 ChildisMale -.027658 .000536 2363664.363 -51.572 .000 -.028710 -.026607 GroupMeanCentered_Child .024957 .000597 2363392.999 41.783 .000 .023787 .026128

PretestInternalizingProbsR everseCoded GroupMeanCentered_Child .060525 .000311 2363402.070 194.677 .000 .059916 .061134

SocialEmotionalCompeten ce GroupMeanCentered_X1R .686055 .000370 2363473.874 1854.111 .000 .685330 .686780

THETK2 a. Dependent Variable: X2 READING THETA-K2 DATA FILE.

Table 14

Estimates of Covariance Parametersa: Random Intercepts Model with Only Child-Level Predictors: Reading

95% Confidence Interval

Parameter Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound

Residual .143226 .000132 1087.040 .000 .142968 .143484 Intercept [subject = S2_ID] Variance .205431 .009500 21.623 .000 .187629 .224922 a. Dependent Variable: X2 READING THETA-K2 DATA FILE.

The equation of the average fitted regression line (across schools) is:

X2RTHÊTK2ij = .454004 + .075408 ChildisAsianij + -.013250 ChildisBlackij + -.017136

ChildisHispanicij + .022378 ChildisWhiteij + -.070708 ChildPovertyij + -.027658 ChildisMaleij +

.024957 GroupMeanCentered_ChildPretestInternalizingProbsReverseCoded ij + .060525

GroupMeanCentered_ChildSocialEmotionalCompetence ij + .686055

GroupMeanCentered_X1RTHETK2ij.

The equation indicates that, as expected, the strongest predictor of end-of-year kindergarten achievement, by far, is beginning-of-year kindergarten achievement. For every one-unit increase in beginning-of-year achievement scores, there is a 0.686-unit increase in end- of-year achievement scores. All of the other predictor variables entered into the model were found to be significant (p < .001). The fitted line for a given school will differ from this average line in its intercept, by an amount û for school j. However, the slope of the school lines is assumed to be fixed; the effect of each predictor variable is assumed to be the same for all schools. Therefore, a plot of the predicted school lines would show a set of parallel lines.

The intra-class coefficient (ICC) for this model is larger than for the null model; this is to be expected, since the model controls for some student-level variation by adding several fixed factors.

0.205431 휌 = = 0.589207 0.205431 + .143226

With this model, almost 60 percent of the total variation in end-of-year kindergarten reading achievement can be accounted for by both the school in which the student was enrolled and the various student-level variables entered.

Comparing the results with the null model, the addition of all the student-level predictor variables has reduced the amount of variance at both the school and student levels. The between-school variance has reduced from 0.232 to 0.205, and the within-school variance has reduced from 0.456 to 0.143. The decrease in the within-school variance is expected because of the addition of all the student-level predictor variables; the reduction in the between-school

88 variance suggests that the distribution of students by each predictor variable differs from school to school.

Random Intercepts Model with Child-Level and School-Level Predictors: Reading

In the next model, level-2 (school-level) predictor variables were entered. All non-binary school-level variables were grand-mean centered, which is the only centering option for top-level variables because group-mean centering them would result in their original values. As with the previous model, binary predictor variables were left as their original values for ease of interpretation. The model is formatted in hierarchical format as:

X2MTHETK2푖푗 = 훽0푗 + 훽1푗ChildisAsian풊풋 + 훽2푗ChildisBlack풊풋 + 훽3푗ChildisHispanic풊풋 +

훽4푗ChildisWhite풊풋 + 훽5푗ChildPoverty풊풋 + 훽6푗ChildisMale풊풋 + 훽7푗InternalizingProblems풊풋 +

훽8푗SocialEmotionalCompetence풊풋 + 훽9푗X1MTHETK2풊풋 + 푒푖푗

β0j = G00+ G01AverageDailyAttendancePct + G02FreeReducedLunchPct +

G03ParentInvolvement + G04PercentNonWhiteinSchool+ G05PercentSpecialEd +

G06SchoolPublic + G07SchoolSize + G08SchoolUrbanicity + uj, where

β1j = G01

β2j through β8j (all slopes fixed as in β1j).

Table 15

Estimates of Fixed Effectsa: Random Intercepts Model with Child-Level and School-Level Predictors: Reading

95% Confidence Interval

Parameter Estimate Std. Error df t Sig. Lower Bound Upper Bound

Intercept .528322 .025196 894.113 20.968 .000 .478871 .577772

ChildisAsian .080112 .001805 1658110.852 44.392 .000 .076575 .083649 ChildisBlack -.022433 .001500 1658112.215 -14.960 .000 -.025372 -.019494 ChildisHispanic -.041668 .001013 1658148.615 -41.132 .000 -.043653 -.039682

ChildisWhite .032228 .001429 1658031.352 22.552 .000 .029427 .035029 ChildPoverty -.073324 .000840 1657966.697 -87.271 .000 -.074970 -.071677 ChildisMale -.020409 .000630 1658011.162 -32.378 .000 -.021645 -.019174

GroupMeanCentered_Chil .015103 .000694 1657734.089 21.774 .000 .013743 .016462 dPretestInternalizingProbs ReverseCoded

GroupMeanCentered_Chil .069218 .000365 1657731.238 189.523 .000 .068502 .069934 dSocialEmotionalCompete nce

GrandMeanCentered_Scho .015396 .006948 617.651 2.216 .027 .001752 .029041 olAverageDailyAttendance Pct

GrandMeanCentered_Scho -.001450 .000674 634.250 -2.152 .032 -.002774 -.000127 olFreeReducedLunchPct GrandMeanCentered_scho .027595 .018885 617.998 1.461 .144 -.009491 .064681 olparentinvolvement GrandMeanCentered_scho -.002721 .000595 630.496 -4.575 .000 -.003888 -.001553 olPercentNonWhiteinScho ol GrandMeanCentered_scho -.005960 .002487 621.112 -2.396 .017 -.010843 -.001076 olPercentSpecialEd

SchoolPublic -.179748 .012379 285028.714 -14.520 .000 -.204011 -.155485 SchoolSize .129644 .032183 621.122 4.028 .000 .066442 .192845 SchoolUrbanicity .048026 .009998 109905.287 4.803 .000 .028429 .067622

GroupMeanCentered_X1R .677658 .000433 1657766.149 1565.163 .000 .676810 .678507 THETK2 a. Dependent Variable: X2 READING THETA-K2 DATA FILE.

Table 16

Estimates of Covariance Parametersa: Random Intercepts Model with Child-Level and School-Level Predictors: Reading

95% Confidence Interval

Parameter Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound

Residual .138801 .000152 910.397 .000 .138503 .139101 Intercept [subject = S2_ID] Variance .154871 .008823 17.552 .000 .138508 .173167 a. Dependent Variable: X2 READING THETA-K2 DATA FILE.

As the data in the tables indicate, most of the predictor variables were strongly statistically significant (with the exception of the average level of parent involvement in the school, which was non-significant). For example, a child in a public school would be expected to have a score that is .180 points lower than a child in a private school (adjusted for all other school- and student-level predictor variables). Interestingly, the sector of the school (public versus private) was by far the strongest predictor variable (other than prior achievement).

Comparing this model to the previous one, there is a reduction in between-school variance. After accounting for the various school-level predictor variables, the between-school variance reduces from 0.205 to 0.155. The intra-class coefficient (ICC) for this model is smaller than for the previous model. This is to be expected, since ICC is a measure of how much of the unexplained variation can be accounted for by which school a student is in; by adding school- level predictors, the model is accounting for a larger portion of the variation among the different schools. Therefore, less variation exists in the random intercept, 푢0푗, for this model than those without any level-2 predictors, and thus the ICC is also smaller.

0.154871 휌 = = 0.52736 0.154871 + 0.138801

With this model, about half of the total variation in end-of-year kindergarten reading achievement can be accounted for by both the school in which the student was enrolled and the various predictor variables entered.

Random Intercepts and Slopes Model, with Poverty used to Examine Cross-Level

Interactions: Reading

The analysis thus far has revealed that reading achievement in the spring of kindergarten is significantly related to the child’s prior achievement, race, ethnicity, socioeconomic status, gender, internalizing problems, and social-emotional competence, as well as the school’s average daily attendance, portion of students with free or reduced lunch, portion of non-White students, portion of students receiving special education services, sector, size, and urbanicity. However, only the main effects of these variables have been considered. In practice, the relationship between an outcome variable and a predictor variable may depend on the interaction effect between the predictor variable and a second predictor variable. Of particular interest to the present study are cross-level interactions between student poverty (level 1) and various school- level variables (level 2).

β6j = G60+ + G61AverageDailyAttendancePct + G62FreeReducedLunchPct +

G63ParentInvolvement + G64PercentNonWhiteinSchool+ G65PercentSpecialEd +

G66SchoolPublic + G67SchoolSize + G68SchoolUrbanicity + u6

For every interaction between school-level predictors and child poverty, the effect was significant (and the estimate was several times greater than the standard error). This means there is evidence that the effect of a child’s poverty on that child’s academic achievement is weaker for students enrolled in public schools than for students enrolled in private schools; is weaker for

92 students enrolled in schools with more than 500 students than for students enrolled in schools with fewer than 500 students; is greater for students in schools that have more students served by free/reduced lunch programs; is greater for students in non-urban schools than for students in urban schools; and is weaker for students in schools that have higher average daily attendance percentages, more parent involvement, more non-White students, and more students receiving special education.

Interestingly, a school’s level of parent involvement was itself not a significant predictor of achievement in this model, even though its interaction with student poverty was indeed a significant predictor of achievement. It is a possible that a variable with a non-significant main effect could be involved in a significant interaction effect. This is one reason that several apparently non-significant predictors were left in the models used throughout this dissertation.

Table 17 Estimates of Fixed Effectsa: Random Intercepts and Slopes Model, with Poverty used to Examine Cross-Level Interactions: Reading

95% Confidence Interval

Parameter Estimate Std. Error df t Sig. Lower Bound Upper Bound

Intercept .516928 .025158 897.642 20.547 .000 .467553 .566304 ChildisAsian .077139 .001804 1658108.048 42.751 .000 .073602 .080675

ChildisBlack -.022538 .001499 1658108.284 -15.036 .000 -.025476 -.019600 ChildisHispanic -.041133 .001013 1658137.818 -40.617 .000 -.043118 -.039148 ChildisWhite .031691 .001429 1658030.274 22.180 .000 .028891 .034492

ChildPoverty -.017814 .004996 1658183.057 -3.566 .000 -.027605 -.008022 ChildSex -.020008 .000630 1658001.483 -31.751 .000 -.021243 -.018773 GroupMeanCentered_Chil .016819 .000695 1657726.983 24.195 .000 .015456 .018181 dPretestInternalizingProbs ReverseCoded GroupMeanCentered_Chil .069474 .000365 1657728.623 190.312 .000 .068758 .070189 dSocialEmotionalCompete nce GrandMeanCentered_Scho .015568 .006931 617.843 2.246 .025 .001957 .029178 olAverageDailyAttendance Pct

GrandMeanCentered_Scho -.001627 .000672 634.668 -2.420 .016 -.002947 -.000307 olFreeReducedLunchPct

GrandMeanCentered_scho .030072 .018838 618.262 1.596 .111 -.006923 .067067 olparentinvolvement GrandMeanCentered_scho -.002399 .000593 630.904 -4.045 .000 -.003564 -.001234 olPercentNonWhiteinScho ol GrandMeanCentered_scho -.005802 .002481 621.344 -2.339 .020 -.010674 -.000930 olPercentSpecialEd SchoolSector -.172277 .012425 283474.045 -13.865 .000 -.196631 -.147924 SchoolSize .134563 .032105 621.408 4.191 .000 .071516 .197611

SchoolUrbanicity .065666 .010037 109260.421 6.542 .000 .045994 .085339 ChildPoverty * -.000835 .000353 1658213.317 -2.365 .018 -.001527 -.000143 GrandMeanCentered_Scho olAverageDailyAttendance Pct ChildPoverty * .001064 4.523336E-5 1658211.619 23.517 .000 .000975 .001152

GrandMeanCentered_Scho olFreeReducedLunchPct ChildPoverty * -.010283 .000978 1658191.001 -10.514 .000 -.012200 -.008366

GrandMeanCentered_scho olparentinvolvement ChildPoverty * -.001449 3.466203E-5 1658217.099 -41.807 .000 -.001517 -.001381

GrandMeanCentered_scho olPercentNonWhiteinScho ol

ChildPoverty * -.000452 .000126 1658136.908 -3.597 .000 -.000698 -.000206 GrandMeanCentered_scho olPercentSpecialEd

ChildPoverty * -.037810 .005274 1658147.410 -7.170 .000 -.048146 -.027474 SchoolSector ChildPoverty * SchoolSize -.023067 .001687 1658212.556 -13.673 .000 -.026374 -.019761

ChildPoverty * -.039867 .001876 1658242.053 -21.247 .000 -.043544 -.036189 SchoolUrbanicity GroupMeanCentered_X1R .677585 .000433 1657763.627 1564.414 .000 .676737 .678434

THETK2 a. Dependent Variable: X2 READING THETA-K2 DATA FILE.

Table 18 Estimates of Covariance Parametersa: Random Intercepts and Slopes Model, with Poverty used to Examine Cross-Level Interactions:

Reading

95% Confidence Interval

Parameter Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound

Residual .138495 .000152 910.395 .000 .138198 .138794 Intercept [subject = S2_ID] Variance .154077 .008778 17.552 .000 .137798 .172280 a. Dependent Variable: X2 READING THETA-K2 DATA FILE.

Comparing this model to the previous one, there is a slight decrease in between-school variance. After accounting for the interaction of poverty with the various school-level predictor variables, the between-school variance decreases only slightly, remaining at about 0.154. The intra-class coefficient (ICC) for this model is only slightly larger than for the previous model.

This suggests that the addition of cross-level interaction effects did not substantially change the amount of unexplained variation that could be accounted for by which school a student is in.

About the same amount of variation exists in the random intercept, 푢0푗, for this model as there is in the random intercept of the previous model where there were student-level and school-level predictors but no cross-level interactions, and thus the ICC is also about the same.

0.154077 휌 = = 0.526629 0.154077 + 0.138495

CHAPTER V

DISCUSSION

This study utilized multilevel modeling to estimate the predictive relationships among school-level variables, student-level background variables, and end-of-year academic achievement among kindergarteners. Prior to this study, it was well established that there exists a relationship between social-emotional competence (SEC) and academic achievement.

However, perhaps due to the various operationalizations of SEC and academic achievement used by researchers, there continues to be less understanding of the interplay between the many components of SEC and how those components come together to influence or predict a student’s success. Researchers who have developed multilevel models predicting academic achievement from the ECLS-K datasets have generally excluded social-emotional variables entirely, despite data being collecting as part of both the originally ECLS-K in 1998 and the ECLS-K: 2011 (e.g.,

Chatterji, 2005). The present study delivers a model by which SEC measured at the beginning of the kindergarten year (along with many other background variables that are more commonly included in predictive models of academic achievement) can be incorporated into predictions of end-of-kindergarten academic achievement. The potential utility of such a model should not be understated; such a model could provide practitioners in the field, including teachers, administrators, and support staff, with the ability to mitigate future academic and behavioral concerns by proactively addressing present social-emotional concerns through a resiliency framework.

Comparisons of the Findings with Extant Literature

Using multilevel modeling with the ECLS-K: 2011 data allowed a deeper examination of achievement gaps and school factors that directly affect or moderate kindergarteners’

96 mathematics and reading achievement levels in isolated subgroups, thus addressing gaps in the extant literature. Several findings in the present study support current educational policy directions; others contradict conventional or theoretical expectations. In conclusion, these findings are discussed along with limitations and areas for further research.

Achievement Gaps

First, in interpreting the achievement gaps revealed by the analyses, it should be borne in mind that gap estimates are regression coefficients that represent differences of a defined group on the outcome measure, as compared to the school means and controlling for other modeled child background factors. This definition is different from a perhaps more common approach, which uses mean differences computed with a specified reference group in mind (e.g., African

American versus White).

The results show that the influence of poverty is consistently negative on both mathematics and reading achievement, even when prior knowledge, gender, race/ethnicity, social-emotional competence, and internalizing problems are controlled. Likewise, prior mathematics preparation (as measured in the fall of kindergarten) has a strong positive and significant effect on subsequent mathematics achievement in the spring of kindergarten (with other factors held constant), and the same is true regarding reading achievement. In addition, there were significant achievement gaps across race and gender. Boys tended to score higher than girls did in mathematics (with other factors held constant), and girls tended to score higher than boys did in reading (with other factors held constant). In both mathematics and reading,

Asian and White children tended to score higher than children who were not members of those groups, and Hispanic and Black children tended to score lower than children who were not members of those groups. Moreover, children’s social-emotional competence (SEC) was

97 predictive of improved mathematics and reading achievement, and children’s internalizing problems were predictive of diminished mathematics and reading achievement (Note:

Internalizing Problems was reverse-coded in the analyses).

The statistically significant advantages estimated for children who start with higher initial mathematics and reading scores (measures taken in fall of kindergarten) are consistent with prior research finding that cognitive and social skills measured in late preschool years are strongly predictive of performance in the same domains in the early school years (Laparo & Pianta,

2000). In addition, the finding that social-emotional competence (SEC) was significantly predictive of later academic achievement was consistent with the extant literature (Oberle,

Schonert-Reichl, Hertzman, & Zumbo, 2014). This finding in particular is consequential for education policy, as there is a common public perception that investing time into fostering social and emotional skills in the classroom will take time away from what is ostensibly the main goal of schooling: academic competence (Malecki & Elliot, 2002). This opinion has been widely criticized by researchers in education and child development (e.g.,DiPerna & Elliott, 2000;

Durlak, Weissberg, Dymnicki, Taylor, & Schellinger, 2011; Elias & Haynes, 2008; Zins,

Weissberg, Wang, & Walberg, 2004). Due to growing evidence that students' SEC and academic success are interrelated, researchers have urged that monitoring and ultimately fostering positive social and emotional development may support academic growth (Greenberg et al., 2003;

Hawkins, Kosterman, Catalano, Hill, & Abbott, 2008; Jones, Brown, & Aber, 2011; Zins et al.,

2004). That being said, it is worth noting that the sizes of the effects of SEC on academic achievement in each model, while statistically significant (due in large part to the extremely large sample size), were quite small; in the level-1 model of mathematics achievement, for example, a one-unit increase in SEC was associated with only a 0.06-unit increase in

98 mathematics achievement. This raises questions regarding the cost- and time-effectiveness of implementing SEC interventions in the classroom, given the weak (though significant) relationship between SEC and academic achievement.

From a school practice perspective, it is also clear that children of different racial/ethnic groups exhibit different patterns of mathematics and reading achievement as early as kindergarten. Consistent with expectations set by prior research on ethnic achievement gaps in both older and younger pupils (NCES, 1995a; NCES, 1995b), Hispanic and Black children showed statistically significant negative achievement gaps, and White and Asian children showed statistically significant positive achievement gaps. These gaps are notable because the models included both prior knowledge and poverty as predictor variables, the latter of which is offered in the literature as one major explanation of achievement gaps among Hispanic and

Black students (NCES, 1995a; NCES, 1995b).

Likewise, that gender differences in reading and mathematics achievement are small but significant as early as in kindergarten should be also noted by both teachers and policymakers.

The findings on mathematics and reading gaps in children from families living in poverty are consistent with results on national tests at all levels of schooling. It is crucial that such gaps are monitored through elementary school and as children start their middle and high school years, and shifts in the size of the mathematics and reading achievement gaps should be closely examined. More importantly, schools should find ways to address domain-specific needs of students as they arise at the classroom level. Timely detection and diagnosis of curriculum- specific needs in students would give schools and teachers the opportunity to prevent mathematics and reading gaps from developing in later years.

School-level Correlates of Achievement

When partitioned, about 15% of the total variability in children’s mathematics and reading achievement scores was between-schools variance. The main effects model for mathematics achievement explained about 51% of that between-schools variance estimate, showing average daily attendance, portion of students receiving free/reduced lunch, portion of non-White students, school sector (where 1 = public, 0 = private), and school urbanicity (where 1

= urban, 0 = suburban or rural) as significant school-level correlates. The main effects model for reading achievement explained about 53% of that between-schools variance estimate, showing average daily attendance, portion of students receiving free/reduced lunch, portion of non-White students, portion of students receiving special education services, school sector, school size, and school urbanicity as significant school-level correlates.

Most of the findings were consistent with the extant literature. Students enrolled in schools with higher average daily attendance had significantly higher mathematics and reading scores (Rothman, 2001; DeKalb, 1999; Ziegler, 1972). Students in schools with a higher proportion of students receiving free/reduced lunch had significantly weaker mathematics and reading scores (Hansen et al., 2011). Students in schools with a higher proportion of non-White students had significantly weaker mathematics and reading scores (Lee, 2002). Students in schools with a larger proportion of students receiving special education services had significantly weaker reading scores, as well as non-significantly weaker mathematics scores (Lee, Shin, &

Amo, 2013). Students in public schools had significantly weaker mathematics and reading scores than students in private schools (Braun, Jenkins, & Grigg, 2006).

One unexpected finding, which contradicted much of the extant literature on the school size, was that students enrolled in schools of more than 500 students exhibited significantly stronger reading achievement than students in schools of fewer than 500 students. As Chatterji

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(2005) noted after finding a similar pattern with the mathematics scores of students who participated in the original ECLS-K study, the positive rather than negative effects of larger school size on achievement may be due to larger schools possessing greater material resources.

In addition, much of the literature on the impact of school size on achievement has focused on older students (Lee & Smith, 1993), so it is possible that larger schools do not have a noticeably negative influence until students reach adolescence.

Perhaps the most surprising finding (at least, to the casual observer) is that students enrolled in urban schools had significantly stronger mathematics and reading scores than students in non-urban schools (adjusted for the other predictor variables included in the model, and where non-urban schools included both suburban and rural schools). Moreover, urbanicity was one of the strongest school-level predictors of mathematics achievement. Although conventional wisdom may hold that urban schools are academically inferior to non-urban schools

(or, at least, to suburban schools), the reality is that this belief does not hold up when the other predictor variables in the model are taken into consideration (e.g., Bohrnstedt, Kitmitto, Ogut,

Sherman, & Chan, 2015). As Webster (2015) commented regarding an analysis of Minnesota mathematics and reading scores that found no appreciable difference between the achievement of middle- and upper-income urban students and middle- and upper-income suburban students, public misunderstanding of the relationships between socioeconomic status, urbanicity, and achievement has contributed to the widespread perception that urban schools are of inferior quality for all students. This, in turn, has damaged urban schools’ reputations, enrollment levels, and faculty morale—not to mention, exacerbated the de facto segregation caused by well- intentioned middle-class parents who believe they are fleeing inferior schools in the urban core for academically superior ones in the suburbs. That being said, the same analysis found that

101 children living in poverty had significantly stronger reading and mathematics scores when enrolled in schools in the suburbs than those in the city; in the outer suburbs, about 64 percent of low-income children met reading standards compared with 43 percent in the core cities. For this reason, the present dissertation examined the interactions of student poverty with various school- level predictor variables.

Cross-level Interaction Effects

Several cross-level interaction results were in expected directions and may point to some school policy or practice actions, keeping in mind that the evidence is correlational. Other cross- level interaction results were unexpected. For example, for children living in poverty (as opposed to their peers not living in poverty), being enrolled in a school with a higher average daily attendance percentage had small but significant negative effects on both mathematics and reading achievement. Moreover, for students living in poverty, being enrolled in schools with higher levels of administrator-reported parent involvement, non-White students, and students receiving special education were also associated with reduced levels of mathematics and reading achievement. However, being enrolled in a school with more students receiving free or reduced lunch had small but significant positive effects on the mathematics and reading achievement of students living in poverty; this may seem counterintuitive, until one considers that schools where a majority of students are low-income tend to have instructional strategies, wraparound programs, social-emotional learning approaches, and community partnerships that are all aligned explicitly to support low-income students and their learning needs, including services such as breakfast, lunch and dinner, as well as an extended school day that runs until 5:30 p.m.

(Camera, 2017).

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As Chatterji (2005) noted, one policy consequence of the finding that students living in poverty tended to perform worse when enrolled in schools with more students receiving special education is that the No Child Left Behind Act’s (NCLB) requirement that schools set common benchmarks for achievement of special versus normally-achieving student populations may not be a reasonable expectation. That being said, many of the effects of the interactions mentioned in the previous paragraph were so small as to be almost trivial, and their significance was likely due to the very large sample size.

Interestingly, the findings for the interactions of poverty with school sector, school size, and school urbanicity were directionally different depending on the outcome variable. For maximizing mathematics achievement, students living in poverty were better served by public schools, schools with more than 500 students, and urban schools, respectively (although the effect for urbanicity was non-significant); for maximizing reading achievement, on the other hand, students living in poverty were better served by private schools, schools with fewer than

500 students, and non-urban schools. Once again, however, many of the effects of the interactions were so small as to be almost trivial, and their significance may have been due to the very large sample size.

Comparing the Models

For principals, superintendents, school support staff, and other practitioners working in the education field, the models presented in this dissertation can potentially assist in the early identification of students who may be at risk of future academic difficulties. For example, converting the model into a user-friendly “red-yellow-green light” system, wherein students with a predicted spring score of more than one standard deviation beneath the mean are assigned a

“red” status and consequently provided with an intensive mathematics or reading intervention, is

103 not a far-fetched application of the models devised in this dissertation. However, determining which of the models presented is most appropriate for an interested practitioner’s school or district goes beyond practical considerations such as the availability of the various student- and school-level data that were collected.

As has been discussed throughout the previous chapter, the models differed from one another in their random residuals, random intercepts, and intraclass correlation coefficients

(ICC). In other words, they differed in their between-schools variability in achievement, within- schools variability in achievement, and variation in achievement attributable to the school in which the student was enrolled. The table below summarizes these statistics for each model side-by-side, for ease of comparison.

Table 19

As discussed in the previous chapter, the ICC for each null model was greater than 0.1, revealing that multilevel modeling was indeed necessary. If the null models had ICCs approaching zero, that would mean the observations within clusters were no more similar than observations from different clusters, and a simpler analysis technique would have therefore been sufficient.

The ICCs for the random-intercept models with only student-level predictor variables were substantially larger than the ICCs for the null models; this is to be expected, since the

104 models control for some student-level variation by adding several fixed factors. There were also decreases in both within-school variance and between-school variance. The decrease in the within-school variance is expected because of the addition of all the student-level predictor variables; the reduction in the between-school variance suggests that the distribution of students by each predictor variable differs from school to school.

The ICCs for the random-intercept models with both student- and school-level predictor variables were smaller than the ICCs for the models with only student-level predictor variables.

In addition, there were reductions in between-school variance. This is to be expected, since ICC is a measure of how much of the unexplained variation can be accounted for by which school a student is in; by adding school-level predictors, the model is accounting for a larger portion of the variation among the different schools. Therefore, less variation exists in the random intercept for these models than those without any level-2 predictors, and thus the ICCs are also smaller.

Finally, the ICCs for the models examining the interaction of student poverty with school were very similar to those for the models without the interaction terms. This means that the interaction terms did not substantially change the proportion of variance accounted for by class.

The table below shows how the models differ when each are used to predict the achievement of an actual student from the ECLS-K: 2011 dataset, who is White, Hispanic, male, and living above the poverty line. This child has slightly above-average prior achievement for his school (i.e., group-mean centered fall theta score in mathematics is 0.38 and group-mean centered fall theta score in reading is 0.84; a theta score is a standardized score used in Item

Response Theory where the mean equals zero and the standard deviation equals one). The child’s ability to cope with internalizing problems is weaker than his school mean, at -0.85 group-mean centered points. The child’s overall social-emotional competence (SEC) is also

105 weaker than his school mean, at -1.64. The child attends a non-urban, public school with more than 500 students, where the average daily attendance percentage and portion of students receiving free or reduced lunch are less than the grand mean, at -6.22 and -19.60, respectively.

However, the school has an administrator-reported level of parent involvement at .93 points greater than the grand mean. Nonetheless, the school has below-average portions of students who are non-White and students who receive special education, at 8.63 less than the grand mean and 1.17 less than the grand mean, respectively. The interactions of child poverty with each school-level predictor are also in the table below, although they are zero for this particular student, since the student lives above the poverty line.

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Table 20

Outcome of Each Model to Predict Achievement of Hypothetical Child Mathematics Reading Random- Random- Random- Model Intercept Intercept Model Intercept Showing Random-Intercept Model with Model with Showing Model with Interaction Hypothetical Child's Model with Student- Student- and Null Model Student- and Interaction of Null Model Student- of Child's Score on Variable Level Explanatory School- School-Level Child's Poverty Level Poverty Variables Level Explanatory with Schools Explanatory with Explanatory Variables Variables Schools Variables Intercept 0.423914 0.424221 0.685532 0.701932 0.431519 0.454004 0.528322 0.516928 GroupMeanCentered_Prior Achievement (math=0.38; reading=0.84) 0 0.659505 0.661766 0.661534 0.686055 0.677658 0.677585 ChildisAsian 0 0.035006 0.03766 0.037956 0.075408 0.080112 0.077139 ChildisBlack 0 -0.081236 -0.07901 -0.079153 -0.01325 -0.022433 -0.022538 ChildisHispanic 1 -0.016949 -0.026258 -0.026108 -0.017136 -0.041668 -0.041133 ChildisWhite 1 0.049606 0.06897 0.068587 0.022378 0.032228 0.031691 ChildPoverty 0 -0.059875 -0.057447 -0.145429 -0.070708 -0.073324 -0.017814 ChildisMale 1 0.01636 0.012548 0.012884 -0.027658 -0.020409 -0.020008 GroupMeanCentered_ChildPretestInternalizingProbsReverseCoded -0.85 0.009891 0.006633 0.006358 0.024957 0.015103 0.016819 GroupMeanCentered_ChildSocialEmotionalCompetence -1.64 0.054394 0.058671 0.058854 0.060525 0.069218 0.069474 GrandMeanCentered_SchoolAverageDailyAttendancePct -6.22 0.019411 0.020299 0.015396 0.015568 GrandMeanCentered_SchoolFreeReducedLunchPct -19.6 -0.00133 -0.001427 -0.00145 -0.001627 GrandMeanCentered_schoolparentinvolvement 0.93 0.014839 0.018444 0.027595 0.030072 GrandMeanCentered_schoolPercentNonWhiteinSchool -8.63 -0.003507 -0.003189 -0.002721 -0.002399 GrandMeanCentered_schoolPercentSpecialEd -1.17 -0.001324 -0.000992 -0.00596 -0.005802 SchoolisPublic 1 -0.407552 -0.414319 -0.179748 -0.172277 SchoolSize 1 0.060636 0.047974 0.129644 0.134563 SchoolUrbanicity 0 0.181667 0.172713 0.048026 0.065666 ChildPoverty * GrandMeanCentered_SchoolAverageDailyAttendancePct 0 -0.003 -0.000835 ChildPoverty * GrandMeanCentered_SchoolFreeReducedLunchPct 0 0.000773 0.001064 ChildPoverty * GrandMeanCentered_schoolparentinvolvement 0 -0.014202 -0.010283 ChildPoverty * GrandMeanCentered_schoolPercentNonWhiteinSchool 0 -0.001136 -0.001449 ChildPoverty * GrandMeanCentered_schoolPercentSpecialEd 0 -0.000829 -0.000452 ChildPoverty * SchoolSector 0 0.057983 -0.03781 ChildPoverty * SchoolSize 0 0.048889 -0.023067 ChildPoverty * SchoolUrbanicity 0 0.000818 -0.039867 Predicted Achievement ActualMath: 0.7325 0.423914 0.37562449 0.24296385 0.23656919 0.431519 0.31111355 0.3107896 0.312045 ActualReading: 1.2227

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As the data in the table above indicate, the models all underestimated this particular student’s actual spring achievement on both mathematics and reading. Nonetheless, each model did accurately predict that the student would have positive theta scores in spring, meaning they correctly predicted that the student would perform better than the average test-taker. For this student’s mathematics achievement, the random-intercept model with only student-level predictor variables was noticeably more accurate than the two models with school-level variables. However, for reading achievement, the three models performed similarly. That being said, the full model should be the most accurate; it is possible that the particular student in the example was something of an outlier.

Limitations

The dataset used for the models was collected as part of a large-scale national study. As

Chatterji (2005) has noted, the secondary analysis of such large-scale national studies does not permit causal interpretations of various school effects; therefore, the evidence presented in this dissertation should be regarded as correlational. The controls instituted were not experimental, but merely statistical. The findings were influenced by factors such as missing data, the particular variables selected, and how those variables were operationalized. Consistent with prior research (Chatterji, 2005), racial predictors with smaller group sizes, including American

Indian/ Native American, Hawaiian/ Pacific Islander, and Multiracial, were excluded from the models for the sake of parsimony (to clarify, this does not mean that students identifying as members of these groups were excluded; rather, the impact of being a member of these groups on academic achievement was not modeled).

Extremely Large Sample Size and Failure to Report Effect Size

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Due to the sample size exceeding 10,000 students and the fact that the inferential tests used in the present study were sample size-dependent, it was found that nearly every predictor variable had a statistically significant influence on academic achievement. As Sullivan and

Feinn (2012) have asserted, “P values are considered to be confounded because of their dependence on sample size. Sometimes a statistically significant result means only that a huge sample size was used” (p. 279). Therefore, the authors recommend that researchers make sure to report effect size, which is independent of sample size.

The tables reported in the present dissertation did not report the effect sizes of individual variables, instead relying on model fit indices to compare whole models. Unfortunately, as

Niehaus, Campbell, and Kurotsuchi Inkelas (2014) asserted, this is a common problem in the

HLM literature, in no small part due to the lack of agreement among scholars regarding how best to report effect sizes that constitute practical significance. Raudenbush and Bryk (2002) stated that even very small amounts of variation at the group level (e.g., as little as 2–3%) could be important to model, but they note that ultimately this is a judgment call left up to the individual researchers. Hedges (2007) called for the use of specialized effect sizes in multilevel designs that take into account within- and between-group variation. Other scholars have discussed the use of model fit indices, such as reduction in deviance (Luke, 2004) or proportional reduction in variance (McCoach & Black, 2008), which both compare models with different predictors to determine whether predictors are significant contributors to the model. Other scholars have discussed multiple methods for effect sizes and how the calculation of effect sizes in HLM is complex and unclear (Roberts & Monaco, 2006). Partly because of the lack of agreement about how to denote practical significance, very few articles in the education literature report such effect sizes regarding proportion of variance explained at each level for specific predictors.

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Non-significant Predictors

There were a few predictor variables that were found to have non-significant effects on some of the models. There is conflicting literature regarding whether researchers should leave non-significant effects in a model or remove them for the sake of parsimony. However, the parsimony of the model is a much greater concern with small sample sizes, where non- significant predictors “use up” degrees of freedom; as Grace-Martin (2018) has argued, this negative impact of non-significant predictor variables is negligible with large sample sizes.

A more important concern is with regard to the interpretation of the model. To ease interpretation, Grace-Martin (2018) recommends eliminating effects that do not serve a purpose; nonetheless, she notes that even non-significant effects can serve a purpose, such as if the predictor is an expected control variable (i.e., race, socioeconomic status, etc.), the predictor has a specific hypothesis associated with it, or the predictor is involved in a higher-order term. For these reasons, all non-significant predictors were left in the models.

Perhaps the best argument for removing any of the non-significant predictors would be with regard to parent involvement. Parent involvement had somewhat weak psychometric properties; it was operationalized in the present dissertation as administrators’ responses to a single five-point Likert-type item in the School Administrator Survey (S2INVOLV), pertaining to the extent to which the administrator agrees parents are active in school programs. The mean for this variable was 4.06 and the standard deviation was 0.93, meaning that administrators generally agreed that parents were, on average, active in school programs. The item was not based on any tangible or quantifiable measure of parent involvement, such as a count of parents attending parent-teacher conferences or other school activities; instead, it was merely based on administrator’s opinions, which varied little among schools. Nonetheless, this item was included

110 in the final models, if only due to the apparent lack of any other measure of parent involvement available in the dataset, as well as the fact that there was an interaction between parent involvement and poverty in the final models.

Lack of General Cognitive Ability as a Predictor

One limitation of the present study is that it ignores the role of general cognitive ability

(i.e., “intelligence”) as a construct separate from academic achievement. As Parker and Benedict

(2002) have pointed out, it is generally believed that intelligence tests measure the general reasoning skills that can predict academic achievement. Unfortunately, no scores on any measure of cognitive ability or intelligence are available for the sample examined. However, despite numerous studies finding moderate or strong correlations between students’ scores on measures of cognitive ability and their scores on standardized achievement tests, some researchers continue to argue such correlations are merely due to the fact that the tests are similar, particularly in the tasks they demand of students (Petrides, Frederickson, & Furnham,

2004; Waterhouse, 2006).

Multilevel Modeling Limitations

Finally, there are limitations inherent in the multilevel modeling approach that was chosen for the analysis. Although multilevel modeling has clear advantages over traditional statistical techniques for analyzing hierarchical data such as disaggregation and aggregation,

Dedrick and colleagues (2009) have pointed out that practitioners of multilevel modeling must take into consideration several methodological concerns in the realms of model specification, data issues, estimation procedures, and hypothesis testing. Studies employing multilevel modeling often fail to report information such as the estimation method used (e.g., restricted maximum likelihood, or REML) or the type of centering used (e.g., group mean). The present

111 study attempted to go beyond what is typically reported in the literature in order to provide results that are both understandable and replicable.

Sample size and weighting. One disadvantage of multilevel modeling, as Woltman and colleagues (2012) point out, is that it requires large sample sizes at each level for adequate power. As Maas and Hox (2005) found, having groups of fewer than 50 could lead to biased estimates of the second level standard errors. Unfortunately, for the present study, there were data collected from an average of about 20 students from each school, thereby violating that guideline. Although the data were weighted to account for patterns of non-response, that weighting raises its own concerns that pertain to the inferential tests used in the models.

Prior to each analysis, the data were weighted to account for non-response to various instruments administered at kindergarten fall and kindergarten spring. Although this made the data more representative of the national population of kindergarten students and helped allay concerns about patterns of systematic non-response among certain respondent subgroups, the weighting also resulted in a dramatically increased sample size (from a sample size of n = 18,174 students before weighting to an estimated population size of N = 4,054,166 students after weighting). Because the inferential tests are sample-size dependent, (i.e., significant results become more likely with increased sample sizes), p-values of less than 0.05 do not necessarily provide the best evidence of the practical utility of any predictor variable. In other words, it is not surprising that almost every predictor variable significantly contributed to the models. It is more worthwhile to examine the estimated strength of those variables (e.g., the expected difference in mathematics scores between students who attended a public school and students who attended a private school, or the amount of improvement in reading scores that accompanies each point of improvement in social-emotional competence).

112

Weighting raises an additional concern. Creating all possible weights for a study with as many components as the ECLS-K:2011 has would be both impractical and financially unfeasible. Therefore, the weights provided in the ECLS-K:2011 dataset accounted for patterns of non-response to only some instruments, based on how likely researchers felt analysts would be to use the data (i.e., which weights would have greatest analytic utility). The sample weight that was used in the present dissertation was selected because it maximized the number of sources of data included in the analyses for which non-response adjustments were made, which in turn minimized bias in estimates, while maintaining as large an unweighted sample size as possible. However, it should be noted that the weight used did not adjust for non-response to all instruments administered as part of the study.

Estimation method. The issue of estimation method remains a methodological concern at the conclusion of this study. Restricted maximum likelihood (REML) was used to estimate all the models’ covariance matrices. REML was chosen over full maximum likelihood (ML). As

McCulloch and Searle (2000) have argued, both ML and REML yield asymptotically efficient estimators for balanced and unbalanced designs, and both therefore have a clear advantage over

ANOVA methods (which produce optimum estimators for balanced designs, due to their minimum variance) in modeling real data, since data are often unbalanced. The reason REML was chosen over ML is that, as Bryk and Raudenbush (1992) asserted, “posterior variances will be larger – and more realistic – under REML than under [ML]” (p. 53). However, the authors went on to “strongly caution the reader that regardless of whether we use [ML] or REML, these tests will be too liberal, with actual significance values substantially exceeding the nominal values, unless J is large” (p. 53). Moreover, although ML produces a negative bias for the estimation of variance components, this bias is greater for smaller sample sizes, and would likely

113 be less of a concern with a sample as large as the one used in the present study. In addition, this bias associated with ML is the cost of having a smaller mean squared error (MSE), meaning that using ML would likely produce estimates that have less error than those produced using REML.

Nonetheless, REML was chosen for the analyses, due to Hoyle and Gottfredson’s (2014) assertion that when when yij is normally distributed, REML is the preferred estimator and inferences about fixed effects can be trusted.

Centering inconsistencies. In addition, different types of centering were used somewhat inconsistently, and it is important to explain why variables were group-mean centered, grand- mean centered, or not centered at all. First, no dichotomous variables were centered; this was simply for ease of interpretation. Notably, there are scholars who differ on whether dichotomous variables should be centered—as Algina and Swaminathan (2011) have pointed out, using the original 0-1 coding in a dichotomous predictor, rather than centering, means the intercept and variance of the intercept represents the mean of the zero group and the variance of the zero group, which may not be desirable in many cases. Nonetheless, again, it was determined that avoiding centering would ease the interpretation of dichotomous variables in the present dissertation.

Non-dichotomous student-level predictor variables were group-mean centered. The decision was made to group-mean center the non-dichotomous student-level predictors because doing so would make it easier to interpret findings related to the theoretical concerns that motivated the research, as well as to remove high correlations between the random intercept and slopes, and high correlations between first- and second-level variables and cross-level interactions (Kreft & de Leeuw, 1998).

114

Finally, non-dichotomous school-level predictor variables were grand-mean centered.

Importantly, it would have been impossible to group-mean center the school-level variables, since the schools are themselves the groups, so group-mean centering would have resulted in unchanged data. The decision was made to grand-mean center the non-dichotomous school-level predictors because doing so would make it easier to interpret findings related to the theoretical concerns that motivated the research, as well as to remove high correlations between the random intercept and slopes, and high correlations between first- and second-level variables and cross- level interactions (Kreft & de Leeuw, 1998).

APPENDICES

APPENDIX A

KENT STATE INSTITUTIONAL REVIEW BOARD APPROVAL

Appendix A

Kent State Institutional Review Board Approval

117

APPENDIX B

PROPERTIES OF COMPUTED VARIABLES

Appendix B

Properties of Computed Variables

Child Variables

First, a measure of social-emotional competence (SEC) was computed. This index was initially based on teacher ratings of students’ social skills in the fall of kindergarten, including interpersonal skills, self-control, internalizing problems, and externalizing problems, as well as a selected set of positive learning behaviors (“Approaches to Learning”), which include things like keeping belongings organized, showing eagerness to learn, and working independently.

Internalizing Problems and Externalizing Problems were reverse-coded prior to Principal

Components Analysis and computation of coefficient alpha (Cronbach, 1951), in order to develop a single SEC variable. The conception of Social-Emotional Competence as a singular psychological construct is consistent with a substantial body of literature (e.g., Denham et al.,

2003). The five items loaded on a principal component with an eigenvalue of 3.324 prior to rotation, and four of the five items had component loadings greater than 0.8. After removing

Internalizing Problems (Reverse-Coded) due to its weaker component loading of 0.446 and its weak inter-item correlations and item-total correlation (all less than 0.4), a new four-item scale was calculated without Internalizing Problems. This new four-item subscale had an improved coefficient alpha of 0.901, as well as other strong psychometric properties. Selected tables from the final reliability analysis are below. As a result of the findings, Internalizing Problems was considered a separate predictor from SEC in the HLMs that are the focus of this dissertation.

Table 21

Descriptive Statistics: Social-Emotional Competence (SEC) Std. N Minimum Maximum Mean Deviation Approaches to Learning 14770 1.00 4.00 2.9435 .68176

119

120

Externalizing Problems (Reverse Coded) 14385 4.00 1.00 3.3985 .62732 Internalizing Problems (Reverse-Coded) 14239 4.00 1.00 3.5379 .49310 Interpersonal Skills 13708 1.00 4.00 2.9902 .63974 Self-Control 13550 1.00 4.00 3.0798 .62870 Valid N (listwise) 12705

Table 22

Inter-Item Correlation Matrix: Social Emotional Competence (SEC) Teacher- Teacher- Reported Externalizing Reported Teacher- Approaches to Problems Interpersonal Reported Self- Learning in fall (Reverse Skills in fall of Control in fall of kindergarten Coded) kindergarten of kindergarten Teacher-Reported Approaches to 1.000 .603 .742 .722 Learning in fall of kindergarten Externalizing Problems (Reverse .603 1.000 .594 .718 Coded) Teacher-Reported Interpersonal .742 .594 1.000 .793 Skills in fall of kindergarten Teacher-Reported Self-Control in .722 .718 .793 1.000 fall of kindergarten

Table 23

Item-Total Statistics: Social-Emotional Competence (SEC) Scale Mean Scale Corrected Squared Cronbach's if Item Variance if Item-Total Multiple Alpha if Item Deleted Item Deleted Correlation Correlation Deleted Teacher-Reported 9.4683 2.883 .770 .610 .876 Approaches to Learning in fall of kindergarten Externalizing Problems 9.0413 3.178 .697 .531 .900 (Reverse Coded) Teacher-Reported 9.4367 2.952 .801 .689 .864 Interpersonal Skills in fall of kindergarten Teacher-Reported Self- 9.3492 2.913 .850 .735 .846 Control in fall of kindergarten

Table 24

Scale Statistics: Social-Emotional Competence (SEC) Mean Variance Std. Deviation N of Items 12.4318 5.131 2.26508 4

121

Next, a poverty index was computed, based on a categorical measure of child poverty

(X2POVTY) provided by NCES that broke down poverty into three categories: Below the poverty line; above the poverty line but below 200% of the poverty line; and 200% above the poverty line. These categories were collapsed into a binary variable, where “below the poverty line” was coded as 1 and the other two categories were coded as 0. This binary measure was used because of its ease of interpretability. In different models, this measure was used as a Level

1 predictor (based on child category) and Level 2 predictor (based on percentage of students in the school below the poverty level).

Table 25

Recoded Binary Poverty – Student-Level Cumulative Frequency Percent Valid Percent Percent Valid Above Poverty Line 10076 55.4 74.5 74.5 Below Poverty Line 3451 19.0 25.5 100.0 Total 13527 74.4 100.0 Missing System 4647 25.6 Total 18174 100.0

The percentage of students in the school who were eligible for free or reduced lunch

(S2LUNCH) was used as a measure of school-level poverty. For this measure, the mean was

50.40% and the standard deviation was 32.32%.

Parent Involvement

Data regarding the average level of parent involvement within a school was derived from an item in the School Administrator Survey (S2INVOLV), a five-point Likert-type item pertaining to the extent to which the administrator agrees parents are active in school programs, where “Strongly Disagree” is coded as 1 and “Strongly Agree” is coded as 5. For the purpose of the HLMs, the item was treated as a continuous variable; this approach is consistent with the

122 work of Glass and colleagues (1972), who found that F-tests in ANOVA could return accurate p- values on Likert-type items treated as continuous variables when statistical assumptions are met.

The mean for this variable was 4.06 and the standard deviation was 0.93, meaning that administrators generally agreed that parents were, on average, active in school programs.

Other Child-level Background Variables

At the child level, several background variables were dummy-coded for analysis. These included gender (Male=1, Female=0) and race/ethnicity in groups of interest (Asian=1, others=0;

African American=1, others=0; Hispanic=1, others=0). In addition, age of the child in months at the beginning of kindergarten (X1AGEENT) was included in the preliminary analysis, with a mean of 66.08 months and a standard deviation of 4.64 months.

Other School-Level Variables

School sector in fall of kindergarten (X1PUBPRI) was coded was 0 (private) or 1

(public).

Table 26

School Sector in Fall of Kindergarten (public vs private) Cumulative Frequency Percent Valid Percent Percent Valid Private 2135 11.7 13.0 13.0 Public 14329 78.8 87.0 100.0 Total 16464 90.6 100.0 Missing System 1710 9.4 Total 18174 100.0

School size in spring of kindergarten (X2KENRLS) was dummy-coded, where 1 indicates 500 students or more and 0 indicates less than 500 students.

Table 27

School Size in Spring of Kindergarten Cumulative Frequency Percent Valid Percent Percent

123

Valid Less than 500 students 8587 47.2 48.3 48.3 500 students or more 9192 50.6 51.7 100.0 Total 17779 97.8 100.0 Missing System 395 2.2 Total 18174 100.0

School urbanicity (X1LOCALE) was coded as 1 (city) or 0 (suburb, town, or rural).

Table 28

School Urbanicity in Fall of Kindergarten Valid Cumulative Frequency Percent Percent Percent Valid Non-Urban (Suburb, Town, or Rural) 10825 59.6 66.8 66.8 Urban 5382 29.6 33.2 100.0 Total 16207 89.2 100.0 Missing System 1967 10.8 Total 18174 100.0

The portion of students in the school who are non-White (X2KRCETH) was also included in the analyses, with a mean of 48.97% and a standard deviation of 34.25%. In addition, the portion of students in the school who receive special education services

(S2SPDPCT) was included in the analyses, with a mean of 5.95% and a standard deviation of

6.27%. Moreover, the average daily attendance (reported as a percentage) for each school

(S2ADA) was included in the analyses, with a mean of 95.32% and a standard deviation of

2.31%.

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