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This is to certify that the
dissertation entitled

THE ASSOCIATION OF TEACHER-STUDENT
RELATIONSHIP QUALITY AND TEACHER SUPPORT WITH
STUDENTS’ SCHOOL SATISFACTION, CLASSROOM
ADJUSTMENT, AND ACADEMIC ACHIEVEMENT

presented by

Hilda Nyougo Omae

has been accepted towards fulﬁllment
of the requirements for the

Doctoral degree in Measurement and Quantitative
Methods

 

 

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THE ASSOCIATION OF TEACHER-STUDENT RELATIONSHIP QUALITY
AND TEACHER SUPPORT WITH STUDENTS’ SCHOOL SATISFACTION,
CLASSROOM ADJUSTMENT, AND ACADEMIC ACHIEVEMENT
By

Hilda Nyougo Omae

A DISSERTATION
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Measurement and Quantitative Methods

2010

ABSTRACT
THE ASSOCIATION OF TEACHER-STUDENT RELATIONSHIP QUALITY
AND TEACHER SUPPORT WITH STUDENTS’ SCHOOL SATISFACTION,
CLASSROOM ADJUSTMENT, AND ACADEMIC ACHIEVEMENT
By

Hilda Nyougo Omae

As children grow, they transition from home to school environments, where they
acquire and master knowledge and skills, and develop an image of themselves as learners
and develop several types of relationships with adults as they grow. As they enter and
remain in school, these relationships expand ﬁom being solely with parents and
caretakers to include their teachers. Due to the large amount of time children spend in
school, it is important to examine and understand how the school environment and its
aﬁ‘ordances, and the relationships that children form while there inﬂuence their lives, and
especially their academic success or failure.

This study examines the inﬂuence of student-teacher relationships and teacher
support on the academic achievement and satisfaction with school for K-S students.
Using longitudinal growth modeling, speciﬁcally, cross-classiﬁed random effects
modeling, the study found that decreased conflictual relationships between teachers and
students were associated with increased achievement in math and reading over time.
Also, there was evidence of the Black-White test gap. Moreover, this gap was greater

during K-3 than it was during 3-5 period.

DEDICATION
This dissertation is dedicated to my parents; my father Samson Nyambane and (to the

memory of) my loving mother, Prisca Nyanchwa Nyansuku for their unrelenting belief in
the value of education, and their unwavering support of my pursuits. Mbuya mono!

iii

ACKNOWLEDGEMENTS

I would like to express my heartfelt gratitude to the faculty, family and friends
that have seen me through this journey. It has been a long one, but it has ﬁnally come to
an end!

To my advisor Dr. Kimberly Maier, thank you for the guidance and support you
have given me throughout. You have been a guiding light and I will be forever grateful.
God bless you.

To Dr. Joyce Grant, a mentor and friend; thank you for believing in me and
getting me through the tough times. I will miss you! To Drs. Sandra Crespo and Chris
Dunbar, thank you for your support. To Dr. Jack Schwille, thank you for believing in me
and giving me a chance at the start of my graduate school.

Special thanks to my brother Gerald. G, I could never have done it without you.
Thank you very much for the prodding, nudging, advise and constant support that you
have provided in a myriad of ways through the years. But especially this last few months,
thank you! We did it!

TO my mother Prisca, wherever you are, thank you. Your love has carried me
through the years — and I am going to depend on it for those to come.

To my father TFS Nyambane, it appears that your dividends are ready! Thank you
for your ﬁrm belief in education, and for giving me the opportunity and encouragement
to pursue it.

To my sisters Millie and Nyaboe, and my brothers Emerson, Nyagami, and

Samaki; thank you for your encouragement.

iv

To the “gals”, thank you for your prayers, words of wisdom and encouragement.
You truly stood in the gap for me. To all my ﬁ'iends, too many to name, thank you! A

million blessings.

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES ........................................................................................................... ix
CHAPTER ONE: INTRODUCTION ............................................................................... 1
1.1 Problem Statement ........................... - - -- - - -_ ---.--1
1.2 Research Question and Hypothesis -- 4
1.3 Organization of dissertation ............................................................................................. 5
CHAPTER TWO: LITRATURE REVIEW ..................................................................... 6
2.1 Introduction ....................................................................................... - -- - 6
2.2 Teacher-student relationship quality and academic achievement - -- ......... 7
2.3 Social environment, student characteristics and teacher-student relationship quality 12
2.4 Race and teacher-student relationship quality ...... .. ..17
CHAPTER THREE: DATA AND METHODS ...................................... 22
3. I Introduction .................................................... -. - - 22
3.2 Data .......................................................................... - - -_.-----.22
3.2.1 Students .................................................................................................................. 23
3.2.2 Teachers ................................................................................................................. 24
3.2.3 Procedures .............................................................................................................. 24
3.3 Measures ......................................................................................................................... 25
3.3.1 Diagnostic Inventory of School Climate (DISC) .................... -- 26
3.3.2 Student-Teacher Relationship Scale (STRS) ......................... 27
3.3.3 Vessels School Climate Survey (V SCS) .............. 27
3.3.4 Behavior Assessment System for Children-Teacher Rating Scale (BASC- TRS). 28
3.3.5 Teachable Pupil Survey (TPS) .............................................................................. 29
3.3.6 Student Survey ...................................................................................................... 29
3.3.7 Academic achievement.......... ......................................... - - ....... 30
3.4 Data Analysis ................................ -- - - - 31
3.4.1 Unconditional Means Model .......................... . - 33
3.4.2 Unconditional Growth Model ..................................................... - --.35
3.4.2 Conditional Growth Models--- - _ ..................... - _ ........ 37
3.4.3 Model Fit ................................................................................................................ 40
3.4.4 Model Variables ...... - - .............................. -- - - 40
CHAPTER FOUR: RESULTS ........................................................................................ 42
4.1 Introduction ........................................................................................ ...... .42
4.2 Descriptive Statistics ............................................................................ 43
4.3 Reading and language achievement In [TBS or SAT9 tests .......... - ---49
4.4 Student report card reading achievement - ----62
4.5 Math achievement in ITBS or SAT9 tests - -66

 

 

4.6 Student report card math achievement ..... 74

 

 

 

 

 

 

4.7 School satisfaction .......................... . - - - - -.79
4.8 Classroom adjustment _ - _ - 85
CHAPTER FIVE: DISCUSSION AND CONCLUSION ............................................. 90
5.1 Introduction .................................................................................................................... 90
5.2 Academic achievement ................................................................................................... 90
5.3 Classroom adjustment and school satisfaction ............................... -- ---_..93
5.4 Limitations ofthe study - - - - ............................................................ 94
5.5 Future research.... - ...... . - - 96
APPENDIX ....................................................................................................................... 98
REFERENCES ................................................................................................................ 102

 

LIST OF TABLES

Table 4.1: Frequencies and Percentages of Students by Grade Levels and Year of

Study ......................................................................................... 44
Table 4.2: Frequencies of Student and Teacher Demographics .............................. 44
Table 4.3: Descriptive statistics of outcome and predictor variables ........................ 46
Table 4.4: Correlations of student and teacher interactional variables ....................... 47
Table 4.5: Intra-class correlation coefﬁcients ................................................... 49
Table 4.6(a): ITBS/SAT9 reading, language achievement .................................... 60
Table 4.6(b): ITBS/SAT9 reading, language achievement .................................... 61
Table 4.7: Report Card Reading Achievement .................................................. 65
Table 4.8(a): ITBS/SAT9 Math Achievement ................................................... 71
Table 4.8(b): ITBS/SAT9 Math Achievement ................................................... 72
Table 4.8(c): ITBS/SAT9 Math Achievement ................................................... 73
Table 4.9: Student Report Card Math Achievement ............................................ 77
Table 4.10(a): School Satisfaction ................................................................. 82
Table 4.10(b): School Satisfaction .................................................................. 83
Table 4.1 1(a): Classroom Adjustment ............................................................ 87
Table 4.11(b): Classroom Adjustment ............................................................ 88
Table 12: Illustration of data i.e. measurements nested in cross-classiﬁcation of teachers

and students ................................................................................ 97
Table 13: Sample questions from students’ survey, fourth and ﬁfth grade ................. 97
Table 14: Sample questions from Student-Teacher Relationship Scale ..................... 98
Table 15: Sample questions ﬁ'orn Behavior Assessment System for Children ............ 99

viii

 

LIST OF FIGURES

Figure 1: Sample questions from students’ survey, grades K-3 ............................... 99
Figure 2: Sample items from the Teachable Pupil Survey .................................... 100
Figure 3: Sample questions from Vessels School Climate Survey .......................... 100

ix

CHAPTER ONE

INTRODUCTION

1.1 Problem Statement

In the beginning of formal schooling, children enter a new environment that can
be quite incomprehensible to them at the time. This marks the start of their
transformation as members of other environments, besides their home. Once in the school
environment, they form an image of themselves as students and embed this image into
their identity. They learn the school mics and regulations and, how to relate with other
students, their teachers, and the school principal. Perhaps more important, they master the
required knowledge and skills. As they make this transition ﬁ'om home to school, they
mainly rely on their parents, siblings, and teachers for emotional support as they navigate

the school system and cope with new challenges.

Students who successfully navigate these early school life challenges gain a
competitive advantage which becomes manifest years later (Entwisle & Hayduk, 1988)
and this advantage may stay with them for the rest of their lives. On the other hand,
students who do not have a positive school experience may develop negative traits that
could linger for a very long time. In fact, both positive and negative teacher-child
relationships observed in kindergarten have been linked to academic and behavioral
outcomes in the eighth grade and beyond (Hamre & Pianta, 2001). This underscores the

importance of early childhood school experiences in shaping the future of students.

How children adjust to school environments is a widely studied topic, in part because
school is where children spend a large portion of their time. Hence, it is an important
context in which they develop (Baker, Dilly, Aupperlee, & Patil, 2003). Indeed, students
that perceive the school’s social environment as warm and psychologically safe (e.g. by
being in a positive classroom environment and having caring and supportive relationships
with their teachers) tend to be satisﬁed with their school experiences, often leading to
good social and academic performance. The reverse is also true (Baker, 1998;

Goodenow & Grady, 1993; Pianta, 1999).

As children grow, both at home and at school, they acquire habits and attitudes that
determine and shape their cognitive development. Because these habits and attitudes
differ across social fabrics, it is imperative for those who seek to understand the
conﬂuence of schools and students’ needs to also learn about the child’s social setting.
Existing literature posits that social structural factors such as gender, socio-economic
status, and majority or minority status, and social contextual factors such as the inﬂuence
of parents, teachers, and one’s peers greatly affect a student’s cognitive development
(Alexander, Entwisle, Blyth, & McAdoo, 1988; Delpit, 1988). It also posits that the most
critical time for shaping the academic future of a student is during the student’s early
years of schooling (Alexander et a1. 1988). This implies that for one to be able to predict
or explain academic achievement gaps among different student groups, one has to
understand both the students’ social settings as well as their early childhood school

experiences in, for instance, preschool, kindergarten, and ﬁrst through third grades.

Early childhood school experiences are greatly inﬂuenced and aﬂ‘ected by the

relationships that students build with teachers. In turn, the nature of such teacher-student

2

 

relationships is inﬂuenced by, among other factors, the student’s behavior, the student’s
family social and demographic background, as well as the teacher’s perception of the
student’s social disposition and academic ability. In general, teachers tend to gravitate
towards, and form relationships with, students who are cooperative, well behaved, and
have a high aptitude (Birch & Ladd, 1998; Henricsson & Rydell, 2004; Pianta, 1994;
Pianta & Nirnetz, 1991). Indeed, it is not uncommon to ﬁnd teachers who behave
differentially, albeit unintentionally, towards high-achieving students compared to their
low-achieving peers. The former group often receives more positive and supportive
interactions and is held to high academic standards, while the latter group has more
negatively affective interactions with low academic expectations placed on them (Baker,

1999; Henricsson & Rydell, 2004; Midgley, Feldlaufer, & Eccles, 1989).

Many studies have explored various factors that affect teacher-student relationships
(Baker, 1998; Goodenow & Grady, 1993; Pianta, 1999) and how these relationships
affect student outcomes (e.g. Pianta & Stuhlman, 2004; Baker, Kamphaus, Horne, &
'Winsor, 2006; Ewing & Taylor, 2009). The overwhelming ﬁnding from these studies is
that teacher-student interactions matter, and the nature and quality of these interactions is
important in predicting student outcomes (see for example Hughes, Gleason, & Zhang,

2005; Hughes & Kwok, 2006; Hughes, Zhang, & Hill, 2006).

However, majority of these studies (on teacher-student relationships) have focused
either on very young children (Alexander, et al., 1988; Birch & Ladd, 1997; Hughes,
Gleason, & Zhang, 2005; Pianta & Stuhlman, 2004), middle school children (Battistich,
Schaps, & Wilson, 2004) or adolescent children (Roeser, Midgley, & Urdan, 1996;

Wentzel, 1998). The elementary school years have received minimal attention, despite

3

 

the importance of this period in the developmental outcomes of children. During these
years, children develop beliefs about schooling, their academic capabilities, and form
identities of who they are as learners (Baker, 1999; Entwisle & Hayduk, 1988). It is
therefore important to study factors (such as interpersonal relationships) that may
enhance (or impede) the processes of learning at this stage, and put measures in place that
would promote student learning and development. Moreover, much of the previous
research on student-teacher relationships uses samples with predominantly large
proportions of Caucasian students relative to students of other races. In contrast, the
sample used in this study is unique because 72% of the children belong to racial minority

groups.

Thus, the purpose of this correlational study is to extend this strand of research by
exploring the associations between the quality of relationships developed between
teachers and their students, and student outcomes. The research questions answered by

this research and hypotheses tested are explained in the next section.

1.2 Research Question and Hypothesis
The objective of this study is to determine how, and to what extent, changes in
teacher-student interaction variables are related to student outcomes. To accomplish this

objective, this study answers the following overarching research question:

What is the relationship, over time, between a student’s overall satisfaction with
school, adjustment to classroom environment, and academic achievement, and the
quality of teacher-student relationships, and teacher support ?

4

 

TO answer this question the following hypotheses were tested empirically:

Hypothesis 1: Close student-teacher relationships and increased teacher support are
strongly and positively related to larger gains in (student) overall
satisfaction with school, adjustment to classroom environments, and
academic achievement for students with behavior problems over time.

Hypothesis 2: Over time, conﬂictual relationships between teachers and students and a
reduction in teacher support are related to smaller gains in (student)
overall satisfaction with school, adjustment to classroom environments,
and academic achievement for students with behavior problems.

The objective is accomplished by analyzing data on students and their teachers from four

elementary schools in a small city in Southeastern United States. The data is analyzed

using a two-level cross-classiﬁed random effects model explained in Chapter three.

1.3 Organization of dissertation
The dissertation is organized into ﬁve chapters. Chapter two contains a
review of selected literature on teacher-student relationships and student
outcomes. The estimation model and data used for analyses are described in
Chapter three with detailed explanations of measures used to construct student
and teacher variables. The results are presented in Chapter four, which are then
discussed and summarized in Chapter ﬁve. The strengths and limitations of the

study are also highlighted, along with suggestions for future research.

CHAPTER TWO

LITRATURE REVIEW

2.1 Introduction

This chapter reviews the literature linking teacher-student relationships and
teacher support to student outcomes. The goal of the review is to enhance understanding
of the current literature and to clarify the contribution this study makes to existing
literature. The overarching theme of the selected literature is that teacher-student
relationships manifested as closeness or conﬂict are related to learning outcomes of
students. The review is divided into three subthemes that highlight different issues related
to teacher-student quality and student learning outcomes.
First, Section 2.2 begins with a review of studies that focus on the evidence that the
quality of teacher-student relationships is related to academic achievement. The studies
reviewed here provide such evidence. Next, Section 2.3 reviews literature linking
students’ social environments to academic achievement. Evidence is provided by this
literature that supports the notion that students’ social environments, including parent-
child relationships, inﬂuence the behavior of students; which in turn, inﬂuence the quality
of teacher-student relationships formed; which in turn affect student outcomes. Last,
Section 2.4 reviews literature providing evidence that race is related to teacher-student

relationships which, are in turn, related to learning outcomes.

2.2 Teacher-student relationship quality and academic achievement

Children develop several types of relationships with adults as they grow (Bowlby,
1982; Hughes, Cavell, & Jackson, 1999). As they enter and remain in school, these
relationships expand from being solely with parents and caretakers to include their
teachers. Existing studies have found that these relationships are important inﬂuences on
a student’s academic success or failure. In effect, one would expect the inﬂuence from
such relationships to span other areas of a student’s life beyond academics. This is true,
especially, for relationships established during the early part of a student’s learning
journey such as kindergarten and elementary school. At that level, teachers play the role
of ‘the adult in the room ’ and, in this way, substitute for parents in shaping the child’s

behavior that would become entrenched in the child’s personality in later years.

Indeed some studies have found that even academic expectations of teachers and
parents for the children are an important inﬂuence on the children’s performance. For
example, Entwisle and Hayduk (1982) found that the nature of childhood teacher-student
relationships are linked to student outcomes; not only in grade school but also in later
years. In that study, the authors focused on a group of students from an earlier study
conducted between 1971 and 1977 when the students were in ﬁrst, second, and third
grades. They examined the 1980 standardized scores for these students to see if observed
variables in the ﬁrst study had any lasting effect four to nine years later. Speciﬁcally,
they considered how the children’s self-expectations and achievement scores, parents’
expectations, peer’s expectations, and absences in early schooling may be related to
outcomes in later years. They found that a parent’s academic expectations for their child

were important in explainmg that child’s performance. Also important was the inﬂuence

 

of teachers. Because this was one of the earliest studies to focus on student-to-adult
relationships, as a factor inﬂuencing student outcomes, its ﬁndings among others,
provided impetus for researchers to focus more on the role of child-parent relationships

and teacher-student relationships in student learning.

In a follow-up study, Entwisle and Hayduk (1988) examined the inﬂuence of
parents and teachers on a child’s long-term school performance. They used the same data
as in the preceding study but utilized regression models allowing them to study both
individual and joint effects of several variables. Consistent with previous studies
reviewed by these authors, they found that the performance expectations of parents and
teachers for students in grades one through three, were good predictors of student
performance on standardized tests, four to nine years later. An important difference of
their study from previous ones is the use of an explicit structural model which was
hitherto uncommon in these types of studies.

Another important ﬁnding of the study was that a child’s social setting inﬂuences
academic performance in later years and, parents and teachers have different relative
inﬂuence on student outcomes depending on the social setting. Speciﬁcally, the study
found that, for a student in a white middle class school, it was the parents’ performance
expectations for the child that had signiﬁcant inﬂuence in the child’s long-term
performance and not the teacher’s expectations. On the other hand, for a child in an
integrated working-class school, it was the teacher’s expectations that had signiﬁcant
inﬂuence while, for a child in a black working class school, it was both the parent’s and
teacher’s expectations that were inﬂuential. The implication of the ﬁnding is that teacher-

child relationships may have different impacts on students of different races and socio-

 

economic backgrounds. Many researchers continue to focus on these relationships and
their inﬂuences on academic achievement of different groups of students.

For example, Baker (2006) examined the contributions that teacher-cth
relationships have on school adjustment during elementary school. She found that
positive teacher-child relationships were beneﬁcial for children across all grade levels in
school adjustment. But students with behavior problems adjusted poorly to school, and
lagged behind academically. In contrast, well behaved students developed close teacher-
student relationships, and performed signiﬁcantly better than those without such
relationships. Buyse, Verschueren, Doumen, Van Damme, & Macs (2008) also found a
similar result for kindergarten students. Similarly, Burchinal, Peisner-Feinberg & Howes
(2002) found that close teacher-student relationships were positively related to
development of language skills and reading competency of children in preschool through
second grade.

Pianta, Steinberg, & Rollins (1995) report too that students who had positive
relationships with their kindergarten teachers adjusted better to classroom environments
when they got to ﬁrst and second grade. Their study followed a group of students in a
small city school district ﬁ'om Kindergarten through second grade and used correlation
analyses to investigate the link between teacher-chﬂd relationships and children’s
adaptation in school. In essence what the study revealed was that children in positive
relationships with teachers displayed lower levels of behavior problems and higher levels
of competence. That is, these children tended (or were more likely) to stay out of trouble
and apply themselves more productively to school work than their counterparts who had

conﬂictual relationships with their kindergarten teachers. The latter group of students

 

exhibited higher levels of behavior problems and had lower levels of competence in ﬁrst
and second grade.

Further evidence in support of the notion that teacher-child relationships play a
role in the academic success of the child is provided by Pianta & Stuhlrnan (2004). Their
study found that teachers assigned higher achievement ratings to students with whom
they shared close relationships than those with whom they experienced conﬂictual
relationships. They used teachers’ and parents’ ratings of social and academic
development of pre-school, kindergarten and ﬁrst grade children to analyze the
relationship between teacher-child relationships and the children’s success. The study
further revealed that students with higher ratings on teacher-child conﬂict were rated
lower on social competence whereas those with close relationships were deemed more
socially competent. This suggests that teachers may gravitate towards children with
whom they relate well and away ﬁ'om those that they have conﬂict with.

Factors inﬂuencing the type of relationships established between teachers and
their students are many and varied. For instance, Hughes, Cavell, & Willson (2001)
highlight gender as one such factor in their study on the quality of teacher-student
relationships among third and fourth grade students. Using sociometric peer ratings of
students ﬁ'om an ethnically diverse school district, they found that girls were perceived as
having received more support ﬁ'om teachers than boys. On the other hand, boys were
perceived as having been in more conﬂictual teacher-student relationships than girls. This
ﬁnding is consistent with Similar previous studies which found evidence that teachers
prefer and, relate positively with children who are cooperative, responsible, and

courteous, as opposed to those that display disruptive and assertive behaviors (Sadker,

10

Sadker, & Klein, 1991; Wentzel, 1991). There is also literature which shows that students
with caring and supportive interpersonal relationships in school are more positively
predisposed in their attitudes and values towards their academic work and are more
academically engaged and satisﬁed with school than their counterparts (Battistich, et al.,
2004; Felner, et al., 1997). With higher levels of engagement in their work, such students
tend to receive relatively more teacher support leading to higher academic performance
(Klem & Connell, 2004). Apparently, these behavioral characteristics are more common
in girls than in boys at the elementary school years, which would also explain the ﬁnding
by Kesner (2000) that teachers rated their relationships with girls as being closer and less
conﬂictual than their relationships with boys. In that study Kesner had interviewed a
sample of pre-service teachers of K-5 students and found that the teachers perceived their
relationships with boys to be more conﬂictual and less close than with girls.

The preceding studies underscore the importance of teacher-student relations in
learning outcomes, especially, in early childhood. However, because this is a very broad
topic many strands of the literature exist. These include, for example, impact of teacher-
child relationships in early childhood education (Entwisle and Hayduk, 1988; Hamre and
Pianta, 2001); impact of school environment and social structural factors on teacher-
student relationships and performance (Alexander and Entwisle, 1988; Baker et al. 2003;
Goodenow and Grady, 1993); and factors inﬂuencing teacher-student relationships
(Baker, 1998; Baker et al., 2006; Ewing and Taylor, 2009; Goodenow and Grady, 1993;
Pianta and Stuhlman, 2004). The current study makes a contribution to this literature by

focusing on teacher-student relationships in the whole range of elementary school years,

11

rather than focusing just on the segmented portions of either pre-school, kindergarten, K-

3, middle school, or high school students.

2.3 Social environment, student characteristics and teacher-student relationship
quality

Student characteristics such as behavior greatly inﬂuence the type of
relationship that develops with their teachers and subsequently the level of support that
these teachers offer. Indeed researchers have found that in general, students with good
behavior tend to receive greater support from teachers which in turn, mediates their
achievement (e.g. Caprara, Barbaranelli, Pastorelli, Bandura, & Zimbardo; 2000). In an
extensive study, these authors used a longitudinal design and structural equation
modeling to investigate the relative impact of early prosocial (e. g. cooperation, helping,
sharing) and aggressive behaviors on performance and found these behaviors to be
instrumental in the academic and social developmental trajectories of children ﬁve years
later.

Because the behavior a student develops is greatly inﬂuenced by the social
environment in which that student is brought up, there is an inevitable overlap in the way
these two topics (social environment and student characteristics) have been presented in
the literature. For instance, Baker (1998) who examined the impact of social
inﬁastructure and the school environment on children’s school satisfaction also examined
student characteristics at the same time. The study focused on children from a large
southeastern metropolitan school district that were considered ‘at-risk’ because of

signiﬁcant poverty rates and its consequences such as violence, substance abuse and

12

disorderly conduct among adults in the community. In addition, the entire sample
consisted of only Aﬁican American children, all in grades three to ﬁve. Using the
Multidimensional Students Life Satisfaction Scale (MSLSS; Huebner, 1994) and path
analysis, Baker assessed the students’ subjective feeling of well-being in order to assess
their level of school satisfaction. She found that among the variables analyzed social
climate in the classroom had the strongest direct effect on school satisfaction. It was also
the only variable with signiﬁcant indirect effect on school satisfaction by inﬂuencing
other variables. This ﬁnding provides evidence that what goes on in the classroom greatly
affects student outcomes. That is, the type of relationships that exist in the classroom
among students as well as between students and their teachers are an important
determinant of whether a student becomes satisﬁed with school or not. The study also
found that the level of the student’s selfesteem was an important factor inﬂuencing
school satisfaction. Clearly, students who are satisﬁed with school are more likely to
have a sense of belonging and, hence, have greater academic success than those who are
dissatisﬁed and have little or no sense of belonging (see also Goodenow and Grady,

l 992).

In a subsequent study, Baker (1999) extended her study of this sample of students
by explicitly measuring and analyzing teacher-student interactions and relations. Again, it
is important to note that all the students and teachers in this study were Aﬁican
Americans. This is noteworthy because some studies have suggested that the teacher’s
race vis-a-vis that of the student is important in determining the nature and quality of
teacher-student relationships established (e.g. Irvine, 1986; see also Section 2.4 below).

Therefore, by design, this study controlled for effects of race on the research ﬁndings.

13

 

The study found that social context of the classroom, even as early as third grade,
inﬂuences whether a student becomes satisﬁed with school or not. In particular, the study
found that students who were dissatisﬁed with school sought academic help by as much
as three times more than their colleagues who were satisﬁed with school. However, these
students also received twice as many behavioral reprimands than their satisﬁed
colleagues. Obviously, the reprimands are in most cases justiﬁed to keep order in the
classroom but as these study ﬁndings suggest, they may have the unanticipated
consequence of alienating the affected children ﬁom school. Hence, to some extent, the
study conﬁrms the conjectm'e that a caring and psychologically safe classroom
environment enhances school satisfaction.

Based on these ﬁndings, Baker reiterated the need for ensuing research to pay
attention to psychological and social outcomes in the early years of schooling rather than
waiting until later years. Doing so would be expected to provide insights into early
intervention strategies to manage and, hopefully reverse students’ negative feelings about
school.

In support of this line of research Baker, Dilly, Aupperlee & Patil (2003)
proposed a ﬁamework to be used in studying psychosocial outcomes associated with
school practices that lead to increased school satisfaction. This framework emphasized
use of a positive psychology approach in which researchers focus on drivers of positive
adjustment to school instead of focusing on developmental problem diagnosis. Hence,
focus is on ‘prevention’ rather than ‘cure’. They assert that when schools ftmction as
psychologically healthy environments for development, they contribute positively to

children’s adjustment in schools, often measured by school satisfaction.

14

In another study, Baker, Kamphaus, Horne, & Winsor, (2006) explored the
association between children’s behavior and educational outcomes. Restricting the study
to general education students only, they found that students with the most signiﬁcant
behavioral problems had the lowest academic achievement scores. These students were
also the least adjusted to classroom environments and scored lowest on teacher-reported
work habits.

In a similar but variant strand of research, Pianta, Nimetz, & Bennett (1997)
studied the association between mother-child relationship quality, subsequent teacher-
student relationships, and outcomes for developmentally at-risk Kindergarten and ﬁrst
grade children. To be classiﬁed as being at-risk, a child had to fall in one or more of the
following categories: come from a low income family; come from a family with low
maternal educational level; be in a family with high level of stress; have low cognitive or
language development level; and/or have poor behavioral adjustment. The results of that
study revealed that children with close mother-child relationships developed relatively
more secure teacher-child relationships than their counterparts. They also adjusted well to
the school environment because they tolerated frustrations better, were less anxious and
better behaved than children with negative mother-child relationships. On the other hand,
children who had problematic relationships with their mothers formed teacher-child
relationships that were wrought with conﬂict and insecurity. They exhibited poor work
habits, poor social skills, less tolerance to ﬁ'ustrations, and were often more anxious with
increased behavioral problems compared to their counterparts. The study reinforces the
notion that a child’s social environment inﬂuences that child’s academic success. In this

case the home environment in which parent-child relationships are formed inﬂuences the

15

 

nature of teacher-student relationship formed which in turn, inﬂuences the student’s
success.

Aikens (2005) also focused on the student’s socioeconomic status (SES) when she
used an Early Childhood Longitudinal Study (ECLS) to investigate socio—economic
factors responsible for differences in reading trajectories of students. She found that
children ﬁ'om low SES backgrounds achieved lower reading scores and had slower
learning growth rates over the K-3 period than students ﬁom more aﬂluent backgrounds.
Even though one would expect family income to be the most important factor responsible
for the achievement gap between low and high SES students (Campbell, 2006), school
and neighborhood contexts were found to be equally signiﬁcant factors in that study. That
is, low SES children attended lower quality schools and lived in poorer neighborhoods
which negatively affected their performance. The reverse was true for the case of high
SES students.

Several more other researchers have focused on student’s social environment as
well as their characteristics and how these factors impact students education (e.g.
Danielsen, Samdal, Hetland, & Wold, 2009; Mantzicopoulos, 2005 ;Van den Oord & Van
Rossem, 2002). For instance, Mantzicopoulos (2005) used a sample of economically
disadvantaged kindergarten students to investigate, among other things, the associatons of
conﬂictual relationships between teachers and students with child characteristics (e. g.
behavior) and found that conﬂictual relationships were prevalent and associated with
decreased academic achievement and higher ratings of behavior misconduct. The current
study also contributes to this strand of literature by focussing on K-5 students from

predominantly low socioeconomic status background. About 70% of the students in the

16

 

participating schools were on ﬁ'ee or subsidized lunch and a majority of them came from

public housing dwellings.

2.4 Race and teacher-student relationship quality

Extant research has also focused on the impact of student race on academic
achievement and documented the existing and persistent achievement gap, especially
between White and Black students. For example, Broh (2003) uses seasonal comparisons
(learning that occurs during summer and that which occurs during the school year), to
investigate the effect of school factors vis-a-vis those pertaining to family background on
the racial test score gap and reports that the gap grew during the school year while
remaining constant over summer break. Such a ﬁnding implies that there are school
factors within the school environment that may favor learning growth for White students
while at the same time negatively affecting learning growth of Black students. Irvine
(1986) argues that one such factor is the nature of teacher-student relationships
established between teachers and students of different races. This suggests that White
teachers, for example, are more likely to form positive relationships with White students
than with Black students, leading to differential academic achievement of these two
groups of students.

Oates (2003) explored this question of whether teacher-student racial congruence
affected teachers’ perceptions of student performance and found that White teachers rated
Black students more negatively than they did White students. In contrast, Black teachers
rated students of both races equivalently. The data used in that study came from a

nationally representative sample of the National Educational Longitudinal Study (NELS)

17

of 1988. In this way, Oates provides some evidence that supports the argument advanced

by Irvine (1986).

In their study, Ladd and Burgess (1999) followed a group of kindergarten
students, using a sample representative of children in American elementary schools,
through second grade and investigated the relationship between students’ behavioral
characteristics and their adj ustment in school environments. They found that children
who were aggressive towards others had lower acceptance from their peers and more
conﬂictual relationships with their teachers than more temperate students. That ﬁnding in
itself was not new; especially in psychology literature. However, additional analyses by
the authors showed that African American children were more likely to experience
chronic peer rejection and were less likely to be afforded certain forms of support such as
teacher-child closeness (Ladd & Burgess, 2001). If African American children are
disproportionately accorded less teacher support because they do not have close teacher-
child relationships then, based on the literature reviewed so far, one can infer that the
academic success of such children is likely to be hindered.

A study by Hughes, Gleason, & Zhang (2005) focused on ethnically diverse and
academically at-risk ﬁrst grade students to examine how teacher perceptions of parent-
teacher and student-teacher relationship quality inﬂuence teacher perceptions of the
children’s academic abilities. These were students who scored below the median of a
state approved literacy test and for that reason were considered to be at-risk academically.
The students were sampled from one urban school and two small city schools in order to
make the study group as diverse as possible. After controlling for the parents’ education

level, these authors found that teachers rated their relationships with Hispanic and White

18

 

students and their parents more positively than those with Aﬁican American students and
their parents. This suggests that race may be an important factor inﬂuencing the quality
of teacher-child relationships and hence, student outcomes. It also suggests that the
quality of these relationships may be relatively (more) compromised for the case of
Aﬁican American students. This is consistent with ﬁndings from other studies showing
more negative teacher perceptions of African American children’s competencies and
personality traits (Horwitz, Bility, Plichta, Leaf, & Haynes, 1998)

To facilitate more understanding of the interaction of teacher and student
demographics, Pigott & Cowen (2000) used closely matched race samples ﬁom several
urban schools to examine the effects of teacher—child racial congruence on teacher ratings
of school adjustment and performance in kindergarten through ﬁfth-grade. Their study
sample consisted mostly (75%) of students from low socio-economic backgrounds.
Because there were very few male teachers in the sampled schools, the authors opted to
have only female teachers in the study. Hence, teachers’ gender was controlled for by
default. Their results showed that both African American and White teachers judged
African American children to have more serious school adj ustment problems, fewer
competencies, more negative stereotypic personalities, and poorer educational prognoses
than White children. This is at variance with the ﬁndings of a recent study by Murray and
Murray (2008) who found that teachers’ ratings of their perceptions of students were
always better for students with whom they shared race than with students from other
races. They also reported that teachers gave more support to students of their race
compared to those of other races. Note, however, that the latter study is one of the few

that have reported such ﬁndings.

19

 

Decker, Dona & Christenson (2007) investigated the importance of student—
teacher relationships for student outcomes, and speciﬁcally behaviorally at-risk Aﬁican
American students. Using a multi-rater, multi-method approach, they collected data from
teachers and students. With increased positive teacher-student relationship quality, as
reported by both teachers and students, there were increased social, behavioral and
engagement outcomes for students. Although teachers viewed their relationships with
students negatively, students viewed their relationships with teachers positively and
wanted to be closer to them.

Focusing on remedial interventions, Murray & Malmgren (2005) investigated the
effect of student-teacher relationships on students’ academic performance and
engagement in school using a teacher-student relationship improvement program in an
all-African American high school. Speciﬁcally the intervention program was designed to
improve the relationships of urban high school adolescents, who had emotional and
behavioral problems, with at least one of their teachers. Although the student sample was
small and purposefully selected, the researchers found that at the end of the intervention
program, academic performance of program participants was signiﬁcantly better than that
of non-participants, suggesting that positive teacher-student relationships have a positive
inﬂuence on students’ academic achievement. Again, their study conﬁrms the ﬁndings
ﬁom other studies of a positive correlation between teacher-student relationships and
academic achievement (e.g. Birch & Ladd, 1997; and Hamre & Pianta, 2001). Overall,
the studies highlighted in this section provide evidence that supports the notion that race
matters in determining the nature and quality of teacher-student relationships which

ultimately impact the performance of, especially, ethnic minority students. The current

20

study also contributes to this strand of literature by using a unique sample with a large
ratio (72%) of ethnic minority students. However, the inﬂuence of teacher’s race on
student outcomes is not explored because not all teachers reported their race and, the

majority of those that did (report) were White.

21

 

CHAPTER THREE

DATA AND METHODS

3.1 Introduction

This chapter addresses several needs. First, data used in this study and how it was
collected are described. Next, measures used for teacher-student interaction, students’
academic achievement, school satisfaction, and classroom adj ustment are discussed in
detail. Speciﬁcally, seven different measures are discussed. Finally, a description of the
data analysis procedure is provided. The model used for analysis is developed by
beginning with a simple unconditional means model which is progressively upgraded to
an unconditional growth model, and, eventually to a conditional growth model. The rest
of the chapter is organized as follows. Data is described in Section 3.2 with subsections
speciﬁc to students and teachers from whom the data were collected, and a subsection on
the data collection procedure. Measures are discussed in Section 3.3 while data analysis

procedures and the models to be estimated are presented in Section 3.4.

3.2 Data

The data used in this study were collected ﬁom students and their teachers in four
elementary schools in a small city in Southeastern United States. This was carried out
under a broader research project on Addressing the Context of Teaching for Behaviorally
At-Risk Young Students (ACT). The aim of the project was to seek an understanding of

the ecological contexts of risk in elementary schools and help teachers acquire the

22

 

necessary and effective classroom skills and, strategies to intervene early in children’s

school careers. ACT is a panel study in which data were collected every fall and spring
semesters over a three-year period; focusing on students in kindergarten through grade
ﬁve and their teachers. Each group of participants in the study project is discussed in

turn.

3.2.1 Students

The sample consists of 1,431 students of which 53% are female. Further, 56% of
these students are Aﬁ'ican American, 28% Caucasian, 10% Hispanic, while 4% belong to
other ethnicities. This is quite representative of the racial and ethnic composition of the
participating schools whose student population consists of 58% Aﬁican American, 27%
Caucasian, 10% Hispanic, and 5% of other groups, mainly Of Asian American descent.

During the entire study period of three years, the student sample consisted of an
average of 15% Kindergarteners, 16% ﬁrst graders, 18% second graders, 16% third
graders, 16% fourth graders, and 19% ﬁfth graders. More detailed discussions of the
descriptive statistics and actual proportions of the students in each year of study are
presented in Chapter 4.

Because students were moving one grade up at the end of each school year, not all
students who started with the study project remained with it for the entire three years.
Clearly, this was expected to occur although school dropouts contributed to missing
outcomes as well. In all, a total of 242 students (19%) remained enrolled with the project

for the entire duration of the study, with others participating for shorter periods. In

23

 

particular, 28% of the students participated for two years while 53% participated for one

year.

3.2.2 Teachers

A total of 68 teachers took part in the study. These teachers were predominantly
of Caucasian descent (62%), with a 10% Aﬁican American representation. Eighteen
teachers (26%) did not indicate their race and two percent reported their race as other.
The teachers were mainly women (96%) and many of them (42%) had been teaching for
more than seven years at the time of recruitment to the project. Seventy three per cent of
them reported their ages which were somewhat uniformly distributed and ranged ﬁom 20
years to 59 years. Further, one third of the teachers reported that they had a master’s
degree while another third said that a bachelor’s degree was their highest level of
education. Clearly, the sampled teachers are representative of a broad range of race,

gender, age, level of education, and teaching experience.

3.2.3 Procedures

Students in Kindergarten through ﬁfth grade in all the participating schools were
recruited for the study. Consent forms in the children’s native languages were sent to the
homes of the children and returned at the beginning of the school year. For those students
whose consent forms were not received after several weeks, teachers sent up to three
reminders in a bid to increase response rates. Because of these efforts the response and

participation rates were over 90% at each of the schools.

24

 

In order to take part in the study, teachers were asked to provide signed informed
consent forms. As a token of appreciation for their participation, they received a stipend.
The participating schools also received a stipend. Whenever teachers in the study took
time off for study-related activities, the project paid for substitute teachers.

As stated earlier, data were collected ﬁ'om both teachers and students in the fall
and spring semesters of each of the three years of study. Teachers responded to
questionnaires regarding school and classroom environments as well as their students’
abilities. The children were assessed on their satisfaction with school, classroom
environments, and relationships with fellow students and teachers. Children in fourth and
ﬁfth grades completed the measures during regular seatwork while the younger ones, in
K through third grade, were put in small groups in the classrooms, media rooms, and
other available instructional spaces, to respond to the questionnaires. Their surveys were
shortened and language was simpliﬁed to be easily understood. In addition, a larger font
size was used with rebuses on three point response scales instead of the four or ﬁve point
scales used with the older children. To control for students’ reading readiness, measures
were projected via overhead projectors and read aloud to them. Furthermore, the
questions were administered to all students in a counter-balanced format to control for

order effects.

3.3 Measures
The measures used in this study are part of a larger series of assessments that the
' teachers completed. In each of the three years of study, teachers were asked to rate

themselves, rate their students, and rate their school environments on a variety of

25

measures discussed in detail below. Teachers were also asked to assess and report
students’ academic performance. The students also carried out similar ratings, albeit on

different measures from those of their teachers. These measures are discussed in turn.

3.3.1 Diagnostic Inventory of School Climate (DISC)

The Diagnostic Inventory of School Climate (DISC) is an instrument that asks
teachers to describe their school setting based on their experiences (O'Neal, et al., 1987).
The survey is composed of 84 questions, all on a four-point Likert scale (never, seldom,

usually, and always). In this measure, school climate is operationalized as a combination

of eight subscales:

(1) clear school mission (school philosophy and instructional goals and
objectives); ‘

(2) safe and well-ordered learning environment (facilities and discipline);

(3) expectations for success (well communicated to staﬂ‘ and students);

(4) high morale (of students and staff);

(5) effective instructional leadership (as perceived);

(6) quality classroom instruction (objectives, expectations, time on-task,
and Opportunities to learn);

(7) monitoring student progress (program modiﬁcations, student progress,

and feedback); and
(8) positive home-school relations (parental support, parental

involvement, and communication).

26

 

Both the scale and the subscales had high internal validity coefﬁcients with

Cronbach alphas of 0.96 for the scale and from 0.78 to 0.92 for the subscales.

3.3.2 Student-Teacher Relationship Scale (STRS)

To assess teacher-child relationship quality, a portion of the Student—Teacher
Relationship Scale (STRS) (Pianta, 1992) was used. The STRS is based on attachment
theory (Bowlby, 1982) and ﬁndings ﬁom teacher-cth interaction research. The items in
this scale are designed to measure the constructs of warmth/security, anger/dependence,
and anxiety/insecmity between teachers and their students (see Appendix Table 14 for
sample items). In order to capture the quality of teacher-student relationships (i.c.
closeness and conﬂict), nine items from this scale were used. The choice to use a short
form of the scale was to reduce the length of the teacher battery included in the larger
study so as not to overburden the teachers. Even so, the items were carefully selected to
ensure that they captured the two constructs, and the brief measure had an internal
consistency of 0.87. Further, a principal components factor analysis with promax rotation
was performed and this revealed that the measure comprised of two factors; a ﬁve-item
subscale measuring closeness (a = 0.80) and a four-item subscale measuring conﬂict (a =

0.86).

3.3.3 Vessels School Climate Survey (V SCS)

The Vessels School Climate Survey (V SCS) (V cssels, 1998c) instrument was
used to assess school climate. It is conceptualized as a combination of the principal’s
leadership style, general quality of interpersonal relationships (teacher-teacher, teacher-

student and student-student), student discipline, character-building activities, the school’s

27

 

physical environment, and the school community (see Appendix Figure 3 for sample
items). The nine subscales are captured in 112 items that teachers rated on a 5-point scale

from strongly disagree to strongly agree. The scale had an alpha coefﬁcient of 0.93.

3.3.4 The Behavior Assessment System for Children - Teacher Rating Scale

(BASC-TRS)

The Behavior Assessment System for Children — Teacher Rating Scale (BASC-

TRS)
(Reynolds & Kamphaus, 1992) is a multidimensional behavior rating scale commonly
used to measure both adaptive and problem behaviors experienced by children in school.
Through the administration of age appropriate versions of the instrument, BASC-TRS
can be used for children from the age of two and a halfycars to 18 years. An earlier
version of BASC was used in this study, and it spans ages four to 18 years (see Appendix
Table 15 for sample items). Depending on the age of the child, respective teachers ﬁlled
out the pre-school form (BASC-TRS-P) for four to ﬁve year olds, the child form (BASC-
TRS-C) for six to 11 year olds or the adolescents form (BASC-TRS-A) for 12 to 18 year
olds.

The instrument has two broad categories; clinical scales and adaptive skills. The
clinical domain is comprised Of an externalizing problems composite (hyperactivity,
aggression, and conduct problems), an internalizing problems composite (anxiety,
depression, and somatization), a school problems composite (attention problems and
learning problems) and a ﬁnal composite for other problems (atypicality and withdrawal).

The adaptive skills scale is comprised of adaptability, leadership, social skills and study

28

skills. In addition to the two broad domains, BASC-TRS gives a broad composite rating;
the behavioral symptoms index, BSI. The BSI is an indicator of the overall level of
problematic behavior in a child, with high scores indicating high levels of behavioral,
academic, and emotional problems. The prc-school, child and adolescent forms had 109,
138 and 148 items, respectively. Each of the items was rated on a four point frequency
scale ranging ﬁ'om never to almost always. In the study, students’ BSI was used as an

indicator of the level of behavioral problems.

3.3.5 Teachable Pupil Survey (TPS)

To assess the degree to which students adj ustcd to the classroom environment,
norms and routines, the School-Appropriate Behavior scale from the Teachable Pupil
Survey (TPS) (Kornblau, 1982) was used (see Appendix Figure 2 for sample items). This
subscale has nine items on a 5-point Likert response format. The subscale is a valid

measure of behavioral adjustment, with an alpha of 0.92.

3.3.6 Student Survey

The student survey was used to assess classroom climate, child’s academic
support (by the teacher and other students), student personal support, classroom teacher
behavior, student’s satisfaction with school, student’s perception of self and the home-
school relationship. Depending on the age of the child, a student ﬁlled out one of two
forms. The items used for the constructs of interest were selected from a variety of
established and commonly used instruments. This decision to use selective items hour the

parent instruments was made because the instruments cover a wide range of constructs,

29

some of which were not relevant to this study. F iﬁeen items from the Vessels Classroom
Climate Scale — Early Elementary (Vessels, 1998a) were used to measure the K-3
children’s view of classroom climate. For the children in fourth and ﬁfth grades, 34
questions from the Vessels Classroom Climate Scale — Late Elementary (Vessels, 1998b)
were used. Sixteen and 21 items ﬁ'om the Classroom Life Instrument (Johnson, Johnson,
& Anderson, 1983) were used for the constructs of teacher academic support, teacher
personal support, peer academic support and peer personal support for the early and late
elementary groups respectively. Students’ satisfaction with school was measured using
six subscale items ﬁ'om the Multidimensional Students’ Life Satisfaction Scale
(MSLSS)(Huebner, 1994). Included in the survey, there were questions concerning
home-school relationships as well as parental relationship with the child (see Appendix

Figure l and Table 13 for sample items).

3.3.7 Academic achievement

Students’ academic achievement is measured using students’ composite scores on
reading and language arts, and mathematics Obtained from either the Iowa Test of Basic
Skill (ITBS) or the Stanford Achievement Test Series — Ninth Edition (SAT9), as well as
their report card grades. Both TTBS and SAT9 are valid, nationally standardized tests
which are widely used in large scale assessments for measuring student academic
achievement in reading, language, mathematics, social studies, and science (Salvia,

Ysseldykc, & Bolt, 2007).

30

3.4 Data Analysis

The data in this study is hierarchical and longitudinal in nature and was analyzed
using multilevel analytic procedures. These techniques model nested sources of
variability in data. They model contextual effects and thus examine how variables
measured at one level affect relationships observed at another level. Speciﬁcally, I used
the hierarchical linear modeling (HLM) technique (Raudenbush & Bryk, 2002) to address
the research hypotheses. HLM has signiﬁcant advantages compared to regular Ordinary
Least Squares (OLS) regression that is commonly used in analyses. HLM does not
require observations to be independent, a stringent assumption for OLS regression
analysis. Nested data, by its very nature, violates this assumption. Consequently, if OLS
is used, it produces small standard errors thereby overcstimating signiﬁcant levels. This
problem is easily solved by using multilevel modeling. Also, HLM allows for the
exploration of cross-level interactions. In this way, we are able to examine how variables
measured at one level affect relationships occurring at another level (Hoffmann, 1997;
Osborne, 2000; Raudenbush & Bryk, 2002).

Although nested, these data are not strictly hierarchical but rather cross-classiﬁed.
In a cross-classiﬁed data structure, a writ is classiﬁed along more than one dimension
(Goldstcin, 1994; Hox, 2002; Rasbash & Goldstcin, 1994; Raudenbush & Bryk, 2002). A
common example in education is One in which students are classiﬁed by the schools they
attend and by the neighborhoods they reside in. Not all students in a particular school live
in the same neighborhood and similarly not all students from a particular neighborhood
attend the same school. The students (ﬁrst level units) are nested in the cross-

classiﬁcation of schools and neighborhoods (second level units). A similar situation is

31

observed in this study. At the start of each academic year, students move to the next
grade level and subsequently have a different classroom (grade) teacher. A student can
therefore only have a maximum of two assessments per teacher i.e. during the fall and
spring of the same year. The assessments (measurement occasions) then form the lower
level units i.e. level-l while teachers and students give the higher level units i.e. level-2.
Speciﬁcally, measrn'ement occasions are nested in the cells formed by the crossing of
students and teachers. See Appendix Table 12 for an illustration of sample data.

The data were analyzed using a two-level cross-classiﬁed random effects model
(HCM2). A two-level HCM2 is similar to a two-level HLM model with the exception
that the latter deals with perfect hierarchy while the former handles cross-classiﬁed
nesting. By using HCM2, correct model parameters for within-cell and between-cell
differences were estimated. Changes in students’ academic performance, their adjustment
to classroom environments and their overall satisfaction with school, both within-year
and across years were modeled.

Three sources of variation are investigated. These are (i) within-student variation
(i.e. individual student growth), (ii) between-students variation, and (iii) between-
teachers variation.l These variations are further partitioned into explained and
unexplained components. Effects of student factors (such as race, gender and behavioral
conduct) and those of teacher interactions with students (such as conﬂict, closeness and
support) were examined.

1 use a piece-wise linear growth approach to estimate learning trajectories of

students between grades K and fall of third grade, and between fall of third grade to ﬁfth

 

’ Additional variation due to interaction between teachers and students could have been possible were it not
for the very small within-cell sample sizes. Each student could only have a maximum of two ratings ﬁorn
the same teacher.

32

grade. Piecewise linear growth models estimate learning growth as a function of time
(Singer & Willett, 2003) and are therefore appropriate for use in this study. The decision
to ‘brcak’ the time into two learning periods was arrived at after close examination of the
empirical growth plots of 20 randomly selected students. Even though a few of them
exhibited quadratic growth trajectories, most had linear trajectories with a natural break
occurring at fall of third grade.

Conceptually, the data can be thought of as a matrix of J rows (of students) and K
columns (of teachers). The indicesi, j and k are used respectively, to represent
measurement occasions (i.e. repeated measurements of students’ scores), students, and
teachers. More speciﬁcally, i=1, 2 occasions within cell jk , for j = 1,...,J = 1431
students, and k =1,..., K = 68 teachers.

I ﬁtted and tested several models before ﬁnding the one that best explains the
data. This included both linear and polynomial models. As is often the case with
multilevel modeling, I started with the simple, unconditional (null) models and
progressively built more complex conditional ones as discussed in the following three

subsections.

3.4.1 Unconditional Means Model

This is the simplest model that is sometimes referred to as the intercept-only
model. It is unconditional because it does not include predictor variables at any level. It
describes and partitions the variation in the outcome variable into its components. In this
case, it estimates the variation that lies between students, between teachers, and within

cells. At level 1 there is a unique set of scores nested within each cell of the cross-

33

classiﬁcation of teachers and students. The within-cell model thus describes the variation

+6..

among these scores and is expressed thus: Y .. = 7r
1 yk

1k Ojk

9

............................................................................... (3.1)

where

12.1.]: is the outcome variable score for student j under teacher k at measurement occasion

1';

7: is the expected outcome score for student j under teacher k; and

Ojk
eij k is the within cell random effect assumed normally distributed with mean 0 and

variance 02 .

At level 2, the between—cell model estimates the variation that is attributable to
student effects and teacher effects. Ordinarily, we would expect student-by-teacher

interaction effects; however, the within-cell sample sizes are too small to distinguish

variances of the interaction effect from the within-cell error, 02. Consequently, such
interactions are omitted ﬁom the model, resulting in the following equations:

+V

”Ojk z 7000 “‘00; 00k, ................................................................ (3.2)

where

u .~N 0,1' .,
00’ i “00]

VOOk ~ N[0,tv00]

7000 is the grand mean score of all children

34

u is the random main effect associated with child j i.e. contribution of child j

00 j
averaged over all teachers, assumed normally distributed with mean 0 and

variance ru ;
00

VOOk is a random teacher effect, i.e. the contribution of teacher k averaged over all

students, assumed normally distributed with mean 0 and variance rv
00 °

Combining the two models (level 1 and level 2) yields a single combined model

+V

00k +8 .

Yijk = 7 000 H001“ ijk ........................................................... (3.3)

3.4.2 Unconditional Growth Model

The unconditional grth model is next to the simplest model after the intercept-
only model. It includes a time predictor in the level 1 model and consequently partitions
variation in the outcome variable as well as n the change trajectory. Based on exploratory
analyses and examination of empirical growth plots and residual plots of 20 randomly
selected students in the sample, the level 1 model assumes a piecewise linear growth
trajectory. As stated earlier, majority of the students had had linear growth trajectories.
Given this observation and in the interest of parsimony, the resulting model has two
pieces, each with its own linear grth rate. In the model, students’ learning trajectories
depend on learning that occurs between grades K to fall of third grade and fall of third
grade to ﬁfth grade. Thus, the conditional growth model to be estimated is expressed as:

Y..

I} k = ”Oj k + ”ljk (Growth K-3fall) +ﬂ2jk (Growth 3sprrng-5) + eijk

, ........... (3.4)

where

35

Yijk is the outcome variable for student j under teacher k at occasion i;

”Ojk is the third grade fall score for student j under teacher k , i.e. the expected

outcome score for a student at the fall of third grade;

7:1]. It is the rate of change for student j under teacher k during K-3fall period;

7: is the rate of change for student j under teacher k during 3fall-5 period;

2 jk

eij k is the within cell random effect assumed normally disu'ibuted with mean 0 and

variance 02 .

Similar to the case of the intercept-only model, the unconditional growth model also
estimates the variation that is attributable to student effects and teacher effects. The
representative level 2 equations are:

+ ’00k,

”Ojk =7000+“00j
”Ijk =7100
”ij = 7200 ...................................................................................... (3.5)

where

u .~N 0, r ,
00’ i “00]
v00k ~N{O’Tv00]

7000 is the expected outcome score at the fall of third grade;

7100 is the average growth rate during K-3f period;

36

7200 is the average growth rate during 3fall-5 period;

u is the random main effect associated with child j i.e. contribution of child j

00,-

averaged over all teachers, assumed normally distributed with mean 0 and variance Tu ;
00

v00]: is a random teacher effect, i.e. the contribution of teacher k averaged over all

students, assumed normally distributed with mean 0 and variance rv
00 .

Combining the two models (level 1 and level 2) yields a single combined model

expressed as:

Yijk = 7000 + 7100 (Growth K-3fall) +7200 (Growth 3sprrng-5) +

u

..................... 3.6
00]. +v00k+ eijk ( )

3.4.2 Conditional Growth Models

Conditional growth models include predictor variables beyond the time variables.
The presence of non-zero variance in the unconditional models indicates that some of the
variability in the outcome variable is due to some of the measured variables. These are
student characteristics (i.e. race, gender, and behavioral conduct) and teacher
characteristics (conﬂict, closeness, and support). Using the unconditional models as
baseline models, I ﬁtted several conditional models, by including student and teacher
variables. However, because almost all the teachers were female (96%) and white (85%),

the effect of teacher’s gender or teacher’s race on student attainment was not explored.

37

By examining signiﬁcance levels of predictors and overall model ﬁt indices, I
determined the ﬁnal models. For instance, in reading or language achievement on ITBS

or SAT9 tests the ﬁnal that best ﬁt the data is as follows:
Reading/Language achievement = 7000 + 7100 (Growth K-3falli’. k )

+7200 (Growth 3spring- -5. rjk ) + 7300 (BSI!) “k j + 7010 {White}. J + 7020 (Hispanicj)

. g _
+7O3O(Oth erj)+7llo(Whrtej) (GrowthK 3fallijk)

- * -
+y120 Hispanic. 1*) (Growth K 3fallijk ) + 7130 (Otherj) (Growth K 3fallijk)

. . * . _
+7210 (White 1.") (Growth BSpring- -S'jk ) + 7220 (I—Irspamcj) (Growth 3sprrng Sijk)
+7230 +1120].}.(Other )* (Growth 3spring- -.5 rjk)” uOOj “‘le [Growth K-3fallijk)

Growth 3spring- -.5 ........................................................ (3.7)

HUNG“ My,
where

7000 is mean reading/language achievement in the fall of third grade of an Aﬁican

American student with behavior misconduct;

7] 00 is the average growth rate in reading achievement during K-3fall;

7200 is the average growth rate in reading achievement during 3fall-5;

7300 is the rate of change in reading achievement due to student behavior;

7010 is the difference in score in third grade fall between Aﬁican American and White

students;

7020 is the difference in third grade fall between Aﬁican American and Hispanic

students;

38

7030 is the difference in third grade fall between Aﬁican American and Other students;

71 10 is the difference in growth rate during K—3fall between African American and

White students;
7120 is the difference in growth rate during K-3 fall between African American and
Hispanic students;

7130 is the difference in growth rate during K-3 fall between Aﬁican American and

Other students;

7210 is the difference in growth rate during 3fall-5 between Aﬁican American and

White students;

7220 is the difference in growth rate during 3fall-5 between Aﬁican American and

Hispanic students;

7230 is the difference in growth rate during 3fall-5 between African American and

Other students;

u

00]. is the is the random effect associated with child j on reading/language

achievement in fall of third grade, assumed normally distributed with mean 0 and

variance tu ;
00

. is the is the random effect associated with child j on reading/language growth rate

ule

during K-3fall, assumed normally distributed with mean 0 and variance ru ;
10

39

u20j is the is the random effect associated with child j on reading/language growth

rate during 3fall-5, assumed normally distributed with mean 0 and variance tu ;
20

VOOk is the is the cumulative random teachers’ effect on a student’s reading/language

growth trajectory, assumed normally distributed with mean 0 and variance Tv ;
00

e1.j k is the within cell random effect assumed normally distributed with mean 0 and

variance 02.

3.4.3 Model Fit

In order to determine the best ﬁtting model, I compared overall model ﬁt statistics
such as the Akaike Information Criterion (AIC) and the Bayes Information Criterion
(BIC) statistics (West, Welch, & Galecki, 2007). Both criteria give an indication Of the
“better” or “worse” model from a group of models that ﬁt the same observations. Lower
values suggest that a given model ﬁts the data better than the alternatives. The advantage
of using the AIC and/ or BIC statistics compared to other ﬁt statistics, such as the
deviance statistic, is that the former do not require the models to be nested.
Consequently, I was able to compare several models and ﬁnd the ‘best’ model without

the constraint of hierarchy.

3.4.4 Model Variables

40

Before nominal variables such as gender and race are included as predictor
variables in estimation models, they have to be either dummy-coded or effect-coded. In
dummy coding, variable categories take on values of 0 for the reference category or 1 for
all other groups. In effect coding, variable categories take on values of -l for the
reference category or 1 or 0 for all other groups. The main difference in the two methods
is the way in which the resulting coefﬁcients are interpreted. In dummy coding, the
intercept is the mean outcome value for the reference group, and the slope coefficients
associated with the dummy variables indicate the difference in the mean outcome score
between those categories and the reference group. When effect coding is used, the
intercept value is the grand mean outcome score and the slope coefﬁcients are the score
deviations from that grand mean.

In these analyses, I use dummy coding because I am interested in looking at
differences in student outcomes based on gender and race. While results based on effect
coding would indicate how far each group of students’ means (by race or gender) are
ﬁ'om the grand mean, the results based on dummy coding go a step further. They give
performance difference between the reference group and the other predicted groups. In
the estimation results reported in chapter Four, gender is coded 1 if a student is male and
0 if a student is female while race is coded l is a student is White, Hispanic or ‘Other’

and 0 if Aﬁican American.

41

CHAPTER FOUR

RESULTS

4.1 Introduction

This chapter reports the results of modeling math and reading or language
achievement, school satisfaction and classroom adjustment for K through ﬁfth grade
students in four elementary schools in a small city in Southeastern United States.
Different models are examined in turn. First, an unconditional model is estimated to
provide information on the average level of academic achievement and overall school
satisfaction across all measurement occasions and across all student groups and, to
examine variance components at each of the levels. Second, an unconditional growth
model is estimated to reveal any signiﬁcant learning growth trajectories experienced in K
through fall of third grade and in fall of third grade through ﬁfth grade. Third, a
conditional growth model is estimated to examine the relationship between race, gender,
and behavior of students and teacher-student relationships with academic achievement,
classroom adjustment and school satisfaction.

Relationships between student outcomes and several variables are investigated.
Achievement on reading or language competency and math is modeled using scores
obtained in both standardized ITBS or SAT9 tests and student report cards.

The rest of the chapter is organized as follows. Section 4.2 provides the
descriptive statistics of the variables in the analysis including demographic summaries of

the students and teachers involved in the study. Correlations of independent variables are

42

also reported there. Section 4.3 gives results on reading and language achievement in
ITBS or SAT9 tests while Section 4.4 gives similar results ﬁom student report cards.
Results on math achievement in ITBS or SAT9 tests and student report cards are
presented in Sections 4.5 and 4.6, respectively. Section 4.7 has results on school

satisfaction while classroom adjustment is covered in Section 4.8.

4.2 Descriptive Statistics

Table 4.1 shows the distribution of grade K-5 students involved in the study. As
described earlier, the students were, to a large extent, evenly distributed across grades and
across years of study. Representation ranged from 11% for Kindergarteners to 21% for
fourth graders, both occurring in year 3. Hence, the study sample was deemed to have
balanced representation for all the grade levels investigated. Similarly, Table 4.2 shows
frequency distributions for these students and their teachers, categorized by gender and
race. These statistics show that a majority of the students (56%) were of African
American descent whereas teachers were primarily Caucasian (62%)2. Furthermore, 96%

of the teachers were female.

 

2 Eighteen teachers (26.5%) did not indicate their race.
43

Table 4.1

Frequencies and Percentages of Students by Grade Levels and Year of Study

 

 

 

 

 

 

 

Grade Year 1 Year 2 Year 3
Frequency Percent Frequency Percent Frequency Percent
Kindergarten 125 18.1 111 14.4 71 11.1
Firstgrade 118 17.1 136 17.6 84 13.1
Second grade 131 19.0 128 16.6 116 18.2
Third grade 111 16.1 121 15.7 105 16.4
Fourth grade 86 12.5 127 16.4 132 20.7
Fifth grade 118 17.1 150 19.4 131 20.5
Table 4.2
Frequencies of Student and Teacher Demographics
Students Teachers
Frequency Percent Frequency Percent
Gender
Male 614 47.3 03 4.4
Female 684 52.7 65 95.6
Race
Aﬁican American 722 56.3 07 10.2
White 370 28.8 42 61.8
Hispanic 133 10.4 - -
Other 58 4.5 01 1.5
NO response - 18 26.5

 

A total of six dependent and four independent variables are used in the study and

their descriptive statistics are reported in Table 4.3 below. Four of the dependent

variables are used to measure academic achievement while the other two measure level of

school satisfaction and classroom adjustment, respectively. To measure academic

achievement ITBS or SAT9 standardized test scores were used together with teacher

report cards on math and reading or language competency. School satisfaction and

44

classroom adj ustnrent variables measure how much the students felt contented with
school and how well they adjusted to the norms, routines, and expectations of the
classroom environment, respectively.

The independent variables are teacher-student interactional variables, a student
behavioral symptoms index, and students’ gender and race. The teacher-student
interactional variables measure level of conﬂict and level of closeness experienced
between teachers and children as well as level of teacher support accorded to children.
The behavioral symptoms index measures student behavior such as hyperactivity,
externalizing and internalizing symptoms, and attentiveness.

With the exception of behavioral symptoms index and classroom adjustment, all
the other variables are reported as z-scores. This is because the measures for these
variables were on different metrics and needed to be standardized to a common metric to
facilitate comparison of performance across different students and measurement

occasions.

45

Table 4.3

Descriptive statistics of outcome and predictor variables

 

 

M SD Min Max N

Independent variables
Teacher-child closeness 0.00 1.00 -4.64 0.84 2968
Teacher-child conﬂict 0.00 1.00 -2.89 0.82 2968
Teacher overall support 0.00 1.00 -4.95 6.44 2981

Behavioral Symptoms Index (T—scores)
Dependent variables

Reading or language achievement (ITBS or SAT9)

Reading or language grade achievement

Math achievement (IT BS or SAT9)

Math grade achievement

School satisfaction

Classroom adjustment

49.90 10.15 32.00 96.00 3178

0.00
0.00
0.00
0.00
0.00

1.00
1.00
1.00
1.00
1.00

-2.42 3.01 1407
-2.82 1.29 2725
-2.45 6.15 1720
-2.84 1.31 2998
-3.99 1.57 2913

35.94 8.63 9.00 45.00 2963

 

Because this study assumed an accelerated longitudinal design, students entered

the study at different points and may have been assessed over a short time relative to the

entire time span of the study. Similarly, due to maturation, some students exited the study

before its completion. Also, some teachers failed to report ratings for students and some

students missed assessments. As a result of these circumstances, we have different

‘sample sizes’ for the variables in table 4.3. Most of the variables were negatively

skewed. For instance, teacher-child conﬂict had a skewness of -l .4 and teacher-child

closeness had a value of -1. An examination of histograms pointed toward generally high

levels of closeness and decreased levels of conﬂict between teachers and students.

Table 4.4 gives the correlation coefficients for the continuous predictor variables

used. All the correlations between student behavior, teacher support, teacher-student

closeness, and teacher-student conﬂict were statistically signiﬁcant at an alpha level of

46

0.01 . Close relationships were positively (even though moderately so) associated with a
decrease in conﬂictual relationships between teachers and students (I = 0.58). Increases in
student behavioral misconduct were associated with few close relationships (r = -0.45),
less teacher support (r = -0.15) and increased conﬂict (r = -0.68) between students and

their teachers.3

Table 4.4

Correlations of student and teacher interactional variables

 

Behavioral Symptoms Teacher-child Teacher-child

 

 

Index T-score closeness conﬂict
Teacher-child closeness -0.446**
Teacher-child conﬂict -0.675** 0.581 * *
Overall teacher support -0.150** 0.166" 0.146"

**p<0. 01.

Even though the design of the study lends itself to multilevel analysis, I also
calculated and examined intra-class correlation coefficients (ICC) to conﬁrm the
tenability of using multilevel models in analyzing these data. Intra-class correlation
coefﬁcients indicate the proportion of variance in the outcome variable that is accounted
for by level 2 units. Altemately, ICC is the expected correlation between any two
randomly chosen units that are in the same group (Hox, 2002; Luke, 2004). In this case,
the level 2 units are students (which give intra-student correlation) and teachers (intra-

teacher correlation). Both ICCS are calculated as follows:

 

3 An increase in the z-scone on teacher-child conﬂict means that there was a decrease in conﬂictual
relationship between teacher and student because conﬂict was reverse coded.

47

 

Intra-student correlation, p = 00 where 2" is the estimate of
S tude m A A A 2 u
tu + rv + 0' 00
00 00
2

student variance, iv is the estimate of teacher variance, and 6' is the estimate of the

00
variance within each cell (between measurement occasions) obtained by ﬁtting a null (i.e.

intercept-only) model. Sinrilarly,

 

1’:
V
Intra-tcacher correlation, p = 00 with the variance estimates
teacher . . . 2
Tu + rv + a
00 00
deﬁned as above.

Using these equations and variance estimates obtained ﬁom ﬁtting an intercept
only model for each of the outcome variables, I obtained ICCS presented in table 4.5.
According to these coefﬁcients, between-student factors would account for 50% - 75% of
the variation in outcome variables while up to 28% would be accounted for by teacher
variables. This means that intra-class correlation exists in these data and therefore, the
traditional linear model is not appropriate. This is because the assumption of independent

observations is violated (Krcft & de Leeuw, 1998).

48

Table 4.5

Intra-class correlation coeﬂicients

 

,0 student ’0 teacher p cell

 

ITBS or SAT9 reading/language 0.72 0.17 0.11
ITBS or SAT9 math 0.57 0.24 0.20
Report card reading/language 0.78 0.02 0.20
Report card math 0.47 0.28 0.25
School satisfaction 0.50 0.02 0.48
Classroom adjustment 0.68 0.05 0.28

 

4.3 Reading and language achievement in [TBS or SAT9 tests
Beginning with this section onwards, I present results obtained after ﬁtting several
multilevel models to the data. The results in this section pertain to reading and language
achievement in ITBS or SAT9 tests while those in subsequent sections pertain to the
remaining dependent variables. In each case, I present at least three models and label
them in ascending order as follows:
i) Model I: the unconditional means i.e. intercept only mode] discussed in
Chapter three section, 3.4.1;
ii) Model 2: the unconditional growth model discussed in Chapter three,
section 3.4.2; and
iii) Model 3: the conditional model also discussed in Chapter three, section
3 .4.3.
In cases where more than three models are presented, the additional models are simply a
variant of the conditional growth model. The speciﬁc differences between these models

are highlighted in the sections in which their results are reported.

49

Models 1 and 2 are both unconditional models (i.e. do not include predictor
variables) and therefore each is expressed the same way mathematically for all the
outcome variables. The equations presented in Chapter three (equations 3.1 - 3.5) and
repeated here (but renumbered) to make it easier for one to follow the results reported
here:

Model 1: unconditional means model

Level I .'

Yijk z ”Ojk +eijk, ............................................................. (4.1)

where

12.]. k is the ITBS/SAT reading/language score for student j under teacher k at

measurement occasion i;

”Oj k is the mean ITBS/SAT reading/language score for student j under teacher

k;

eijk is within student random effect assumed normally distributed with mean 0

and variance 02.

Level 2:

”M = 7000 +"001' ”00k, ....................................................... (4.2)

uOOj ~ N[0, tum J ,

50

v00k ~ NLOJVOO]

where

7000 is the grand mean ITBS/ SAT reading/language score for all children

uOOj is the random main effect associated with child j i.e. contribution of child j

averaged over all teachers, assumed normally distributed with mean 0 and variance

Tu ;
00

v00 k is a random teacher effect, i.e. the contribution of teacher k averaged over all

students, assumed normally distributed with mean 0 and variance rv
00 .
Combined model:

+V

00k +6..

Yijk =7000+"00j yk ......................................... (4.3)

Model 2: Unconditional growth model

Level I .'

Yijk = ”Ojk + ”ljk (Growth K-3fall) +ﬂ2jk (Growth 3spnng-5) + eijk
, ....................... (4.4)

where

Yij k is the ITBS/SAT reading/language score for student j under teacher k at occasioni ;
”Oj k is the ITBS/SAT reading/language score for student j under teacherk , i.e. the

expected ITBS/SAT reading/language score for a student at the fall of third grade;

51

”ljk is the rate of change (i.e. growth rate) for student j under teacher k during K-3fall

period;

n2]. k is the rate of change (i.e. growth rate) for student j under teacher k during 3fall-5
Period;

eij k is the within student random effect assumed normally distributed with mean 0 and

variance 02 .

Level 2:
'%ﬁ=%m+%w’hm,
hﬁzhm

5ﬁ=ﬁm
........................................................................................... as

where

u .~N0,r ,
00’ i “00]

VOOk ~ N[0,rv00]

7 000 is the mean ITBS/SAT reading/language score at the fall of third grade;
7100 is the average growth rate during K-3fall period;

7200 is the average growth rate during 3fall-5 period;

52

u is the random main effect associated with child j i.e. contribution of child j

OOj

averaged over all teachers, assumed normally distributed with mean 0 and variance ru ;
00

v0 0 k is a random teacher effect, i.e. the contribution of teacher k averaged over all

students, assumed normally distributed with mean 0 and variance tv
00 .

Combined model:

Yijk = 7000 + 7100 (Growth K-3fall) +7200 (Growth BSprrng-S)

+ e ..................................................................................................... (4.6)

+"001' + ’00]: yk

Model 3: Conditional growth model

Level I :

ITBS/SAT Reading / language achrevementijk =7r0j k + ”ljk (Growth K-3fallijk)

+ﬂ2jk (Growth 3sprrng-5ijk )+ ”3jk (BSIijk ) + eijk .............................................. (4.7)

where

7: is the mean ITBS/ SAT reading/language score for student j categorized as one

Ojk
with behavior misconduct, under teacher k , at the fall of third grade;

7:1]. k is the rate of change (i.e. growth rate) for student j under teacher k during K—3 fall
Period;
n2]. k is the rate of change (i.e. growth rate) for student j under teacher k during 3fall-5

peﬁod;

53

ﬂ3jk is the average increase (or decrease) in ITBS/SAT reading/language score for

student j under teacher k accompanying a one unit change in BSI score;

eij k is the within student random effect assumed normally distributed with mean 0 and

variance 02 .

Level 2:

”Ojk = 7000 + uOOj + v00k + 7010 {White}. J + 7020 {Hispanic}. ) + 7030 (Otherj)
”ljk = 7.100 (Growth K-3falliik ) + 71 10 (Whitej ) * (Growth K-3fallijk ) +

7120 {Hispanic}. ) * (Growth IK-3fallijk ) + 7130 {Other}. ) “' (Growth K-3fallijk ) +

u1 Oj (Growth K'3fauzjk)

7tij = 7200 (Growth 3spring-5ijk ) + 7210 (Whitej ) * (Growth 3spring-5ijk)

+7220 {Hispanic}. ) * (Growth 3spring-5ijk ) + 7230 (Otherj ) * (Growth 3spring-5ij k )

+u20j (Growth 3spnng-5ij k )

BSI..

”3jk =7300( 11k) ........................................................................ (4.8)

where

7000 is mean reading/language achievement in the fall of third grade of an Aﬁican

American student with behavior misconduct;

54

7100 is the average growth rate in reading achievement during K-3fall;

7 200 is the average growth rate in reading achievement during 3fall-5;

73 00 is the rate of change in reading achievement due to behavior;

7010 is the difference in third grade fall between African American and White students;

7020 is the difference in third grade fall between Aﬁican American and Hispanic

students;

7030 is the difference in third grade fall between African American and Other students;

71 10 is the difference in growth rate during K-3 fall between Aﬁican American and

White students;

7120 is the difference in growth rate during K-3 fall between African American and

Hispanic students;

7130 is the difference in grth rate during K—3 fall between Aﬁican American and

Other students;

7210 is the difference in growth rate during 3fall-5 between African American and

White students;

7220 is the difference in growth rate during 3fall-5 between Aﬁican American and

Hispanic students;

7230 is the difference in growth rate during 3fall-5 between Aﬁican American and

Other students;

55

uOOj is the random effect associated with child j on reading/language achievement in

fall of third grade, assumed normally distributed with mean 0 and variance tu
00

u1 Oj is the is the random effect associated with child j on reading/language growth rate

during K-3fall, assumed normally distributed with mean 0 and variance ru
10

u20j is the random effect associated with child j on reading/language growth rate

during 3fall-5, assumed normally distributed with mean 0 and variance ru ;
20

v00 k is the cumulative random teachers’ effect on a student’s reading/language growth

trajectory, assumed normally distributed with mean 0 and variance rv ;
00

Combined model:

ITBS/SAT Reading / language achrevementijk = 7000 + 7100(

Growth K-3fallij k )
+7200 (Growth 3spring-5ijk ) + 7300 (BSIijk ) + 7010 {White}. ) + 7020 {Hispanic}. J +
7030 [Other]. ) + 7] 10 {White}. J * (Growth K-3fallijk ) + 7120 (Hispanicj J * (Growth K—3fallijk )
+7130 (Other). ) * (Growth K-3falliik ) + 7210 {White}. ) * (Growth 3spring—5iik )

+7220 [Hispanic]. ) * (Growth 3spring-5ijk ) + y230 [Other]. ) * (Growth 3spring-5ijk J + uo0 . +

J

u1 0]. (Growth K—3fallijk ) + u20j (Growth 3spnng-5iik ) + v00 k + eijk (4.9)

 

56

Tables 4.6(a) and 4.6(b) Show the ﬁxed effects and variance component estimates
for reading and language in ITBS or SAT9 achievement, respectively. Based on the
likelihood ratio tests and the information criteria of AIC and BIC, model 3 best ﬁts the
data and is therefore preferred over models 1 and 2.

The results ﬁom model 1 show that during the fall of third grade overall average
reading and language achievement in ITBS or SAT9 tests are signiﬁcantly different ﬁom
zero. This result simply means that if all possible predictors are ignored, the mean
reading achievement of all students across all measurement occasions is statistically
signiﬁcant. However, once a time variable is included as an explanatory variable, as in
model 2, the conditional mean of achievement becomes statistically insigniﬁcant
suggesting that reading achievement scores are time-dependent. Speciﬁcally, model 2
includes two time variables which capture the effects of learning trajectories during K
through fall of third grade (K-3fall) and fall of third grade through ﬁfth grade (3fall-5).
Model 2 results suggest that learning that occurs between K-3fall and between 3fall-5
accounts for 27% of the variability in reading achievement initially attributed to within-
student characteristics. Model 3 explains an additional 47% of the within-student
variance and- 14% of the teacher variance".

Model 3 builds upon model 2 by including a behavioral symptoms index (BSI)
variable and taking into account the student’s race. I investigated the role of students’

gender, and teacher related variables (teacher-student closeness, teacher-student conﬂict

 

" The ﬁgures of 27% and 14% represent the percentage change in the within-student variance between
0.081 — 0.059

models 1 and 2 computed as (
0.081

)x 100% and teacher variance between models 2 and 3

0.029 — 0.025

x 100% , res ivcly.
0.029 ) pect

computed as (

57

and teacher support) in reading achievement on the ITBS or SAT9 tests by including
them as predictors. Also, I investigated student-teacher interactions, such as student
gender by teacher support, to examine any inﬂuence they might have on student
achievement. Their coefficients were not statistically signiﬁcant. Therefore, these
variables are not included in Model 3.

As discussed in Chapter three, race was dummy—coded with the Aﬁican American
students’ dummy variable used as the reference group in analyses. Results ﬁom model 3
reveal that there were signiﬁcant differences in the mean reading achievement associated

with students’ race and behavior. Speciﬁcally, these results show that in the fall of third

grade, Aﬁican American students had a lower average reading score (7000= -0.39) than

their White counterparts whose average score was 0.59 (i.e. 0.98-0.39).5 Similarly,
students whose race is classiﬁed as ‘Other’ had a higher average score than African
American students. The performance of Hispanic students in reading was, however, not
signiﬁcantly different ﬁ'orn that of Aﬁican American students.

After controlling for behavioral conduct and learning growth during fall of third
grade — ﬁfth grade, results indicate that African American, White and Hispanic students
improved while Other students declined in their performance during K-fall of third grade.
The growth rates were signiﬁcantly different. White students exhibited a considerably

higher growth rate (71 10 = 0.10, p<0.001) than their African American counterparts. No

signiﬁcant differences were evident between the growth rates for Hispanics or Other
students relative to Aﬁican Americans. During fall of third grade — ﬁfth grade, learning

growth rates for White and Hispanic students declined while that of African American

 

5 The coefﬁcients of each dummy variable is equal to the difference between the mean of the group coded 1
and the mean of the reference group.

58

and Other students increased. Relative to Aﬁican American students, the decrease for

White students was signiﬁcant, 7210 = -0.17, p<0.001. There was a moderate positive

correlation (r = 0.67) between achievement at third grade fall and growth rate during K-
third grade fall indicating that students with faster growing rates in the early grades
attained higher levels of achievement by the beginning of third grade than those with
slower growth rates. But, this trend was reversed during the fall of third —to ﬁfth grade
period, resulting in a negative correlation with the score at fall of third grade.
Furthermore, students who exhibited faster learning rates in K-third grade fall
experienced a remarkable decline in their growth rate between fall of third grade and ﬁfth
grade, r = -0.89. The behavioral symptoms index coefﬁcient is negative and statistically

signiﬁcant (7300 = -0.01). This suggests that students with elevated behavioral problems

experienced a decrease in their reading achievement.

59

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4.4 Student report card reading achievement

This section presents results from four models on the ﬁxed effects and variance
component estimates for reading achievement as measured by students’ report card
scores. The results are summarized in Table 4.7. Models 1 and 2 are similar to those
presented in section 4.3 except for the dependent variable which has changed to student
report card reading scores. In addition to a time variable, both models 3 and 4 include
students’ gender, race, and behavioral symptoms as predictors. Additionally, model 4 has
a teacher-child conﬂict variable as a predictor. Teacher-child closeness and teacher
support were considered and dropped as predictors because they were not statistically
signiﬁcant. Similarly, interactions between teacher and student variables were
considered. These were found to be statistically insigniﬁcant, and dropped as predictors.
Based on the likelihood ratio tests and the information criteria of AIC and BIC, model 4
best ﬁts the data and is therefore preferred over models 1, 2 and 3. Level 1 and level 2
model equations are similarly expressed as outlined by equations 4.7 and 4.8. Similar to

equation 4.9, the combined model equation for the ﬁnal model is expressed thus:

Report card reading achievement Growth K-3fallijk)

ijk=7000+7100(

+y200 (Growth 3sprrng-5Uk ) + 7300 (138ka ) + 7400 (Conﬂictijk ) + 7010 (Malej)

 

+7020 {White}. ) + 7030 (Hispanicj ) + 7040 {Other}. ) + uOOj + v00 k + eijk (4.10)
where

7000 is the mean reading/language achievement in the fall of third grade of an Aﬁican

American female student with behavior misconduct;

62

7100 is the average growth rate in reading achievement during K-3fall;

7200 is the average growth rate in reading achievement during 3fall-5;

7300 is the rate of change in reading achievement due to behavior;

7400 is the rate of change in reading achievement due to student-teacher conﬂict;

7010 is the difference in third grade fall between male and female students;

7020 is the difference in third grade fall between African American and White students;

7030 is the difference in third grade fall between Aﬁican American and Hispanic

students;

7040 is the difference in third grade fall between African American and Other students;

u is the random effect associated with child j on reading/language achievement,

OOj

assumed normally distributed with mean 0 and variance tu ;
00

v00]: is the cumulative random teachers’ effect on a student’s reading/language growth

trajectory, assumed normally distributed with mean 0 and variance rv ;
00
eijk is the within student random effect assumed normally distributed with mean 0 and
variance 02 .
As more variables were progressively added in models 2, 3, and 4, they explained
increasingly more and more of the variability in reading achievement previously

attributed only to student and teacher factors. The unconditional means only mode] (in

this case model 1) is the baseline for level 1 variance comparisons, while the

63

unconditional growth model (mode12) is the baseline for level 2 variance comparisons.
For instance, 78% of the variability observed in student reading achievement under
model 2 was attributed to between-student factors. By including behavioral conduct,
students’ race and gender (model 3), the between student variance decreased by causes
the between-student effect to decrease by 48% i.e. from 0.78 to 0.37. Similarly,
variability attributed to teacher factors decreased by 35%. .

Coefﬁcient estimates of models 3 and 4 are relatively similar in both magnitude
and statistical signiﬁcance. Consequently, only those of model 4, the better ﬁtting model,
are discussed because similar inferences would apply to those of model 3. The results
show that reading scores on student report cards differ signiﬁcantly by race and by
gender. Speciﬁcally, the results show that White female students outperform all other
categories of students. Their z-score is 0.52 (0.82-0.30)6 compared to 0.28 for White
male, 0.02 for ‘Other’ female, -0.04 for ‘Other’ male, -0.3 for Aﬁican American female,
and -0.54 for African American male students. Hispanic students’ reading scores were
not statistically different ﬁ'om those of their Aﬁican American counterparts. Clearly,
regardless of race, female students outperform their male counterparts. It is encouraging
to note that decreased conﬂictual relationships between teachers and students were

accompanied by increased reading achievement, 7400 = -0.08, p<0.01. Even so, an

increase in student misbehavior was positively related to deereased achievement in

reading, = -0.02, p<0.001.

7300

 

6 African American female students are the reference group.
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4.5 Math achievement in ITBS or SAT9 tests

Models 1, 2, 3, 4 and 5 in tables 4.8(a), 4.8(b) and 4.8(c) give the estimates of the
ﬁxed effects and variance components and correlation coefﬁcients for math achievement
in ITBS or SAT9 tests. Similar to the models discussed above, models 1 and 2 are the
unconditional means and unconditional growth models, respectively. Models 3, 4, and 5
all have a time variable as well as race as predictors. In addition, model 3 has a
behavioral symptoms index as a predictor while model 4 has teacher-conﬂict instead;
model 5 has teacher-child closeness.

Based on the likelihood ratio tests and the information criteria of AIC and BIC,
model 3 best ﬁts the data and is therefore preferred over models 1, 2, 4 and 5.Even
though the teacher-child conﬂict variable in model 4 is statistically signiﬁcant, the model
has a slightly worse ﬁt than model 3. Furthermore, when the behavioral symptoms index
was included as an additional predictor, the AIC and BIC values increased.
Consequently, the ﬁnal results discussed in this analysis are for model 3. It is noteworthy
however, that the parameter estimates in both models are relatively similar in magnitude
and statistical signiﬁcance. Level 1 and level 2 model equations are similarly expressed
as outlined by equations 4.7 and 4.8. Similar to equation 4.9, the combined model

equation for the ﬁnal model is expressed thus:

66

ITBS/SAT math achievement. Growth K-3fallijk ) + 7200 (Growth 3sprrng-5ijk)

jk =7000+7100(

BSlrjk ) + 7010 (Whitej ) + 7020 [Hispanic]. )+ 7030 (Otherj)

. . t _
+7110(Whitej)*(Growth K- 3fall. rjk ) + 7120 (Hrspamcjj (Growth K 3fallijk)
o . . -
+y130 {Other}. )* (Growth K- 3fall. zjk ) + 7210 (Whitej) (Growth 3sprmg 51.1%)

t ' _
+7220 [Hispanic]. )* (Growth 3spring- -5. jk ) + 7230 (Otherj) (Growth 3sprrng 51.1%)

+u00j+10.(Growth K- 3fall. 11W) u20j (Growth 3spring-5ijk)+v v00k+ eijk ..................... (4.11)
where
7000 is mean ITBS/SAT math achievement in the fall of third grade of an African

American student with behavior misconduct;

7100 is the average growth rate in ITBS/SAT math achievement during K-3 fall;

7200 is the average growth rate in ITBS/SAT math achievement during 3fall-5;

7300 is the rate of change in ITBS/SAT math achievement due to behavior;

7010 is the difference in third grade fall between Aﬁican American and White students;

7020 is the difference in third grade fall between Aﬁican American and Hispanic

students;

7030 is the difference in third grade fall between Aﬁican American and Other students;

67

7110 is the difference in growth rate during K-3fall between Aﬁican American and

White students;

7120 is the difference in growth rate during K-3fall between Aﬁican American and

Hispanic students;

7130 is the difference in growth rate during K-3fall between Aﬁican American and

Other students;

7210 is the difference in growth rate during 3fall-5 between Aﬁican American and

White students;

7220 is the difference in growth rate during 3fall-5 between Aﬁican American and

Hispanic students;

7230 is the difference in growth rate during 3fall-5 between Aﬁican American and

Other students;

u is the random effect associated with child j on ITBS/SAT math achievement in

00j

fall of third grade, assumed normally distributed with mean 0 and variance Tu ;
00

ul 0j is the is the random effect associated with child j on ITBS/SAT math growth rate

during K-3fall, assumed normally distributed with mean 0 and variance Tu ;
10

u20j is the random effect associated with child j on ITBS/SAT math growth rate

during 3fall-5, assumed normally distributed with mean 0 and variance ru ;
20

68

VOOk is the cumulative random teachers’ effect on a student’s ITBS/SAT math growth

trajectory, assumed normally distributed with mean 0 and variance 1v ;
00

eijk is the within student random effect assumed normally distributed with mean 0 and

variance 02 .

The results show that at the fall of third grade, mean math scores in ITBS or

SAT9 tests were statistically different from zero ( 7000= -0.28, p<0.001), with signiﬁcant

differences associated with race. African American students’ mean score was lower
compared to White and ‘Other’ students, although their performance was not
signiﬁcantly different from that of Hispanic students. During K-3fall period, students’
performance improved considerably with variations observed by race. During the 3fall-5
period, students’ learning rates declined, varying by race. In particular, White students

exhibited faster learning rates (y1 10 = 0.15, p<0.001) during the early years of schooling
(K-3fall) but lower rates (7210 = -0.l9, p<0.001) in later years (3fall-5) relative to

African American students. Overall, elevated behavioral problems among students were
accompanied by a decrease in math performance, even though the decrease was relatively

small (7300: -0.01).

After controlling for student variables, the results show that teacher-student
closeness, teacher-student conﬂict and teacher support had no signiﬁcant effect on
students’ ITBS or SAT9 math achievement. Also, none of the interactions between

student variables (i.e. gender and race) and teacher factors (i.e. support, conﬂict, and

69

closeness) were statistically signiﬁcant. Consequently, they were dropped ﬁom the
models.

By including time and BSI as predictors, 65% of variability in math achievement
initially attributed to within-student factors, and 17% to teacher factors, were explained.
There was a high positive correlation between performance at fall of third grade and
growth rate during the K— fall of third grade period (r = 0.85), suggesting that students
with faster growing rates in the early grades attained higher levels of achievement by the
fall of third grade. Again, this trend was reversed during the fall of third to ﬁfth grade

period, resulting in a negative correlation with the third grade fall (r = -0.77).

70

 

 

 

 

 

 

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4.6 Student report card math achievement

Table 4.9 shows the estimates of the ﬁxed effects and variance components for
math achievement as reported in student report cards. Based on the likelihood ratio tests and
the information criteria of AIC and BIC, model 3 best ﬁts the data and is therefore
preferred over models 1, and 2. While the level 1 and level 2 model equations are similar to

equations 4.7 and 4.8., the combined equation for the model is as follows:

Report card math achrevementijk = 7000 + 7100 (Growth K-3fallij k )

+7200 (Growth 3sprmg-5ijk ) + 7300 (88117]:ij 7400 (Suppﬂijk ) + 7010(Wh1tej)
. o * . -
+y020 {Hispanic}. ) + 7030 {Other}. ) + 1100}. + u20j (Growth 3spnng 51.11:)

+v00k + eijk ................................................................................................................ (4.12)

where

7000 is mean report card math achievement in the fall of third grade of an Aﬁ'ican

American student with behavior misconduct;

y“ 00 is the average growth rate in report card math achievement during K-3fall;
7200 is the average growth rate in report card math achievement during 3fall-5;
7300 is the rate of change in report card math achievement due to behavior;

7400 is the rate of change in report card math achievement due to teacher support;

7010 is the difference in third grade fall between African American and White students;

74

yOZO is the difference in third grade fall between Aﬁican American and Hispanic

students;

7030 is the difference in third grade fall between African American and Other students;

u is the random effect associated with child j on report card math achievement,

OOj

assumed normally distributed with mean 0 and variance ru ;
00

u20j is the random effect associated with child j on math growth rate during 3fall-5

period, assumed normally distributed with mean 0 and variance Tu ;
20

v0O k is the cumulative random teachers’ effect on a student’s report card math growth

trajectory, assumed normally distributed with mean 0 and variance rv ;

’ 00
eij k is the within student random effect assumed normally distributed with mean 0 and
variance 02.

Model 1 appears to have underestimated the average math achievement of

students, 7000= 0.35 relative to model 3, 7000: 1.12. The results in model 3 show that

there were signiﬁcant mean differences in math achievement associated with students’
race. White and ‘Other’ students had higher scores than Aﬁican American students but
there were no signiﬁcant differences in performance between Aﬁican American and
Hispanic students. This is the same order in performance evident in the standardized math

achievement.

75

There were notable declines in students’ learning rates during K—3fall (7100 = -

0.05, p<0.001) and fall of third and ﬁfth grade, 7200 = -O.24, p<0.001. And, after taking

into account growth rates and third grade fall, there were signiﬁcant, albeit small, positive
inﬂuences of teacher support while student behavioral conduct had a negative inﬂuence
on report card math performance.

As predictors, time, BSI and teacher support explained considerable variance in
students’ report card math achievement. Time alone explained 21% of variance initially
attributed to within-student factors i.e. the difference between models 1 and 2. By
including BSI and teacher support (model 3), an additional 7%, 47%, and 18% of initial

within student, between student teacher variance was explained.

76

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4.7 School satisfaction

Models 1, 2, and 3 in tables 4.10(a) and 4.10(b) give the ﬁxed effects,
variance components estimates and correlation coefﬁcients for students’ overall
satisfaction with school. Based on the likelihood ratio tests and the information criteria of
AIC and BIC, model 3 best ﬁts the data and is therefore preferred over models 1, and 2.

Level 1 and level 2 model equations are similar to equations 4.7 and 4.8. The combined equation

for model 3 is as follows:

School satisfaction ..

y k = 7000 + 7100 (Growth K-3fally.k ) + 7200 (Growth 33pr1ng-5ijk)

* -
+7300 (Supportijk ) + uOOj + u1 Oj (Growth K 3fallijk ) +

I! ' _ *
u20j (Growth 3sprmg Sijk ) + u30j (Supportﬁk ) + VOOk + eijk ......................... (4.13)

where

7000 is mean school satisfaction in the fall of third grade of an Aﬁican American

student with behavior misconduct;

7100 is the average growth rate in school satisfaction during K-3fall;

7200 is the average growth rate in school satisfaction during 3fall-5;
is the rate of change in school satisfaction due to behavior;

7300

7300 is the rate of change in school satisfaction due to teacher support;

79

u is the random effect associated with child j on school satisfaction, assumed

001'

normally distributed with mean 0 and variance Tu ;
00

u1 Oj is the random effect associated with child j on school satisfaction growth rate

during K-3fall period, assumed normally distributed with mean 0 and variance tu ;
10

u is the random effect associated with child j on school satisfaction growth rate

20j

during 3fall-5 period, assumed normally distributed with mean 0 and variance ru ;
20

. is the random effect associated with child j on school satisfaction growth rate due

“30,

to teacher support, assumed normally distributed with mean 0 and variance tu ;
30

v0 0 k is the cumulative random teachers’ effect on a student’s school satisfaction growth

trajectory, assumed normally distributed with mean 0 and variance tv ;
00

eij k is the within student random effect assumed normally distributed with mean 0 and

variance 02 .

The results show that students’ mean school satisfaction is not signiﬁcantly
different ﬁom zero. Also, there was no evidence of signiﬁcant change in school

satisfaction during the early years of schooling (7100 = 0.02, p>0.05). However, later

years were characterized with a signiﬁcant, albeit small, decline in school satisfaction,

7200 = -o.09, p<0.05.

80

School satisfaction does not vary with race or gender of student, nor the
interaction of student variables (race and gender) and teacher variables (conﬂict,
closeness and support). Also, students’ behavior did not inﬂuence it. The main factor that
seems to be inﬂuential is teacher support. That is, the greater the level of teacher support,

the greater the level of school satisfaction, holding all other things constant, 7300 = -0.3 8,

p<0.00 1 .

By including time and teacher support as predictors considerable variance in
school satisfaction initially attributed to within student, between student, and teacher
factors was explained. Model 3 resulted in the explanation of an additional 21% within
student variance, 16% between student variance, and 67% teacher variance. Although
growth rate during K-3fall was not statistically signiﬁcant, signiﬁcant variance

components (ru = 0.40, p<0.001 and Tu = 0.03, p<0.05) suggest that individual
00 10

student growth trajectories vary. In addition, students’ growth trajectories are different
during later years of schooling, as well as due to varying levels of teacher support.
Correlation coefﬁcients in table 4.8(b) indicate a moderate to strong positive
correlation between third grade fall and growth rate during K-3fall period, r = 0.75. This
means that students with faster growth rates during K-3fall period attained higher levels
of school satisfaction by the fall of third grade compared to their counterparts. However,
higher levels of school satisfaction at the fall of third grade were moderately associated
with declining growth rates during fall-5 period, r = 0.60. While increased teacher
support was positively (albeit small correlation coefﬁcients) related to high levels of

school satisfaction at third grade fall (r = 0.27), and improvement in school satisfaction

81

during K-3fall period (r = 0.28), it was associated with a decline in satisfaction growth

rated during 3fall-5 period.

82

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84

4.8 Classroom adjustment

Models 1, 2, 3, 4 and 5 in tables 4.11(a) and 4.1 1(b) show the ﬁxed effects and
variance component estimates on modeling students’ classroom adjustment. Of the ﬁve,
models 4 and 5 ﬁt the data equally well, based on likelihood ratio tests and information
criteria of AIC and BIC statistics. However, slightly more variability in classroom
adjustment is explained in model 4 although there are no substantive differences in the
magnitudes of parameter estimates as well as their statistical signiﬁcance. Nonetheless,
the results ﬁom model 3 are used in the discussion that follows, since it ﬁts the data
better.

Level 1 and level 2 equations for modeling classroom adjustment are expressed as
outlined by equations 4.7 and 4.8. Similar to equation 4.9, the combined equation for the

ﬁnal model is expressed as follows:

Classroom adjustment Growth K-3fall . )+ 7200 (Growth BSpﬁng-Sijk)

ijk=7000+7100( yk

+7300 (BSIz'jk J + 7010 {Male}. ) + 7020 (Whitej J + 7030 [Hispanic]. ) + 7040 (Otherj)

 

 

+1.00]. +v00k +eijk ................... - -- ..................................... (4.14)

where

7000 is mean classroom adjustment score in the fall of third grade of an Aﬁ'ican

American female student with behavior misconduct;

7100 is the average growth rate classroom adjustment during K-3 fall;

7200 is the average growth rate in classroom adjustment during 3fall-5;

85

7300 is the rate of change in classroom adjustment due to behavior;

7010 is the difference in third grade fall between male and female students;

y020 is the difference in third grade fall between African American and White students;

7030 is the difference in third grade fall between African American and Hispanic

students;

7040 is the difference in third grade fall between Aﬁican American and Other students;

u is the random effect associated with child j on classroom adjustment, assumed

OOj

normally distributed with mean 0 and variance tu ;
00

vOOk is the cumulative random teachers’ effect on a student’s classroom adjustment

growth trajectory, assumed normally distributed with mean 0 and variance rv ;
00

eij k is the within student random effect assumed normally distributed with mean 0 and

variance 0' 2 .

The results show that mean classroom adjustment scores at the fall of third grade
were signiﬁcantly different ﬁ'om zero, and that there were signiﬁcant differences due to
student race and gender. Compared to Aﬁ'ican American students, White and Other
students had considerably higher average scores of classroom adjustment. There were no
signiﬁcant differences in adjustment between African American and Hispanic students.

The results also show that in general male students have higher classroom adjustment

scores than their female counterparts, y010=1.28, p<0.01.

86

By adding time, student race, student gender and student behavior as predictors of
classroom adjustment (model 3), there were notable decreases in the model variance
components. While within student variance decreased by 19%, between student variance

decreased by 65%, and teacher variance decreased by 17%.

87

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89

 

 

 

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CHAPTER FIVE

DISCUSSION AND CONCLUSION

5.1 Introduction

This chapter synthesizes the study’s ﬁndings in light of existing literature,
discusses its limitations and gives implications for practice and suggestions for possible
future research. The discussion is organized broadly under the performance measures
topics of academic achievement on one hand and classroom room adjustment and school
adjustment on the other. These topics are covered in Section 5.2 and 5.3, respectively,
while Section 5.4 highlights the limitations of the study and Section 5.5 presents

suggestions for future research.

5.2 Academic achievement

{Students’ academic achievement was inﬂuenced by both student factors and
teacher factors. For reading/language and mathematics, irrespective of whether it was
standardized (ITBS/SAT9) testing or report card scores, student’s race was an important
predictor of performance. This ﬁnding is in line with what other researchers have found
(Cheadle, 2005; Irvine, 1986; Newell, 2007; Perez-Johnson, 2008; Riordan, 2002;
Rippeyoung, 2006). By the fall of third grade, African American and Hispanic students
performed equivalently in reading/language and mathematics. However, White and Other
students consistently outperformed Aﬁ'ican American students in both subjects. Other

students were primarily of Asian American descent. Existing research suggests that most

90

Asian American parents, relative to other races, instill in their children the traditional
ethic of hard work and a clear sense of the association between success and hard work
(Begum, 2007; Cheadle, 2005; Kim, 2008; Sy, 2002). It is possible then that these
children come to class more prepared and employ themselves in their work more than
students of other races. Consequently, such disposition to academic work results in high
academic achievement. The attaimnent gap between White and Aﬁican American
students is one that has received considerable attention. Several researchers have
suggested possible reasons for these differences. Some explanations put forth for the
differences include differences in family structure and socio-economic status (Brooks-
Gunn & Duncan, 1997; Mayer, 1997), differential teacher’s perceptions and! or racial
bias in testing (Delpit, 1995; Ferguson, 1998), and differences in socialization, culture or
behavior (Fordham & Ogbu, 1986). Any of these reasons are plausible explanations for
the achievement gaps in this study.

Student gender proved'an inﬂuential factor only for report card reading/language
attainment at the fall of third grade. Female students performed signiﬁcantly better than
their male counterparts. Some researchers have suggested that this is the case because
oﬁen times boys have tended to learn to read at an older age than girls. Also, boys have
been thought to take longer to learn, with greater difﬁculties in comprehending narrative
texts (Simpson, 1996; Smith & Wilhelm, 2002).

Over time, students’ academic growth trajectories were varied. In general,
students’ performance improved during the early years of schooling (K-3 fall) but
declined during the later years, i.e. 3fall-5 period. From the ITBS/SAT results in

reading/language and mathematics, students’ rates of improvement varied by race during

91

K-3fall period. Although all students exhibited an overall improvement in learning, the
rates for White students were signiﬁcantly higher than those of African American
students. This is possibly due to the oft advanced notion that the mainstream culture in
schools is very similar to what most White students are exposed to at home and quite
different ﬁom the live experiences of most African American students (Delpit, 1995;
Kohl, 1994; Ogbu, 1983).

During the 3fall-5 period, there was a general decline in the students’ growth
trajectories in both reading/language and mathematics. Although there were no racial
differences on report card scores, there were signiﬁcant ones in standardized
reading/language and math scores. In both subjects, the decline for White students was
much higher than that of Aﬁ'ican American students. A possible explanation for the
decreased performance is that during this period, possibly the fourth-grade slump in
reading may have occurred (Chall, October, 1988; Chall & Jacobs, Spring, 2003). The
reading slump is premised on the change in academic language needed for reading grade-
level content material. From around fourth grade, there is a shift in reading ﬁom learning
to read to reading to learn often characterized by more extensive vocabulary and heavier
content load (Coles, October 23, 2007). As such, this shift oﬁen leads to decreased
performance since most students are unprepared for the cognitive demands of the work.
Another possible explanation for such a decline is that, during third to ﬁfth grade,
children are becoming older and beginning to have behavioral problems that have a
negative impact on their learning.

Teacher-student relationships and teacher support had small effects on students’

performance. None of them explained academic attainment in standardized

92

reading/language or mathematics. However, decreased conﬂictual relationships with
teachers led to increased performance in report card reading achievement, while
increased teacher support was linked to increased report card math attainment. This is not
surprising. It is in agreement with what other researchers have found, i.e. that students
who get support ﬁom their teachers perform better than those that do not (Baker, 1999;
Hughes, Cavell, & Willson, 2001; Meehan, Hughes, & Cavell, 2003). Also, students with
high levels of behavioral misconduct tended to perform poorly. Again, this is not out of
the norm. Conventional wisdom would lead to the conclusion that children who exhibit
disruptive behavior and are socially maladjusted often have a difficult time beneﬁtting
from instructional processes. This then results in poor student outcomes, and in this case,

decreased achievement in reading/language and mathematics.

5.3 Classroom adjustment and school satisfaction

The results show that there were signiﬁcant differences in classroom adjustment
among students of different races and gender, at the fall of third grade. Overall, White
and Other students had higher classroom adjustment scores relative to their African
American counterparts. Also, male students had higher classroom adjustment scores than
their female counterparts. Over time, levels of adjustment increased. This suggests that
the longer students spent time in school, the better adjusted they became with classroom
routines. It was surprising though that teacher support, teacher-student closeness or
teacher-student conﬂict did not impact student’s sense of adjustment. This is especially
so given that some studies have found these relationships signiﬁcant (Pianta, Steinberg,

& Rollins, 1995; Van den Oord & Van Rossem, 2002).

93

From the results there were no signiﬁcant differences in school satisfaction
among the students. Also, unlike in reading and math achievement or classroom
adjustment, school satisfaction does not vary with race or gender of the students. The
main factor that seems to inﬂuence school satisfaction is teacher support. That is, the
greater the level of teacher support, the greater the level of school satisfaction, holding all
other things constant. This ﬁnding is logical. Because students’ main interaction with
school is with their teachers, if they feel well supported by these teachers then they can
be expected to be generally content with their school experiences and consequently report
that they are satisﬁed. Although students’ satisfaction increased during K-3 fall period, it
signiﬁcantly declined during 3fall-5 period. The decline is possibly due to the fact that as
students mature into their adolescence, they face newer challenges that may cause them
to be disgruntled with school. For instance, increased peer pressure and need for peer and
adult acceptance are heightened (Hughes & Kwok, 2006; Kohl, 1994). Along with these,
students experience increased isolation and feelings of inadequacy (Kohl, 1994). Taken

together, these two situations would easily create an environment of dissatisfaction.

5.4 Limitations of the study

This study had some limitations. First, the measures used did not collect
information on student’s home/ family variables such as level of education of parents,
whether or not a child came from a single or two parent family background, level of
parental involvement, parenting practices and a child’s involvement in enrichment

activities in and out of the home environment. Among others, these factors have been

94

found to be important predictors and contributors to a child’s academic achievement and
social adjustment (Begum, 2007; Cheadle, 2005; Lareau, 2003).

Second, the student sample is a purposive sample; schools with large percentages
of racial minority students, large proportions of students on free or reduced lunch, and
low on-time and overall graduation rates. While this sample helps us study an important
population of students, inferences cannot be generalized to the population of students in
US schools.

Third, a majority of the students (56%) were of Aﬁican American descent
whereas teachers were primarily Caucasian (62%)7. Furthermore, 96% of the teachers
were female. Previous studies have suggested that the race and gender of a teacher vis-a-
vis that of the student is an important factor in explaining variability in student
performance (Irvine, 1986; Pigott & Cowen, 2000). This study was unable to test this
hypothesis.

Fourth, the study used data from teacher and student self-reports, with no data
ﬁ'om other sources, such as independent observers in the classrooms, to corroborate the
self-reported information. Self-reports are potentially susceptible to social desirability
response bias (Arnold & Feldman, 1981). In this case, teachers and/ or students may
have, for instance, overstated the quality of their relationships in order to present
themselves in favorable light. This begs the need for caution in interpreting the results.

Fifth, several studies have linked student performance to school factors besides
teachers. Characteristics such as school culture and climate, student-teacher ratios and
leadership styles of administrators have been found to inﬂuence student performance

(Baker et al., 2003; Danielsen, Samdal, Hetland, & Wold, 2009; Sweetland & Wayne,

 

7 Eighteen teachers (26.5%) did not indicate their race

95

2000; Tian & Gilman 2009). Additionally, these factors may inﬂuence the nature and
quality of teacher - student relationships, one of the foci of this study. Unfortunately, the
study did not collect data on such school variables and were therefore not included in the

analyses.

5.5 Implications for practice and future research

Teacher support and decreased conﬂictual relationships between teachers and
students was related to students’ academic performance. This ﬁnding has implications in
the practice of teaching and also in the preparation of student teachers for their
profession. Ideally, since teachers are the adults in schools, students look to them for
guidance, and oﬁen times view them as role models. Consequently, it is important that
they (teachers) are conscious of this power that they wield and use it in ways that are
beneﬁcial to their students. One such manner, in light of the study’s ﬁnding, would be for
the teachers to be aware of the nature of the relationships they have with their students
and be deliberate at cultivating positive, less conﬂictual and supportive relationships with
them. Several studies document that (most) teachers and student teachers care about their
students and their work, an aspect manifested in myriad ways. However, one way that
such ‘caring’ could be translated into meaningful and tangible outcomes would be for
teachers to actively and deliberately pursue positive relationships with their students thus
affecting students’ performance.

Results from this study showed differential learning rates in math and
reading/language achievement associated with student race. This ﬁnding of White-Black

achievement gap is not new, and has received considerable attention. However, further

96

research needs to be done to examine speciﬁcally the reasons for positive trajectories
during K-3fall period, which are followed by negative trajectories during 3fall-5 period.
Also, race and socio-economic status were confounded in this study, and thus it would be

worthwhile to situate a similar study in more economically diverse schools.

97

APPENDIX

Table 12

Illustration of data i. e. measurements nested in cross-classiﬁcation of teachers and students

 

Student 1:
Complete data

Student 2: Incomplete data,
dropped out

Student 3: Incomplete
data , matured

 

Measurement
occasion

I

23456

123456

 

Kindergarten
Teacher

X

X

 

First Grade
Teacher

 

Second Grade
Teacher

 

Third Grade
Teacher

 

Fourth Grade
Teacher

 

Fifth Grade
Teacher

 

 

 

 

 

Table 13

Sample questions ﬁom students’ survey, fourth and ﬁfth grade.

 

ﬁrn with us

 

Never Sometimes

We have worked together in my class to help
others who really need help like the homeless a b

Our teacher is always joking with us and having

I can talk to my classmates and teacher about
my family and my feelings

It is easy to make friends in my classroom, and
everyone seems to have ﬁiends

a b
a b
a b

Often Almost always

c d
c d
c d
c d

 

98

 

 

Table 14

Sample questions ﬁom Student- Teacher Relationship Scale.

 

 

Please reﬂect on the degree to which each of the following statements currently applies to
your relationship with this student. Please “bubble in” one mp0nse for each item on the
scanth sheet.

Deﬁnitely not Not Neutra Applies Deﬁnitely

really I somewhat does

I share an affectionate 1 2 3 4 5
relationship with this child
This child and I seem to l 2 3 4 5
frequently struggle with each
other
This child feels that I treat 1 2 3 4 5
him/her fairly
I often feel myself becoming 1 2 3 4 5
frustrated with this child
This child accepts help ﬁom 1 2 3 4 5
me when I offer it
It is easy to joke and have 1 2 3 4 5
fun with this child
Dealing with this child 1 2 3 4 5
drains my energy
Despite my best efforts, I am 1 2 3 4 5
uncomfortable with how this
child and l have gotten along
This child openly shares 1 2 3 4 5
his/her feelings and
experiences with me

 

 

99

Table 15

Sample questions ﬁ'om Behavior Assessment System for Children.

 

[Please mark every item. Ifyou don‘t know or are unsure, give your best estimate, based on your
bbservations. A "Never" response does not mean that a child "never" engages in the behavior,
only that you have not observed the child to behave that way. Ifyou wish to change an answer,
erase the ﬁrst answer completely, then mark your new answer. (N=Never, S=Sometimes,
O=Often, A=Always)

Bites nails

Stares blankly

 

Adjusts well to new teachers

Argues when denied own way

hives up easily when learning something new

Shows a lack of concern for others' feelings

Stays disappointed a long time if a favorite activity is cancelled

N S O A
N S O A
N S O A
N S O A
N S O A
N S O A
N S O A

 

 

 

 

 

 

 

 

 

 

1. ﬁ Yes Sometimes No
2. 9 Yes Sometimes No
3. ‘( Yes Sometimes No
:4. a, Yes Sometimes No
5. 3 Yes Sometimes No
. 6. ” Yes Sometimes No

 

 

............................................................ ‘
I

The kids in my class help each other.

Kids in my class laugh when I mess up.

I
------------------------------------------------------------ ‘
I

There are mean kids in my class.

Kids say “thank you” in my room.

My class is a really ﬁm place to be.

Figure 1. Sample questions from students’ survey, grades K-3.

100

 

Items 1—19 are scored as follows

1 Never

2 Not Usually
3 Sometimes
4 Often

5 Always

Academic achievement for this student is appropriate for age
This student is able to begin and complete classroom tasks

This student is alert and attentive to classroom proceedings
This attention span for this student is appropriate for age

This student completes his/her work on time

This student is eager and enthusiastic about classroom activities
This student enjoys schoolwork

This student follows directions

This student willingly participates in classroom activities

\OWQOtM-bUJNu—t

 

 

 

Figure 2. Sample items ﬁom the Teachable Pupil Survey.

 

 

Teachers are patient with students who progress slowly due to a disability or lack of discipline

Cooperative learning is routinely used to build character and social skills, and to promote
learning.

There is a free exchange of ideas and opinions among teachers.

Teachers are encouraged by fellow teachers to develop their knowledge and skills.
Teachers are friendly and affectionate toward students.

Students respectfully correct peers who are unfair, impatient, selﬁsh, destructive, or hurtful.

Teachers and counselors encourage students to think about and plan for their future.

 

Figure 3. Sample questions from Vessels School Climate Survey.

101

 

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