jiang he 200908 phd0717 - University of Georgia

EVALUATING SCHOOL-LEVEL AND STUDENT-LEVEL EFFECTS ON STUDENT

ACHIEVEMENT: EVIDENCE FROM THE EDUCATION LONGITUDINAL STUDY OF

2002

by

JIANG HE

(Under the Direction of Eric Houck)

ABSTRACT

This dissertation is grounded in the empirical and theoretical literature on student

achievement. Using the Education Longitudinal Study of 2002 (ELS:2002), this dissertation

sought to contribute to a better understanding of what factors explain the educational outcomes

in an education production function.

This dissertation aims to examine the relationship between educational expenditure and

student achievement, accounting for student, school, and family characteristics. Another aim of

this dissertation is to take a close look at students and their educational behaviors in relation to

achievement. This research model brings empirical evidence to test the effects of student

motivation and attitudes toward learning.

Findings indicate that student socioeconomic status and expectation and attitude about

learning are the three strongest factors positively related to student achievement. These effects

are significant on both the student and the school levels. Comparatively, school resource, teacher

quality, and school poverty variables do not show significant impact on learning outcomes. An

important finding derived from hierarchical linear modeling is that low performing students may

benefit greatly when they are in schools where expectation and attitude about learning are high.

These effects are typically strong for Black and Hispanic students.

INDEX WORDS: Student Achievement, Educational Expenditure, Student Motivation,

Education Production Function, Hierarchical Linear Modeling



2002

by

JIANG HE

B.S., Peking University, China, 2003

M.P.A., University of North Carolina at Pembroke, 2004

A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial

Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

ATHENS, GEORGIA

2009

© 2009

Jiang He

All Rights Reserved



2002

by

JIANG HE

Major Professor: Eric Houck

Committee: Sally Zepeda Catherine Sielke

Electronic Version Approved:

Maureen Grasso Dean of the Graduate School The University of Georgia August 2009

iv

ACKNOWLEDGEMENTS

I wish to extend my deep gratitude to my major professor, Dr. Eric Houck. His constant

support made this dissertation possible. I also want to thank Dr. Catherine Sielke, who critiqued

my thinking and writing while encouraging me to press on. I am thankful for Dr. Sally Zepeda’s

patience, unfailing support, and tremendous editing efforts. Her investment further helped to

improve the research.

This dissertation would never have been completed without the assistance from the

Lifelong Education, Administration, and Policy Department for providing secure office for my

data. I am also indebted to the National Center for Education Statistics for allowing me to use the

Education Longitudinal Study: 2002 to conduct my research.

I want to thank my mother and my mother-in-law for their unselfish help whenever we

needed the most. Their child support was a huge relieve on us so that we can focus on our

studies. A special thanks to my wife, Dr. Lei Cheng, who always stands by me from the

beginning to the end of my doctoral journal.

v

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ........................................................................................................... iv

LIST OF FIGURES ...................................................................................................................... vii

LIST OF TABLES ....................................................................................................................... viii

CHAPTER

1 INTRODUCTION .......................................................................................................... 1

Statement of the Problem ......................................................................................... 1

Definition of Key Terms .......................................................................................... 3

Conceptual Framework ............................................................................................ 4

Purposes of the Study ............................................................................................... 5

Research Questions .................................................................................................. 7

Methods .................................................................................................................... 8

Significance of the Study ....................................................................................... 10

2 REVIEW OF THE LITERATURE .............................................................................. 12

Overview ................................................................................................................ 12

Education Production Function .............................................................................. 12

Issues and Future Directions of Education Production Function ........................... 28

Student Learning Motivation Theories ................................................................... 32

Empirical Findings on Student Achievement.......................................................... 44

Other Factors Affecting Student Motivation ........................................................... 48

vi

3 DATA AND METHODS.................................................................................................. 55

Overview .................................................................................................................... 55

Data ............................................................................................................................ 55

Hierarchical Linear Modeling .................................................................................... 60

Methods ....................................................................................................................... 63

4 FINDINGS OF THE STUDY.......................................................................................... 68

Overview .................................................................................................................... 68

Data Description ......................................................................................................... 68

Factor Analysis ........................................................................................................... 70

Treating Missing Values ............................................................................................ 75

Variables..................................................................................................................... 81

Hierarchical Linear Modeling .................................................................................... 84

Summary of Findings ............................................................................................... 112

5 CONCLUSION............................................................................................................... 119

Review of Findings .................................................................................................. 119

Research Implications .............................................................................................. 124

Policy Implications ................................................................................................... 126

Data Limitations ....................................................................................................... 127

Future Steps .............................................................................................................. 128

vii

LIST OF FIGURES

Page

Figure 1. Conceptual Framework of Education Production Function ............................................ 5

Figure 2. Math and reading scores vs. Black plot with focus of mean expectation ...................... 91

Figure 3. NAEP scores vs. Hispanic Student plot with focus of mean expectation ..................... 98

Figure 4. Range of plausible values for math and reading test scores ........................................ 113

Figure 5. Range of plausible values for NAEP test scores ......................................................... 114

Figure 6. Range of plausible values for SAT scores ................................................................... 114

Figure 7. Range of plausible values for academic GPA ............................................................. 114

Figure 8. Percent of Variance in Achievement at Student and School Levels by Four Measures

..................................................................................................................................................... 117

viii

LIST OF TABLES

Page

Table 1. Research Findings on Educational Expenditure and Achievement ................................ 18

Table 2. Research Findings on Class Size and Achievement ....................................................... 24

Table 3. Selected Variable Description ........................................................................................ 58

Table 4. Summary of Variables and Factor Loadings matrix of FEXP ........................................ 72

Table 5. Summary of Variables and Factor Loadings matrix of FMOV ...................................... 73

Table 6. Summary of Variables and Factor Loadings matrix of FATD ....................................... 74

Table 7. Summary of Variables and Factor Loadings matrix of FPAR ........................................ 74

Table 8. Results of Bartlett's and Kaiser-Meyer-Olkin Tests ....................................................... 75

Table 9. Case Numbers of Factors ................................................................................................ 75

Table 10. Factor Analysis Missing Values Check (FEXP) ........................................................... 76

Table 11. Factor Analysis Missing Values Check (FMOV) ......................................................... 76

Table 12. Factor Analysis Missing Values Check (FATD) .......................................................... 77

Table 13. Factor Analysis Missing Values Check (FPAR) .......................................................... 77

Table 14. ANOVA test of Factors with and without Missing Values .......................................... 79

Table 15. Means, Standard Deviations, and Descriptions of Student-Level Variables ................ 82

Table 16. Means, Standard Deviations, and Descriptions of School-Level Variables ................. 83

Table 17. Results for Four Model (Standard Coefficient) on Student Math, Reading Test Score 92

Table 18. Results for Four Model Estimates (Standard Coefficient) on Student NAEP scores ... 99

Table 19. Results for Four Model Estimates (Standard Coefficient) on Student SAT Score ..... 105

Table 20. Results for Four Model Estimates (Standard Coefficient) on Academic GPA .......... 111

Table 21. Two-Level HLM Estimates (Standard Coefficient) over Four Outcome Measures ... 116

1

CHAPTER 1

INTRODUCTION

Statement of the Problem

The relationship between educational expenditure through tax dollars and student

academic achievement is not a new topic, and the results so far are mixed (Goldschmidt &

Eyermann, 1999). Theoretically, increasing educational expenditure should improve school

conditions, teacher salaries, student/teacher ratios, and educational facilities; thus, granting

students a better educational opportunity. Coleman et al. (1966) first adopted education

production functions to explain the relation between expenditure and achievement. They found

that educational resources have very little impact on student achievement in general, except for

the pupil/teacher ratios. Rather, family characteristics had a much greater influence on student

achievement. Hanushek (1989, 1994, 1996, 2003), through a serious of individual studies and

meta-analyses, concluded that public spending only slightly improved student performance.

Although this point-of-view faced challenges from other scholars (Hedges, Laine, & Greenwald,

1994; Hedges & Greenwald, 1996; Greenwald, Hedges, & Laine, 1996a, 1996b; Goldschmidt &

Eyermann, 1999), the field of education finance gained increased attention from both educational

researchers and practitioners (Rolle & Houck, 2004).

Further evidence has emerged from studies using state and local data which examines the

role of educational expenditures on student academic achievement (Marlow, 1999; Tobier,

2001). Education finance studies often lead to a unique situation in that the effects of money are

not quite the same on different demographic groups even within one particular region

(Rumberger & Palardy, 2005). However, blurred as the picture appears to be, expenditures in

general have not yet made an impressive impact, which drives scholars to ponder whether things

2

are left out of the theoretical framework or whether money falls to the right spot, such as teacher

salary or school facilities.

The dissertation develops a new model accounting for student behaviors on learning (i.e.,

motivation, attitude, and expectation). Several researchers have laid the ground work of how

motivation toward learning works for students. Lareau (2003) and her research team observed

different patterns from the children of various social classes and racial groups. The key finding

was that self-entitlement, such as the pursuits of individual preference, helped student learn

better. Sirin’s meta-analysis (2005) implied that, learning motivation of students influenced by

parental education level and family structure, leads to high academic achievement; however, the

relationship was not very strong. Rothstein (2000) argued that students were affected by the

educational institution, which was eventually affected by students themselves. This loop

emphasized the importance of peer effect and how students perceived themselves and each other.

In explaining how motivation relates with achievement from students of different racial

background, a similar idea raised by Ogbu (2004) suggested that the lack of achievement from

Black students was caused by the burden of “acting White.” Black students “lacked the

motivation to study hard in order not to be viewed by their peers” as “acting White.” Mickelson

(1990) also observed the education achievement disparities between White students and Black

students controlling for other factors. The survey findings suggested that Black students had a

dual-value system. What every student in general believed was that education was a good way to

a better life and it should provide a vital opportunity to everyone for success. But this “abstract

attitude” or “external attitude” conflicted with the real world obstacles that Black students face

and truly believe, namely the “concrete attitude” or “internal attitude.” Further, Mickelson

3

(1990) found that the concrete attitude contributed more than the abstract attitude with regard to

student academic achievement.

Few have investigated how educational resources affect student groups characterized by

attitudes toward learning. Controlling for race, gender, and other demographic information, the

author believes that student attitude may endogenously affect academic achievement more than

other exogenous factors such as teacher quality, class size, and school characteristics. This is

important, in particular, because the education psychology literature has proved that student

motivation and other behavioral factors significantly affect student achievement (Duncan,

Featherman, & Duncan, 1972; Hanson, 1994). Incorporating these motivational factors into the

education production function and testing it will lead to the answer of the classic question: what

matters the most to student achievement? The author hopes this dissertation can help to develop

a new line of inquiry in the field of school finance indicating how educational resources make

the most sense to the most students according to their learning attitudes.

Definition of Key Terms

The following terms are used in this dissertation. This section provides the explanations

of these terms.

Education Production Function: A mathematical construct that models the relationship between a

given set of educational resource inputs and a set of educational outputs.

Input Variables: Variables or factors that are potentially impacting education process that

ultimately impacting educational outputs.

Output Variables: Variables or measurements that are the outcome of the education process.

Teacher Quality: A term capturing teachers’ characteristics based primarily on teacher education

and experience (Grubb, 2008).

4

Student/teacher Ratio: The number of students divided by the number of certified FTE staff in

one educational unit.

Student Achievement: High school standardized tests, NAEP equalized tests, high school

academic GPA, SAT scores.

Conceptual Framework

The conceptual model guiding this study draws from literature on education production

functions. The input measurements of the function are on the left side of the Figure 1. On the

right side, there are output variables such as high school grade point average (GPA), Scholastic

Aptitude Test (SAT), and math and reading test score.

In this model, student-level independent variables such as gender, race, and

socioeconomic status (SES) will be examined. School-level characteristics such as teacher

quality, student/teacher ratio, school type, and percent minority will also be examined. Student

attitude and motivational factors will be created through factor analysis on a number of

independent variables taken from Education Longitudinal Study of 2002 (ELS:2002) dataset.

These factors will be applied to both student-level and school-level in the hierarchical linear

modeling analysis.

Figure 1. Conceptual Framework of Education Production Function

Education, with its complex structure and high stakes, is always

researchers. The U.S. public education system has drawn more and more attention from

educators, school administrators, and politicians over the last

that education generally prepares human capital in various

(Becker, 1992). Abundant education

advantages for the potential employees

5

. Conceptual Framework of Education Production Function

Purposes of the Study

Education, with its complex structure and high stakes, is always attractive


educators, school administrators, and politicians over the last few decades. First, it is recognized

that education generally prepares human capital in various sectors of the macro economy

educational experience and an advanced degree generate comparative

potential employees entering the labor market. According to the

attractive to policy


, it is recognized

macro economy

advanced degree generate comparative

ccording to the Digest of

6

Education Statistics, men with bachelor degrees earn $24,230 more annually than men with high

school degrees; women with college degrees earn $18,530 more annually than women with high

school degrees; and the earning gaps have increased steadily since 1990 (Snyder, Dillow, &

Hoffman, 2009). Therefore, it is important to understand theoretically and empirically what the

gaps represent in the education process, especially in the early stages of education.

Secondly, public education is funded largely by tax revenues at state, local, and federal

levels. Many taxpayers, if not all, expect that their money is spent effectively on education. Thus,

not only students and parents, but also the general public, has reason to care about public

education. It is in the interest of the majority to make sure that students learn from certain

educational programs and interventions funded by taxpayers. This dissertation, in its unique way,

examines a national sample of students, teachers, parents, and school administrators to identify

what factors work best to improve student achievement, and under what condition(s), either

institutional or individual, that affects these factors.

The current focus of educational reform is on school accountability and student

achievement as the No Child Left Behind ACT1 progresses along. It is reasonable to believe that

external incentive or sanction stimulates teachers to teach close to the tested curriculum and that

students learn about the materials that are being tested. One issue with this type of schooling is

that students tend to ignore other useful elements of learning such as social cohesion and other

progressive perspectives of education. On the other hand, one alternative to this external reform

model is internal motivation of student learning. The hypotheses being tested in this dissertation

include three student behavioral constructs, specifically, locus of control (Rotter, 1966),

motivation (Pintrich & Schunk, 2002), and self-concept and self-esteem (Rosenberg, 1986).

1 ED.gov at http://www.ed.gov/policy/elsec/guid/states/index.html, accessed on 2009/03/26

7

Theoretically, these variables all show positive correlations with student achievement. However,

very few studies have included all three constructs and fewer are in the realm of education

production function. This dissertation adds to this research area by using sophisticated research

methods and examining large-scale dataset in the analysis.

A recent development in the field of education finance is that educational researchers

noticed a primary objection with education production function, which is a single variable or few

variables research design (Carpenter, 2000; Ilon & Normore, 2006; Odden, Borman, &

Fermanich, 2004). Contemporary education research tends to study student achievement based

on student, classroom, or school variables in isolation from other important factors. Such

research from the field of education finance generates critical findings. For example, Lee and

Smith (1997) investigated the NELS:88 dataset using Hierarchical Linear Modeling (HLM)

methods to find that students achieve the maximum test score gains at schools enrolling between

600 and 900 students. Glass and Smith (1979) undertook an extensive meta-analysis of class-size

research and identified non-linear effect of class size of 20 students is the tipping point for this

class size effect. Coleman et al. (1966) concluded that family characteristics of students are most

influential to student achievement. Most of the existing research paid attention to control

variables to identify the key variables that have effects on student learning; however, research

rarely covered the whole picture of educational processes. This dissertation advances research

through multiple level analysis that takes consideration of individual student factors and teacher

and school factors. Moreover, each level of analysis consists of a host of variables and factors

generated from factor analysis.

Research Questions

Specifically, this dissertation attempts to address the following research questions:

8

1. In the realm of education production function, what factors affect student academic

achievement the most?

2. Specifically, how do the motivation and attitude affect student academic

achievement?

3. Do these factors have the same effect at the student level and the school level?

4. What portion of variance do factors from each of the two level of analysis explain?

Methods

The analysis was built on data from the ELS:2002. To obtain key school resource

variables, this dissertation acquired the restricted data license which contained certain variables

that are linked from the F-33 Common Core of Data to the ELS dataset. Since ELS:2002

includes both the individual student information, and aggregate level information from teachers

and schools, this type of dataset was ideal for multi-level modeling.

ELS:2002 is on-going, and is also the fourth longitudinal study conducted by the NCES

Longitudinal Studies Program. The first three waves of surveys were finished by 2006. Base-

year data collection for the study was in 2002, with approximately 20,000 10th grade students

selected from 750 public and private high schools. Policy issues to be studied through ELS:2002

include the identification of school attributes associated with achievement; the influence of

parent and community involvement on student achievement; and the transition of different racial-

ethnic, gender, and socioeconomic groups from high school to postsecondary institutions and the

labor market (Bozick & Lauff, 2007).

Math and reading test score composites from the base year study is included in this

dissertation analysis, specifically, high school standardized tests. Each of the next two follow-up

studies had special contributions as well, especially for the student achievement measurement.

9

The first ELS follow-up study was conducted in 2004, when high school transcripts were

collected. The second follow-up study, which was administrated in 2006, contains college

enrollment information of the same cohort in 2002. The ELS:2002 datasets allow a number of

input and output measures which are used in the education production functions for this

dissertation. Coming from the two follow-up studies, high school GPA, dropout information,

SAT scores, ACT scores, and college enrolment information are also used as output

measurements.

Compared with other datasets, ELS:2002 had apparent advantages for this dissertation.

First, ELS:2002 is relatively new to the research arena, in both the time of data release, and the

infrequent usage. A search through academic databases revealed that over 10,000 publications

were written from previous NCES studies. For example, the NELS series, ELS:2002, is seldom

seen in the academic fields. Secondly, as the NCES longitudinal studies get more sophisticated in

data collection, many of the sampling issues were taken into consideration when the datasets are

released to researchers. Thirdly, the large-scale dataset yields tremendous statistical power to the

analysis.

The common trend of existing research holds educational expenditure variables as

exogenous factors that exert influences from outside of the student learning process. However,

synthesizing literature from education theories of public spending, this study sought to add

critical endogenous factors such as student attitude toward class and school, and self-esteem

effects into the education production function.

These factors exert influences from inside of the student learning process. Adopting

appropriate statistical techniques with the ELS dataset, the author believes that the empirical

results should support the hypotheses this dissertation raises. The new research direction is to

10

add the peer effect, student attitude factors, as well as the public expenditures into the traditional

model to predict student academic achievement. With feasible data, the new model will illustrate

how the educational expenditure has the desirable effect on student academic achievement.

The dependent variables are standardized test composite scores in reading and math,

NAEP equalized test scores, student SAT scores, and student academic GPA. These variables

also take into consideration the weight variables representing the national sample. The

explanatory variables include gender, race, socioeconomic status composites, attitudes about

oneself, future educational expectation, teacher experience, teacher credentials, school level

spending, poverty, school size, school type. The motivation and attitude variables are reduced to

a small number of factors by factor analysis.

Based on the nested nature of the education process, where students are grouped in

classrooms, and classrooms are grouped in schools, HLM analysis is most appropriate. This

research will run the HLM analysis on student and school level.

Significance of the Study

The essential contribution of this dissertation to policy makers is to refresh the focus of

educational expenditures. This research may indicate new directions for effective school

spending that improves student academic achievement. In addition, the new theoretical

framework sorts out other influencing factors related to educational investment. Furthermore, the

application of HLM onto the ELS:2002 dataset examines the issue from both the individual and

institutional perspectives. The large dataset and sophisticated quantitative research are among the

new directions for school finance (Plecki, 2006). This will provide scientific based evidence to

back the funding decisions for specific education spending and could be used to guide either

greater investment, or less investment, in some particular students' education. Specifically, this

11

dissertation points out different ways it could or would change people's perceptions about

education, since motivation is itself a factor that many see as beyond the immediate reach of

public policy.

Another implication from this research is that it helps to evaluate existing educational

policies. For example, in coping with the No Child Left Behind (NCLB) Act, many local

education authorities develop strategies to improve student academic achievement. Some of

these may involve extra spending that may be futile to the current system. Combined with both

attitude and monetary concerns, this research should inform policy makers about what

components a good policy should include.

In general, school curricula do not necessarily mandate teachers to motivate students to

learn, although many good teachers do so anyway. One of the implications for policy makers is

that educational expenditure could be spent on encouraging teachers to help students build a

positive attitude. Policy makers should take the results from this research to prioritize the usage

of educational expenditure. The public education system is all about making choices with limited

resources. Scientific based strategies are set to start policy-makers to observe from multiple

angles to the matter of education. Improving student attitudes, on the one hand, may improve

student achievement. On the other hand, it may accomplish the same end result at a lower cost,

compared with traditional spending patterns.

Building on this theoretical framework, the author believes that the fundamental question

lies within the social value of education. If the stakes for education are high enough, students and

parents should have higher motivation to seek better education opportunities and therefore push

for higher educational standards. The motivation to learn is a reflection of social value of

education that is definitely worth investing in the long run.

12

CHAPTER 2

REVIEW OF THE LITERATURE

Overview

This chapter reviews prior literature on various aspects of the education process related to

student achievement. First, this chapter introduces education production functions and the

applications over time. The next section summarizes specific issues that emerged when using

these functions. This chapter then turns to the work of student motivation theories before

synthesizing findings from prior studies. The last section discusses other important factors

affecting student motivation which also potentially affect student achievement.

Education Production Function

This section summarizes the field of education finance with a concentration on student

achievement. The focus of this literature is the education production function and its various

applications. The first section defines and describes education production function. The

following sections break down the literature by the key research area and common variables used

to conduct these studies.

Education is a complicated process because there are many people involved – students,

parents, teachers, school administrators, and educational policy makers. Each part of the process

has a certain amount of input to the outcome, which usually is measured in terms of student

academic achievement. Among all the inputs, there is money that pays for the education process

and covers the expenses from school where education of all forms occurs. Needless to say,

money is important, in both the amount and the way it is spent. Many educators and policy

makers study the dynamic of how to make the best use of every dollar on education, and others

13

focus on how the amount of money is distributed among different groups of students (Rolle &

Houck, 2004).

At school, students learn from teachers and interact with peers, but after school, students

spend a significant amount of time with their family members. Therefore, parents and family

characteristics can certainly shape students’ attitude toward the learning process. Many

researchers have been investigating the impact from various factors such as students’ family

characteristics, parents’ education background, family socioeconomic status (SES), school class

characteristics, and school characteristics on students’ academic achievements (Coleman et al.,

1966). Most of the outcome measures are characterized by test sores.

Such research studies are broadly viewed as education production function which

contains the input factors to predict the outcomes of education. The most often seen research

methods are regression analyses of various patterns. There is a long lasting investigation of the

relationship between educational inputs and output as illustrated in equation 2-1.

Equation 2-1 O → F (S, X, C) + V

O represents outputs of various forms. S, X, and C are inputs of school characteristics,

student characteristics, and community characteristics. Since equations are only proxies to the

real world, V captures other information as well as errors.

The outputs from education production function are student achievement. Test scores are

the commonly used measurement from many existing studies. Other researchers use graduation

rate, dropout rate, percentage of students going to college, or the passage of one particular exam

as output measurements (Rowan-Kenyon, 2007; Rumberger, 1995). Some studies targeting the

long term effects of education use average salaries in the workforce as outcome of prior

education. There are also abstract variables used to capture student achievement, such as the

14

cognitive ability measurement that is not always in the form of a test. Comparatively, the inputs

can be a series of different measures. The general categories for inputs in education production

function are student inputs, teacher inputs, and school inputs.

Student input variables may include innate student ability (intellectual quotient, academic

attitude, etc.), demographic information (race, gender, etc.), parental background (family living

patterns, parental education level, etc.), and the socioeconomic status (family income,

neighborhood information, etc.) of the student. Teacher input variables may include teachers’

degree and education, years of experience, teachers’ licensures, teachers’ professional

development, teachers’ classroom practices, and teachers’ salaries. School input variables may

include classroom size, school size, school type (public, private, catholic, or charter), school

leadership status, school expenditure, geographic location of the school, and wealth of the school

district. The teacher and school input variables can be aggregated to classroom or school level in

a multi-level environment.

Other important input variables that are directly related with student, teacher, and school

are also commonly seen in the education production function. Based on the specific research

agenda, these variables may be federal expenditure on education (such as Title-I funding), state

and local investment, or one particular policy implementation (such as the NCLB Act). No

matter what variables are in place, people seldom include all the input and output measurements

due to availability of information and time and resource considerations. The variables that are

directly related with the research questions are the explanatory variables, and the ones that are

important but not being studied directly are kept in the education production function as control

variables.

15

Educational Expenditure

Various scholars had studied the relationship between public education expenditure

through tax dollars and student academic achievement (Coleman et al., 1966; Hanushek, 1989,

1994, 1996, & Hedges & Greenwald, 1996). The results were mixed. Theoretically, increasing

education expenditure should improve the school condition, teacher salary, teacher/student ratio,

and educational facilities. Thus, the students can have a better environment to study. Coleman et

al. (1966) first used educational production function to explain the relationship between

expenditure and achievement. After surveying students from grades 1, 3, 6, 9, and 12, they

concluded that the resources had very little impact on student achievement in general, except that

the student-teacher ratio had negative significant effect.

Hanushek (1989) had long studied this issue and found little evidence to support public

spending enhanced student achievement. Based on Hanushek’s research, Hedges et al. (1994)

conducted a meta-analysis of education production function model and found positive

relationships between educational resources inputs and student outcomes, which started this

academic debate. Hanushek (1994) soon wrote a reply mentioning different viewpoints of his,

and he also pointed out some of the statistical errors that Hedges et al. (1994) had made. The

disagreement included that the quantity of educational expenditure did not matter much unless it

was spent efficiently. Hedges and Greenwald (1996) claimed that the vote-counting technique

used in Hanushek’s meta-analysis was not appropriate and their combined significance tests were

better.

Greenwald et al. (1996a) conducted a meta-analysis on the effect of school resources on

student achievement. They found a broad range of resources that are positively related to student

outcomes such as per-pupil expenditure, teacher ability, teacher salary, teacher/student ratio, and

16

class size. Hanushek (1996) published his article toward the same issue and directly pointed out

several statistical misinterpretations. He confirmed his previous finding that lack of resources is

not the largest problem facing schools and that more fundamental reforms are needed in schools.

Greenwald et al. (1996b) extended the debate with a rejoinder confirming the accuracy of their

former research.

In more recent years, Hanushek (2003) reviewed the U.S. and international evidence on

the effectiveness of educational policies and found that increased educational expenditures, and

that student achievement did not show significant improvement. In addition, he also mentioned

that the variation in teacher quality caused the variation in student performance. The common

problem with Hanushek’s work and his debaters are that aggregate measures for student

achievement and public expenditure seem plausible because the amount of unobserved

heterogeneity is hard to control (Goldschmidt & Eyermann, 1999).

On a separate level, Tobier (2001) conducted analysis on New York City’s public schools

and found that students are still underperforming despite the increased funds and personnel. The

author did point out the problem could be the way resources are spent, in particular, teacher

training should be a key factor in improving student achievement. By applying Oklahoma data

into the education production function, Jacques and Brorsen (2002) found that different

expenditure patterns have different impact on student test scores, but the most effective approach

is to target the spending toward classroom instruction.

Analyzing district level and student level data, Ferguson and Ladd (1996) investigated

Alabama schools using education production function and found that instructional spending had

a large effect on test scores. They also concluded the effect is non-linear, in that the most

17

significant effect accrued to districts where per-pupil instructional spending is the lowest, and no

effect to districts where instructional spending is above the median.

Other scholars have found that money hardly makes any difference or even makes the

matter worse. Marlow (1999) studied spending on public schools in California about school

structure and public education quality. He also found that the public expenditure had negative

impacts on student achievement when the expenditure was defined as spending per pupil or

personnel salaries. He also pointed out that school size matters because it costs more for smaller

schools to raise student achievement than that of bigger schools.

Applying education production function with eight large Texas school districts, Clark

(1998) found that teacher salaries are the biggest factor for resource difference. However, the

strongest predictor for student achievement is not directly related with expenditure, but the non-

monetary variables such as student SES that are directly related with the expenditure. This tells

us that only looking at money spent in the educational institutions may not be sufficient. At least

we need to look for better measurement of educational expenditure.

Overall, the findings of educational expenditure research is disunity (See Table 1).

Researchers have different opinions on which variables to use to capture the educational

expenditure information. Meta-analysis showed discrepancy, mainly caused by different research

methods. One theme coming out of the education production function that is close to an

agreement, though, is the strong impact of student family characteristic.

18

Table 1

Research Findings on Educational Expenditure and Achievement

Author Data Method Variables Used Funding

Coleman et al. (1966)

Students of 1,3,6,9, and 12 grades were surveyed and tested for achievements

Education Production Function, Regression

Student/teacher ratio, SES, school resources

Resources made little difference to student achievement

Hanushek (1989)

38 studies with 187 estimates of relationships between resources and achievement

Vote counting Per pupil expenditure, teacher experience, teacher education, teacher salary, teacher student ratio, administrative input, and facilities

No strong, or systematic relationship between educational expenditure and academic achievement

Hedges, Laine, & Greenwald (1994a)

Same as Hanushek (1989)

Meta-Analysis, Inverse chi-square test

Same as Hanushek (1989)

School spending and achievement were associated with one another

Greenwald, Hedges, & Laine (1996a)

Updated data from Hanushek’s (1989) research

Meta-Analysis, Combined significant testing and effect magnitude estimation

Per pupil expenditure, teacher experience, teacher education, teacher salary, teacher student ratio, administrative input, and facilities

A broad range of resources were positively related with student outcomes

Ferguson & Ladd (1996)

Alabama schools Education Product Function, Regression

Instructional spending Instructional spending had a larger but non-linear effect on test scores

Marlow (1999)

California public schools

Education Product Function, Regression

Spending on school infrastructure, school enrollment

Spending defined as spending per pupil or personnel income had negative impacts

Tobier (2001)

New York City’s public schools

Education production function, Regression

Funding, personnel, and teacher’s training

teacher’s training is a key factor in improving achievement

Jacques & Brorsen

Oklahoma School Districts

Education production

Expenditures on instruction,

Spending toward classroom

19

(2002) function, Regression

instructional support, administration, and facilities

instruction on student is most effective.

Student Factors

Existing research shows that the socio-economic status (SES) is an important factor to

predict student achievement. Research finds that students from low-SES background typically

underachieve compared to students from high-SES backgrounds (Nye & Hedges, 2001; White,

1982). Coleman (1996) argued that SES was the single dominant factor affecting student

learning. Forty years later, research still holds that production function for education needs more

variables for student learning dynamics such as SES and the interaction between home and

school (Stiefel, 2006).

Lareau (2003) and her research team observed different patterns of children from

different social classes. Regardless of race, rich children have a sense of entitlement which

means that they have the rights to pursue individual preference such as asking questions in class,

and sharing information with others. Children from poor families have shown pattern of sense of

constraint in the interactions with others in an institutional setting. These children are reluctant to

try new things and to ask questions. Lareau also concludes that the children with the sense of

entitlement are more individualist than the ones with the sense of constraint.

Sirin (2005) reviewed literatures published between 1990 and 2000 on SES and academic

achievement. At first the author introduces three new trends of the research direction. Firstly, the

range of the SES indicators has expanded. Specific factors such as mother’s education

background and family structure are more likely to be included in the measurements. Secondly, a

greater percentage of children are living with parents who are better educated with strong family

structures over the past 20 years. This might be because of the entire education level of the

20

nation has increased. Thirdly, many moderate factors such as race/ethnicity, neighborhood

characteristics, student grade level, etc. have been included into the model in recent years.

Needless to say, the more variables in the model, the more accurate the model is supposed to be.

But the many factors have moderated the magnitude of the relationship between SES and

academic achievement as Sirin (2005) concludes in his meta-study.

Analyzing the Illinois School Report Card, Sutton and Soderstrom (1999) discovered that

low income and percentage minority are the two most significant predictors for student test

scores with the same direction, while average class size, elementary pupil-teacher ratio, teacher

salary, teacher experience, and expenditure per pupil have weak relationships with the dependent

variable. These results are similar to Coleman et al. study (1966).

Similarly, Okpala, Okpala, and Smith (2001) applied the education production function to

North Carolina data and revealed that poverty and socioeconomic status are good predictors for

mathematics scores of elementary students. The greater the percentage of free and reduced-price

lunch students in schools, the lower the student test scores are. There is an inverse relationship

between socioeconomic status and student achievement. The study further finds that there is no

significant correlation between the instructional supplies expenditures and the test scores.

Race is another widely studied factor with education production function. There is a

commonly observed gap between the White students and the minority students in terms of

academic achievement. This pattern has been reflected from a number of studies using national

represented samples (Coleman et al., 1966; Campbell, Hombo, & Mazzeo, 2000; Jencks &

Philips 1980).

Gender difference is one unique aspect in academic achievement. Research finds that

girls tend to have higher educational attainment than boys in general (Lee et al., 2008); however,

21

boys tend to have better practical abilities than girls and have better scores in mathematics and

science subjects (Hedges & Nowell, 1995). Other research shows that male students have more

apparent advantages over their female counterparts to exceed in class as grade levels increased

(Ethington, 1992; Linn & Hyde, 1989).

In summary, student level factors have significant influences on student achievement.

Socioeconomic status and parental education background are among the strongest variables in

education production functions. White students in general perform better than minority students.

Gender is another strong predictor of student achievement; however, the relationship seems to be

non-linear.

Class Size

Education takes place in classrooms. Students learn from the teacher as well as from their

fellow students within the classrooms. The peer effect on student learning is reflected by class

size. Class size not only determines how students are learning and interacting with each other but

also how teachers are interacting with students. Teacher can spend more time on each student if

the class size is small and less time per student if the class has many students.

Glass and Smith (1979) undertook an extensive meta-analysis of class-size research and

sorted from more than 100 articles on class size. The findings did confirm that small class size is

beneficial for students. The fewer students in calss (e.g. 20), students do better. But after 20

students, the difference between a class of 20 and a class of 40 does not very significantly impact

student achievement. This non-linear effect also implies 20 students are the critical point for

class size effect.

Hanushek (1986) reviewed previous studies using education production function to study

the effects of class size on student achievement, and he found that out of the 112 estimates, only

22

23 had statistically significant relationships with student outcomes, and only 9 of them showed

positive impacts. But most of the measurements were using pupil/teacher ratio instead of real

class size. There is a sharp distinction between the two terms. According to Finn (2002), “The

‘pupil/teacher ratio’ is the ratio of the number of students in an educational unit to the number of

full-time-equivalent professionals assigned to that unit” (p. 557). Therefore ,the class size which

is the average number of students per classroom is a better measure, and Hanushek’s conclusions

can be challenged.

Elliot (1998) took a similar approach using HLM and investigated with NELS:88 on the

direct effects of school expenditures on math and science achievement. The findings suggest that

unlike in the direct uses of simply hiring more teachers and spending on capital investments,

resources are most effective in promoting student achievement when they are targeted to

encourage teachers to use effective teaching strategies which emphasize higher order thinking

and inquiry skills.

Using Hierarchical Linear Modeling (HLM), Nye and Hedges (2001) studied class size

effects on student learning with the Tennessee Project STAR randomized experiment and found

positive effects on reading and mathematics achievement across all grade levels. They also

concluded that there are cumulative effects on academic achievement for small classes, which

indicates the earlier small class setting will benefit students over the course of early education

process.

Applying similar research methods, Nye and Hedges (2004) analyzed the Tennessee

Project STAR again and found four years of positive lasting benefit on minority students in small

classes in reading. However, there were five years of negative lasting benefit for girls in small

classes in mathematics. Based on the Tennessee two year longitudinal dataset, Finn and Achilles

23

(1990) also found that small class size yields lasting advantages for minority and for

economically disadvantaged students. These findings indicate that class size can have

differentiated effects among various student populations within the classroom. Class size effects

may also vary by different subjects.

In reviewing the studies on class size, especially the ones with the Tennessee Project

STAR, Hanushek (1999) confirmed the class size effect should be non-linear at large and the

benefit does not appear until the class size decreases to a certain point. The implication of his

finding led to the discussion of the difference that teacher quality makes on student learning. And

policy makers should not just focus on reducing class size but also pay attention to the teacher

and the instruction quality. Rice (1999) confirmed this implication and based on the data from

National Education Longitudinal Study: 1988 (NELS:88), her findings suggested that class size

is positively correlated with the use of class time on non-instructional tasks such as maintaining

class order.

More recently, Borland, Howsen, and Trawick (2005) found evidence to confirm the non-

linear relationship between class size and student achievement based on Kentucky schools. This

study further concluded that the optimal class size is different based on subject areas, therefore

the impact of one class size can be positive for one subject and negative for the other. The other

important finding is that as the class size increases, peer effects actually help student to compete

for better achievement. But the effects may differ from one type of student to another.

Many state and local educational authorities have implemented class size reduction

programs, such as the Project STAR in Tennessee, the Project Prime Time in Indiana, the Project

SAGE in Wisconsin, the class size reduction program in California, the class size reduction

program in Florida, and the class size reduction project in Burke County, North Carolina.

24

Researchers have been looking into what the results from these experiments (Biddle & Berliner,

2002; Finn 2002; Ilon & Normore, 2006). The current knowledge about class size is that if

funded adequately, small classes benefit students in their early stage of schooling and the effect

can carry over to higher grade levels. The magic number is around 20 which mean classes with

less than 20 students tend to improve student learning. The benefits from small class are greater

for minorities and economically disadvantaged students. In addition, small class size improves

teacher morale, and gives teachers more individual time with students (Biddle & Berliner, 2002;

Finn, 2002; Ilon & Normore, 2006).

The rationales for the class size reduction in earlier grades are that students in their early

age of education require more attention and behavior assistance than when they are older and

more acquainted with the class setting. The research does shed lights on where to spend the

money. As Hoxby (2000) noted in her study of class size effect, some of the benefits from class

size reduction are simply too costly for most schools to consider, because the policy

implementation for cutting class size also means hiring more teachers, and building more

classrooms, which ultimately means increasing the budget of the schools. This ties closely to the

impact that schools bring to the education production function since the inputs of education are

the independent variables which affect the outputs of education. The overall summary of this

section can be seen in the Table 2.

Table 2

Research Findings on Class Size and Achievement

25

Author Data Method Variables Used Finding

Glass & Smith (1979)

More than 100 articles on class size

Meta-Analysis Class size of 20 Small class (less than 20) size is beneficial for students, non-linear relationship after 20 students

Hanushek (1986)

1960-1980, 112 estimates from 147 studies of the relationships between pupil/teacher ratio and achievement

Vote counting of regression estimates of the partial effect of given input

Pupil-teacher ratio, teacher education, teacher experience, teacher salary, and expenditure/pupil

Few pupil-teacher ratio variables showed significant relationships but the directions are different

Elliot (1998)

NELS: 88 Dataset Education production function, HLM

Promoting student achievement, and effective teaching strategies

Teachers’ encouragement has positive impact on student learning

Rice (1999) NELS: 88 Dataset Education production function, Regression

Class size, teacher experience, instructional time, and non-instructional time

Class size has positive impact on class time; teacher experience has negative impact on student learning

Nye & Hedges (2001)

Tennessee Project STAR

Education Product Function, Randomized experiment

Class size Small class has positive effect on student learning and math achievement

Nye & Hedges (2004)

Tennessee Project STAR

Education Product Function, Randomized experiment

Class size Small class has positive effect on minority student but negative effect on girls

Borland, Howsen, & Trawick (2005)

Kentucky Department of Education data

Education Product Function, Regression

Class grade, rank, experience, salary, and student innate ability

non-linear relationship between class size and achievement

School Effects

One of the strongest indicators of school effects on student learning is the fiscal ability of

the school district. The implication is that high SES schools can spend the money on improving

26

the teacher quality and reduce classroom size. Studies on school effects have pointed out that

school funding in part depends on the historical heritage of the school district (Bowles &

Bosworth, 2002). Their study calculated the costs of 17 Wyoming school districts and revealed

that on average it costs more in smaller schools than in larger schools for students to achieve

similar outcomes. But this research used ordinary least square regression on mainly school level

data, and the characteristic of students and teachers were not presented to get the more complete

picture.

A number of studies have found that school level resources do affect student

achievement. Wenglinsky (1997) conducted a study based on selected nationally datasets, which

provided empirical evidence that school level expenditures in some areas matter to student

achievement. The study showed that more money used to hire more teachers leads to greater

student achievement, while increased spending on school administration or raising teachers’

salary did not.

Using a national representative data, Ram (2004) found that school level resources are

positively correlated with mathematics and verbal SAT scores. Jacques and Brorsen (2002)

studied Oklahoma school districts and used education production function to find that school

level spending is positively related with student achievement, especially when the money is spent

on instruction related areas.

Another trend in the research of school resource is to look at school size effect on student

achievement. To answer this complex question, Lee and Smith (1997) investigated the NELS:88

dataset using HLM methods to find that school size exerts influences in two ways. One comes

from the theory of economies of scale in that large schools promote specialty in curriculum

skills. In other words, these skills are positively correlated with school size. Therefore, student

27

achievement goes up as the size of the school increases. School size also exert influence on that

schools also function as social communities, and as the size of school increases, teachers and

school administrators have reduced the ability to teach all the students and provide

individualized care. Therefore, as the school size increases, students may suffer. The two

competing effects influence students at the same time to make the optimal student number

between 600 and 900, which means students at such schools can enjoy fairly good instruction

and social care to make the most achievement (Lee & Smith, 1997).

Teacher Effects

Teachers are the most important factors in the schooling process: children can somehow

learn without books, or even without classrooms, but they can hardly learn without a teacher.

Indeed, research has proven that teacher and classroom effects have the biggest impact on

student learning (Goldhaber, 2002; Goldhaber & Brewer, 1997, Xu & Gulosino, 2006).

There are different perspectives of teacher and classroom effects. Teachers are

categorized in terms of teaching degrees, teaching experience, and teaching certifications. There

is research showing that the teachers’ degrees have a non-linear impact on student learning.

Summarizing from existing research, Odden, Borman, and Fermanich, (2004) found that the

impact increases as teacher degree goes up, and then the effect fades to a flat line after teachers

getting a bachelor degree. Years of experience have little impact except that the teachers with

three or more years of teaching showed stronger impact than teachers with less than three years

of teaching. The findings for teacher licensure indicated the certification has a positive impact on

student learning (Odden et al., 2004).

On the one side, there is research arguing that teachers have substantial impacts on

student learning and that there is a large variation in the impact of individual teachers across

28

classrooms even within the same school (Odden et al., 2004). Therefore, educational spending

targeting these teacher characteristics should contribute to student achievement.

However, there is other research saying the opposite. Podgursky and Springer (2007)

summarized past literature of teacher effects and found that the type of teaching certification,

teacher education, licensing exam scores, and experience are generally weak predictors of

student achievement. Ballou and Podgursky (2000) claimed that most of the teacher preparation

and licensing research are misrepresented which Darling-Hammond (2000) found to be untrue

due to the different research methods they used. Later, Darling-Hammond (2007) pointed out

that qualified teachers are the key to student success, and she also called for more federal and

local support for highly effective teachers.

Teacher’s salary seems to matter little to student achievement. Through the research on

teacher pay and focusing nationally and in 66 metropolitan areas, Greene and Winters (2007)

concluded that even though on average public school teachers are paid more than their private

school counterparts and most white collar workers, increasing their pay did not increase student

achievement.

In summary, research has shown that a number of student, school, and teacher factors

influence student achievement. However, discrepancies exist within the application of education

production function. One reason for that is the imperfect nature of the research method, which is

introduced in the next section.

Issues and Future Directions of Education Production Function

The fundamental problem with the educational production function is that many

researchers have been applying single-variable designs with the function. As Odden, Borman,

and Fermanich (2004) pointed out, too much previous research has tended to examine student

29

achievement based on student, classroom, and school variables in isolation from other important

factors. Others (Carpenter, 2000; Ilon & Normore, 2006) noted that research designs that only

used one variable to emphasize the educational outcome was one of the problems of the recent

education reforms.

Those who use education production functions to study the relationship between

expenditures and student achievement, often commit a common mistake in that they often over

look the critical process variables such as curriculum setting, and classroom instruction. This

leads to the criticism of the over simplification of the education production function (Odden &

Picus, 1992). There are a number of procedures in between having the money to spend on

education and the students learning more or gaining better scores. If these variables representing

teacher and classroom behaviors are missing, the education production function is definitely

misused.

Odden and Picus (1992) also pointed out another potential threat to education production

function that is the mismatch between educational goal that the school is carrying along and the

assessment for which students are held accountable. Most of the existing education finance

research that deals with data and analysis does not always address whether the curriculum

assignment and the tests are in the mission statement of the school district. If the tests are not a

priority of the school agenda, students low test scores may not lead directly to the conclusion that

“money does not matter.”

The solution of these critiques may not be very complicated. One way to improve the

usage of education production function is to increase more variables in the model. For example,

examining the relationship between educational expenditure and student academic achievement,

it would be problematic if the researchers only used expenditure variables as explanatory

30

variables. There should be at least some control variables such student race, gender, and socio-

economic status, among some of the instructional characteristics. The premise for this strategy is

the availability of dataset with ample variables, either through the requesting of large national

datasets or the collections of first hand dataset by education researchers.

Problems with the education production function may also occur in the misrepresenting

the relationships between the explanatory variables and the dependent variable. In a recent study,

Harris (2007) examined the Trends in International Mathematics and Science Study (TIMSS)

1999 dataset and found educational expenditure has a diminishing effect to student achievement.

This non-linear relationship between input and output is not new. Ferguson (1991) analyzed

school expenditures in Texas school districts and found among elementary school teachers, the

positive teacher effects turned insignificant at around five years of experience, and additional

years of teaching experience did not improve student test scores. Similar effects occur in other

studies from the Alabama experience (Ferguson & Ladd, 1996).

Since most of the existing researchers use some sort of linear regression methods along

with the education production function, determining whether there is a linear association

between the input and output can be problematic. The interpretation of the findings must be

careful and the insignificant impact from explanatory variables to student outcome can tell one of

the two things. One, money of different forms does not matter to student achievement. Two,

money matters in some non-linear way, such as teaching experience having a positive correlation

with student learning under the first five years and the effect fades out after five years of

teaching experience (Ferguson, 1991). One solution for this problem is a careful assessment of

the true relationship before concluding whether money matters or not. The other solution is

adopting a more sophisticated statistical approach to the education production function to capture

31

the subtle change in the direction of the relationship between educational expenditure and

outcome.

One other issue with the education production function is from the application of this

model in analyzing student achievement. Fowler and Monk (2001) pointed out that expenditure

is not the best indicator for student learning outcomes using the education production function. It

is the actual cost associated with the educational activities that should be used to predict student

achievement. They also noted that educational cost is the minimum expenditure spent on

education. The more appropriate approach to study education finance it to use cost function

instead of education production function.

Looking from the cost side of education, one interesting implication is that like many

other public institutions, public schools tend to spend as much of the available resources they

have in one fiscal year. Therefore, the reality is that more spending does not necessarily lead to

better outcomes (Hanushek, 1989). In the education production function, if the spending

variables are included, the results may be skewed because these spending variables are likely to

be more than the actual cost of education production.

However, the superiority of cost function also brings the challenge of measuring the real

cost of education. One must have known the amount for adequate funding for as certain degree

of education to claim the amount of cost. Anyone studying in the field of education finance

understands that it is difficult to define adequate funding.

Even though the application of the education production function may include a range of

student, teacher, school, and other variables, sometimes the relationship between the explanatory

variables and the dependent variable can be spurious if all the variables are on the same level of

analysis (Odden & Picus, 1992). For example, individual and aggregate students’ social-

32

economic status may have different effect on student achievement. In another instance, teacher

experience has unique influence to student learning, but using average experience in one school

and treating all the teachers as one variable reduces the explainatory power from individual

teacher experience.

Furthermore, incorporating all the student level and school level variables still does not

suffice to capture a full picture of student achievement. In addition to these exogenous factors of

schooling, education production functions should be more powerful in predicting student

academic achievement by adding endogenous variables which are innate or closely related with

family characteristics of the students. Student behavior characteristics such as locus of control,

motivation, and attitude within the education production function should explain part of the

schooling myth.

Student Learning Motivation Theories

Distilling from the literature on student behavioral research, there are three major

concepts that are believed to have influence on student achievement: locus of control,

motivation, and attitude. Locus of control, motivation, and attitude have different effects on

student learning. And they also have internal influence with each other. This section reviews the

relevant theories on each of the three concepts and the next section draws empirical evidence that

these theories are based. Most of the findings are generated from the education production

function settings.

Locus of Control

The locus of control construct originated from Rotter’s (1966) social learning theory,

which was defined as a person’s belief in the amount of control a person has in life, either in

general or in a specific area. Locus of control has impact on learning, motivation, and behavior

33

(Pintrich & Schunk, 2002). There are two types of orientation for locus of control. An internal

locus of control refers to a belief or expectancy that one’s behavior or stable personal

characteristic will control specific events or outcomes (in other words, self-belief). External

locus of control refers to a belief or expectancy that events or outcomes are controlled by

external forces to oneself (such as luck or other people’s power).

When talking about influence on something, people usually regard that as the internal

locus of control. Previous research generally shows that internal locus of control has positive

impact on student achievement and that internal locus of control is a powerful variable both in

predicting and explaining educational achievement (Shepherd, Owen, Fitch, & Marshall, 2006;

Sterbin & Rakow, 1996). James Coleman’s widely cited Equality of Educational Opportunity

Study proved that locus of control is a one of the strongest predictors for student achievement

(Coleman et al., 1966).

In addition, internal locus of control influences individual motivation to some extent

(Graham, 1994), because locus of control is also an element of attribution theory besides social

learning theory (Autry & Langenbach, 1985). The causality, in the form of many successes or

failures, is attributed to the choices of different behaviors. although the two theories all make

predictions regarding the influence of causal factors on the expectancy of success, there are sharp

differences between social learning theory and attribution theory in terms of theoretical origins.

Social learning theory is more abstract; while attribution theory uses concrete concepts (Weiner,

1976). The two theories will be discussed in detail in the motivation section.

Motivation

Derived from the Latin verb movere (to move), “motivation is the process whereby goal-

directed activity is instigated and sustained” (Pintrich & Schunk, 2002, p. 5). The central element

34

for motivation is an anticipated goal, which provides impetus for and direction to action. Goals

may not be well formulated and may change with experience. Goals are something individuals

have in mind that they try to achieve or avoid. Motivation also requires activity, either mental or

physical. Physical activities include effort, persistence, and other overt actions; while mental

activities involve cognitive actions such as planning, rehearsing, organizing, monitoring, making

decisions, solving problems, and assessing progress (Pintrich & Schunk).

As Tollefson (2004) described, motivation comes from cognitive psychology, in which

people believe cognitions cause behavior. Cognitive psychology deals with the process of how

people obtain information and how they interpret and give personal meaning to situations or

events in their lives. Cognitive theories of motivation start from the premise that people try to

bring order into their lives by developing personal theories about why things happen the way

they evolve. There are three major cognitive theories explaining motivation: expectancy value

theory, attribution theory, and social learning theory.

Expectancy value theory hypothesizes that the degree to which people will devote effort

at certain things, such as learning is a function of two variables: expectancy construct and value

components. Expectancy construct reflects individual’s beliefs and judgments about his or her

capabilities to finish the task successfully. Value components of motivation are linked to the

results of the task; they are the rewards on completion of the task (Pintrich & Schunk, 2002;

Tollefson, 2004).

According to Tollefson (2004), there are two types of rewards that are commonly

associated with completion of the task. One is external reward, which is the rewards from other

people such as teachers, parents, and peers. The other reward is internal reward, which is a sense

of self-fulfillment.

35

In the case of education, it is similar to a two-part test. A student will have a good sense

of motivation if he or she first anticipates whether the learning process is feasible as planned by

the teacher or curriculum. Second, the student understands what kind of consequences he or she

will receive from successful completion of the learning process. Most of the time, the

consequences are good, although sometimes students are motivated to learn to avoid bad

consequences such as being punished for bad grades. These are external rewards. The internal

rewards may be that the student feels something is accomplished, and he or she is mentally

happy or has a sense of pride with the educational achievement.

The second motivational theory is social learning theory which is generated from Rotter’s

(1954) and Bandura’s (1986) work. As Rotter pointed out, “The major or basic modes of

behaving are learned in social situations and are inextricably fused with needs requiring for their

[sic] satisfaction the mediation of other persons” (p. 84). The theory comprises four basic

variables: behavior potential in a given situation, expectancy of a consequence following a

specific behavior, reinforcement value of outcome, and the psychological situation in which the

context of behavior is captured (Pintrich & Schunk, 2002)

In the field of education, there are also two premises for this theory. One is that students

make personal interpretations according to their past accomplishments and failures to set goals

based on these interpretations. The second premise is that students set individual goals which

become their personal standards for evaluating their performance (Tollefson, 2004).

An important element in the motivational process is self-efficacy, which Bandura defined

as “People’s judgments of their capabilities to organize and execute courses of action requires to

attain designated types of performances” (1986, p. 391). There are four principal sources from

which people develop their personal sense of efficacy: “performance accomplishment,

36

observation of the performance of others, verbal persuasion and related types of social influence,

and states of physiological arousal from which people judge their personal capabilities and

vulnerability” (Tollefson, 2004, p. 209).

In the case of education, for example, a student may take a course and the student will

have an anticipated grade based on information such as how hard the course is, and what the past

achievement is for the student. After first setting the goal for the course, the student will use this

as this goal to assess the current endeavor.

Social learning theory shares some similarity from the expectancy value theory. The

social learning theory argues that an individual undertakes self evaluation first, and then sets up a

goal based on the evaluation. The next step is to work toward the goal. In expectancy value

theory, the individual understands the goal first. Based on all the information of the goal and

what the expected reward is, the individual then decides whether to work on the goal or not. The

major difference is that in the expectancy value theory, incentive plays an important role for the

individual, whereas in for the social learning theory, the individual is more likely to receive an

internal incentive of meeting the goal during the process of working toward the goal.

Expectancy value theory and social learning theory all point out that individuals are

motivated to perform certain tasks based on the expectancies for success and the values

connected to the success. These theories assume that individuals are rational thinkers who plan

things before they seek out the task challenges. These theories also assume individuals have

good sense of their ability in certain task areas. However, in the realm of education of school

children, these assumptions are not always satisfied.

The third motivational theory is the attribution theory which is concerned with

perceptions of causality and with the consequences of these perceptions (Tollefson, 2004).

37

Attribution theory believes individual human beings who are trying to understand their

environment and the causal determinants of their own behavior as well as the behaviors of others

(Pintrich & Schunk, 2002).

Attribution theory also looks at both thoughts and feelings as motivators of human

learning. The key for the attribution theory is on the individual’s search for understanding the

conditions for success or the reason for failure. These conditions can be personal or

environmental. Environmental conditions include specific information as well as social norms.

Personal conditions include a variety of schemas, prior experience, and knowledge of the

individual’s ability. Furthermore, prior knowledge and beliefs, and individual differences are the

two major factors to influence the attribution process (Pintrich & Schunk, 2002).

Derived mostly from Weiner’s (1972) work, attribution theory has four elements that

people commonly use to explain why they have been successful or have failed at an academic

task. These causes are ability, effort, task difficulty, and luck. Weiner also developed dimensions

to categorize these causes. On the one dimension, the ability and task difficulty causes are stable,

while the effort and luck causes are unstable. On the other dimension, the ability and effort

causes are internal, while the task difficulty and luck causes are external. Empirically, Uguak,

Elias, Uli, and Suandi (2007) found that the majority of students contribute their causes of

success as internal rather than external.

In a piece by Weiner (1972), the attribution theory was applied to the study of the

educational process. Weiner specifically pointed out that attribution theory can be used to

examine the influence of causal beliefs on both teacher and student behaviors. Students may seek

to understand why they failed or passed an exam; a teacher may attempt to understand the

reasons why students have different behavior and performance over a variety of tasks in class.

38

The teachers have two instruments that they can use to motivate students: rewards and

punishments. So do the students to themselves. Achievement motivation is developed through

the instruments and the ability for the students to understand the causal linkages from striving to

the achievement activities – either reward or punishment.

Besides the three major theoretical frameworks, there are other terms used to express the

meaning of motivation such as aspiration and expectation. Academic expectation means the level

of education that students expect to achieve, while academic aspiration means the education they

hope to achieve (Hanson, 1994). Educational aspiration is among the most significant predictors

of educational attainment (Duncan, Featherman, & Duncan, 1972). Parallel to this, student’s

academic expectation, in the next step, is an important variable both in predicting and explaining

educational attainment (Hanson, 1994).

Human and financial capital from parents can provide a cognitive environment and

physical resources for the child that aid performance and aspirations (Qian & Blair, 1999; Sewell

& Shah, 1968). Expectation, like aspiration, belongs to the category of motivation (Hanson,

1994; Trusty, 2000). Trusty (2000) used the NELS:88 dataset and logistic regression to find that

there are a number of factors influencing student academic expectation such as socioeconomic

status, ethnic group, prior achievement, parental expectation, locus of control, parental

involvement of school extracurricular activities.

Similar findings emerge from other research. Flowers, Milner, and Moore (2003) visited

the issue of locus of control and its impact to student aspiration. The authors argued that to

examine the relationship, the theoretical framework must include three aspects of education:

family characteristic, student characteristic, and school characteristics. The family aspect is

important because parents are vital to provide academic support and motivation. In addition,

39

successful parents are in a good position to stay active in their children’s education process and

get involved with students and schools when needed. The student aspect of education process is

that when they have good attitude in learning, they tend to enjoy many of the school activities

which in return help them learn more. The school aspect of education is usually connected to the

resource of various sorts that schools are able to allocate. The school facilities and in-school

programs are important to stimulate student learning.

Locus of control is the top level of behavioral concept and it is believed to have influence

on motivation. Employing regression analysis to the NELS dataset and the first two follow-up

surveys, and controlling for family characteristic, student characteristic, and school

characteristics, Flowers, Milner, and Moore (2003) found that African American high school

seniors with higher levels of locus of control were more likely to have higher educational

aspirations than African American high school seniors with lower levels of locus of control.

Synthesizing from existing learning frameworks, Walberg (1984) studied nearly three

thousand research articles in the U.S. and internationally and concluded that nine important

factors are influencing student learning: 1) the ability or prior achievement, 2) the childhood

development, 3) the student motivation, or self-concept, 4) the amount of time students engage in

learning, 5) the quality of the instructional experience, both psychological and curricular wise, 6)

the home factor, 7) the classroom social group, 8) the peer group outside the school, and 9) the

out-of-school time on studying. These findings suggested that not only these nine factors have

significant impact on student learning, but they also have impact to each other.

Walberg’s (1984) famous Educational Productivity Model divides these nine factors into

three categories. First, the attitude, motivation, and prior learning ability are internally affecting

student learning outcomes. Another category consists of other factors, the classroom social

40

group, the peer group outside the school, and the out-of-school time on studying as

environmental factors that are affecting student learning externally. Third, the amount of time in

learning and instructional quality are the school factors which are usually unalterable compared

with the other two categories. The research concluded with that these three major categories all

have a positive impact on student achievement.

Attitude

Attitude has a much broader meaning than motivation and locus of control, from the field

of psychology to education, and it usually consists of the following components: persistence or

perseverance, and self-esteem or self-concept.

Self-concept means “the totality of the individual’s thoughts and feelings having

reference to himself as an object” (Rosenberg, 1986, p. 7). Rosenberg went on to clarify the

definition by providing what the self-concept is not. On the one hand, self-concept is not as

cognitive as Freud’s ego, which consists of a set of intellectual processes enabling the individual

to think, perceive, remember, reason, and attend to deal with reality. Ego does work to protect

and enhance the self-concept; however, it does not constitute the self-concept. On the other hand,

self-concept is not as real as the “real self,” since the person may have a disposition to love, to

write, to compose, or to excel. In other words, the self concept is only the picture of the real self

(Rosenberg, 1986).

There are a few motives for self-concept. Self-esteem as the first motive is “the wish to

think well of oneself” (Rosenberg, 1986, p. 53). Rosenberg did suggest that self-concept and

self-esteem vary across a range of factors, such as age, race, social class, birth order, sex,

religion. Therefore it will be useful to put these two concepts into specific context.

41

Self-esteem or self-concept is the factor often studied in the educational field about how

students view themselves in regard to study. Self-concept consists of the strength of a student's

sense of self-worth and overall self-esteem (Lee, Daniels, Puig, Newgent, & Nam, 2008, p. 309).

Slavin (1997) stated that self-concept includes the way people perceive the self strengths,

weaknesses, abilities, attitudes and values. Similarly, self-esteem is about how people evaluate

self skills and abilities.

One of the most studied aspects in attitude is the race factor, that students of different

races should have different educational attitude. Since Ogbu and Fordham’s (Fordham, 1988;

Fordham & Ogbu, 1986; Ogbu, 1978; 1983; 1991) series of writings about the ethnic-

achievement dilemma in the U.S. education system, they also developed the oppositional culture

theory. The theory states that some African Americans purposefully choose to expect less effort

than they would otherwise do because of the opposition to the behavior of the majority White

students. As Ogbu (2004) pointed out, the lack of achievement from Black students can be

explained by the burden of “acting White.” The oppositional culture theory views this type of

behavior as blocked opportunity.

To explain why some minorities succeed while others tend to underperform, Ogbu (2004)

distinguishes between two types of minorities: voluntary minorities and involuntary minorities.

Voluntary minorities are those who migrated more or less voluntarily from their homeland to

America. Asian Americans are often cited as an example of immigrant minorities since a

significant portion of the first generation migrations came to the U.S. in seeking better

opportunities.

On the contrary, involuntary minorities are those who did not originally choose to arrive

at American land. Instead, they unwillingly left home and to come to the U.S. These differences

42

of entry into American society result in differences in adaptation and differences in the

perception of cultural and social barriers usually confronted by new migrants. Voluntary

minorities are more willing to adapt to American society as a means for upward mobility and

they believe the possibility to achieve better social status through hard work like the Asian

Americans (Qian & Blair, 1999). Involuntary minorities, however, perceive American culture as

a threat to their own identity, and view the historical and contemporary social structures as

barriers for them to move up the social ladders. They usually have lower educational aspirations

compared with voluntary minorities.

More specifically, Ogbu (2004) reasoned two types of burden the involuntary African

Americans may face. One type of the burden is from the past history. During the slavery era,

Blacks were forced to do whatever the Whites told them to do. As part of the history which can

never be easily forgotten, the Black people now are looking at this past period as bitter

experience. Traditionally, Black people do not want to follow the mainstream people because

they do not want to comply with the Whites. The second type of burden of “acting White” is

more practical in the modern society. It is commonly observed that Blacks are rewarded a lot less

than their Whites counterparts with the same skill, education and ability. Perhaps this occurs

because real segregation still exists. Black students learn these facts in the real world or they are

told by their parents who suffer from this kind of unequal treatment will be reluctant to invest

their full strength at school work. They do not believe education will benefit them the same as it

will benefit to the White students (Ogbu, 2004).

Past research has successfully explained the reason why students of different race have

different achievement levels holding other things constant. Mickelson (1990) observed the

education achievement disparities between White and Black students and found the achievement

43

gap was closely associated with student attitudes toward school. Through a series of surveys, the

findings suggested that the Black students have a dual-value system. What every student in

general believes is that education is the only way to a better life and it will provide an equal

opportunity to everyone. But the belief conflicts with the real world observation that Black

students face. The fact is that every student may have a good attitude toward education

regardless of color, however, the Black student has another attitude that education will not work

for them.

According to Mickelson (1990), the first type of attitude is abstract attitude or external

attitude, and the second type of attitude is concrete attitude or internal attitude. The research

results showed that the concrete attitude outweighed abstract attitude when the common belief

conflicts with the individual observation. This explains the education achievement disparity very

well. Associate with this concept, the current educational achievement can be explained partially

by student attitude. Because students also spend out-of-school time at home. If they have a

positive attitude toward studying, they may work hard at home. This improves their academic

achievement but it has nothing to do with educational expenditure.

Mickelson (1990) also suggested that attitudes are less effective in improving

achievement when they are too abstract. Abstract attitudes are formed from the prevalent belief

that hard work leads to better pay, and ultimately leads to higher social status. In school, this

kind of abstract ideology is translated that anyone can become successful by studying hard in

school. Mickelson views these concepts as too abstract, and they are not linked to the reality

because one man’s case can be completely different to another’s. Therefore, such belief in hard

work does not automatically lead to student achievement. Concrete attitudes, on the other hand,

are formed from students’ daily experiences. They see the life of the people around them. In the

44

case of African Americans, they are most likely to interact with other African Americans. If they

see real examples around them and still fail to achieve desired goals through hard work, the

concrete attitude outweighs the abstract attitude and the students may lose faith in working hard.

Theoretically, it is reasonable to believe that if a student holds a positive attitude of him

or herself, the student should routinely exhibit positive or persisting behaviors toward learning,

such as attending school regularly, participating in extracurricular activities, and completing

required work in and out of school. These positive or persisting behaviors should give the student

more chance to achieve more academically.

Empirical research has demonstrated that the influence from attitude is directly correlated

with student achievement. Applying the educational productivity theory, Walberg, Fraser, and

Welch (1986) studies the factors affecting student performance. The findings showed that

student achievement was related persistence, and persistence is positively correlated with

motivation, among other things.

In addition, research has proved that self-concept is among the most significant

predictors for student achievement in mathematics (O’Conner & Miranda, 2002; Reynolds &

Walberg, 1992; Thomas, 2000). Reynolds and Walberg (1992) also found that parents have

greater amount of influence to children’s self-concept.

Empirical Findings on Student Achievement

Many of the prior studies used the National Education Longitudinal Study of 1988

(NELS:88) and its follow-up studies to examine the relationship between student educational

behaviors and achievement of various measurements (Cook & Ludwig, 1997; Finn & Rock,

1997; Lan & Lanthier, 2003; Lee, Daniels, Puig, Newgent, & Nam, 2008; Muller, Stage, &

45

Kinzie, 2001; O’Conner & Miranda, 2002; Reis & Park, 2001; Singh, Granville, & Dika, 2002;

Sterbin & Rakow, 1996; Thomas, 2000).

Sterbin and Rakow (1996) applied path analysis and regression analysis to investigate the

impact from locus of control and self-esteem on student achievement. Specifically, they used

three variables to compose the locus of control scale:

“good luck is more important than hard work for success;

every time I try to get ahead, something or somebody stops me;

planning only makes a person unhappy, since plans hardly ever work out anyway.”

For self-esteem, they used four variables:

“I take a positive attitude toward myself;

I feel I am a person of worth, on an equal plane with others;

I am able to do things as well as most other people;

on the whole, I am satisfied with myself.”

The results showed that both locus of control and self-esteem are significantly correlated with

standardized test scores. In addition, they found that self-esteem and locus of control are highly

correlated with each other.

Another way to study the student behavior impacts to achievement is the examination of

different effects by gender. Reis and Park (2001) investigated the relationship between self-

concept, locus of control and math and science achievement with NELS:88 dataset. The factor

analysis sorted eight variables into the self-concept factor and five other variables into the locus

of control variable. The regression results indicated that the best predictor for distinguishing

between high-achieving males and females is locus of control. Finn and Rock (1997) used

identical dataset and similar statistical procedures except that they looked at particular at-risk

46

students. Their findings showed that the self-esteem and locus of control factors distinguish

students in terms of academic success.

Using the similar strategy to break down the student population by race and gender

subgroups, Muller, Stage, and Kinzie (2001) found locus of control to be strongly related to

students’ science achievement for all subgroups except Asian American males.

Cook and Ludwig (1997) took the issue of unequal motivation toward school wok

between Black and White students and tested there hypotheses. First, do Black students

experience greater alienation toward school than non-Hispanic Whites? Second, do Blacks incur

social penalties from their peers for succeeding academically? And third, if yes, are these

achievement penalties greater than those for the Whites? The research found all three questions

have negative answers after controlling for socioeconomic status and other family characteristics.

However, the findings did not provide evidence to verify that Black students would be rewarded

for “acting White” either. If they see no benefit for working harder for good grades or lack of

“concrete attitude (Mickelson, 1990),” even they would not be punished for succeeding. In other

words, they might still choose to be less motivated toward school work.

Applying a different outcome measurement to the NELS datasets, Lan and Lanthier

(2003) detected very similar results. The authors found that the student motivation composite had

a significant relationship with dropout decisions while the self-esteem composite did not. The

locus of control composite failed to show significant impact either. This research confirmed

some of the prior findings that prior academic performance, relationship with teachers, and

participation in school activities were significantly related with student attainment. Lee et al.

(2008) studied the relationship between motivation and postsecondary educational attainment

among low socioeconomic status students. Building on the categorical regression analysis and

47

path analysis, their research found no direct or indirect impact from student attitude toward

educational attainment. However, high academic expectation does have a significant effect on

student attainment (Lan & Lanthier, 2003).

In another study used the NELS:88 dataset, Singh, Granville, and Dika (2002) tested the

influence of motivation, attitude, and academic engagement on mathematics and science

achievement. They applied confirmative factor analysis and incorporated two motivation factors,

one attitude factor, and one academic engagement factor into the structural equation models to

predict achievement. In both the science and mathematics models, they found positive results

from all these factors. The authors further implied that since the three aspects of student learning

inputs are relatively alterable compared with fiscal spending and family characteristics, it may be

a wise choice to improve these motivation and attitude factors to improve student achievement.

Combining the NELS:88 and its first two follow-up studies, O’Conner and Miranda

(2002) selected 10 variables as proxies of student attitude of mathematics. Six of these items

were composed into the self-concept factor, and the other four were composed into the effort

factor. The regression analysis showed that these two attitude factors were the strongest

predictors of student mathematics performance. Using exactly the same datasets and regression

analysis, Thomas (2000) also found that motivation and attitude measurements are positively

correlated with student science achievement.

In the same study, Thomas (2000) found that attitude affects science achievement. In

observing the achievement gap among students of different ethnicity, his research also revealed

that the impact sizes of attitude among the major student ethnic groups are inseparable, however

the way attitude affects student learning is not the same across ethnic groups. The explanation of

this may come from Ogbu’s study (1983), which recognized the difference expectation of their

48

future among each ethnic group. Asian Americans are optimistic where as African Americans are

pessimistic about their future, because Asian Americans immigrants compare their current

conditions with their peers in their home county, in which case they are better off, but African

Americans compare theirs with the White peers in the United States, in which case they are

worse off. This different reference group theory gives the two ethnic population different

attitudes toward education since they view their future differently.

The other study used ELS:2002 dataset aimed to look at locus of control, motivation, and

attitude simultaneously in regard to student achievement (Sciarra & Seirup, 2008). Teacher and

student survey items were composed into factors to predict math achievement scores. The

findings showed that among the five major ethnicity groups locus of control and attitude explain

more variance of student achievement than motivation does.

Other Factors Affecting Student Motivation

From the previous discussion it is summarized that motivation and other behavioral

characteristics toward learning are heavily correlated with student race. In addition, these factors

are also influenced by gender, peer effect, prior ability, and parental role. This section briefly

discusses these factors in relation to student achievement.

Gender

Other than the race factor which has been studied to a great extent, gender, on the other

hand, is also an important factor in student motivation toward learning. Evidence shows that girls

and boys have different reactions toward motivation. Marsh, Martin, and Cheng (2008) studied

964 Year 8 and 10 high school students in their mathematics, English, and science classes in 5

49

Australian coeducational government schools. Their analysis of classroom motivation suggested

that girls are easier motivated than boys, and teacher’s gender has little impact on student

motivation.

However, O’Conner and Miranda (2002) summarized prior research and concluded a

mixed message: “gender differences in self-concept overwhelmingly report that males’

mathematics self-concepts were higher than females’ mathematics self-concepts and females’

verbal self-concepts exceed that of males’ although females had higher achievement grades in

both core areas” (p. 77). Achievement wise, boys do have apparent advantages over girls,

especially in mathematics and science. Another finding is that girls in higher grades are less

interested in taking mathematics and problem-solving courses, compared with their male

counterparts.

Goldsmith (2004) studied eighth graders from NELS:88 and found that female students

tend to have greater educational and occupational aspirations than male students. The findings

also showed that Black and Latino students are more likely than White students to have high

educational and occupational aspirations. Combining these two factors, Goldsmith (2004) found

an even bigger gap between White males and Black females. The model also predicts that in

terms of educational aspirations, Black females have a greater advantage over White females

than Black males have over White males.

Research on gender-achievement issues borrows the concept of gender difference and to

explain the disparities between the girls and boys. Lundy (2003) selected student samples from

the NELS:88 dataset and analyzed the race and gender effect on student achievement. The

findings show that African American students are less likely to express hard working behavior

50

than the White and Asian American students. although there is evidence that African American

students have pro-education attitudes, over all, they still achieve less than other ethnic groups.

More importantly, Lundy’s (2003) study found that there is a clear gender factor among

high school students, in that male students appear to be more resistant to school work, and they

receive poorer grades than female students. Lundy offered a hypothesis that male students view

hard-working female students as girlish, and girls resist the image of girlish by not study hard

intentionally. Furthermore, the study has controlled parent and other family characteristics

because these factors are often associated with race but not gender (Lundy 2003).

Peer Effect

Most of research about the peer effects of learning has been focused on the race and

gender factors. Others have been looking further at the sub-groups of ethnicity and gender

combined (O’Conner & Miranda, 2002). Still there is important reason to understand the peer

effect by controlling race, gender, socioeconomic status, among other factors. Rothstein (2000)

wrote that students are not only affected by the educational institution, but also affected by their

fellow students. Peer effect cannot be neglected when studying the student learning process. Peer

effect coming from students of similar background usually contributes to the achievement and

underachievement of students. A positive peer environment has been found to have a positive

impact on attitude and small to moderate impact on learning outcomes (Walberg, 1984). Reis and

McCoach (2000) found that high-achieving students had a positive influence on gifted high

school students who began to under-achieve.

On the other hand, students with low academic performance usually find themselves with

negative attitude, and this attitude in return is among the strongest predictors of student

underachievement (Clasen & Clasen, 1995). Their study also showed that about two thirds of the

51

participating students mentioned peer pressure or attitude of the other kids is the primary force

against them obtaining good grades.

One intriguing fact is that the notion of high-achieving and low-achieving are always

relative in a specific context. For example, in a school of hundreds of students, no matter where

to draw the achievement line is drawn, it is reasonable to assume that there are always students

above the line and students below the achievement bar. When studying the impact of one group

of students to the other group of students, the separation criteria is critical to the results,

especially if the students are from a homogeneous population.

Prior Ability

Researchers have tried to detect whether attitudes influence achievement or prior

achievement influences attitudes. Adopting the second follow-up survey (NELS:92), Qian and

Blair (1999) studied the factors that were influencing student motivation which ultimate by

influencing student achievement. They revealed that prior educational performance has a strong

impact on student motivation. Through their research, O’Conner and Miranda (2002) found that

prior ability is highly correlated with student attitude toward learning, and this holds true for any

demographic subgroup: gender or ethnicity. Similar effects were found among African American

male and female students. Prior academic performance is the strongest predictor for education

expectations, and then the high expectations tend to lead to high educational attainment (Trusty,

2002).

Wilson (1983) conducted a meta-analysis covering research on kindergarten through

college students and found that successful achievement leads to positive attitudes. Using

structural equation modeling, Reynolds and Walberg (1992) studied science achievement and

attitudes among eleventh graders. Their findings confirmed prior research in that prior

52

achievement is among the factors that influence attitudes about science. In addition, Reynolds

and Walberg’s (1992) results showed that science achievement influences science attitudes but

not the other way. Another important finding from this research is that high motivation also leads

to good attitude toward learning (Reynolds & Walberg, 1992).

Examining both the prior achievement and attitude together, research has identified that

prior achievement plays a more important role than learning attitude or socioeconomic status

(Ma & Williams, 1999). The fact that student’s prior ability explains present achievement is

intuitively understandable. If the effect is direct, the lag effect shows that student performance

does not change dramatically unless unexpected things happen. On the contrary, if the effect

from prior ability to student achievement is indirect, and then theoretically there may be a loop

between achievement and motivation. Prior academic achievement enhances student self-esteem,

therefore enhances student motivation toward learning. As research has shown, enhanced

motivation correlates with current student achievement.

Parental Role

Typically, educational aspirations from parents have been captured as parental

expectation of their children’s highest education level. Trivette and Anderson (1995) concluded

that this is one of the ways parents can improve student motivation. Parental characteristics and

other social variables also have high a correlation with student motivation, and research

suggested the effects come through parental involvement in students’ school activities (Qian &

Blair, 1999). In addition, the findings further suggest that the role of parental status is stronger

for White students than for African Americans in educational attainment.

George and Kaplan (1998) conducted research with the NELS:88 dataset. Their path

analysis discovered that parental involvement has significant direct as well as indirect effects on

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student science attitudes. The indirect effect is mediated through science activities and

library/museum visits. The study also concluded that science activities have a significant direct

effect on science attitudes toward learning (George & Kaplan, 1998). Evidence suggests that

other formats of parent involvement of school activities are also helping to improve student

achievement. These activities include active involvement in parent-teacher organizations, and

home-based partnerships or projects (Trivette & Anderson, 1995).

These findings agree with some of the empirical studies on student behavior patterns

(Qian & Blair, 1999; Sewell, & Shah, 1968; Smith-Maddox, 2000), and the reason that parents

matter is not only because the high parental expectation serves as motivation that passes to the

students (Fan, 2001; Fan & Chen; 2001), but also because parents with high levels of education

are able to provide financial and human capital to support students to learn more (Hanson, 1994;

Trusty, 2000). Trusty (2002) later studies this issue with NELS:88 dataset and found that

parental education level is a proxy for socioeconomic status factor to influence student

motivation on learning.

In addition to the parental aspirations to improve student achievement and parental

participation in school activities to enhance student achievement, Trivette and Anderson (1995)

found two other components of parental involvement that are useful for students learning.

Summarizing from prior research, they identified that parent-child communication about school

and school activities increases student aspirations and expectations positively. Such

communication can be simply a verbal interaction, or cues of problem-solving strategies.

The other important component is home structure or environment. The research on the

relationship between home environment and cognitive development has shown that parents are

able to set the “hidden” curriculum for success. Children coming out of a study-friendly home

54

environment tend to spend more time on studying. This type of motivation is unconsciously

working toward children overtime. On the other hand, if parents spend most of the time watching

TV at home or the home environment is noisy, children will not feel motivated to study at home

(Trivette & Anderson, 1995).

One other way parents can influence their children come from the influence they have on

the teachers. In a study about teacher quality, Xu and Gulosino (2006) found evidence to support

that the positive feelings about students’ parents not only encourages teachers to establish a

better teacher parent partnership, but also boosts teacher morale in classroom teaching.

In summary of this chapter, education production function provides a desirable platform

to analyze the relationships between various input variables and output measures. Most of the

methodological approach is regression on student and school data. The findings on school

expenditure, teacher quality, and various other student or school variables do not paint the same

picture as results from empirical studies are not consistent. Research using education production

function is not new; however, very few people conducted this type of research with the addition

of student behavior variables. The current understanding of the research is that to reach sound

results, the education production function needs to embody a broader than ever set of factors,

both the traditional ones and the new ones that this dissertation proposes. Student expectation,

motivation, and expectation on learning as education psychology proves, is among the best

predictors of student academic achievement. The addition of student behavioral factors

potentially leads to new finding of how to improve student learning through school expenditure.

The next chapter provides the detailed scope of the research.

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CHAPTER 3

DATA AND METHODS

Overview

This chapter reviews the data and research strategies this dissertation uses to address the

research questions:




achievement?



The analytical procedures of this dissertation are mainly building on the Education

Longitudinal Study of 2002 (ELS:2002) acquired from the National Center for Education

Statistics (NCES). Due to the nested nature of the data, the Hierarchical Linear Modeling (HLM)

is the most appropriate research methods for this dissertation. HLM has two level of regression

analysis: one on student level and the other on school (district) level. In sorting out of the

multiple independent variables, factor analysis of various formats is performed.

Data

ELS:2002 Description

The Education Longitudinal Study of 2002 (ELS:2002) is the fourth in the NCES

national longitudinal high school cohort series and is designed to build on the multiple policy

objectives of NLS-72, HS&B, and NELS:88. Base-year data collection for the study was in

56

2002, with approximately 20,000 10th grade students selected from 750 public and private high

schools. Policy issues to be studied through ELS:2002 include the identification of school

attributes associated with achievement; the influence of parent and community involvement on

student achievement; the dynamics and determinants of dropping out of the educational system;

changes in educational practices over time; and the transition of different racial-ethnic, gender,

and socioeconomic groups from high school to postsecondary institutions and the labor market

(Bozick & Lauff, 2007).

Like the earlier NCES studies, ELS:2002 examines students’ values and goals,

investigates factors affecting risk and resiliency, and gathers information about participation in

social and community activities. The study also contains teacher evaluations of the effort and

ability of each student, school administrator questionnaires, school library and media center

questionnaires, and parent questionnaires. In the ELS:2002 series, the first follow-up was

administrated in 2004, and high school transcripts were collected covering the span of the high

school years (Bozick & Lauff, 2007).

As in NELS:88, ELS:2002 includes measures of school climate, each student’s native

language and language use, student and parental educational expectations, attendance at school,

course and program selection, use of technology, planning for college, interactions with teachers

and peers, perceptions of safety in school, parental income, resources, and home education

support system (Bozick & Lauff, 2007).

The longitudinal study is also designed to support both longitudinal and cross-cohort

analyses and to provide a basis for important descriptive cross-sectional analyses as well.

However, priority was given to the longitudinal aspects of the study, with survey items chosen

for their usefulness in predicting or explaining future outcomes as measured in later survey

57

waves. The ELS:2002 content is also designed to provide comparability, where possible, to the

prior NCES high school studies to facilitate cross-cohort comparisons. For example, trends over

time can be examined by comparing the data from 1980, 1990, and 2002 high school

sophomores, collected with HS&B, NELS:88, and ELS:2002, respectively; or data from 1972,

1980, 1982,8 1992, and 2004 high school seniors, collected from NLS-72, HS&B, NELS:88, and

ELS:2002 (Bozick & Lauff, 2007).

There are seven survey components of the base-year design: assessments of students in

mathematics and reading; a survey of students; a survey of parents, teachers, school

administrators, and librarians; and a facilities checklist (completed by survey administrators,

based on their observations at the school). The student assessments measured achievement in

mathematics and reading and were based on the test frameworks used in NELS:88. The

assessments designed for ELS:2002 used items from NELS:88, the National Assessment of

Educational Progress (NAEP), and the Program for International Student Assessment (PISA).

The baseline scores from these assessments can serve as a covariate or a control variable for later

analyses. Mathematics achievement was reassessed in the first follow-up, so that achievement

gain over the last two years of high school can be measured and related to school processes and

mathematics course taking. The student questionnaire gathered information about the student’s

background, school experiences and activities, plans and goals for the future, employment

experience, in and out-of-school experiences, language background, and orientation toward

learning (Ingels, 2007).

The ELS:2002 also contains transcripts and grade point average (GPA) information that

were collected from sample members in late 2004 and early 2005, about 6 months to 1 year after

most students had graduated from high school. Collecting the transcripts in the 2004–05

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academic year allowed for more complete high school records. Transcripts, both academic and

general, were collected from the school that the students were originally sampled from in the

base year (which was the only school for most sample members) and from their last school of

attendance if it was learned during the first follow-up student data collection that they had

transferred. Transcripts were collected for regular graduates, dropouts, early graduates, and

students who were homeschooled after their sophomore year. School course offerings data were

also collected (for base-year schools only) (Ingels, 2007).

Data and Variables from ELS:2002

Table 3 illustrates the selected variables the author will use and the hypotheses related to

student academic achievement. Among all the variables, the author particularly interested in the

attitude and motivation variables (e.g. how much students like school, how far in school students

think will get, and how far in school parents expect). The author want to test how attitude toward

education will affect academic achievement with controlling for other factors such as family

background, race, and gender. The author also interested in the relationship between educational

expenditures and student academic achievement. In this study, the educational expenditure

variable is represented by teacher’s education and teaching experience.

Table 3

Selected Variable Description

Variable Name Variable Coding Hypothetic

Relation

Explanations

Standardized test score (Math, Reading)

From low to high in a 100-point scale

N/A N/A

High School GPA Continuous number on a 4.00 scale

N/A N/A

Gender of student Male=1, Female=0 – Males usually have higher scores in secondary schools

Race of student Asian, Black, Hispanic, and White

? Asian and White students tend to perform better than black

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students students

SES composition From low to high + The rich have more to spend on education than the poor

How much students like school

From “not at all” to “a great deal”

+ The more students like school, they tend to study harder to get better grades

How far in school student think will get

From high school degree to Ph.D. degree

+ The higher the expectation from students, the harder students may try to study

How far in school parents expect

From high school degree to Ph.D. degree

+ The higher the expectation from parents, the harder students may try to study

Discuss school related things with parents

From never to often + More discussion about things in school will help students understand school materials better

Teacher has master degree or above

Master=1, not=0 + The higher degree, the higher credentials teachers have to teach students

Teacher’s experience From 1 year to 40 years

+ The more years teachers have taught, the better the teachers might be

School size From low to high ? Not sure about the relationship

Free and reduced-price lunch student percentage

Free and reduced-price lunch student percentage increases

– The higher the percentage students are in free and reduced-price lunch, the less money the school may have to spend

Is the school in urban area Urban = 1 – Urban schools may have lower performance than rural schools

Percentage of minority students

Between 0 and 1 – The higher minority students in school, potentially the lower the overall achievement

ELS:2002 has more than 100 student behavior variables. Based on the literature and prior

research, the author use factor analysis to sort these variables into two or three factors. Factor

analysis is a typical way to reduce large number of variables into a few factors that make sense

of which variables each factor includes. The original variables load onto factors based on the

pattern of correlations. In this dissertation, these factors were categorized as “motivation” or

“attitude” depending on the factor loadings on each of them. The regression analysis in the later

stage incorporated these factors along with other explanatory variables.

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Hierarchical Linear Modeling

One particular focus of the dissertation was to bring in the student motivation aspect of

education input. The next section states the problems associated with the design, application, and

interpretation of education production function before offers a number of solutions. To

demonstrate one of the solutions, the final section discussed hierarchical linear modeling, its

merits as well as its potential problems.

A better way to refine the education production function is to employ the Hierarchical

Linear Modeling (HLM). Education takes place in classroom with teachers; therefore, teacher

quality, experience, and certification have direct impact on student learning. Classrooms are in

schools buildings and each school has its own unique characteristic such as school leadership,

school type, school size, district fiscal ability, and geographical location of the school. These

factors also have direct or indirect impact on student learning. Based on the nested nature of

education, it will be helpful not only to include all these variables, but also to build them into

different layers.

Using HLM had distinct advantages over other statistical procedures. Cohen (1983) was

one the first few scholars that brought the attention of the multiple level modeling in education

research. Cohen (1983) called for a statistical framework that incorporated measurements of

multilevel structure of schools. Starting from the 1980s, more researchers had been considering

conducting education research using the nested model. As the techniques became more mature,

scholars recognized the importance of setting student, teacher, and school effects in a multilevel

framework by which to examine the improvements in student learning emerge from these three

different levels.

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Burstein (1980) stated schooling activities occur within hierarchical groups, and

individuals belong to every level of such groups. Each of these groups has a specific

arrangements such as the learning group within classrooms, the classrooms within schools, the

schools within districts, the families within communities, and schools within communities. These

groups also have a specific influence on the group members in terms of thoughts, behavior, and

feelings of their members. In other words, members in one group may be quite different from

members in other groups even though they are on the same hierarchical level. This is the case for

students taught by different teachers; the teacher factor may have unequal contribution to student

achievement, even they are in the same school and same community.

To explain the complex influences of group settings on individual student behavior, the

hierarchical structure brings the chance to evaluate the effects of higher level organizational units

(such as schools) on their lower level subgroups (such as classrooms) (Burstein, 1980). Two

important advantages rise from this specific research technology: “(1) variables can have

different meanings at different levels of analyses, and (2) measures of group outcomes other than

the group mean warrant careful attention in analyses involving group-level outcomes” (Burstein,

1980, p. 161).

Raudenbush and Bryk (1986) summarized the merits of using HLM was the application

of slopes as outcomes. Take the usage of educational expenditure to explain the student

achievement for example: the first step will be running regression on student achievement based

on a spending variable within each school. By applying slopes as outcomes, the estimated slopes

from this step will be the outcomes in the second step which is the analysis of variances in slopes

on the basis of other factors within classrooms.

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Raudenbush and Bryk (1986) also pointed some technical difficulties in conducting such

procedures. First, regression coefficients usually have greater sampling variability than sample

means. If the sample size is small, the regression coefficient may result in a large sampling error.

Therefore the beginning of the second step has less statistical power. Second, the sampling

precision of the estimated slopes varies across units depending on the data collection design used

within each unit. The regression analysis that is used in the second-stage usually assumes equal

variances across cases on the dependent variable. For example, the unequal variance at

classroom level, may bias the prediction at school level.

As the techniques mature, researchers are able to solve some of the difficulties to use

HLM. Beyond two-level hierarchical modeling, the emergence of three-level equations extended

the understanding of education from within school effects, between school effects, to within

classroom effects (Bryk & Raudenbush, 1988). Therefore the whole picture of education, and in

statistical terms, levels of the education system – the student, the classroom, and the school are

all under a closer examination.

Hierarchical linear modeling was used to analyze a range of education issues, one of

which being the relationship of educational expenditure and student achievement. Archibald

(2006) studied elementary schools of one school district in Nevada and applied three-level HLM

to students, teachers, and schools. She found that most of the per-pupil expenditure effects on

student achievement were explained at student level, and a small portion of the variance was at

school level while a much smaller portion was from the teachers.

A number of studies were carried out with the NELS:88 dataset because of the very

nested structure of the information collected. School finance has been an important topic for

educators for years. The application of NELS:88 in this area has been tremendous. After 20 years

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of the first wave of data collection, researchers are still using these datasets. Grubb (2008)

summarized previous knowledge about the field of education finance and pointed out one of the

often neglected aspect of research is not paying attention to the education process. Using the

NELS:88 datasets, his study investigated various aspects of school finance and found that the

most significant factor to influence student achievement is family characteristics such as SES

and parental involvement in education. In addition, the research discovered from students’

perspective that motivation and engagement, such as doing home work on time and liking school

are important to student outcomes.

There are two bold policy implications coming out of this recent study. First, the simple

statement of “money matters to education; or, money does not matter to education” is not the

right way to describe the relationship between education and expenditure, even though the results

may come out of credible empirical evidence. Based on the fact that many factors are involved in

the education process, researchers should emphasize the process of determining where money is

spent and how the money is spent before making the conclusion. Second, because almost every

school finance research has found that family characteristics are important to student

achievement, the direction for school finance reform may turn to ways to improve these family

characteristics, such as housing policies to improve family stability and welfare policies to

guarantee income (Grubb, 2008).

Methods

This dissertation employed primarily HLM analysis on the relationship among various

factors to student academic achievement. The dependent variables are a standardized test

composite with reading and mathematics, and high school GPA. These variables are also

properly weighted to represent the sample population before being used. The explanatory

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variables include gender, Black or White, SES, whether students have positive feeling about

themselves, negative feeling about themselves, time spent on study, attitude toward class, future

educational expectation, school expenditure, and student-teacher ratio. The student motivation

variables are reduced to a few factors using factor analysis.

The ELS:2002 data are nested with two levels; therefore, HLM is appropriate for the

analysis. Developed in the early 1980s, HLM is useful in this context because it allows the

researcher to use teacher and school level variables to explain variation in the individual level

parameters and provides a test for main effects and interactions between and within levels or

groups (Bryk & Raudenbush, 1988). For instance, at the student level, a basic question of interest

is whether the number of science courses taken by students positively predicts science

achievement within schools. At the school level, interest may focus on learning whether the level

of curriculum implementation within schools predicts mean science achievement across schools.

Another possibility concerns cross-level inferences, such as testing whether the level of

curriculum implementation within schools has any different effects across schools.

The first step of the dissertation research is the HLM analysis of student and school

levels. The results of the multiple linear regressions and the HLM models will be compared since

one of the critiques of education production function analysis with multiple linear regressions is

that it overlooks the nested nature of the education process, where students are grouped in

classrooms, and classrooms are grouped in schools.

Basic Regression Model

Yi = β0 + βi Xi + ri (1)

The intercept β0 is the expected value of Y when the starting point of independent

variable X is zero. βi is the parameter estimate of the independent variable X. The error term r is

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the unexplained variance by the regression function. The “i” behind each explanatory variable

and the dependent variable represents the observation number of the dataset.

Level One Model

Most people use level one model for the individual level analysis, and more often than

not, that will be student level regression. Of course, there can be more than one independent

variable shown in this single regression model. Then the regression model with “l” independent

variables will be:

Yi = β0 + β1i X1i + β2i X2i + β3i X3i + . . . +βli Xli + ri (2)

There are several forms of the models depending on the research question and the data

availability. The simplest possible hierarchical model can be the random-intercept model in

which only the intercept parameter is in the level one model. Compared with model (1), the βi in

this model is simply zero now, and it is equivalent to a one-way ANOVA which tests the random

effect.

Yi = β0 + ri (3)

Level Two Model

The next level should be the groups that the individual cases reside in. One of the merits

of HLM is that HLM estimates a set of random effects associated with each higher level unit. In

the realm of education, the second level regression can be the analysis of school characteristics.

ELS:2002 dataset provides adequate school information so the author choose the second level to

be school analysis.

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If the explanatory variables of the student level and the school level are exclusive, the

second level of regression will decompose the β0 of the level one model. For example, if the first

level is examining the student demographic impact to student test scores, the regression model

will have race (RACE), gender (GEND), socioeconomic status (SES), and student motivation

(MOV). Therefore the model will look like:

Yi = β0 + β1i (RACE)i + β2i (GEND)i + β3i (SES)i + β4i (MOV)i + ri (4)

And if the school level regression is examining the teachers’ average experience (EXP)

within school, teachers’ average education level (EDU) within school, and school funding

(FUND), the level-two model will look like:

β0 = γ00 + γ1j (FUND)j + γ2j (EXP)j + γ3j (EDU)j + rj (5)

Here the γ0 designates the expected value of β0 when all the school parameters are zero.

In other words, if the school has certain amount of funding, and default years of teaching

experience and default level of education, the value of γ0 will be the explained variance this level

two model has for the β0. The other γs are the regression coefficients of each of the level two

independent variables. The “j” means the number of schools in this dataset.

However, if the level two and level one model have overlapping explanatory variables,

for example, the research also examines the school level SES (M_SES), race (M_RACE), and

motivation (M_MOV), the level two model will be a bit complex. Beside the model (5), there

should be another model to decompose the β3 using the mean SES at school level to explain the

variance at the student level. The model should look like:

β1 = γ01 + γ1j (FUND)j + γ2j (EXP)j + γ3j (EDU)j + γ4j (M_SES)j + γ5j (M_RACE)j + γ6j

(M_MOV)j + rj (6)

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Depending on the specific nature of the research, the level two model(s) can be as many

as the independent variables in the level one model plus the intercept. After writing down all the

level two regression models, take them to the level one model and use the parts to the right of the

equations to replace the parameter estimates in the level one model. This will be the combined

model for two levels:

Yi = [γ01 + γ1j (FUND)j + γ2j (EXP)j + γ3j (EDU)j + γ4j (M_SES)j + γ5j (M_RACE)j + γ6j

(M_MOV)j + rj ]i (RACE)i + [γ02 + γ1j (FUND)j + γ2j (EXP)j + γ3j (EDU)j + γ4j (M_SES)j + γ5j

(M_RACE)j + γ6j (M_MOV)j + rj ]i (GEND)i + [γ03 + γ1j (FUND)j + γ2j (EXP)j + γ3j (EDU)j + γ4j

(M_SES)j + γ5j (M_RACE)j + γ6j (M_MOV)j + rj ]i (SES)i + [γ04 + γ1j (FUND)j + γ2j (EXP)j + γ3j

(EDU)j + γ4j (M_SES)j + γ5j (M_RACE)j + γ6j (M_MOV)j + rj ]i (MOV)i + γ01 + γ1j (FUND)j +

γ2j (EXP)j + γ3j (EDU)j + γ4j (M_SES)j + γ5j (M_RACE)j + γ6j (M_MOV)j + ri + rj (7)

In summary, the main research technique this dissertation employs is HLM on student

and school levels. The ELS:2002 dataset contains numerous variables, and the independent

variables of interest are student demographic, teacher quality, school characteristics, and other

control variables. Generated by factor analysis, student behavior factors will be included in the

model. The dependent variables are learning outcome measurements such as math and reading

test score, NAEP score, SAT score, and high school academic GPA.

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CHAPTER 4

FINDINGS OF THE STUDY

Overview

The purpose of this study was to explore the relationship between student behavioral

factors to student academic achievement in the realm of education production function. Other

factors of interest are school expenditure variables. The research employed Hierarchical Linear

Modeling (HLM) which has student level predictors and school level predictors. The adoption of

HLM enabled the research to look at a more complete picture of the education production

process as it happens with students and in schools.

To follow the research method discussion in the previous chapter, this chapter carries out

as the following: the first section described the processes of cleaning up the dataset, including

selecting variables, coding and recoding values, and checking missing values. The second

section focused on the procedures of creating factors through a set of factor analyses. The final

section rested on the HLM analysis with a series of different models which center around the

different outcome measurements.

Data Description

Data for this dissertation came from the Education Longitudinal Study of 2002

(ELS:2002) restricted version. The difference between the restricted and publicly available

datasets is that the restricted version has more extensive race/ethnicity categorization. Variables

used in this study, such as student/teacher ratio, percent free and reduced-price lunch, and

number FTE teachers are only available from the restricted-use dataset. One of the apparent

advantages is that the restricted dataset contains school resources, student enrollment, and school

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poverty information which were drawn directly from the Common Core of Data (CCD).

Therefore there is no need to merge the ELS:2002 with CCD to get the necessary variables.

Education Longitudinal Study currently has three waves in 2002, 2004, and 2006,

respectively. Some of the outcome measurements in this dissertation are taken from the 2004

follow-up (F1) and 2006 follow-up (F2) studies. These variables are the NAEP-equated

ELS:2002 math score (F1), GPA for all academic courses (F1), student ever dropped out (F2),

and highest level of education attempted (F2). Most of the independent variables are drawn from

the base year study. The sample weight variable is the student expanded sample weight from the

base year restricted dataset. This variable has a more accurate reflection of the entire student

population then the regular sample weight from the public dataset, although these two weight

variables do not show significant difference statistically. The adoption of the restricted weight

variable enable the dataset to represent the actual student population nationally.

The data for the present study has a sample of about 16,000 students. These students are

nested in more than 700 schools, which have an average of 23 students per school. The average

student number is usable, and the school number is big enough for multilevel models (Bickel,

2007). Due to the nature of the survey, there are 5%-30% missing values for the variables this

dissertation uses. During the data preparation stage with SPSS software, the statistical procedures

choose pairwise technique whenever possible to maximize the number of students. At the stage

of factor analysis, some cases are dropped because of the missing value, and basic statistical tests

are adopted to show that the cases in use and the cases excluded from the factor analysis do show

significant difference in terms of mean value and standard deviation. Linear trend at a point

imputation technique is used to replace missing values so that the new factors are statistically

alike to the original ones.

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Factor Analysis

As Meyers, Gamst, and Guarino (2006) pointed out, factor analysis has two distinct

advantages. The usage of factor analysis can reduce a relatively large number of variables to a

much smaller number of factors. The final factors, through appropriate factor analysis

procedures, are also the constructs that best represent the inventory of the set of variables.

Furthermore, factor analysis is a useful tool for researchers to organize or conceptualize a set of

measures. The final version of factors should have meanings that best represent the research

purposes.

Factor analysis separates the total variance of each variable into two parts. The first part

is the common or shared variance with other variables in the analysis. The second part is the

variance unique to the variable itself. During the extraction process, factor analysis adopts only

the commonly shared variance. Multiple factors constitute a factor matrix, which displays how

much each variable has its variance loaded on the factors. A good measure of the magnitudes of

factors extracted from the process is the amount of common variance each factor accounts for.

Each variable has a portion of variance captured by the factor. This portion of variance is the

loading score of a factor matrix (Kim & Mueller, 1979). The dissertation uses the Principal Axis

Factoring method in SPSS to create all the four groups of factors.

There are a number of criteria to gauge the quality of factors produced by factor analysis.

The first criterion is the problem of multicollinearity, which is tested by looking at the initial

communalities. The rule of thumb is to make sure all the initial communalities are all less than

0.8 to clear the potential multicollinearity problem (Kim & Mueller, 1979). The second criterion

is the problem of outlier, which is also checked from the initial communalities. The rule of

thumb is that none of the initial communalities is less than 0.1 to clear the potential outlier

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problem (Kim & Mueller, 1979). The third test is the factorability of a set of variables. This test

is to check the correlation matrix and if some of the correlations are greater than 0.3, then the

factor analysis is a good method for this set of variables (Kim & Mueller).

Bartlett's Test of Sphericity is an important test in factor analysis. It calculates the

determinate of the matrix of the sums of products and cross-products from which the inter-

correlation matrix is derived. The determinant of the matrix is converted to a chi-square statistic

and tested for significance (Kim & Mueller, 1979). The null hypothesis is that the inter-

correlation matrix comes from a population in which the variables are non-collinear (i.e. an

identity matrix, which is a matrix repeats itself diagonally). If the significance level is less than

0.05, the null hypothesis is rejected (Kim & Mueller).

It is also important to check the Kaiser-Meyer-Olkin (KMO) test for the final factor(s). It

measures the degree of common variance among the variables. Usually, the closer the number is

to one, the better the factor(s) may be. In other words, the factors extracted account for a

substantial amount of variance when KMO is high (Kim & Mueller, 1979). The last criterion is

to check the final factor matrix and examine the factor loadings of each of the variables included

in the factor. The factor loading is the portion of variance the factor captures from each of the

variables. If the loading is greater than 0.5, that means the variable is properly loaded onto the

factor. Otherwise the variable should be dropped from the factor. If there are multiple factors

extracted, it is suggested to go with the factor that has the strongest loading (Kim & Mueller,

1979).

This dissertation included four sets of factor analysis. The target factors were in the area

of expectation on learning, motivation on learning, attitude on learning, and parental

involvement on student learning. Each factor analysis used about 15 variables, and only the

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variables with a factor loading above 0.45 were kept in the factor. The following sections are

factor analysis processes carried out exactly according to the six criteria discussed above.

Meyers, Gamst, and Guarino (2006) mention that no factor should have fewer than three

variables, and it is not the case here for the four sets of factor analysis.

Table 4 shows the results of the first set of factor analysis on student expectation on

learning. There were two factors formulated based on the variables used. Comparing the two

factors, the first one captured much more variable information in terms of factor loadings.

Therefore, the final factor for expectation was only the first factor.

Table 4

Summary of Variables and Factor Loadings matrix of FEXP

Variables Used in Student Educational

Expectation Factor (FEXP)

Factor Loadings Initial

Communalities 1 2

Can do excellent job on math tests .656 -.487 .670

Can understand difficult math texts .653 -.476 .708

Can understand difficult English texts .635 .412 .635

Can learn something really hard .684 .039 .496

Can understand difficult English class .705 .459 .700

Remembers most important things when studies .654 .175 .473

Can do excellent job on English assignments .725 .485 .724

Can do excellent job on English tests .719 .470 .724

Can understand difficult math class .708 -.482 .717

Can master skills in English class .729 .445 .699

Can get no bad grades if decides to .683 .022 .499

Can get no problems wrong if decides to .679 -.134 .485

Can do excellent job on math assignments .746 -.477 .744

Can learn something well if wants to .752 .009 .602

Can master math class skills .752 -.457 .739

Extraction Method: Principal Axis Factoring. 2 factors extracted. 5 iterations required.

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Table 5 shows the results of the second set of factor analysis on student motivation on

learning. There were three factors formulated based on the variables used. Comparing the three


Therefore, the final factor for motivation is only the first factor.

Table 5

Summary of Variables and Factor Loadings matrix of FMOV

Variables Used in Student Educational

Motivation Factor (FMOV)


Communalities 1 2 3

How much likes school .656 -.487 .318 .318

Classes are interesting and challenging .653 -.476 .470 .470

Satisfied by doing what expected in class .635 .412 .470 .470

Education is important to get a job later .684 .039 .276 .276

Importance of good grades to student .705 .459 .398 .398

Importance of getting good education .654 .175 .303 .303

Gets totally absorbed in mathematics .725 .485 .225 .225

Mathematics is important .719 .470 .289 .289

Studies to get a good grade .708 -.482 .497 .497

Studies to increase job opportunities .729 .445 .581 .581

Studies to ensure financial security .683 .022 .534 .534


Table 6 shows the results of the second set of factor analysis on student attitude on

learning. There were four factors formulated based on the variables used. Comparing the three


Therefore, the final factor for attitude was only the first factor.

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Table 6

Summary of Variables and Factor Loadings matrix of FATD

Variables Used in Student Attitude Toward

Learning Factor (FATD)


Communalities 1 2 3 4

How many times late for school .496 -.036 .442 .070 .496

How many times cut/skip classes .478 -.058 .406 .085 .478

How many times got in trouble .467 -.006 .188 .301 .467

How often student completes homework (English) .710 .257 -.144 -.169 .710

How often student completes homework (math) .704 -.328 -.208 -.116 .704

How often student is absent (English) .525 .151 .122 -.365 .525

How often student is absent (math) .511 -.207 .121 -.293 .511

How often student is tardy (English) .561 .248 .090 -.020 .561

How often student is tardy (math) .560 -.170 .078 .045 .560

How often student is attentive in class (English) .666 .395 -.189 -.053 .666

How often student is attentive in class (math) .688 -.380 -.253 .005 .688

How often student is disruptive in class (English) .540 .301 -.140 .315 .540

How often student is disruptive in class (math) .543 -.156 -.177 .323 .543


Table 7 shows the results of the second set of factor analysis on student attitude on

learning. There were just one factor formulated based on the variables used. The factor loadings

were relatively high comparing with 0.45. This factor was also the final factor for parental

involvement on student learning.

Table 7

Summary of Variables and Factor Loadings matrix of FPAR

Variables Used in Student Parental School Involvement

Factor (FPAR)

Factor Loading Initial

Communalities 1

How often discussed school courses with parents .714 .461

How often discussed school activities with parents .705 .457

How often discuss things studied in class with parents .740 .475

How often discussed grades with parents .647 .383

How often discussed prep for ACT/SAT with parents .594 .331

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How often discussed going to college with parents .687 .429

How often discussed current events with parents .595 .313

How often discussed troubling things with parents .561 .283


For all the four factors, the initial communalities show that there was no multicollinearity

problem or outlier problem. All the four sets of the factor analyses were factorable, which meant

that the correlation matrix had at least one correlation that is greater than 0.3. The results of the

Bartlett's Test of Sphericity and the Kaiser-Meyer-Olkin test were shown in Table 8. The results

showed that these factor analyses were valid and statistically solid.

Table 8

Results of Bartlett's and Kaiser-Meyer-Olkin Tests

Factor Bartlett's KMO

FEXP 0.000 0.938

FMOV 0.000 0.850

FATD 0.000 0.866

FPAR 0.000 0.899

Treating Missing Values

Pairwise case selection is adopted to maximize the most number of cases in the process

of factor analysis. The overall cases left in the factors are shown in Table 9.

Table 9

Case Numbers of Factors (rounded to closest hundreds)

Factor FEXP FMOV FATD FPAR

Valid Cases 10000 9900 9200 12000

The case numbers indicate that there are significant amount of cases left out of the

factoring process. To make sure the cases used and the cases not used do not have statistical

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difference, descriptive analysis of these cases against the other variables, and T-test are

performed. The results are shown in Table 10 – Table 13.

Table 10

Factor Analysis Missing Values Check (FEXP) (rounded to closest hundreds)

Variables N (In) N (Out)

Mean (In)

Mean (Out)

SD (In) SD (Out)

T-Test

Gender 10000 5400 0.53 0.46 0.499 0.498 0.000 Race 10000 5300 6.34 5.72 2.294 2.376 0.000

Total years teaching/K-12 7300 3700 14.67 14.38 7.858 7.831 0.064

Highest degree earned by the teacher

7400 3800 3.99 3.98 0.772 0.785 0.767

Type of certification held 7300 3700 4.55 4.5 0.913 0.958 0.017

Standardized test math and reading

10000 6000 52.00 48.39 9.717 9.737 0.000

NAEP-equated ELS:2002 math score

8500 5100 156.89 145.99 32.512 34.255 0.000

GPA for all academic courses

8100 4800 14.03 13.32 28.125 27.415 0.158

Most recent SAT composite score

3900 1900 1051.66 997.31 200.662 218.735 0.000

Table 11

Factor Analysis Missing Values Check (FMOV) (rounded to closest hundreds)

Variables N (In) N (Out)

Mean (In)

Mean (Out)

SD (In) SD (Out)

T-Test

Gender 10000 5400 0.53 0.46 0.499 0.498 0.000 Race 10000 5300 6.34 5.72 2.294 2.376 0.000



7400 3800 3.99 3.98 0.772 0.785 0.234



10000 5900 52.00 48.39 9.717 9.737 0.000


8500 5100 156.89 145.99 32.512 34.255 0.000

GPA for all academic 8100 4800 14.03 13.32 28.125 27.415 0.251

77

courses


3900 1900 1051.66 997.31 200.662 218.735 0.000

Table 12

Factor Analysis Missing Values Check (FATD) (rounded to closest hundreds)

Variables N (In) N

(Out)

Mean

(In)

Mean

(Out)

SD (In) SD

(Out)

T-Test

Gender 10000 5400 0.53 0.46 0.499 0.498 0.226

Race 10000 5300 6.34 5.72 2.294 2.376 0.000



7400 3800 3.99 3.98 0.772 0.785 0.654



10000 5900 52.00 48.39 9.717 9.737 0.000


8500 5100 156.89 145.99 32.512 34.255 0.000


8100 4800 14.03 13.32 28.125 27.415 0.001


3900 1900 1051.66 997.31 200.662 218.735 0.000

Table 13

Factor Analysis Missing Values Check (FPAR) (rounded to closest hundreds)

Variables N (In) N

(Out)

Mean

(In)

Mean

(Out)

SD (In) SD

(Out)

T-Test

Gender 10000 5400 0.53 0.46 0.499 0.498 0.000

Race 10000 5300 6.34 5.72 2.294 2.376 0.000



7400 3800 3.99 3.98 0.772 0.785 0.395



10000 6000 52.00 48.39 9.717 9.737 0.000


8500 5100 156.89 145.99 32.512 34.255 0.000


8100 4800 14.03 13.32 28.125 27.415 0.055

78


3900 1900 1051.66 997.31 200.662 218.735 0.000

These tables show that missing values caused about 30% – 35% of cases to be excluded

from the four factors created by factor analysis. The results of these tests, especially the T-test

showed that there were significant differences between the cases in the four factors and the cases

out of the four factors. In other words, the cases in and out of the factors had different means and

standard deviations, according to some of the variables used in the analysis. This could be a

potential bias to the reliability of these factors.

To improve the quality of these four factors, the problem of missing values needed to be

addressed. The easiest method to fix missing values is the deletion method, which included

listwise deletion and pairwise deletion. The author viewed deletion as the last resort of treating

missing values; therefore, this dissertation did not use either of them to fix the missing value

problems for the factors.

Another strategy to solve the missing value problem is to use the single imputation

technique, which replaces the missing value with something else. McKnight, McKnight, Sidani,

and Figuerudo (2007) discussed three types data replacement: constant, random, and nonrandom.

The first type may include the mean or median values of the variable or even zero. Random

replacement is related with a random function. Nonrandom replacement brings in part or all of

the other cases in the variable to be fixed. The missing value can be replaced by a mathematical

calculation of adjacent values or by a regression model using all of the non-missing values. This

dissertation adopts the regression replacement method to improve the missing value conditions

of the factors.

SPSS offers a number of single imputation strategies to replace missing values. The

series mean strategy replaces missing values with the mean of the entire variable. The mean of

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nearby points replaces missing values with the mean of valid surrounding values, which are the

valid values above and below the missing value. Similarly, median of nearby points replaces

missing values with the median of valid surrounding values. Linear interpolation replaces

missing values using a linear interpolation that is based on the last valid value before the missing

value and the first valid value after the missing value. Linear Trend at Point (LTP) method

replaces missing values with the linear trend for that point based on the regression of the entire

series. The missing values are replaced with their predicted values.2

The first four strategies rely heavily on either the mean value of some or part of the data,

or the median of part of the data. The LTP method projects the missing value be regression and

on the entire variable. Therefore, the LTP method is adopted to fill in the missing values in this

study. The new factors with no missing values and the original factors are compared by ANOVA

test. The results are shown in Table 14.

Table 14

ANOVA test of Factors with and without Missing Values

Factor F Value Significance

FEXP 0.054 0.947

FMOV 0.154 0.858

FATD 0.000 0.995

FPAR 1.028 0.358

These results indicated that the four new factors were statistically inseparable from the

four original factors. The new factors still had the identities of valid factor analysis but were

immune from the missing value problem.

2 Source: SPSS Help Function. Topic: Estimation Methods for Replacing Missing Values.

80

The technique to handle missing value problems employed in this dissertation was by no

means the most advanced. Besides single imputation method which was used in this study and

deletion method discussed briefly in the previous section, there were also model-based

procedures to correct missing value. According to McKnight et al. (2007), model-based

procedures include maximum likelihood, expectation maximization, Markov chain Monte Carlo,

and other adjustments. These procedures are usually derived from underlying distribution,

probability, or theoretical models; and these procedures treat the missing data as if they can be

observed to produce robust parameter estimates (McKnight et al., 2007). The model-based

procedures are complex in nature, and some techniques can be quite cumbersome for analyses

using multiple iterations. Therefore, this study did not adopt these procedures.

Another option is the multiple imputation (MI), which is available from SAS software.

Although this analysis did not use this method, but considering the importance of its application,

some of the usages from multiple imputations to deal with missing values were explained.

Multiple imputation (MI) on the other hand, is viewed as the “gold standard” of current

research (Treiman, 2009). The critical feature of MI is the ability to estimate the influence of the

missing data on parameter estimation (McKnight et al., 2007). Proposed by Rubin (1977), MI is

a method of generating multiple simulated values for each incomplete dataset, and then

iteratively analyzing datasets with each simulated value substituted in turn. The purpose is to

generate estimates that better reflect true variability and uncertainty in the data than do

regression methods. MI procedure replaces each missing value with a set of plausible values that

represent the uncertainty about the right value to impute. These multiple imputed data sets are

then analyzed by using standard procedures for complete data and combining the results from

these analyses (Yuan, 2000).

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Variables

To fulfill the research purposes, the data were used to construct a comprehensive set of

individual-level and school-level variables to measure the various effects on student

achievement. The way most of the variables in ELS:2002 were coded are not directly useable for

dissertation analysis; therefore, additional steps were needed to clean up the raw data. These

additional steps included adjusting missing values, reversing values to proper order, and

conducting factor analysis to create necessary factors.

Student-level variables were shown in Table 15. There were three types of variables:

continuous variables, dichotomous variable, and factors. Several classes of student-level

variables were constructed. The first was demographic including gender, race, and

socioeconomic status (SES) variables. The SES variable was a composite measure developed by

NCES that captures father’s education level, mother’s education level, family income, father’s

job type, and mother’s job type3.

The next class of factors was created through factor analysis (See factor analysis section

for the detailed procedures and lists of variables used to generate the factors). There were four

type of student learning behavior factors. The first factor was the student educational expectation

(FEXP) that measured how much students want to pursue higher level of education. The second

factor was the student educational motivation (FMOV) that measures how motivated students

were to learn. The third factor was the student attitude toward learning (FATD) that measures

how much effort students put in learning. The last factor was the parental school involvement

(FPAR) that measured the degree of involvement of parents to students learning. The difference

between this factor and the SES composite variable was that the SES was about the financial

3 Source: ELS Electronic Code Book variable description.

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capital and educational background of the family, while the FPAR was about the behavior of

parents on student learning. The inclusion of FPAR intends to covered a broader range of family

characteristics.

The third class of variables was output measures. They included standardized test

composite math and reading, NAEP-equated ELS:2002 math score, GPA for all academic

courses, and most recent SAT composite score. Each of them became a separate dependent

variable in the later part of the analysis. Overall, the school-level variables showed median range

variance.

Table 15

Means, Standard Deviations, and Descriptions of Student-Level Variables

Variable Mean SD Type Description from ELS:2002

Demographic Variables

GENDR 0.50 0.500 D Female = 1

ASIAN 0.09 0.289 D Asian = 1

BLACK 0.13 0.339 D Black = 1

HISPN 0.15 0.353 D Hispanic = 1

WHITE 0.17 0.495 D White = 1

SESC 0.42 0.743 C Socioeconomic Status Composite

Student Learning Behavior Factors (missing value treated)

FEXP 0.02 0.768 F Student Educational Expectation Factor *

FMOV 0.00 0.741 F Student Educational Motivation Factor *

FATD 0.05 0.703 F Student Attitude Toward Learning Factor *

FPAR 0.01 0.802 F Parental School Involvement Factor *

Student Academic Achievement Variables

TCMR 50.66 9.880 C Standardized test composite math and reading

NAEP 152.81 33.591 C NAEP-equated ELS:2002 math score (F1)

GPA 2.57 0.835 C GPA for all academic courses (F1)

SATC 1034.2 208.161 C Most recent SAT composite score

C = Continuous Variable, D = Dichotomous Variable, and F = Factor * See Table 4 - 7 for the lists of variables used in the factor analysis

School-level variables are shown in Table 16. There were three types of variables:

continuous variables, dichotomous variable, and factors. Several classes of school-level variables

83

were constructed. The first was student composite which were the mean values of student-level

variables: Mean Socioeconomic Status Composite (MSESC), Mean Student Educational

Expectation Factor (MFEXP), Mean Student Educational Motivation Factor (MFMOV), Mean

Student Attitude Toward Learning Factor (MFATD), and Mean Parental School Involvement

Factor (MFPAR).

The next class of variables was measures of teacher characteristics. They were the mean

total years teaching/K-12, the mean type of certification held, and the mean highest degree

earned by the teacher. These variables were also proxies for part of school expenditures.

The last class of variable is school structural characteristics which included school type

(public or private), school urbanicity (urban or rural), total school enrollment, percent minority,

student/teacher ratio, % full-time certified teachers, percent free and reduced-price lunch. Among

these, student/teacher ratio, % full-time certified teachers were two of the school expenditure

proxies. All the school-level variables were included in the second level model of the HLM

analysis (see HLM section for more technical details).

Table 16

Means, Standard Deviations, and Descriptions of School-Level Variables

Variable Mean SD Type Description from ELS:2002

Student Composites

MSESC 0.04 0.434 C Mean Socioeconomic Status Composite

MFEXP 0.02 0.227 F Mean Student Educational Expectation Factor

MFMOV 0.01 0.212 F Mean Student Educational Motivation Factor

MFATD 0.05 0.245 F Mean Student Attitude Toward Learning Factor

MFPAR 0.01 0.255 F Mean Parental School Involvement Factor

Teacher Characteristics

MTEXP 14.60 5.661 C Mean total years teaching/K-12

MTCRT 4.51 0.824 C Mean type of certification held

MTDEG 4.00 0.601 C Mean highest degree earned by the teacher

Structural Characteristics

SURB 0.33 0.471 D School urbanicity (Urban = 1)

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SENR 1245.86 846.904 C Total school enrollment

SPMN 34.05 31.471 C Percent minority

SSTR 16.46 4.367 C Student/teacher ratio

SPTC 91.21 19.917 C % full-time teachers are certified

SPFL 24.91 19.462 C Percent free and reduced-price lunch

C = Continuous Variable, D = Dichotomous Variable, and F = Factor

Hierarchical Linear Modeling

Schreiber and Griffin (2004) reviewed academic articles using multilevel modeling in

The Journal of Educational Review for 10 years (1992-2002). They generalized a common

framework of carrying out multilevel modeling and a standardized reporting style. This

dissertation referred to their modeling and reporting approaches in the HLM stage. Schreiber and

Griffin (2004) introduced three models of HLM. The first model is the basic model with no

predictors in either level. It is also referred as the one-way ANOVA model or the “fully

unconditional model” (Raudenbush & Bryk, 2002). This model provides the critical information

of whether multilevel research is necessary by checking the Intraclass Correlation Coefficient

(ICC). “ICC measures the proportion of the total variance that occurs systematically between

groups (Raudenbush & Bryk, 2002, p. 36).” Multi-level methods need to be used when the ICC

is greater than 10%, which means there is more than 10% of the total variance coming from

between groups (Lee, 2000). Later in this analysis the results demonstrate that across all four

outcome measures, each of them satisfies the threshold of ICC, in that more than 10% of the total

variation is from the school level (see Figure 8 for details).

Referred to as the means-as-outcome model (Raudenbush & Bryk, 2002), model 2 has

only school-level predictors and leaves the student level empty. The purposes of this model is to

test whether controlling for school-level variables, ICC shows any change. The anticipated

change is for ICC to decrease, which means the school-level predictors are capturing significant

variances in explaining the outcome variables.

85

Although not included by Schreiber and Griffin (2004), this dissertation adds a third

model for each of the outcome variables. Model 3 is also called the random coefficient model

(Raudenbush & Bryk, 2002). This model only has student-level variables to test the effects of the

individual predictors on the outcome measures.

The final model is an intercepts & slopes-as-outcome model (Raudenbush & Bryk, 2002).

Model 4 contains both student-level and school-level predictors. The four models altogether not

only show the proportion of variance on each level, but also show the change in the explanatory

power of model overall as more variables are added to the models. The following sections are

description of the 4 models by each outcome measures: math and reading test score, NAEP

score, high school GPA, and SAT score.

Math and Reading Test Score

One-way ANOVA Model (Model I)

Model I is a one-way ANOVA model. There is no predictor at both student level and

school level. The dependent variable is math and reading standardized test score composite. This

test score is a norm-referenced measurement of achievement based on the estimate of

achievement relative to the population4. This model is to partition the total variance in the

student achievement into within and between school components, and to see if there is

significant difference in test scores among schools.

The results show that the grand mean student achievement is 50.06. The reliability of the

sample means for the true school mean is 0.855, which indicates that the sample means are quite

reliable as indicators of the true school mean.

4 Source: ELS Electronic Code Book variable description.

86

Results also show that the variability exist across schools (23.33) is statistically

significant at 0.000 level, so that the null hypothesis that the variance across schools equals 0 is

rejected. The intraclass correlation coefficient ρ = τ00 / (τ00 + σ2) = 23.33 / (23.33 + 77.03) =

0.23. This suggests that 23% of the total variance in math and reading standardized test score

exists across schools. Since this number is greater than 0.1, the dataset qualifies for multilevel

analysis. In other words, the results of this empty model show that math and reading test score

has enough variability at the student and school levels for further analysis with HLM.

Means-as-outcome Model (Model II)

Model II is means-as-outcome model. To account for the variance across schools, the

Mean Socio-Economic Status (MSES), the Mean Student Expectation (MFEXP), the Mean

Motivation (MFMOV), the Mean Attitude (MFATD), Mean Parent Involvement (MFPAR),

Mean Teacher Experience (MTEXP), Mean Teacher Certification (MTCRT), Mean Teacher

Highest Degree (MTDEG), School Urbanicity (SURB), School Enrollment (SENR), School

Percent Minority (SPMN), School Student-Teacher Ratio (SSTR), School Percent Teacher

Certified (SPTC), and School Percentage of Student Receive Free and reduced-Price Lunch

(SPFL) variables are included in the level 2 model. All these school-level variables are grand

mean centered. The results show that the grand mean of math and reading standardized test score

composite is 49.37, which is relatively the same as in Model I.

MSES, MFEXP, and MFATD all show significant effects on school mean test scores at

.000 level. MFMOV and MFPAR show insignificant effect on school mean test scores. These

results mean that higher mean SES, educational expectation, and attitude toward learning, tend to

have higher level of mean test score composite. Among the teacher characteristics and school

characteristics variables, only the SPMN and SPFL show significant impact to student

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achievement. These relationships are both negative meaning that the higher the percentages of

minority and free and reduced-price lunch students in the school, the lower the students score in

the tests.

The reliability 0.523 is a conditional reliability with which we can discriminate among

schools with the same mean predictors at the school level. Controlling these school level

variables, the variance in mean student achievement among schools decreases dramatically,

which is also suggested by the decreased intraclass correlation coefficient ρ = τ00 / (τ00 + σ2) =

4.08 / (4.08 + 79.22) = 0.05 (was 0.23 in Model 1). Comparing with the one-way ANOVA

model, adding school-lever predictors decreases the variance among schools from 23.33 to 4.08.

In other words, 82.5% of the variance in mean math and reading standardized test score

composite between schools is explained by the school-level variables {[τ00(ANOVA) -

τ00(current)] / τ00(ANOVA) = (23.33 – 4.08) / 23.33 = 0.825}. Overall, Model II has more

predicting power then Model I at school level.

Random Coefficient (RC) Model (Model III)

Model III is a random coefficient model. In this model, students’ Socio-Economic Status

Composite (SESC), Expectation Factor (FEXP), Motivation Factor (FMOV), Attitude Factor

(FATD), Parent Involvement Factor (FPAR), Student Gender (GENDR), and racial variables are

included as predictors at student level. All these variables are group centered. There is no school-

level predictor in this model. The average intercept is quite reliable with reliability at 0.878.

The grand mean math and reading standardized test score composite is a bit higher at

50.08. All the student-level predictors, except for the gender variable, are significant at 0.000

level. The results show that, on average, students who have higher SES tend to do better in the

tests. Students who have higher expectations of their education and higher attitude tend to have

88

higher test scores. However, surprisingly, the results also show that students who have stronger

motivations of education tend to have lower test scores. The parent involvement factor is

significant too. White and Asian students tend to have better test scores than Black and Hispanic

students. Overall, Black students have significantly lower test scores than others. Student SES,

expectation, and attitude all show very strong positive impact on test scores.

The inclusion of student level variables decreases variances at student level from 77.03 to

52.21. That is, 33.2% of the variance at student level is explained by these student level variables

altogether {[σ2 (ANOVA) - σ2 (current)] / σ2 (ANOVA) = (77.03 – 52.21) / 77.03 = 0.332}.

Comparing the proportions of variances explained by these variables at student level (33.2%) in

the current model and at school level (82.5%) in the means-as-outcome model, it seems these

variables have stronger effects at school level than at student level. The mean math and reading

standardized test score composite still varies significantly across schools at 0.000 level.

The random part of the student level model as a whole shows that mean levels of math

and reading scores still vary across schools after controlling for the ten student-level variables.

Although insignificant, the random part of gender variable does indicate heterogeneity of

regression slopes exists for gender. Similarly, regression slopes vary across school for Hispanic

and all the student behavior variables.

Intercepts & Slopes-as-outcome Model (Model IV)

Model IV is an intercepts & slopes-as-outcome model. In this model, school level

predictors MSES, MFEXP, MFMOV, MFATD, MFPAR, MTEXP, MTCRT, MTDEG, SURB,

SENR, SPMN, SSTR, SPTC, and SPFL are included. The conditional reliability of the average

intercept is 0.595, and the conditional reliability of the other slopes is around 0.10. This number

is low because these predictors as a whole have explained much variance in the achievement

89

slope, making it more difficult to detect additional variance; hence the individual slopes are not

very high. Student level predictors SESC, FEXP, FMOV, FATD, FPAR, GENDR, and four

racial variables are included.

Overall the results reflect the means-as-outcome model and the random coefficient model

in terms of the significance of school-level and student-level predictors. On the school level, the

results show that that the grand mean math and reading standardized test score composite is

49.42. Schools with higher mean SES tend to have higher level of student achievement (γ01

=6.33). Students in schools where there are higher mean learning expectations tend to have

higher level of achievement (γ02 =4.04). Students in schools of higher mean learning attitude tend

to show higher level of learning outcome (γ04 =4.26). Students in schools with higher percentage

minority students tend to have lower level of student achievement, but the relationship is weak

(γ011 = – 0.04). Schools with higher percentage of free and reduced-price lunch tend to have a

lower level of student achievement, but again the relationship is weak (γ014 = – 0.03). The other

school level predictors do not present statistical significance.

On the student level, the Asian Student (ASIAN) variable turns to be insignificant. White

Student (WHITE), Black Student (BLACK), and Hispanic Student (HISPN) variables remain

significant, and the directions of the relationships are the same as in the random coefficient

model. SESC, FEXP, FMOV, FATD, and FPAR variables are all significant. The school-level

composites under each student-level variable in general show little impact since very few of

them are statistically significant. The heterogeneity of regression slopes still exists for the

student-level variables, although the scale decreases for most of these variables. This is an

indication that certain amount of variance picked up by the decomposition of school-level

predictors.

90

Since there are two levels of inferences, student-level variables are modeled with the

school-level variables in Model IV. Eight variables – Black student, Hispanic student, White

student, expectation, motivation, attitude, and parental involvement – were observed to vary

among schools, and because of this variability, these eight variables can be modeled with school-

level variables. This decomposition means that each randomly varying coefficient at student-

level becomes a model. The school-level variables that are observed to be significantly related to

the random coefficients, or in other words, some school-level variables show influences to

student-level slopes.

Among the eight significant student-level variables, five of them were observed to have

significant school-level predictors. Take Black student variable for example, school mean

expectation and mean teacher experience accounted some of the variability in BLACK slope.

The result implies that, on average, the impact of Black students on math and reading scores

increases from negative to positive if the students are in schools where students have higher

expectations and teachers have a bit more experience, although the impact from mean teacher

experience is smaller than that of student expectation. Figure 2 illustrates the fact that although

being a Black student tends to have a negative impact on achievement, however, Black students

in a school of high education expectation usually have better chances of learn more.

91

Figure 2. Math and reading scores vs. Black plot with focus of mean expectation

Also, the impact that student expectation has toward achievement tends to drop a little if

students are in schools where more teachers have certification, while the impact may increase a

little if students are in schools where there are more minority students. Among all the student-

level variables that are modeled by school-level variables, BLACK shows the strongest effect

from mean expectation variable. Examining the random effects, 14.4% the proportion of

variance of the BLACK coefficient is explained by school mean expectation {τ03 (Model III) -

τ03 (Model IV) / τ03 (Model IV) = (8.83 – 7.56) / 7.56 = 0.144}.

The school level predictors as a whole explain 79.9% of the variance in student math and

reading standardized test score composite among schools {[τ00(RC) - τ00(current)] / τ00(RC) =

(24.02 – 4.82) / 24.02 = 0.799}. All the results from the four models are shown in Table 17.

92

Table 17

Results for Four Model (Standard Coefficient) on Student Math, Reading Test Score

I II III IV Fixed Effects School Mean, γ00 50.06*** 50.74*** 50.08*** 49.42*** School-level Variables Mean SES, γ01 6.24*** 6.33*** Mean Expectation, γ02 4.14*** 4.04*** Mean Motivation, γ03 -0.71 -0.26 Mean Attitude, γ04 3.97*** 4.26*** Mean Parent Involvement, γ05 -0.53 0.74 Mean Teacher Experience, γ06 0.02 0.03 Mean Teacher Certification, γ07 -0.05 -0.05 Mean Teacher Degree, γ08 0.16 0.08 School Urbanicity, γ09 -0.20 -0.22 School Enrollment, γ010 -0.00 -0.00 School % Minority, γ011 -0.05*** -0.04*** School Student/Teacher, γ012 -0.05 -0.06 School % Teacher Certified, γ013 -0.00 0.00 School Free Reduced Lunch, γ014 -0.03* -0.03 Student-level Variables Gender, γ10 -0.06 0.06 Asian Student, γ20 1.81*** 0.94 Black Student, γ30 -3.16*** -3.31*** Mean Expectation, γ32 6.66* Mean Teacher Experience, γ36 0.19* Hispanic Student, γ40 -1.98*** -1.92*** White Student, γ50 2.16*** 2.18*** SES, γ60 3.14*** 3.19*** Expectation, γ70 2.91*** 2.80*** Mean Teacher Certification, γ77 -0.93* School % Minority, γ79 0.75* Motivation, γ80 -0.92*** -0.92*** Mean Teacher Degree, γ88 -0.64* School Urbanicity, γ89 -1.14** Attitude, γ90 2.36*** 2.38*** School % Minority, γ911 -0.01* Parent Involvement, γ100 0.43*** 0.52*** Mean Expectation, γ102 -1.63*

Random Effects τ00 23.33*** 4.08*** 24.02*** 4.82*** τ01 1.81* 1.10* τ02 5.84 6.60 τ03 8.83 7.56 τ04 13.87* 11.53* τ05 11.81 13.54 τ06 2.27*** 1.65** τ07 1.28*** 1.18** τ08 1.96*** 2.17*** τ09 1.25** 0.73* τ10 1.04* 0.92* σ

2 77.03 79.22 52.21 52.78 ρ 0.23 0.05

93

*** p<0.000, ** p<0.01, * p<0.05; All school-level predictors are grand mean centered; All student-level predictors are group mean centered.

NAEP Scores



school level. The dependent variable is student NAEP score. This test score information is from

the first follow-up survey in 2004. This model is to partition the total variance in the student

achievement into within and between school components, and to see if there is significant

difference in test scores among schools.

The results show that the grand mean student achievement is 149.78. The reliability of

the sample means for the true school mean is 0.817, which indicates that the sample means are

quite reliable as indicators of the true school mean.

Results also show that the variability exists across schools (236.56) is statistically


rejected. The intraclass correlation coefficient ρ = τ00 / (τ00 + σ2) = 236.56 / (236.56+ 887.14) =

0.21. This suggests that 21% of the total variance in NAEP score exists across schools. Since this

number is greater than 0.1, the dataset qualifies for multilevel analysis. In other words, the

results of this empty model show that NAEP scores have enough variability at the student and

school levels for further analysis with HLM.





94






mean centered. The results show that the grand mean of NAEP score is 147.19, which is

relatively the same as in Model I.

MSES, MFEXP, and MFATD all show significant effects on school mean NAEP scores

at .000 level. MFMOV and MFPAR show insignificant effect on school mean test scores. These

results mean that higher mean SES, educational expectation, and attitude toward learning, tend to

have higher level of mean test score composite. Among the teacher characteristics and school

characteristics variables, only the SPMN and SPFL show significant impact to student

achievement. These relationships are both negative meaning that the higher the percentages of

minority and free and reduced-price lunch students in the school, the lower the students score in

the tests.





45.73 / (45.73 + 908.69) = 0.05 (was 0.21 in Model I). Comparing with the one-way ANOVA

model, adding school-lever predictors decreases the variance among schools from 236.56 to

45.73. In other words, 80.7% of the variance in mean NAEP score between schools is explained

95

by the school-level variables {[τ00(ANOVA) - τ00(current)] / τ00(ANOVA) = (236.56 – 45.73) /

236.56 = 0.807}. Overall, Model II has more explanatory power than Model I at school level.







The grand mean NAEP score is a at 150.16. All the student-level predictors, except for

the parental involvement variable, are significant at 0.000 level. The results show that, on

average, students who have higher SES tend to do better in the tests. Students who have higher

expectations of their education and higher attitude tend to have higher test scores. However, the

results also show that students who have stronger motivations of education tend to have lower

test scores. White and Asian students tend to have better test scores than Black and Hispanic

students. Overall, Black students have significant lower NAEP scores than otherwise. Student

SES, expectation, and attitude all show very strong positive impact on NAEP scores.

The inclusion of student level variables decreases variances at student level from 887.14

to 589.26. That is, 33.6% of the variance at student level is explained by these student level

variables altogether {[σ2 (ANOVA) - σ2 (current)] / σ2 (ANOVA) = (887.14 – 589.26) / 887.14 =

0.336}. Comparing the proportions of variances explained by these variables at student level

(33.6%) in the current model and at school level (80.7%) in the means-as-outcome model, it

seems these variables have stronger effects at school level than at student level. The mean NAEP

score still varies significantly across schools at 0.000 level.

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The random part of the student level model as a whole shows that mean levels of NAEP

scores still vary across schools after controlling the 10 student-level variables. Although

insignificant, the random part of parental involvement variable does indicate heterogeneity of

regression slopes exists for parental involvement. Similarly, regression slopes vary across school

for HISPAN, WHITE, SES, motivation, and attitude variables.




SENR, SPMN, SSTR, SPTC, and SPFL are included. The conditional reliability of average

intercept is 0.543, and the conditional reliability of the other slopes are around 0.10. This number







results show that that the grand mean NAEP score is 147.73. Schools with higher mean SES tend

to have higher level of student achievement (γ01 =20.61). Students in schools where there are

higher mean learning expectation tend to have higher level of achievement (γ02 =13.92). Students

in schools of higher mean learning attitude tend to show higher level of learning outcome (γ04

=10.56). Schools with higher percentage of minority students tend to have lower level of student

achievement (γ011 = – 0.11). Similarly, schools with more free and reduced-price lunch students

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tend to have lower level of student achievement (γ014 = – 0.14). The other school level predictors

are not statistically significant.

On the school level, only some of the variables are significant. Students in schools where

there is higher mean learning expectation tend to have a higher level of achievement (γ02 =4.04).

Students in schools of higher mean learning attitude tend to show higher level of learning

outcome (γ04 =4.26). In schools with higher percentage minority students, students on average

tend to have lower level of student achievement, although the relationship is weak (γ011 = – 0.04).

Schools with higher percentage of free and reduced-price lunch tend to have lower level of

student achievement, and the relationship is weak too (γ014 = – 0.03). The other school level

predictors do not show statistical significance.

On the student level, gender, the Asian Student (ASIAN), White Student (WHITE),

Black Student (BLACK), and Hispanic Student (HISPN) variables remain significant, and the

directions of the relationships are the same as in the random coefficient model. SESC, FEXP,

FMOV, and FATD variables are all significant. FPAR is not significant as shown in Model III.

The school-level composites under each student-level variables in general show little impact

since very few of them are statistically significant. The heterogeneity of regression slopes still

exist for the student-level variables, although the scale decreases for most of these variables. This

is an indication that certain amount of variance picked up by the decomposition of school-level

predictors.


school-level variables in Model IV. Nine out of the 10 variables–gender, Asian student, Black

student, Hispanic student, White student, SES, expectation, motivation, and attitude–were

observed to vary among schools, and because of this variability, these nine variables can be

98

modeled with school-level variables. This decomposition means that each randomly varying

coefficient at student-level becomes a model. The school-level variables that are observed to be

significantly related to the random coefficients, or in other words, some school-level variables

show influences to student-level slopes.

Among the nine significant student-level variables, five of them were observed to have

significant school-level predictors. For Asian, Black, Hispanic, and White students, school mean

expectation accounted a great amount of the variability in these racial variable slopes, and the

directions are positive. For Black and White students, school mean motivation accounted a great

amount of the variability in these racial variable slopes, and the directions are negative. Figure 3

illustrates that although Hispanic students overall have a negative impact on NAEP score,

attending a school with high educational expectation increases the chance of having better NAEP

scores than being in a school with low expectation.

Figure 3. NAEP scores vs. Hispanic Student plot with focus of mean expectation

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Student SES can also be modeled be school urbanicity and student/teacher ratio,

however, the relationships are relatively small. Among all the student-level variables that are

modeled by school-level variables, school-level expectation shows the strongest effect toward

Hispanic student variable. Examining the random effects for Hispanic students, 18.8% the

proportion of variance of the HISPAN coefficient is explained by school mean expectation {τ03

(Model III) - τ03 (Model IV) / τ03 (Model IV) = (177.99 – 149.85) / 149.85 = 0.188}.

The school-level predictors as a whole explain 79.8% of the variance in student NAEP

score composite among schools {[τ00(RC) - τ00(current)] / τ00(RC) = (248.14 – 50.19) / 248.14 =

0.798}. This number is quite close to the number using math and reading scores as outcome

measure (79.9). All the results from the four models are shown in Table 18.

Table 18

Results for Four Model Estimates (Standard Coefficient) on Student NAEP scores

I II III IV Fixed Effects School Mean, γ00 149.78*** 147.19*** 150.16*** 147.73*** School-level Variables Mean SES, γ01 20.15*** 20.61*** Mean Expectation, γ02 13.75*** 13.92*** Mean Motivation, γ03 -5.36 -3.90 Mean Attitude, γ04 9.66*** 10.56*** Mean Parent Involvement, γ05 -2.11 -2.34 Mean Teacher Experience, γ06 0.06 0.09 Mean Teacher Certification, γ07 0.75 0.46 Mean Teacher Degree, γ08 0.52 0.18 School Urbanicity, γ09 -0.61 -0.51 School Enrollment, γ010 0.00 0.00 School % Minority, γ011 -0.13*** -0.11*** School Student/Teacher, γ012 -0.04 -0.07 School % Teacher Certified, γ013 -0.02 -0.04 School Free Reduced Lunch, γ014 -0.11* -0.14** Student-level Variables Gender, γ10 -5.07*** -4.74*** Asian Student, γ20 8.95*** 8.08** Mean Expectation, γ22 30.90* Black Student, γ30 -11.93*** -10.89*** Mean Expectation, γ32 38.82** Mean Motivation, γ33 -34.04* Hispanic Student, γ40 -5.89** -4.3**

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Mean Expectation, γ42 46.13*** White Student, γ50 5.77*** 6.29** Mean Expectation, γ52 33.74** Mean Motivation, γ53 -34.88** SES, γ60 10.35*** 10.92*** School Urbanicity, γ69 -3.43* School Student/Teacher, γ612 -0.40* Expectation, γ70 9.78*** 9.49*** Motivation, γ80 -1.88*** -2.31*** Attitude, γ90 9.68*** 9.76*** Parent Involvement, γ100 0.35 0.59

Random Effects τ00 236.56*** 45.73*** 248.14*** 50.19*** τ01 33.84** 18.64*** τ02 122.96 107.18 τ03 129.99 126.40 τ04 177.99** 149.85** τ05 164.46* 166.92* τ06 33.96*** 25.82*** τ07 6.91 4.65 τ08 13.27* 19.08* τ09 16.40* 10.60* τ10 8.03* 6.93* σ

2 887.14 908.69 589.26 598.70 ρ 0.21 0.05


SAT



school level. The dependent variable is student SAT score. This model is to partition the total

variance in the student achievement into within and between school components, and to see if

there is significant difference in test scores among schools.

The results show that the grand mean student achievement is 981.77. The reliability of

the sample means for the true school mean is 0. 857, which indicates that the sample means are

quite reliable as indicators of the true school mean.



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rejected. The intraclass correlation coefficient ρ = τ00 / (τ00 + σ2) = 10526.85 / (10526.85 +

31899.76) = 0.25. This suggests that 25% of the total variance in SAT scores exists across

schools. Since this number is greater than 0.1, the dataset qualifies for multilevel analysis. In

other words, the results of this empty model show that SAT scores have enough variability at the

student and school levels for further analysis with HLM.










mean centered. The results show that the grand mean of SAT score is 1000.09, which is


MSES, MFEXP, and MFATD all show significant effects on school SAT scores at .000

level. These results mean that higher mean SES, educational expectation, and attitude toward

learning, tend to have higher level of mean test score composite. Among the teacher

characteristics and school characteristics variables, only mean teacher experience, school

student/teacher ratio, and school free and reduced-price lunch variables show significant impact

to student achievement. However, these relationships are weak compared with MSES, MEXP,

and MATD variables.

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3193.49 / (3193.49 + 32355.19) = 0.09 (was 0.25 in Model I). Comparing with the one-way

ANOVA model, adding school-lever predictors decreases the variance among schools from

10526.85 to 3193.49. In other words, 69.7% of the variance in mean SAT between schools is

explained by the school-level variables {[τ00(ANOVA) - τ00(current)] / τ00(ANOVA) =

(10526.85 – 3193.49) / 10526.85 = 0.697}. Overall, Model II has more explanatory power then

Model I at school level.







The grand mean SAT score is 981.41. All the student-level predictors, except for the

parental involvement variable, are significant. The results show that, on average, students who

have higher SES tend to do better in the tests. Students who have higher expectations of their

education and higher attitude tend to have higher test scores. However, the results also show that

students who have stronger motivations of education tend to have lower test scores. White and

Asian students tend to have better test scores than Black and Hispanic students. Overall, Black

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students have significant lower SAT scores than otherwise. Student SES, expectation, and

attitude all show very strong positive impact on SAT scores.

The inclusion of student level variables decreases variances at student level from 887.14

to 589.26. That is, 35.9% of the variance at student level is explained by these student level

variables altogether {[σ2 (ANOVA) - σ2 (current)] / σ2 (ANOVA) = (32355.19 – 20728.06) /

32355.19 = 0.359}. Comparing the proportions of variances explained by these variables at

student level (35.9%) in the current model and at school level (69.7%) in the means-as-outcome

model, it seems these variables have stronger effects at school level than at student level. The

mean SAT score still varies significantly across schools at 0.000 level.

The random part of the student level model as a whole shows that mean levels of SAT

scores still vary across schools after controlling the ten student-level variables. Among the ten

student-level variables, only motivation indicates heterogeneity of regression.












104

results show that that the grand mean SAT score is 147.73. Schools with higher mean SES tend

to have higher level of student achievement (γ01 =126.96). Students in schools with higher mean

expectation tend to have higher level of student achievement (γ02 =81.59). Similarly, students in

schools with higher mean attitude toward learning tend to learn more (γ04 =32.37). Interestingly,

schools with more experienced teachers may lead to lower level of student achievement,

although the relationship is weak (γ06 = 1.97). Schools with higher percentage of minority

students and higher level of free and reduced-price lunch students tend to have lower level of

student achievement, again with weak relationships (γ11 = -0.97, γ014 = -1.09). The other school

level predictors are not statistically significant.

On the student level, gender, Asian Student (ASIAN), White Student (WHITE), Black

Student (BLACK), and Hispanic Student (HISPN) variables remain significant, and the

directions of the relationships are the same as in the random coefficient model. SESC, FEXP,

FMOV, and FATD variables are all significant. FPAR is not significant as shown in Model III.

The school-level composites under each student-level variable in general show little impact since

very few of them are statistically significant. The heterogeneity of regression slopes becomes

more for the student-level variables.


school-level variables in Model IV. Nine out of the 10 variables–gender, Asian student, Black

student, Hispanic student, White student, SES, expectation, motivation, and attitude–were

observed to vary among schools, and because of this variability, these nine variables can be

modeled with school-level variables. This decomposition means that each randomly varying

coefficient at student-level becomes a model. The school-level variables that are observed to be

105

significantly related to the random coefficients, or in other words, some school-level variables

show influences to student-level slopes.

Among the nine significant student-level variables, eight of them were observed to have

significant school-level predictors. Mean student behavior variables remain strong predictors on

school level, although student motivation has a different direction from student expectation and

attitude. Among all the student-level variables that are modeled by school-level variables,

school-level expectation shows the strongest effect toward Black student variable. Examining the

random effects for Black students, 41.8% the proportion of variance of the HISPAN coefficient

is explained by school mean expectation {τ03 (Model III) - τ03 (Model IV) / τ03 (Model IV) =

(8815.53 – 5126.19) / 8815.53 = 0.4188}.

The school-level predictors as a whole explain 69.0% of the variance in student NAEP

score among schools {[τ00(RC) - τ00(current)] / τ00(RC) = (11233.76 – 3476.79) / 11233.76 =

0.690}. All the results from the four models are shown in Table 19.

Table 19

Results for Four Model Estimates (Standard Coefficient) on Student SAT Score

I II III IV Fixed Effects School Mean, γ00 981.77*** 1000.09*** 981.41*** 959.88*** School-level Variables Mean SES, γ01 126.84*** 126.96*** Mean Expectation, γ02 62.94* 81.59** Mean Motivation, γ03 14.29 6.21 Mean Attitude, γ04 36.73* 32.37* Mean Parent Involvement, γ05 -16.50 -23.62 Mean Teacher Experience, γ06 2.36** 1.97* Mean Teacher Certification, γ07 -15.92 -3.83 Mean Teacher Degree, γ08 2.87 -1.92 School Urbanicity, γ09 -13.22 -12.18 School Enrollment, γ010 -0.01 0.00 School % Minority, γ011 -0.24 -0.97*** School Student/Teacher, γ012 4.28** 2.00 School % Teacher Certified, γ013 -0.65 -0.50 School Free Reduced Lunch, γ014 -1.83*** -1.09** Student-level Variables Gender, γ10 -14.25** -10.98*

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Mean Teacher Experience, γ16 -3.01** Mean Teacher Degree, γ16 20.55* Free Reduced Lunch, γ114 1.11* Asian Student, γ20 37.31** 36.15** Mean Attitude, γ24 222.57** School Student/Teacher, γ212 8.80* Black Student, γ30 -110.31*** -108.25*** Mean Expectation, γ32 210.14* Mean Attitude, γ34 138.90* Hispanic Student, γ40 -31.81** -27.08 Mean Expectation, γ42 246.10** Mean Attitude, γ44 154.25* Free Reduced Lunch, γ414 3.16* White Student, γ50 31.17** 36.46** Mean Expectation, γ52 170.68* Mean Motivation, γ53 -218.76* SES, γ60 57.24*** 56.86*** Expectation, γ70 68.84*** 68.23*** Mean Expectation, γ72 48.15* School % Minority, γ711 -0.57** Motivation, γ80 -22.87*** -22.25*** Mean Attitude, γ84 38.94* Attitude, γ90 58.19*** 55.94*** Mean Teacher Experience, γ96 2.40 * Mean Teacher Degree, γ98 -19.13* Parent Involvement, γ100 4.15 5.94 Mean Expectation, γ102 -44.79* School Student/Teacher, γ1012 -2.48 *

Random Effects τ00 10526.85*** 3193.49*** 11233.76*** 3476.79*** τ01 1604.43 644.28** τ02 826.75 1415.48** τ03 8815.53 5126.19** τ04 3693.65 3508.49*** τ05 3696.62 4784.87** τ06 1638.90 1568.82*** τ07 404.95 504.83*** τ08 842.02** 703.32*** τ09 1116.84 1527.82** τ10 803.19 848.19** σ

2 31899.76 32355.19 20728.06 20696.96 ρ 0.25 0.09


High School GPA



school level. The dependent variable is student high school GPA for all academic courses. The

107

GPA information is from the first follow-up survey in 2004. This model is to partition the total

variance in the student achievement into within and between school components, and to see if

there is significant difference in student GPA among schools.

The results show that the grand mean student achievement is 2.51. The reliability of the

sample means for the true school mean is 0.762, which indicates that the sample means are quite

reliable as indicators of the true school mean.



rejected. The intraclass correlation coefficient ρ = τ00 / (τ00 + σ2) = 0.12 / (0.12 + 0.60) = 0.17.

This suggests that 17% of the total variance in student GPA exists across schools. Since this

number is greater than 0.1, the dataset qualifies for multilevel analysis. In other words, the

results of this empty model show that student GPA has enough variability at the student and

school levels for further analysis with HLM.










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mean centered. The results show that the grand mean of high school GPA is 2.48, which is


MSES, MFATD, SENR, SPMN, SSTR, SPTC, and SPFL all show significant effects on

school mean GPA at .000 level. MFEXP, MFMOV, MFPAR, SURB, and the teacher

characteristics variables show insignificant effect on school mean GPA. These results mean that

higher mean SES and mean educational expectation tend to have higher level of mean GPA.

SENR, SPMN, SSTR, SPTC, and SPFL show significant impact to student achievement, but the

relationships are very small. These relationships indicate that bigger schools and schools with

more minority students tend to decrease student GPA, while schools with higher student/teacher

ratio, more teachers are certified, and schools with higher percentages free and reduced-price

lunch tend to increase student GPA.





0.03 / (0.03 + 0.62) = 0.05 (was 0.17 in Model I). Comparing with the one-way ANOVA model,

adding school-lever predictors decreases the variance among schools from 0.12 to 0.03. In other

words, 75% of the variance in high school GPA between schools is explained by the school-level

variables {[τ00(ANOVA) - τ00(current)] / τ00(ANOVA) = (0.12 – 0.03) / 0.12 = 0.75}. Overall,

Model II has more explanatory power then Model I at school level.




109




The grand mean GPA score is a bit higher at 2.53. All the student-level predictors, except

for the Hispanic student variable, are significant at 0.000 level. The results show that, on

average, students who have higher SES tend to do better in the tests. Students who have higher

expectations of their education and higher attitude tend to have higher GPA. Girls in general tend

to have higher GPA than boys. White and Asian students tend to have better test scores than

Black students. The strongest predictor at student level is the attitude factor, and one unit

increase of student attitude tends to increase GPA by 0.45.

The inclusion of student level variables decreases variances at student level from 0.60 to

0.32. That is, 46.7% of the variance at student level is explained by these student level variables

altogether {[σ2 (ANOVA) - σ2 (current)] / σ2 (ANOVA) = (0.60 – 0.32) / 0.60 = 0.467}.

Comparing the proportions of variances explained by these variables at student level (46.7%) in

the current model and at school level (75%) in the means-as-outcome model, it seems these

variables have stronger effects at school level than at student level. The mean GPA still varies

significantly across schools at 0.000 level.

The random part of the student level model as a whole shows that mean levels of NAEP

scores still vary across schools after controlling the ten student-level variables. Although

insignificant, the random part of Hispanic student variable does indicate heterogeneity of

regression slopes exists for Hispanic student. Similarly, regression slopes vary across school for

GENDR, BLACK, WHITE, SES, expectation, motivation, attitude, and parental involvement

variables.

110












results show that the grand mean GPA is 2.50. Schools with higher mean SES tend to have

higher level of student achievement (γ01 =0.38). Students in Schools with higher learning attitude

tend to have higher level of achievement (γ04 =0.47). Although SENR, SPMN, SSTR, and

MTCRT variables are statistically significant, the relationships are minimal to student GPA (γs

=0.00).

On the student level, gender, Asian Student (ASIAN), White Student (WHITE), and

Black Student (BLACK) variables remain significant, and the directions of the relationships are

the same as in the random coefficient model. SESC, FEXP, FMOV, FATD, and FPAR variables

are all significant. Hispanic student is not significant as shown in Model III. The school-level

composites under each student-level variables in general show little impact since very few of

them are statistically significant. The heterogeneity of regression slopes still exist for the student-

111

level variables, although the scale decreases for most of these variables. This is an indication that

certain amount of variance picked up by the decomposition of school-level predictors.


school-level variables in Model IV. Nine out of the 10 variables–gender, Black student, White

student, SES, expectation, motivation, and attitude–were observed to vary among schools, and

because of this variability, these nine variables can be modeled with school-level variables. This

decomposition means that each randomly varying coefficient at student-level becomes a model.

The school-level variables that are observed to be significantly related to the random

coefficients, or in other words, some school-level variables show influences to student-level

slopes.

Among the nine significant student-level variables, three of them were observed to have

significant school-level predictors. Student expectation can be modeled by school mean teacher

certification; in that students with high expectation have lower GPA in schools that more

teachers are certified. Students with high attitude will have higher GPA is they are in schools

with high mean motivation and attitude.

The school-level predictors as a whole accounts for 58.3% of the variance in student high

school GPA among schools {[τ00(RC) - τ00(current)] / τ00(RC) = (0.12 – 0.05) / 0.12 = 0.583}.

All the results from the four models are shown in Table 20.

Table 20

Results for Four Model Estimates (Standard Coefficient) on Student Academic GPA

I II III IV Fixed Effects School Mean, γ00 2.51*** 2.48*** 2.53*** 2.50*** School-level Variables Mean SES, γ01 0.38*** 0.38*** Mean Expectation, γ02 0.03 0.03 Mean Motivation, γ03 0.11 0.13

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Mean Attitude, γ04 0.47*** 0.47*** Mean Parent Involvement, γ05 -0.04 -0.05

Mean Teacher Experience, γ06 -0.00 -0.00 Mean Teacher Certification, γ07 0.02 0.03 Mean Teacher Degree, γ08 -0.04 -0.04 School Urbanicity, γ09 -0.04 -0.04 School Enrollment, γ010 -0.00*** -0.00*** School % Minority, γ011 -0.00*** -0.00*** School Student/Teacher, γ012 0.01* 0.01** School % Teacher Certified, γ013 0.00** 0.00* School Free Reduced Lunch, γ014 0.00* 0.00 Student-level Variables Gender, γ10 0.27*** 0.27*** Asian Student, γ20 0.32*** 0.31*** Black Student, γ30 -0.17*** -0.13** Hispanic Student, γ40 -0.01 -0.00 White Student, γ50 0.17*** 0.19*** SES, γ60 0.24*** 0.23*** Expectation, γ70 0.13*** 0.12*** Mean Teacher Certification, γ77 -0.08** School % Minority, γ79 -0.00* Motivation, γ80 0.08*** 0.08*** Attitude, γ90 0.45*** 0.45*** Mean Motivation, γ93 0.16* Mean Attitude, γ94 0.17*** Parent Involvement, γ100 0.04*** 0.05*** School Student/Teacher, γ1012 -0.01*

Random Effects τ00 0.12*** 0.03*** 0.12*** 0.05*** τ01 0.02** 0.01* τ02 0.08 0.07 τ03 0.09** 0.06** τ04 0.13** 0.08* τ05 0.10** 0.10* τ06 0.02*** 0.01** τ07 0.01** 0.01** τ08 0.01*** 0.01** τ09 0.01 0.00 τ10 0.00*** 0.00** σ

2 0.60 0.62 0.32 0.32 ρ 0.17 0.05


Summary of Findings

School-level Effects versus Student-level Effects

One of the interesting findings is related to the achievement differences on individual and

school levels can be observed by calculating the plausible value range. The plausible value range

can be used to gauge the magnitude of the variance among students or among schools in terms of

113

student mean achievement (Raudenbush & Bryk, 2002). Figure 4 through Figure 7 illustrate the

95% confidence interval of each of the four outcome measures on school and student levels. It is

obvious that the school mean values of student achievement have a large range. Comparing with

the mean value of each outcome measures, the plausible range for the math and reading test

scores is 38%, the NAEP scores is 40%, the SAT is 41%, and the academic GPA is 54%.

Of course the plausible value range for students is larger than that of schools. These

results together suggest that where students attend high school has a great to do with how much

they learn, although these estimates do not account for the student background, teacher and

school characteristics.

Figure 4. Range of plausible values for math and reading test scores

20

30

40

50

60

70

80

School Student

114

Figure 5. Range of plausible values for NAEP test scores

Figure 6. Range of plausible values for SAT scores

Figure 7. Range of plausible values for academic GPA

60

110

160

210

School Student

200

400

600

800

1000

1200

1400

School Student

0

1

2

3

4

5

6

School Student

115

Student Behavior Factors versus School Resource Variables

The results of all the Model IVs are compiled into Table 21. This table also summaries

the answers to the first research question this study raises–what factors affect student academic

achievement the most? Overall, the results from the four outcome measures are quite close. The

school-level variables show consistent patterns in that the mean SES, mean student expectation,

and mean student attitude are the three strongest predictors to student achievement. Just like

some of the existing literatures found that SES has the most impact on student achievement, this

dissertation suggests that SES has the strongest positive influence on student learning on school

level. This means that students in schools of high SES tend to have higher academic achievement

than those students in schools of low SES. Similarly, students in schools of high educational

expectation and attitude tend to have higher test scores than those students in schools of low

educational expectations and attitude.

The results also show that teacher characteristics including mean teacher experience,

mean teacher certification, and teacher education background do not have significant impact on

student achievement. School urbanicity, school enrollment, student/teacher ratio, and percent

teacher certification do not have significant impact on student achievement either. School

percent minority and percent free and reduced-price lunch show significant relationships on

some outcome measures, however, the coefficients are small and limited.

On the student level, almost all the predictors have significant relationships with student

achievement measures. Racial variables including Asian, Black, Hispanic, and White all have

strong impacts to student learning outcomes. Asian and White students on average tend to have

higher achievement than Black and Hispanic students. Similar to school-level mean SES,

student-level SES proved to the strongest positive variable among all the predictors. Student

116

behavior factors also have significant impact to student achievement. Expectation and attitude

have strong positive influences while motivation has weak negative influence on student learning

outcomes. Parental involvement shows inconsistent relationships with 2 of the 4 outcome

measures, and the influences are not strong.

Table 21

Two-Level HLM Estimates (Standard Coefficient) over Four Outcome Measures

Math & Reading

NAEP Score Academic GPA

SAT Score

Model V Model V Model V Model V Demographic Variables Gender, γ10 0.06 -4.74*** 0.27*** -10.98* Asian Student, γ20 0.94 8.08** 0.31*** 36.15** Black Student, γ30 -3.31*** -10.89*** -0.13** -108.25*** Hispanic Student, γ40 1.92*** -4.3** -0.00 -27.08 White Student, γ50 2.18*** 6.29** 0.19*** 36.46** SES, γ60 3.19*** 10.92*** 0.23*** 56.86*** Mean SES, γ01 6.33*** 20.61*** 0.38*** 126.96*** School Resource Variables Mean Teacher Experience, γ06 0.03 0.09 -0.00 1.97* Mean Teacher Certification, γ07 -0.05 0.46 0.03 -3.83 Mean Teacher Degree, γ08 0.08 0.18 -0.04 -1.92 School Urbanicity, γ09 -0.22 -0.51 -0.04 -12.18 School Enrollment, γ010 -0.00 0.00 -0.00*** 0.00 School % Minority, γ011 -0.04*** -0.11*** -0.00*** -0.97*** School Student/Teacher, γ012 -0.06 -0.07 0.01** 2.00 School % Teacher Certified, γ013 0.00 -0.04 0.00* -0.50 School Free Reduced Lunch, γ014 -0.03 -0.14** 0.00 -1.09** Educational Behavioral Variables Expectation, γ70 2.80*** 9.49*** 0.12*** 68.23*** Motivation, γ80 -0.92*** -2.31*** 0.08*** -22.25*** Attitude, γ90 2.38*** 9.76*** 0.45*** 55.94*** Parent Involvement, γ100 0.52*** 0.59 0.05*** 5.94 Mean Expectation, γ02 4.04*** 13.92*** 0.03 81.59** Mean Motivation, γ03 -0.26 -3.90 0.13 6.21 Mean Attitude, γ04 4.26*** 10.56*** 0.47*** 32.37* Mean Parent Involvement, γ05 0.74 -2.34 -0.05 -23.62

*** p<0.000, ** p<0.01, * p<0.05; All school-level predictors are grand mean centered;

All student-level predictors are group mean centered;

117

Where Students Go to School Matters

Using both the school-level and student-level variables, these models across the four

outcome measures indicate that more variance exist on school level than on student level. In

other words, the school-level variables altogether predict more proportion of the student

achievement than the student-level variables combined. To address the research question 4 –

What portion of variance do factors from each of the two level of analysis explain? The results

presented in Figure 8 demonstrate the percent variance in four different student achievement

measures between student and school levels. Between 58.3% and 79.9% of the total variability in

achievement is related to the differences among schools the students attend, and between 20.1%

and 41.7% is due to the differences among students themselves. This finding implies that where

students go to school and who the students go to school with has tremendous impact on student

achievement. Students learn by themselves, however, the school environment, teachers and other

students who they interact everyday also related to their learning outcomes.

Figure 8. Percent of Variance in Achievement at Student and School Levels by Four Measures

20.1 20.231.0

41.7

79.9 79.869.0

58.3

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Math and

Reading Scores

NAEP Scores SAT Scores High School

Academic GPA

118

Combining the findings from Table 21, these school variation come mostly the school-

level SES, student expectations of education, and student attitudes of learning. This directly

address the research questions 2 this dissertation raises, in that student behavior factors have the

most contribution to student achievement, both individually, and collectively in schools.

Furthermore, to answer the research question 3, the mean school-level student behavioral factors

have more influences on student learning than student-level factors.

The results from the four sets of HLM analyses contribute to the understanding of which

factors at the school level influence the student level predictors, in other words, the changes

school-level to the student-level slopes. Across the four output measures, mean student

expectation has the strongest positive effect on a number of student-level variables including the

racial and student behavior variables. School-level mean SES, on the other hand, has very little

influence to any of the student-level variables. Some of the school characteristics variables, such

as student/teacher ratio, teacher experience, and school enrollment have limited impact on

student-level predictors.

119

CHAPTER 5

CONCLUSION

Review of Findings

This dissertation raised four research questions:




achievement?



Findings from the HLM analysis indicated that on the student level, race and SES had

strong relationships with student achievement. Asian and White students tended to have better

test scores than Black and Hispanic students. Students with higher SES were more likely to have

higher achievements. Gender variable had significant impact to student learning over three of the

four outcome measures. The pattern was not consistent on whether boys or girls have better

achievements. The three student behavior variables demonstrated significant influences on all

four learning outcomes. Expectation and attitude had positive impact while motivation had

negative impact to students. Parental involvement had a weak positive influence on two of the

four outcome measures, (i.e. math and reading test scores and academic GPA).

The results also illustrated that school-level variables were showing consistent patterns

over four different outcome measures. Mean SES, mean student expectation, and mean student

attitude were the top three positive predictors of student achievement. School characteristic

120

variables such as school urbanicity, school enrollment, student teacher ratio, percent teacher

certified, and school free and reduced-price lunch eligibility possessed very little impact, if any,

to student learning. The school percent minority variable was consistent over the four models

with negative impact to student achievement; however, the relationship was weak. Teacher

quality variables including teacher experience, teacher degree, and teacher certification all had

minimal influence on student learning. Similar to student level results, school level mean SES,

expectation, and attitude displayed strong positive impact to student learning. Mean student

motivation on school level was insignificant.

These findings across the four outcome measures showed that more variation exists at the

school level than at the student level, which means that school-level variables collectively

predicted more proportion of the student achievement than the student-level variables

collectively do. Between 58.3% and 79.9% of the total variability in achievement was related to

the differences among schools the students attend, and between 20.1% and 41.7% was due to the

differences among students themselves.

Furthermore, strong school effects may alter the impact of student-level variable.

Evidence emerged from the second outcome measure–the NAEP score. Hispanic students tend to

have low achievement, but Hispanic students in high educational expectation schools

outperformed their counterparts in low educational expectation schools significantly. This

pattern also held true for Black students using NAEP and SAT as outcome measures. On the

other hand, Asian and White students tended to have even higher achievement if they were

placed in schools where students had higher expectation and attitude of learning.

121

The sections that follow address other areas that are not directed related with the research

questions in this dissertation, however; these results relate back to the literature this dissertation

draws from and the findings are of important implications.

Student Behavior Factors

Among the three student behavioral factors, expectation and attitude on learning showed

strong and positive impact to student learning on student and school levels across the four output

measurements. Motivation factor, on the other hand, displayed inconsistent patterns. On the

student level, motivation was negatively associated with three of the four student achievement

variables (except GPA). All the relationships were weak compared with expectation and attitude

factors. The fact that high level of motivation on learning did not lead to high achievement is

contrary to student behavior literature. Unlike on the student level, the motivation factor on the

school level became insignificant across all four outcome measures. The discrepancy on student

and school levels was an indication that motivation factor in this dataset might not fully capture

the concept of motivation on learning.

Parental involvement, the fourth factor in this dissertation, had limited influence on

student learning. This factor was significant on math and reading scores and student GPA on the

student level, and the size of the effects is small. Parental involvement was insignificant on all

four outcome measures on the school level.

Teacher quality in this study consisted of three variables: teacher experience, teacher

certification, and teacher degree. All the three variables were on the school level, and all three

variables were insignificant across four student achievement variables except teacher experience

that had a weak positive effect on SAT scores. This consistent lack of impact from teacher

122

quality variables indicated that school resources spent on these areas might not lead to desirable

results, at least compared with student expectation and attitude on learning factors.

Gender

The effect from the gender variables in this study fluctuated across different outcome

variables. It was insignificant on math and reading test scores, negatively associated with NAEP

scores and SAT scores, and positively associated with academic GPA. The size of the effects

ranged from medium to large. The inconsistency reflected the fact that the effects were mixed on

different tests and different group of students.

Race

Most of the race variables showed significant influence to student learning. In general,

Asian and White students tended to have higher achievement, while Black and Hispanic students

tended to have lower achievement. These effects ranged from medium to large depending on the

outcome variable. Socioeconomic status had the strongest positive impact on student

achievement on both student and school levels. Take math and reading test score for example, on

average, one unit increase of student SES tended to increase the test score by 3.14 points, and

one unit increase of school SES tended to increase school mean score by 6.24 points.

School Characteristics

School level variables included school urbanicity, school enrollment, percent minority

students, student/teacher ratio, percent teacher certified, and percent free and reduced-price lunch

students. Urban schools in general had lower student achievement than non-urban schools; the

relationship was not significant though. Student enrollment variable only became significant at

the GPA measurement, and the relationship was very weak. Similar to that was student/teacher

and percent teacher certified variables.

123

The only school level variables had certain influence on student learning were the percent

minority students, and percent free and reduced-price lunch students variables. High levels of

minority and free and reduced-price lunch students were both associated with low level of

student achievement. Still the strength of the relationship was weak compared with school level

SES variable and expectation factor.

Since HLM allows two levels of analysis, the school level decomposition in this study

yielded some interesting findings. The student-level race variables were further explained by

school-level learning behavior factors multiple times across the four outcome measures. The

decomposition occurred mostly with the race variables.

School Level Decomposition on Math and Reading Test Score

On the math and reading test score outcome measure, Black students in general tend to

have a 3.31 points disadvantage compared with otherwise. However, Black students in high

expectation schools tend to gain 6.66 points advantage - that is a net 3.35 points benefit. There

are other pairs of variables involves school-level decomposition. Similarly, Black students in

schools with experienced teachers, their test score then to increase by 0.19 points. This small

increase means that experienced teachers help Black students learn a bit more. There are other

school-level decompositions, but due to the fact that they are not significant at school level, these

decompositions are not as important as from the student behavior factors.

School Level Decomposition on NAEP Test Score

On the NAEP test score outcome measure, all four race variables had decompositions

from student behavior factors. Students in schools with high expectations on learning, regardless

of the race, the students tended to have test scores gain of 30 to 40 points. Motivation factor

tended to reduce the test scores by about 34 points.

124

School Level Decomposition on SAT Test

On the SAT score outcome measure, the student behavior variables remained the patterns

as shown in previous outcome measures. Students in schools with high expectation, and attitude

had a significant score gain regardless of race. Motivation had an opposite impact on White

students, however; this factor was not significant on school level. Teacher experience showed a

little positive impact on students in schools with high attitude on learning. Teacher degree had a

bigger negative impact than teacher experience. This indicated that resources spent on

experienced teachers may generate better learning outcomes than spent on well-educated

teachers. However, either teacher experience or teacher degree did not present significant

relationships with student achievement on the school level.

School Level Decomposition on Academic GPA

On the high school academic GPA outcome measure, student expectation had

decomposition by teacher certification. Students with high expectation on learning tended to

have high achievement, however; these students might have a significant GPA drop if they were

in schools with high level of teacher certification. Again, teacher certification was not significant

on student level.

Research Implications

Lee (2000) stated that the school environment, in which students learn, had a great deal

of influence on the learning outcome. “Specifically, these school factors are school type, school

effectiveness, and school organizational style” (Lee, p126). The results from this dissertation

have reinforced the argument that schools make a difference. Across the four outcome measures,

the results proved once again that where students attend school impacts how much they learn.

The school contribution does not come from school resources or from teacher quality variables.

125

What really matters is student educational expectation on both the individual level and the school

level. This implies that to help students achieve more, the solution may not come from reforming

the education system but may exist from the ways in which students view their educational

opportunities and the interaction with peers and teachers.

Another implication from this research is that it helps to evaluate existing educational

policies, especially school finance policies. The findings in this study add to the long-lasting

debate of whether money matters to student learning. If educational resources can be used to

increase student educational expectations, the impact is considerable.

Along with school resource allocation policies, findings from this dissertation imply that

student assignment policies may include more elements. One recent Supreme Court case5 ruled

that race cannot be used alone in student assignment policies. To achieve student diversity,

policy makers may consider student expectation or attitude on learning. These factors are as

strong as race or SES factors in predicting student achievement.

This study has also shown that the attempts to increase validity by including four

different outcome measures are working. All the four student achievement variables yielded

similar results from the same set of student-and school-level variables. In addition, two of the

four student achievement variables are from the first follow-up survey: NAEP score and

academic SAT. These two variables were constructed 2 years after the math and reading test

score, which was extracted from the base year survey when all the students were 10th graders at

the time. The similarity of results from outcome measures of different times may suggest that

student achievement of high school students tend to have lasting effects.

5 Parents Involved in Community Schools v. Seattle School District No. 1, 127 S. Ct. 2738 (2007)

126

Policy Implications

“Learning is a product of schools, but also of families, communities, and peers”

(Rothstein, 2000, p. 5). The education production function has at least five inputs: peer effects

from fellow students, school and teacher characteristics, family SES and parental involvement,

community properties such as minority and urbanicity, and student themselves, specifically the

learning behavior factors. All five aspects have been included in this analysis to predict effects

on student achievement. As expected, the strongest variables are SES and student expectation

and attitude on learning. None of these are within school systems and none of them are directly

related to school expenditure. SES has been an important predictor to student achievement since

the Coleman et al. study (1966). Student behavior variables, as significant as they are in this

study, pave the way to a new focus of educational policy.

One policy implication from this study is that examining relations between school

characteristics and student academic achievement could help parents to choose schools that

would be most appropriate for their children. In addition, administrators could make more

accurate decisions regarding which schools in the district best serve students based on

examination of the relationship between school characteristics and student academic

achievement.

Since there is no empirical linkage from school resource and teacher quality variables,

another policy implication from this study is that school finance policy should not be formulated

principally on the amount of money to spend to project student learning. This is not by any

means to claim that school expenditures of various sorts are negligible. In fact, school finance

policy may be framed toward creative ways to increase student learning behaviors (i.e., student

educational expectation and learning attitude).

127

It comes as no surprise that SES has the most positive impact to student achievement on

both the student and school levels. School policy has very limited influence on student SES. The

results also show that learning occurs at school but learning outcome is not only related to school

factors. In this study, SES is not merely a measure of family capital; it is a composite of parents’

education background, parents’ working status, and family income.

Data Limitations

As with all research, there are a number of limitations which may undermine the results

of this study. First, significant numbers of cases were dropped out during the factor analysis

stage due to missing values. The factor analysis uses linear trend at a point regression method to

replace missing data. However, as pointed out in chapter 4, further steps of this research should

adopt more sophisticated techniques such as multiple imputation to address the missing value

problem.

Secondly, since this is a longitudinal study, it will be useful to test the lasting effects of

all the variables used here in relation to student achievement. For example, the ELS:2002 is still

on-going, and there will be future data on college academic achievement. Testing the earlier (10th

grade) student demographic and educational behavior variables indicates what kind of impact

these variables had onto students’ later achievement.

Additionally, students’ present academic achievement is related with initial achievement

to a certain degree, and prior ability is also highly associated with achievement (Qian & Blair,

1999; Trusty, 2002). Therefore the current student achievement from this study may possibly be

overestimated. One approach to make a better inference is to use growth modeling to account for

the prior ability in the future research design.

128

Teacher salary was not included in this dissertation. The reason is that ELS:2002 is a

national data and pure dollar amount may not reflect the difference among different living

standards of the school locations. The inclusion of teacher salary without controlling the income

difference may incur bias into the analysis. However, teacher salary takes up a considerable

amount of total school expenditures,6 not including benefits and other type of spending on

teaching staff. Taking this variable into the consideration is believed to increase the explanatory

power of the study. A better way to handle this problem is to link the current ELS:2002 data to

external data to include the necessary variables.

Future Steps

This study shows that student educational expectation and attitude are among the

strongest predictors of academic achievement. In the future, this research may point to student

expectation and attitude into more depth. First, whether or not prior ability has any correlation

with either expectations and motivations or learning outcomes was not addressed in this research.

It will be beneficial to incorporate prior ability into the model as a control variable. Therefore the

relationship from expectation and attitude can be further purified. Second, ELS:2002 is a

longitudinal study with multiple survey points. This research may test the student expectation

and attitude effects over time to see whether or not schools alter these student-level variables,

and how.

6 Source for raw data: National Education Association, "Rankings & Estimates" published December 2008.

http://www.nea.org/home/29402.htm

129

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