Copyright © 2012, Gaylon Craig Spinn

Instructional Leadership: The Efficacy of Student Performance with CSCOPE

Curriculum Implementation

by

Gaylon Craig Spinn, BS, MEd

A Dissertation

In

EDUCATIONAL LEADERSHIP

Submitted to the Graduate Faculty

of Texas Tech University in

Partial Fulfillment of

the Requirements for

the Degree of

DOCTOR OF EDUCATION

Approved

Clint Carpenter

Chair of the Committee

Charles Crews

Eugene Wang

Peggy Gordon Mill

Dean of the Graduate School

May, 2012

Copyright © 2012, Gaylon Craig Spinn

Dedication

In my favorite vingette from All I Really Need to Know I Learned in

Kindergarten, Robert Fulghum writes, “Hold hands and stick together”. As I

progressed through the doubts and certainties of this journey, my wife, Kelle Spinn,

has been my greatest fan, my toughest critic, and the loving, supportive confidant I

needed to complete this dissertation and my doctoral degree. Thank you Kelle for

holding my hand and being at my side, ever present and ever vigilant, as I pursued this

opportunity in my life. I love you for all that you have done for me and our family.

My favorite daughters, Megan and Kristen Spinn, have been there for me

throughout this process as well. Megan was there to make me laugh when I thought

this journey would never end. Kristen was there cheering me on and pulling me along

whenever I was convinced that I could never do this. Thank you both for being patient

with me and sacrificing with our family as I worked to complete this goal in my life.

Finally, I have to say that my mother, Merlene Waters, and my father, James

Spinn, are the best parents a son could ever have. My father is my greatest hero,

teaching me the value of hard work and motivation for a higher level of education.

Thanks Dad for being such a great influence in my life and always encouraging me to

better myself through education. My mother may deserve the most credit for this

accomplishment in my life. You always believed in me and taught me that I could

accomplish anything I set my mind to. You were right, again.

Acknowledgements

“When you go out into the world to examine what’s offered, always carry a

green pencil with you,” is one of my favorite musings by Robert Fulghum. The

graduate school faculty I have had the pleasure of working with at Texas Tech

University has “raised questions to encourage me to think” rather than “leav[ing] me

defeated…” as you taught, challenged, extended, and at times corrected my thinking in

providing me with a world class education. I want to thank you who have been a part

of my journey in completing my dissertation and degree for Doctor of Education. Each

of you has carried a green pencil in revealing to me that “from here, it’s possible”.

I would like to thank the members of my dissertation committee for your

support, encouragment, and wise counsel. To Dr. Clint Carpenter, I owe a debt of

gratititude for serving as my committee chairman, for guiding me during my studies,

and for helping me see the potential in my study. Your boundless energy and powerful

ideas were a source of inspiration for me. To Dr. Eugene Wang, thank you for your

patience, tireless work, and relentless pursuit of knowledge and the truth in guiding me

through intermediate statistics and learning Mplus. You brought discipline, focus and

understanding to me and my study; for this I am truly grateful. To Dr. Charles Crews,

your guidance and support ensured that my study had meaning and produced a

document of the highest quality. You pushed and encouraged me through every barrier

along the way; many thanks.

Texas Tech University, Gaylon Craig Spinn, May 2012

v

Table of Contents

Dedication .................................................................................................................... iii

Acknowledgements ...................................................................................................... iv

Abstract ........................................................................................................................ ix

List of Figures .............................................................................................................. xi

List of Tables .............................................................................................................. xii

Chapter I ....................................................................................................................... 1

Introduction and Problem Statement ........................................................................ 1

Statement of the Problem ...................................................................................................................... 2

Significance of the Study ...................................................................................................................... 3

Theoretical Framework ......................................................................................................................... 4

Purpose of the Study ............................................................................................................................. 4

Research questions. .......................................................................................................................... 6

Delimitations of the study................................................................................................................. 6

Limitations of the study. ................................................................................................................... 7

Assumptions. .................................................................................................................................... 8

Definition of Terms .............................................................................................................................. 8

Overview of the Study ........................................................................................................................ 12

Chapter II ................................................................................................................... 14

Review of the Literature ............................................................................................ 14

Introduction ......................................................................................................................................... 14


vi

Educational Reform and Accountability ............................................................................................. 15

CSCOPE Curriculum Development.................................................................................................... 16

Leadership Theories ............................................................................................................................ 19

Principal leadership. ...................................................................................................................... 19

Instructional leadership. ................................................................................................................ 21

Curriculum leadership. .................................................................................................................. 22

Teacher leadership. ........................................................................................................................ 25

Studies Related to the Research Question ........................................................................................... 29

Chapter Summary ............................................................................................................................... 31

Chapter III .................................................................................................................. 32

Methodology ............................................................................................................... 32

Introduction ......................................................................................................................................... 32

Participants ......................................................................................................................................... 33

Measures ............................................................................................................................................. 35

Procedures ........................................................................................................................................... 36

Research Design ............................................................................................................................ 36

Cohorts ........................................................................................................................................... 37

Data Collection .............................................................................................................................. 38

The Proposed Model ........................................................................................................................... 39

Chapter Summary ............................................................................................................................... 41

Chapter IV .................................................................................................................. 42

Data Analysis .............................................................................................................. 42

Introduction ......................................................................................................................................... 42

Latent Growth Modeling..................................................................................................................... 43

Goodness-Of-Fit ................................................................................................................................. 44


vii

Modeling ............................................................................................................................................. 47

Summary of Findings .......................................................................................................................... 56

Summary ............................................................................................................................................. 57

Chapter V .................................................................................................................... 58

Conclusions ................................................................................................................. 58

Introduction ......................................................................................................................................... 58

Summary of findings .......................................................................................................................... 60

Limitations .......................................................................................................................................... 62

Recommendations ............................................................................................................................... 63

Implications for further study ............................................................................................................. 64

Summary ............................................................................................................................................. 65

References ................................................................................................................... 67

Appendix A. Sample Descriptive Statistics .............................................................. 77

Appendix B. LGM1 Hypothesized Model ................................................................ 82

Appendix C. LGM2 Linear Growth Model ............................................................. 95

Appendix D. LGM3 Piecewise Growth Model ...................................................... 102

Appendix E. LGM4 Piecewise Growth Model ...................................................... 109

Appendix F. LGM5 Piecewise Growth Model ....................................................... 116

Appendix G. LGM6 Piecewise Growth Model ...................................................... 124

Appendix H. LGM7 Piecewise Growth Model ...................................................... 132

Appendix I. LGM8 Piecewise Growth Model........................................................ 140


viii

Appendix J. LGM9 Piecewise Growth Model ....................................................... 151

Appendix K. LGM10 Piecewise Growth Model .................................................... 159

Appendix L. LGM11 Piecewise Growth Model .................................................... 168

Appendix M. LGM12 Piecewise Growth Model ................................................... 177

Appendix N. Institutional Review Board Approval Letter .................................. 185

Appendix O. TESCCC Confidentiality Oath ........................................................ 187

Appendix P. TESCCC Agreement to Submit Final Research Findings ............. 189

Vitae ........................................................................................................................... 191


ix

Abstract

As of May 25, 2010, over 800 school districts across the state of Texas have

adopted CSCOPE as their curriculum. The CSCOPE curriculum management system

has become the defacto curriculum management system of choice for public schools in

Texas. The purpose of this study was to evaluate, via latent growth modeling, the

effects of CSCOPE curriculum implementation upon student academic performance in

mathematics as measured by the Texas Assessments of Knowledge and Skills (TAKS)

tests.

The population consisted of 4,847,844 public school students in Texas. A

purposively selected sample (N=468) of Texas public school students were taught

using the CSCOPE curriculum management system; the sample also included students

taught using a non-CSCOPE curriculum during the study period. A priori assumption

was made regarding a causal relationship between curriculum and instruction and the

resulting student performance.

Existing research shows that when the written, taught, and tested curriculum

are tightly aligned student performance increases. There is scarce research to

substantiate the effects of CSCOPE on student performance. What effect does

CSCOPE as a model for a guaranteed and viable curriculum have over time on student

performance in mathematics as defined by measures included in the Academic

Excellence Indicator System? Results reveal that CSCOPE had a .958 of a standard

deviation effect on growth in student performance in mathematics during the three


x

year period of interest in the study. CSCOPE has a positive effect on student

performance over time.


xi

List of Figures

Figure 3.1 Hypothesized Model ................................................................................... 40

Figure 4.1 Mean Curve ................................................................................................ 49

Figure 4.2 Individual Curves........................................................................................ 49

Figure 4.3 Hypothesized Model (LGM1) .................................................................... 51

Figure 4.4 LGM2 ......................................................................................................... 52

Figure 4.5 LGM12 Final Model ................................................................................... 54


xii

List of Tables

Table 2.1 Types of Curriculum .................................................................................... 24

Table 3.1 Texas Statewide Enrollment, 2004-2005 through 2009-2010 ..................... 33

Table 3.2 Sample and State Demographic Summary ................................................... 34

Table 3.3 Sample Demographic Summary by District ................................................ 35

Table 4.1 Sample Means .............................................................................................. 47

Table 4.2 Sample Covariances ..................................................................................... 47

Table 4.3 Sample Correlations ..................................................................................... 48

Table 4.4 LGM Fit Indices ........................................................................................... 55

Table 4.5 State TAKS Math Score Summary .............................................................. 57


1

Chapter I

Introduction and Problem Statement

An enduring call for educational reform and improvement in America’s public

schools has spawned a myriad of change in the last quarter century. From A Nation at

Risk to No Child Left Behind, America’s public schools have embraced and at times

endured waves of change intended to improve schools and student academic

performance. Codifying the lofty goals of excellence and equity for all students in

public schools has become a regular endeavor of the elect. “A major focus of federal

policy has been improving the education of disadvantaged children. No Child Left

Behind is the latest federal effort to reach the goal of equal educational opportunity”

(Murnane, 2007, p. 178). However, Murnane (2007) adds that “rhetoric rather than

reality” (p. 161) has dominated the debate and subsequent policies targeting the

American idea of equality.

While advocating for change in the federal Title I program, President Bush

(2004) asserted, “The challenge to educate future Americans can be called the

essential work of democracy. Making America safer, stronger, and better demands a

world-class education system” (p. 114). Rose (2004) adds that there is a strong

consensus that we must close the achievement gap between white, black, and Hispanic

students.


2

In Texas, the Legislature expects the principal to be the instructional leader of

the school (Education Code 11.202[a]), while the State Board of Educator

Certification expects a principal to be the educational leader who promotes the success

of all students by facilitating the design and implementation of curricula that enhance

teaching and learning (State Board For Educator Certification, 2009). Clearly, school

leaders have a significant impact on student achievement (English, 2003; Robert J.

Marzano, Waters, & McNulty, 2005; York-Barr & Duke, 2004), and the leader’s

impact can be sustained (Fisher, 2007, pp. 178-180). It is incumbent upon principals

and other school leaders to analyze and observe the effects of curriculum and

instruction in determining its effects on student achievement.

Statement of the Problem

In 2006 the State of Texas began a substantial rewrite of Chapters 110-114 of

Title 19 Texas Administrative Code (TAC). Concluding in 2010, the State of Texas

adopted Chapter 110 Texas Essential Knowledge and Skills (TEKS) for English

Language Arts and reading, Chapter 111 TEKS for mathematics , Chapter 112 TEKS

for science, and Chapter 113 TEKS for social studies (Secretary of State,

Texas Education Agency, & State Board of Education, 2010). The mathematics

TEKS were implemented in 2006, with the new English TEKS implemented in 2009

and science TEKS implemented in 2010. The social studies TEKS were implemented

in 2011.

In School Leadership That Works, Marzano, Waters, and McNulty (2005)

assert that a “guaranteed and viable curriculum” (p. 22) is the most significant school


3

level factor in determining student performance outcomes, while English (2003) and

English and Steffy (2001) maintain that the written, taught, and tested curriculum must

be tightly aligned. In the classroom, teacher expertise with classroom curriculum

design and instructional methods is the most significant teacher level factor affecting

student academic achievement (Robert .J. Marzano, 2003b; Robert J. Marzano,

Pickering, & Pollock, 2001).

In response to the revised TEKS, Texas Assessment of Knowledge and Skills

(TAKS), and the state’s Academic Excellence Indicator System (AEIS) accountability

system, school and district leaders began searching for the tools and resources

necessary for teacher and student success in meeting this complex plethora of new

challenges. A curriculum management system called CSCOPE emerged in response

to these new challenges. Designed around the TEKS and over 30-grounded theories

and best practices in curriculum, instruction, and school leadership, CSCOPE has

become the curriculum of choice for most schools and districts in the state of Texas.

Significance of the Study

As of May 25, 2010, nineteen of twenty educational service centers across the

state of Texas have adopted CSCOPE as the curriculum for implementation and

support in local independent school districts. Over 800 school districts in Texas have

implemented CSCOPE at some level. In a relatively short period, CSCOPE has

become the defacto statewide curriculum for mathematics, science, social studies and

language arts in grades K-12 in Texas. While most districts have chosen to maintain a

separate curriculum for Pre-Advance Placement, Advanced Placement, and Dual


4

Credit courses at the high school level, clearly, most students in Texas are receiving

curriculum and instruction driven by CSCOPE in Texas public school classrooms.

The material and human capital expended in a curriculum implementation of this

magnitude and significance merits study.

Theoretical Framework

In articulating the meta-analysis research on school effect, Marzano (2003a)

identified five school level factors that affect student achievement. These include “a

guaranteed and viable curriculum, challenging goals and effective feedback, parent

and community involvement, safe and orderly environment, and collegiality and

professionalism” (p. 10). Clearly a guaranteed and viable curriculum arises as the

most powerful school-level factor in determining student performance (Robert .J.

Marzano, 2003b, p. 15). The Texas Educational Service Center Curriculum

Cooperative (TESCCC) purports to provide a guaranteed and viable curriculum via the

CSCOPE curriculum management system (2010). English and Steffy (2001) explain

that an aligned curriculum is one in which the students are tested over what is taught

(p. 14).

Purpose of the Study

The State of Texas maintains a comprehensive school accountability system

known as the Academic Excellence Indicator System (AEIS). The AEIS system holds

districts and schools publically accountable for student performance on the Texas

Assessment of Knowledge and Skills (TAKS) test. TAKS is drawn from standards

that have been established for each course/grade level in mathematics, science, social


5

studies, and English Language Arts in grades Pre-Kindergarten through 12. Student

performance data are disaggregated based upon students’ ethnicity/race, sex, special

education status, low socio economic status, and limited English proficiency status.

Finally, statistics such as dropout rate and completion rate are calculated and assigned

to campuses and districts.

The revision of the Texas Essential Knowledge and Skills (TEKS) that began

in 2006 and concluded in 2010, coupled with changes in state exams and high school

graduation requirements, prompted most districts and schools to begin searching for

the means to efficiently and effectively meet the rising tide of standards and the

profusion of new requirements for students, teachers, schools, and districts. The time

and energy demands, as well as the financial and human capital needed to meet these

extensive new requirements, prompted most districts to turn to third party partners for

assistance with curriculum management. The multiple simultaneous tasks of rewriting

curriculum, developing appropriate benchmark assessments, training teachers, and

providing support for campuses and teachers appeared daunting in light of the scope of

changes and the implications for district and campus accountability.

While participating in the Texas Association for Supervision and Curriculum

Development (ASCD) Curriculum Boot Camps offered by Dr. John Crain,

participating district leaders and Education Service Center (ESC) personnel asked why

1000+ independent districts invest time and resources to write and rewrite curriculum

based upon the same state standards and exams? Participating ESC’s saw a need to

develop and support a curriculum that could be adopted and used at the local level


6

(Crain, 2011). The CSCOPE curriculum management system developed as a Texas

Educational Service Center (ESC) cooperative product and related services has

emerged as the curriculum management system of choice in Texas.

The purpose of this study was to analyze the effects of CSCOPE

implementation on student academic performance over time. The material and human

capital expended via CSCOPE in response to the state’s sweeping school improvement

efforts begs the question: What effect has the implementation of CSCOPE had on

student academic performance?

The hypothesized model postulates a priori that curriculum and instruction will

have an effect on student performance and produce growth in student academic

achievement over time. Variables related to race/ethnic status, low socio economic

status, and English language learner status were examined.

Research questions.

The study was guided by the following research questions:

What effect does CSCOPE have on student mathematics performance?

What effect does CSCOPE have on student sub-populations mathematics

performance?

Delimitations of the study.

Parameters for this study include a district in Texas that implemented the

CSCOPE curriculum management system for three or more years. A multi-year

implementation timeline is needed to calculate student growth over time. A control


7

district that had not implemented CSOPE during the same period was also identified

and used in connection with the study. Student results from 2005-2010 TAKS

mathematics exams were collected from participating districts. Student demographic

information consistent with the AEIS accountability system was also collected. While

the CSCOPE curriculum management system includes curricula for English Language

Arts, science, social studies, and mathematics, with the revision of TEKS at the state

level, the mathematics and social studies curriculum components were the only

curricular components that had been implemented for the five-year period needed to

meet the parameters for the study. Student performance in mathematics emerges as

the most pressing need in Texas public schools; therefore, this study was further

delimited to student performance in mathematics.

Limitations of the study.

This study does not include a sampling of all curriculum products or resources

developed or available to Texas school districts. Other locally developed or

commercially available curriculum products may produce different results. A latent

growth structural equation model makes clear causal relations among constructs. A

priori assumption is made regarding a causal relationship between the implementation

of curriculum and instruction and the resulting student performance as measured by

the TAKS test.


8

Assumptions.

This study assumes that the Texas Assessment of Knowledge and Skills is free

from bias in measuring students’ academic achievement and that student performance

data obtained from participating districts are accurate. Findings may be generalizable

because the study was based upon statewide standards, curriculum, and exams.

Definition of Terms

Academic Excellence Indicator System (AEIS) The AEIS dates back to 1984,

when the Texas Legislature took its first steps towards requiring an emphasis on

student achievement as the basis for school and district accountability. House Bill 72

provided for student academic performance indicators to drive the accountability

system. This marked a dramatic shift from a process driven accountability system to a

student results driven system. System indicators include the following:

Results of Texas Assessment of Knowledge and Skills (TAKS*); by grade, by

subject, and by all grades tested;

Participation in the TAKS tests;

Exit-level TAKS Cumulative Passing Rates;

Progress of Prior Year TAKS Failers;

Results of the Student Success Initiative;

English Language Learners Progress Measure;

Attendance Rates;

Annual Dropout Rates (grades 7-8, grades 7-12, and grades 9-12);

Completion Rates (4-year longitudinal);


9

College Readiness Indicators;

Completion of Advanced / Dual Enrollment Courses;

Completion of the Recommended High School Program or Distinguished

Achievement Program;

Participation and Performance on Advanced Placement (AP) and International

Baccalaureate (IB) Examinations;

Texas Success Initiative (TSI) – Higher Education Readiness Component;

Participation and Performance on the College Admissions Tests (SAT and

ACT), and

College-Ready Graduates;

“Performance on indicators is then disaggregated by ethnicity, sex, special

education, low income status, limited English proficient status (since 2002-03), at-risk

status (since 2003-04, district, region, and state), and, beginning in 2008-09, by

bilingual/ESL (district, region, and state, in section three of reports)...”

(Texas Education Agency, 1984).

CSCOPE (not an acronym) is a comprehensive web based curriculum

management system that includes components for establishing the curricular scope,

sequence, vertical alignment, and student performance indicators based upon Texas

Essential Knowledge and Skills, exemplar lessons, and assessments. System

components include the following:


10

Vertical Alignment Documents (VAD) The VAD provides the grade

level/course standards for the year’s instruction, graphically representing aligned

TEKS among and across grade levels and courses. Additionally, the VAD adds

specificity and clarity to the TEKS.

Year at a Glance (YAG) provides a brief overview or “snapshot” of the entire

instructional plan for the year.

TEKS Verification Matrix graphically verifies that all TEKS are accounted for

within each grade level or course.

Instructional Focus Documents (IFD) groups grade level or course standards

into logical, coherent units for instruction.

Exemplar Lessons are designed around the 5E model of instruction, except in

English Language Arts, and provide a comprehensive resource for planning and

implementing instructional activities.

Performance Indicators provide evidence of student attainment of or progress

toward student learning expectations.

Unit Tests are designed to assess the student expectations found in the IFD’s.

Lesson Planner is used to develop and share high quality plans for instruction.

Leadership Tools and Resources include walkthrough forms, instructional

monitoring tools, resources for professional learning communities, and reports that

support the monitoring of the curriculum and instruction.


11

Educational Service Center (ESC) Professional Development Activities and

Support includes providing any professional development needs that member districts

or schools may have related to the implementation and support of the CSCOPE

curriculum management system.

Principal is operationally defined as the instructional leader of the school

(Education Code 11.202(a) 1995).

Student Performance is operationally defined as the student’s achievement as

demonstrated on the Texas Assessment of Knowledge and Skills (TAKS) test in

mathematics in grades 3-8. Student level test scores and related student demographic

information were gathered from participant districts.

Texas Assessment of Knowledge and Skills (TAKS) measures a student’s

mastery of the state-mandated curriculum, the Texas Essential Knowledge and Skills

(TEKS). TAKS is administered for Grades 3–9 reading, Grades 3–10 and exit level

mathematics, Grades 4 and 7 writing, Grade 10 and exit level English language arts

(ELA), Grades 5, 8, 10, and exit level science, Grades 8, 10, and exit level social

studies (Texas Education Agency, 2003a).

Texas Essential Knowledge and Skills (TEKS) are a set of standards developed

by the Texas Education Agency that are required elements of each state approved

grade level/course offered in Texas public schools. The TEKS provide the essential

knowledge and skills to be learned in the grade level/courses as well as the expected

student performance level for the knowledge and skills (Texas Education Agency,

2009, 2010). TEKS are the state standards assessed on TAKS exams.


12

Overview of the Study

The study was organized into five chapters. Chapter I Introduction and

Problem Statement provided the background and context for the study. The problem

statement, significance of the study, and theoretical framework were each identified.

Additionally, the purpose of the study along with with a study overview analyzed and

explained the theoretical framework for student performance with CSCOPE

implementation.

Chapter II Review of the Literature examined the literature related to

educational reform and accountability and specifications of the Texas academic

excellence indicator system. The schema and process for CSCOPE curriculum

development was discussed. Principal leadership, instructional leadership, curriculum

leadership, and teacher leadership, and the achievement of student sub-populations

were reviewed.

Chapter III Methodology examined and explained the methodology used in the

study. A description of how the data are gathered was provided. The hypothesized

model was presented. Methodological elements such as population, sample, and

generalizeability of the study were discussed.

Chapter IV Data Analysis was presented and discussed the data to be used in

the study. Structural equation model statistics were presented and discussed. Model

fit indices were presented as well as the empirical rational of the indices. Statistical

results of the structural equation models and associated variables were presented and

discussed.


13

Chapter V Conclusion discussed the findings of the research. Effects on the

explored variables were discussed as well as consideration of the results on the

research questions. Recommendations for action and further study related to findings

were made.


14

Chapter II

Review of the Literature

Introduction

The call for the reform and improvement of America’s public schools stems

from the highest seat of American government. In 2004, President George W. Bush

asserted, “The challenge to educate future Americans can be called the essential work

of democracy. Making America safer, stronger, and better demands a world-class

education system” (Bush, 2004, p. 114). While researchers point out that U.S. student

performance lags behind that of our international counterparts in mathematics and

science, “the fact is that these results signify something real” (Hanushek, 2004, p. 2).

Lagging behind our international counterparts casts doubt on America’s workforce

and long-term economic welfare (Hanushek, 2004).

In 2011, President Barack Obama declared, “We must reform our schools to

accelerate student achievement, close achievement gaps, inspire our children to excel,

and turn around those schools that for too many young Americans aren’t providing

them with the education they need to succeed in college and a career” (p. 1).

President Obama asserted that congress should reform No Child Left Behind.

Building upon what worked best in The Race to the Top, President Obama declared,

“Our challenge now is to allow all fifty states to benefit from the success of Race to

the Top. We need to promote reform that gets results while encouraging communities

to figure out what’s best for their kids” (Obama, 2011, p. 1).


15

Educational Reform and Accountability

Research shows that schools focused on reform and accountability can

improve student achievement. Schools engaged in capacity building, including

improving professional knowledge and competency, coupled with a supportive

organizational structure, produce significant results in student achievement. The local

education agency, outside consultants, and external partners, such as colleges and

universities, can be important partners for providing assistance and support to the

school (Ross, Gray, & Sibbald, 2008, p. 22). Harris and Herrington’s (2006, p. 29)

study on accountability, standards, and the growing achievement gap, found that

policies that have increased school capacity, provided students exposure to rigorous

content, increased time i.e. longer school day, summer school, after school, etc. and

content standards have helped close the achievement gap. Of necessity, school reform

policy and efforts must have an effect in the classroom. “Educators - practitioners and

policymakers - recognize what discerning parents have always known: The quality of

individual teachers matters” (Danielson, 2001, p. 12).

Research surrounding school reform and accountability points toward several

social-political implications associated with policies aimed at school reform. Low

controversy policies with high visibility are viewed as having a greater positive impact

on schools. Policies focused on professional development or decentralized

governance are less controversial and have the most political appeal, while policies

that alter core practices are viewed as burdensome and threatening. While aggressive

improvement policies may produce positive learning outcomes, they are also likely to

produce low staff morale. This results in a loss of confidence and commitment from


16

staff. This leaves policymakers at all levels with the dilemma of improving schools

while maintaining staff morale (Torres, Zellner, & Erlandson, 2008, p. 7). Schools

engaged in aggressive reform efforts cannot lose sight of what matters to teachers.

Leaders must remain aware of and responsive to teacher needs related to working

conditions - gathering, analyzing, and responding to data surrounding teacher views of

working conditions. “Teachers who intend to leave their schools and teaching are

more likely than those who intend to stay to have concerns about their lack of

empowerment, poor school leadership, and the low levels of trust and respect inside

their buildings” (Berry, Wade, & Trantham, 2008, p. 80). Policy makers and school

leaders should consider the possibility and implications of “teachers being emotionally

exhausted” (Berryhill, Linney, & Fromewick, 2009, pp. 8-9). “This may cause

teachers to leave the profession or decrease their commitment and

enthusiasm”(Berryhill et al., 2009, pp. 8-9). Neither of these results lead to what

accountability policies seek in improving student performance (Berryhill et al., 2009,

p. 9).

CSCOPE Curriculum Development

Currently, over 800 of 1237 Texas public school districts have partnered with

CSCOPE as their curriculum management system, born of work led by Dr. John

Crain, Region XIII, and the Hill Country Curriculum Consortium. Dr. Crain also

developed six days of leadership training for the school administrators within the six

regions who initiated and participated in the collaborative. Two days of the training


17

focused on curriculum within the TEKS framework, two days on instructional design,

and two days on leading and coaching staff (Crain, 2011).

The Texas Educational Service Center Curriculum Cooperative (TESCCC)

began development of CSCOPE during the 2005-2006 academic year.

Implementation of CSCOPE began during the 2006-2007 school year. The TESCCC

originally consisted of Education Service Centers 2, 6, 8, and 19. Regions 1 and 6

joined soon after the cooperative was formed. In 2007, Regions 13, 20, 10 and 7

partnered with the cooperative. Since 2007, Regions 3, 5, 9, 11, 12, 14, 15, 17, and 18

have also committed to the cooperative.

Originally conceived as a curricular scope and sequence, developers responded

to the needs of local districts. The financial and human capital needed to implement

improved curricula around the revised state standards, imminent changes in state

exams and the state accountability system appeared daunting and costly for most

districts across the state. Additionally, the need persists to respond to the mobility

subset population of students across Texas. Historically, the mobility subset

population of students moves to other schools within a district or even to neighboring

districts and gets lost in differences in curricular scope and sequence. The resulting

loss in student learning can have a lasting effect on individual students. In turn this

can have effects on campus, district, and state completion rates (Wade N. Labay &

Drumm, 2011).

As the curricular scope and sequence became popular among early adopters,

more districts across Texas began adopting CSCOPE. As more districts became


18

involved with CSCOPE, the demand for a fuller more robust curriculum management

system emerged. The TESCCC team, including ESC personnel, and other content

area experts, developed research-based curricular components that support teaching

and learning based upon Texas standards. System components include professional

development, curriculum, assessment, and the innovative use of technology. The

current curricular components of the CSCOPE include the Vertical Alignment

Document, Year at a Glance, Instructional Focus Documents, and the TEKS

Verification Matrix.

Guided by the work of Marzano, English, Bybee, Jacobs, and Wiggins and

others, the CSCOPE curriculum management system provides a guaranteed and viable

curriculum that is conceptually organized to provide both vertical and horizontal

alignment in clearly articulated periods of time. The curriculum provides for an

emphasis of “key spiraling components which represent the major competencies,

ideas, and skills that students are expected to develop” (Hamilton, 2008, p. 2) within

and across grade levels/courses “with growing levels of competency, proficiency, and

depth of understanding” (Hamilton, 2008, p. 2). Additionally, the system provides

exemplar lessons “to inspire decision making, teacher creativity, and the appropriate

use of available resources” (Hamilton, 2008, p. 9). Irrespective of what curriculum a

school or district uses, at the lesson level teachers employ their expertise,

incorporating knowledge of individual students and their needs and interest. Exemplar

lessons provide a model for the standard of rigor, relevance, and essential questions


19

crucial for student learning. Teachers use their expertise to provide differentiation or

accommodations for students as appropriate (Hamilton, 2008, p. 2).

Leadership Theories

Principal leadership.

A free democratic society requires ethical living and social justice. Principals

must build upon a sense of community, recognizing an interdependent nature and a

need to work toward the common good (Reames, 2010, p. 440). Recognizing and

building upon the features and people in the school organization allow the leader to

build unity and coordination. Principal leadership focusing schools around a mission

and goals, encouraging trust and collaboration among stakeholders, and actively

supporting and improving instruction produces the greatest effect on student

achievement (Supovitz, Sirinides, & May, 2010, p. 34). Well-functioning

organizations develop a culture, beliefs, and values that allow individual workers and

teams to focus individual and collective actions based upon common objectives

(Greenwald, 2008, pp. 426-427). In response to business interest and the No Child

Left Behind Act, many states have adopted legislative policy and “high stakes” testing

requirements designed to put pressure on schools, principals, teachers, and students to

perform at high levels. While Gruber openly questions the merits of high stakes

testing, he acknowledges that such reforms are here to stay (Gruber, 2006, p. 2).

When confronted with high stakes accountability, the role of principal as a curriculum

leader is essential for school and student success (Allan A. Glatthorn, 1997, p. 4).

Current trends in principal preparation expect that school leaders be proficient with


20

pedagogy, curriculum, instructional practices, data analysis, as well as capable of

creating and sustaining a culture of professional learning (Reames, 2010, p. 439). As

Schmoker (Schmoker) notes, the impact of the actual taught curriculum in schools is

“indescribably important” (p. 36). The taught curriculum has the most profound

impact on student learning and school success. It is incumbent upon teachers and

principals to ensure that the written and taught curriculum are aligned (Schmoker,

2006, p. 36).

Principals must be effective communicators, providing information and

developing an ecology of knowledge, planning, and expectations within the school.

As schools manage the uncertainties of change, communication is essential for

building and maintaining a positive school climate (Halawah, 2005). Principals with

the highest levels of student achievement exhibit qualities of organizational oversight

and judgment. High performing principals recognize the primacy of perspective over

managerial skill in building and leading successful learning communities. Student

achievement increases when leadership is collaborative. The most effective principals

focus on student guidance/development, thoughtful instructional management, and

staff development. These skills require “utilizing resources, prioritizing, and drawing

informed conclusions to make quality decisions” effecting the school (Erwin, Winn,

Gentry, & Cauble, 2010). Informing practice and thinking that leads to desired results

requires preparation, inquiry, and action. A “data wise” improvement process

provides a framework for tackling the complex technical and strategic problems

associated with school leadership in an era of high stakes accountability (Boudett,


21

City, & Murnane, 2010). Data driven principals and data driven decision making

teams function best when data are viewed as valid and reliable, data are readily

available, and data and assessment literacy have been developed (Mingchu Luo, 2008,

pp. 629-630).

Instructional leadership.

Effective school leaders create and implement a plan for executing the

curriculum required by the state and local district, focusing on achieving the learning

outcomes established in the curriculum. The plan should focus on meeting the needs

of all students and allocate resources including staff to support student success in the

curriculum. The plan should align all school systems with student achievement.

Systems should include building capacity within the school to create teaching teams

with the expertise to meet student needs, including data driven processes for school

improvement (Ruebling, Stow, Kayona, & Clarke, 2004). Feedback provided to

schools and teachers around planned performance indicators includes an analysis of

identified strengths and weaknesses, analysis of provision of resources, programs for

teaching and learning, and student achievement results. School administrators and

leadership teams should focus on performance data and continuous improvement,

building a shared commitment to strategic and continual improvement at all levels

within the school (Rowe & Lievesley, 2002).

Professional learning communities (PLCs) have surfaced as one of the best and

most agreed upon organizational arrangements to improve instruction and student

academic performance. Teacher teams should work from “common curricular


22

standards” and plan for implementation based upon a “roughly common schedule.”

Teams should meet regularly and maintain a focus on teaching and learning working

collaboratively to ask and answer questions based upon data derived from common

assessments related to improving student learning and academic achievement.

Common assessments and “assessment literacy” (Schmoker, 2006, p. 107) by

individual teachers and teacher teams are critical for the success of PLC’s. “With

common assessments and results, teachers can conduct what Eaker calls “active

research” where “a culture of experimentation prevails” (Schmoker, 2006, p. 107).

Teacher teams “succeed where typical staff development and workshops fail”

(Schmoker, 2006, p. 106). PLCs can provide a vital link and necessary support during

new teacher induction. New teacher induction experiences are the most successful

when they allow teachers to effect their own professional development initiatives

aligned to their unique needs. This bridges teacher needs with training and subsequent

implementation in the classroom (Cherubini, 2007). PLCs lend themselves to building

professional capacity, providing teacher leadership opportunities, supporting new

teacher induction, and improving student achievement.

Curriculum leadership.

Challenging the status quo in most schools, Schmoker (2006) asks aloud why

students attend schools “where instruction is largely unsupervised?” (p. 163). “Why

would the quality of curriculum a student receives depend upon which teacher a child

happens to get?” (Schmoker, 2006, p. 163). Pointing to the elephant in the room,

Schmoker (2006) presses, “Should we continue to deny tens of millions of students the


23

opportunity to read and write and learn in ways that engage the intellect - while their

enthusiasm for learning, their intellectual and career prospects suffer irretrievably?”

(p. 163).

Acknowledging that working with curriculum is laden with disagreement,

Glatthorn (2008) explains that with “good judgment” and “creative coping” (p. 27)

teachers can develop plans that address the most pressing concerns associated with

state and district level expectations associated with the written, taught, and tested

curriculum while simultaneously integrating curriculum components that allow

teachers to use their creativity to develop plans that are interesting for students.

Curriculum work should first begin with analysis and development of the written

curriculum and mastery units that are essential for student success. An expanded

concept of alignment then includes purposeful consideration of eight other curriculum

types - hidden curriculum, excluded curriculum, recommended curriculum, written

curriculum, supported curriculum, tested curriculum, taught curriculum, and the

learned curriculum. Developing a teacher wise and robust curriculum should include

alignment with the eight types of seemingly competing curriculum found in Table 2.1

below (1999).


24

Table 2.1 Types of Curriculum

Types of Curriculum

Type Definition

Hidden curriculum The unintended curriculum - what students learn from the

school's culture, climate, and related policies and practices.

Excluded curriculum What has been left out of the curriculum, either intentionally or

unintentionally.

Recommended curriculum The curriculum advocated by experts in the subject fields.

Written curriculum The document(s) produced by the state education agency, the

school system, the school, and/or the classroom teacher

specifying what is to be taught.

Supported curriculum The curriculum that appears in textbooks, software, and

multimedia materials.

Tested curriculum The curriculum that is embodied in state tests, school system

tests, and teacher-made tests.

Taught curriculum The curriculum that teachers actually deliver; it is the

curriculum that is enacted or put into operation.

Learned curriculum The "bottom-line" curriculum - what students learn.

(Allan A. Glatthorn, 1999, pp. 29-30)

Pointing to solutions in curriculum leadership in this brave new world of high

stakes testing and accountability requires developing data and assessment literacy for

campus leaders and teachers. While there is no one complete framework for data

analysis, school data generally falls into the categories of demographic data,

perceptions data, student learning, and school processes (Bernhardt, 2004).

Curriculum leaders, including principals and teachers, need to be literate in making

meaning of the various types of data gathered, transforming it into information for

planning and action. This requires schools to develop an agreed upon framework and

culture of collaboration around data analysis and the resulting plans and efforts for

school improvement (Crum, 2009). The increased use of formative assessments is

central to plans for improving curriculum and instruction. Formative assessments are


25

used to improve the learning of the students who complete the assessment. This has

led some researchers and practitioners to rename formative assessment “assessment

for learning” (Assessment Reform Assessment Reform Group, 2002, p. 1).

“Assessment for learning is the process of seeking and interpreting evidence for use by

learners and their teachers to decide where the learners are in their learning, where

they need to go and how best to get there” (Assessment Reform Group, 2002, p. 1).

This makes explicit the idea that the intention of the assessment is to evaluate and

improve upon what the student has learned (Glasson, 2008).

Teacher leadership.

After reviewing over 20 years of research and literature on teacher leadership,

it is clear that teacher leadership over this period focused upon pedagogy,

relationships, routines and expectations, engagement, and “improving curricular,

instructional and assessment practices” (Robert J. Marzano et al., 2005, p. 290), which

have significant impact on student learning and result in high levels of student

achievement (English & Steffy, 2001; Robert J. Marzano et al., 2005; York-Barr &

Duke, 2004). Advances in the design and capabilities of statistics software reveal

empirically “that the single largest factor affecting student academic growth is

differences in the effectiveness of individual classroom teachers” (Holloway, 2000, p.

84). Numerous scholars and researchers view these and other teacher competencies

as a matter of social justice for all students. A theory of justice “has three key ideas

that are imbricate and integrated with one another: (1) Equity of learning opportunity,

(2) Respect for social groups, (3) Acknowledging and dealing with tensions.”


26

(Cochran-Smith, Feiman-Nemser, McIntyre, & Association of Teacher Educators.,

2008, p. 13) These lofty democratic ideas presuppose a high level of teacher

competency and proficiency (Cochran-Smith et al., 2008).

Teacher leadership in professional development improves teacher collaboration

and fosters a sense of community within the school. Teachers who were involved with

leading and learning from peers reported that teacher leadership builds school culture,

improves morale, and can improve student achievement (Hickey & Harris, 2005).

Volante and Cherubini (2010) assert that educators must improve their assessment

literacy and data driven decision-making. Developing the assessment capacity of

teachers is essential for schools to make effective use of assessment data for school

improvement purposes (2010, pp. 22-23). Ivie, Roebuck and Short (2001) add that

while experienced teachers insist that teaching is primarily a science, attention to the

aesthetic qualities of teaching should not go undeveloped, stating (aesthetically), “A

spoonful of sugar (art) might just help the medicine (science) go down in the most

delightful way” (Ivie et al., p. 532).

Critics of standardized testing point to the fact that standardized testing takes a

great deal of time during the school year, can have a tendency to narrow the

curriculum, and originates (illegitimately) from the federal or state government,

arguing that politicians and bureaucrats do not know or understand what is happening

in the classroom. Regardless of where educators stand in their view on state mandated

standardized testing, they are best served by acknowledging that standardized tests are


27

here to stay and learn to interpret, analyze, and apply the results to improve classroom

practice and student performance (Mertler, 2007, pp. 26-27).

Analysis of teacher and administrator views of various types of assessment of

student achievement reveal a significant difference between teacher views and those of

administrators. Teachers think that teacher observations, portfolios, and teacher-

developed assessments are some of the most valuable forms of assessment while

administrators view portfolios of student work, student exhibits, and teacher-

developed assessments as the most legitimate types of student assessment. Both

groups tend to rank nationally normed standardized exams, end of course exams, and

other forms of state assessment lower in terms of validity and reliability, with

administrators taking a more favorable view of state assessments and end of course

exams than teachers. From a formative viewpoint, it is recommended that both

teachers and administrators be willing to consider multiple sources of data in

evaluating student achievement. Multiple sources bring perspective, clarity, and

direction to improvement efforts. Comparing results can provide a richer and deeper

insight into student performance. The combined perspectives of both internal and

external measures of student achievement can bring teachers and administrators

together regarding the value attached to differing sources of evidence of student

achievement (Guskey, 2007, pp. 25-26).

The shift from evaluating educational “inputs” as a measure of the quality of

education to measuring educational “outputs” in the form of student achievement has

presented challenges. Issues of alignment, validity, and reliability, as well as the


28

related implications associated with curriculum and instruction, have left practitioners,

researchers, and reformers with multiple interpretive problems. Iwanicki (2001)

asserts that one way to address these apparently confounding issues is to develop and

align teacher evaluation systems to answer to the following three questions:

Q1. Were the objectives of the lesson worthwhile and challenging?

Q2. Did the teacher treat the students with dignity and respect?

Q3 To what extent did all students achieve the objectives of the lesson?

Reflecting on these questions captures three crucial aspects of

instruction - intents, processes, and outcomes. (pp. 57-59)

Iwanicki (2001) explains that when a group of teachers were presented with the choice

of a more traditional system or a new integrated system of teacher evaluation they

chose the latter rather than the former. The study on this type of integrated evaluation

revealed, “Teachers developed more ownership for student learning, the quality of

their reflective judgment improved, and, yes, the students' scores on the state exams

went up” (Iwanicki, 2001, p. 59). Other researchers have observed that “the quest for

valid and consistent measures of teacher behaviors that are related to student learning”

(Kimball, 2004, p. 55) has been a longstanding pursuit in educational research . The

Washoe County study examined relationships between teacher evaluations and student

performance on standardized tests. The results revealed “weak” or “mixed” findings

between ratings on teacher evaluations and student achievement as measured by

standardized exams (Kimball, 2004, pp. 54-78).

Reflecting upon the persistent problem of standardized testing having a

tendency to narrow the curriculum, reformers have noted - tongue in cheek -


29

“WYGWYA” - that “What You Get is What You Assess.” Teachers and reformers

have advocated for improved quality of test to include “thinking skills” and “test

worth teaching to” reasoning that proper alignment with standards necessitating higher

order thinking, instruction, and assessment should require “assessments” to include

open-ended items that call upon students “to compose or explain” answers in

demonstrating higher and more complex cognitive skills (Haertel & Herman, 2005,

pp. 16-25). The inclusion of open ended items on assessments serve to reduce the

effect of narrowing the curriculum due to standardized assessments.

Studies Related to the Research Question

Merritt’s (2011) study, CSCOPE’s Effect on Texas’ State Mandated

Standardized Test Scores in Mathematics, explored the effects of CSCOPE

implementation on mathematics scores using a Fischer t-test to compare the effects of

a group of districts who had implemented CSCOPE to those who had not. Results

revealed a statistically significant (P < .05) effect on the mean passing percentage at

the all student level in grades 3-8 (2011).

Opening doors of opportunity for all students and closing the achievement gap

for traditionally underrepresented student populations are the altruistic and utilitarian

goals of education and related educational policy. The goal of federal assistance

programs in education is to “improve student learning and achievement, especially

among economically disadvantaged children” (Kirby, 2002, p. 122). Methods and

measures for attaining these goals have been a matter debate and policy decisions

years.


30

Historically, policies that focus on time and content standards for all students

including minorities have had a positive effect on student achievement. The gains

produced as a result of these policies have been considerable for minority students.

Government accountability measures focused on promotion and graduation

expectations including standardized exams have also produced significant gains in

closing the achievement gap. Policies that focus on takeovers/oversight/reconstitution,

school report cards, vouchers/charters/school-choice have only produced small or

mixed gains in achievement for minority students. Increased standards, policy related

to increased (more rigorous) course taking, and resulting higher academic achievement

hold for all racial/ethnic groups (Harris & Herrington, 2006). “In short, standards

affect academic rigor that, in turn, drives achievement” (Harris & Herrington, 2006, p.

11). Further, “school responses to increased promotion and graduation expectations

and standardized exams disproportionately benefit disadvantaged students” (Harris &

Herrington, 2006, p. 12). An increased focus on student achievement coupled with

increased resources have produced a significant effect in closing the achievement gap

(Harris & Herrington, 2006, p. 23).

Research shows that when curriculum is “focused on and connected to, as well

as aligned with tests, the influence of socioeconomic level on test performance

declines” (English, 2010, p. 6). Poor students can perform well on tests if they are

taught properly (English, 2010, p. 7). Teachers who promote understanding in the

classroom recognize and respond when a student’s understanding in a particular

domain grows. Skillful teachers use this information in ever more powerful ways,


31

using a domain-based approach to assessment of knowledge in the classroom and then

focusing attention to the levels of reasoning students apply in using the ideas of the

domain. Assessment opportunities involve students in using the mental activities

appropriate for the domain while providing increasingly complex levels of reasoning:

reproduction, connections, and analysis (Fennema & Romberg, 1999, p. 162).

Teachers who recognize these connections and build upon them with students in the

classroom produce significant results in terms of student growth in learning and

academic achievement.

Chapter Summary

It is clear that student learning in the curriculum is why schools exist (Ruebling

et al., 2004, p. 243). Expectations continue to mount for schools to produce high

levels of student achievement for all students including closing the achievement gap

for economically disadvantaged and minority students. Leadership focused upon the

instructional core - what teachers and students do in the presence of content - is where

the elusive holy grail of school improvement and student achievement is found

(Elmore, 2009). It is clear that curriculum and instruction as well as stakeholder

leadership converge upon research findings related to the improvement of student

academic performance.


32

Chapter III

Methodology

Introduction

As articulated for over a decade, principals and teachers must exhibit high

functioning and effective leadership behaviors as well as curriculum and pedagogical

proficiency in providing a tightly coupled curriculum. While there is significant

research to substantiate this claim and this study acknowledges that the CSCOPE

curriculum management system is designed with a strong research-based foundation,

there is sparse research to examine the effects of CSCOPE on student academic

performance as measured within student sub-populations and demographic

characteristics identified in the Academic Excellence Indicator System (AEIS). The

study used latent growth modeling to fill a need for further study regarding the effect

of CSCOPE implementation on student academic performance as measured by student

Texas Assessment of Knowledge and Skills (TAKS) mathematics scores.

The purpose of the study was to evaluate student academic performance as

measured on the TAKS test. Student mathematics TAKS scores were used as the

dependent variable in evaluating student academic performance. The study sought to

answer the following research questions: (1) What effect does CSCOPE have on

student mathematics performance? (2) What effect does CSCOPE have on student

sub-populations mathematics performance?


33

Participants

The population for this study is public school students in Texas. The State of

Texas maintains 1,265 public school districts (Texas Education Agency, 2003b) with a

student population of 4,400,644 in the 2004-2005 school year. By the 2009-2010

school year the population had grown to 4,847,844 students. See Table 3.1 for the six

year public school enrollment for the study’s population. A comparison of the number

and percent of the population’s demographic characteristics with the sample’s

demographic characteristics are provided in Table 3.2.

Table 3.1 Texas Statewide Enrollment, 2004-2005 through 2009-2010

Texas Statewide Enrollment, 2004-2005

through 2009-2010

Year Number

Annual

Change (%)

2004-2005 4,400,644 1.7

2005-2006 4,521,043 2.7

2006-2007 4,594,942 1.6

2007-2008 4,671,493 1.7

2008-2009 4,749,571 1.7

2009-2010 4,847,844 2.1

(Texas Education Agency, 2010a)


34

The sample selected for this study was a set of students from Texas public

schools (n = 468). The samples and the state’s demographic characteristics can be

seen in table 3.2. Student TAKS mathematics test scores and related demographic

information were drawn from two school districts in Texas. An array of student

demographic characteristics including student gender, race/ethnicity, LEP status and

economically disadvantaged status were represented in the sample.

Table 3.2 Sample and State Demographic Summary

Sample and State Demographic Summary

Sample a State

b

Demographic N Percent N Percent

Male 242 51.7 2,489,328 51.3

Female 226 48.3 2,358,516 48.7

White 355 75.9 1,615,459 33.3

Black 5 1.1 679,351 14.0

Hispanic 97 20.7 2,354,042 48.6

LEP 15 3.2 817,074 16.9

EcoD 214 45.7 2,853,177 58.9 a Sample N = 468.

b Statewide Enrollment in 2009-2010 N = 4,847,844.

The first group of students (District 1) received curriculum in mathematics for

three years based upon a non-CSCOPE curriculum followed by three years of

curriculum based upon the CSCOPE curriculum. The second group of students

(District 0) received curriculum in mathematics from the non-CSCOPE curriculum

during the entire 6-year period of the study. The sample’s demographic characteristics

are summarized by district in table 3.3.


35

Table 3.3 Sample Demographic Summary by District

Sample Demographic Summary by District

District 1a District 0

b

Demographic n Percent n Percent

Male 76 51.7 166 51.7

Female 71 48.3 155 48.3

White 109 74.1 246 76.6

Black 0 0.0 5 1.6

Hispanic 32 21.8 65 20.2

LEP 2 1.4 13 4.0

EcoD 76 51.7 138 43.0

a District 1 n = 147.

b District 0 n = 321.

Measures

The Texas Education Agency (TEA) reports TAKS mathematics scores using

two different metrics for scores. The first type of score is a four digit “scale score”

(Texas Education Agency, 2010b, p. 1) with a metric ranging from 1200 to 3300. The

second type of score is a “vertical scale score” (Texas Education Agency, 2011, p. 1);

the vertical scale score employs a four digit metric ranging from 1 to 1,000.

Beginning in the 2009-2010 school year, only the vertical scale scores were reported

for grade 8 TAKS.

Test score data obtained included student scale scores for grades 3-7. The

grade 8 student scores obtained were vertical scale scores. To standardize the two

types of scales of the obtained student scores, the scores were converted to a z score

using IBM SPSS Statics 19 (IBM SPSS, 1989, 2010). The center point for the z

scores was set at the met standard cut point for both types of scales. The met standard

cut point for the scale score is 2100, while the met standard cut point for the vertical


36

scale score is 700 (Texas Education Agency, 2005a, 2006a, 2007a, 2008a, 2009a;

2010b, p. 31). Because campus accountability ratings and student success on the

exam are based upon this cut point, z scores were centered at the met standard cut

point for both scales School level and classroom level interventions focus on the

needs of students near the met standard cut point.

For comparison, a district using the CSCOPE curriculum management system

was identified, as well as a non-CSCOPE district during the same period. Through the

use of curriculum implementation and the resulting student performance data, the

effects of curriculum implementation on student performance were analyzed.

Analysis of student demographic characteristics and student sub-populations identified

in the AEIS and student performance were also completed. These variables included

district, gender, White, Hispanic, African-American (Black), limited English

proficiency (LEP) status, and economically disadvantaged (EcoD) student status.

Procedures

Research Design

This quantitative study used latent growth modeling to examine whether

CSCOPE implementation affects TAKS math scores. Student TAKS mathematics

scores were used to measure student performance. Changes in the slope growth factor

following CSCOPE implementation provided evidence of CSCOPE's impact on

student performance.

A claim for exemption was made to the Institutional Review Board (IRB) of

Texas Tech University. The IRB approved the claim for exemption on May 24, 2011.


37

The study was exempt because participant scores and demographic information were

collected from existing data which was collected in a manner conistent with the

Family Educational Rights and Privacy Act. Participating student names or related

demographic information cannot be identified in conjunction with the study.

Cohorts

Two student cohorts were established based upon the district the students were

enrolled in during the course of the study. The first cohort, non-CSCOPE, was taught

using the non-CSCOPE mathematics curriculum for the entire six-year period of the

study. The second cohort, CSCOPE, was taught for three years using the same non-

CSCOPE curriculum as the non-CSCOPE district. During the next three years of the

study, the students in CSCOPE received curriculum and instruction based upon the

CSCOPE curriculum management system. Student performance was measured using

z scores from the student TAKS mathematics scores from grades 3 through 8.

Student mathematics performance was modeled from grades 3 through 8 using

a latent growth modeling framework using Mplus 6.1 (Muthen & Muthen, 1998-

2010). The latent growth model uses the growth factors of random slope and intercept

as the latent variables in measuring student growth in academic performance over time

(Muthen & Muthen, 1998-2010, p. 115). Using a latent growth framework is

preferred over a longitudinal framework because the latent growth framework allows

for the exploration of student performance irrespective of each individual students

starting point or previous performance. Student or “sub-populations” were identified

as covariates in the model. Sub-population characteristics such as gender,


38

race/ethnicity, economically disadvantaged student status, and LEP student status were

explored.

Data Collection

The data were collected from two public school districts in Texas. Student

TAKS scores and related demographic information were maintained in each school

district's student information system. Student scores were obtained for grade 3 (2004-

2005), grade 4 (2005-2006), grade 5 (2006-2007), grade 6 (2007-2008), grade 7

(2008-2009), and grade 8 (2009-2010) for each student enrolled in the school districts

participating in the study. In grades 3, 5, and 8, multiple administrations of the TAKS

test are offered; scores obtained for these grade levels were from the first

administration of the test. The requested TAKS mathematics test scores and

associated student demographic information were down,loaded into a Microsoft Excel

workbook. The data obtained included a unique student identification number (ID) for

each student record. The student ID served to protect student confidentiality in the

study and maintained referential integrity of the data when processing cases for the

study. Student names were not associated with the student ID, so individual students

or related student demographic information cannot be identified in conjunction with

the study. Student cases contained the student’s TAKS mathematics scores from

grades 3-8 and demographic information including the student’s gender,

race/ethnicity, LEP status, and economically disadvantaged status. After the data were

obtained from each district, a district identifier, 0 for the non-CSCOPE district and 1

for the CSCOPE district, was added to each case for study purposes.


39

The Proposed Model


1. What effect does CSCOPE have on student mathematics performance?

2. What effect does CSCOPE have on student sub-populations mathematics

performance?

A hypothesized model was a six year linear growth model for continuous

outcomes including covariates associated with the student demographic

characteristics. The model explored the relationships and growth of student

mathematics scores using the latent factors of slope and intercept for a diverse group

of students who were instructed using both the CSCOPE curriculum and the non-

CSCOPE curriculum. (Muthen & Muthen, 1998-2010, p. 115) See Figure 3.1 for the

hypothsized model.


40

I Pre-CSCOPE CSCOPE

Figure 3.1 Hypothesized Model

MATH4SS MATH5SS MATH6SS MATH7SS MATH8SS MATH3SS

District Race\Eth EcoD LEP Gender


41

Chapter Summary

Chapter III presented a methodological overview of the study. High

functioning leadership, curriculum, and pedagogical knowledge and skills from both

teachers and administrators along with a well-articulated, tightly aligned curriculum is

essential for improving student performance. The population of Texas public school

students was identified as well as the purposefully selected sample of student TAKS

mathematics scores from cooperating districts. A discussion of study participants

demographic characteristics and confidentiality followed. The generalizabilty of the

sample to the population in this study with regard to efficacy of CSCOPE

implementation on student performance was discussed. The study’s quantitative

design using a latent growth structural equation model was discussed. Data collection

and z score conversion was explained. The relationship between the established

student cohorts’ treatment with curriculum and instruction within the selected districts

was described. Chapter III concludes with a description of the hypothesized latent

growth model and a representative diagram of the relationships identified and explored

by the model (Muthen & Muthen, 1998-2010).


42

Chapter IV

Data Analysis

Introduction

The purpose of the study described herein was to analyze and explore the

relationships between two variations of curricular implementation in mathematics and

the resulting student performance on standardized exams. Student test scores on the

Texas Assessment of Knowledge and Skills (TAKS) mathematics exam in grades 3-8

were used as the dependent measure to explore the effect of the curricular inputs on

student achievement over time. A latent growth structural equation model (SEM) was

used to explore the relationship between curricular implementation and the resulting

student performance over time. The latent growth SEM uses the growth factors of

random slope and intercept as the latent variables in measuring student growth in

academic performance over time (Muthen & Muthen, 1998-2010, p. 115). Covariates

such as gender, race, ethnicity, economically disadvantaged (EcoD) student status, and

limited English proficient (LEP) student status as well as the all student (District)

groups were added as independent variables and explored.

With the popular implementation of the CSCOPE curriculum management

system, over 800 school districts across Texas have adopted CSCOPE as their

curriculum management system of choice. The quality and effectiveness of the

system have been matters of heated debate among educators and other stakeholders

across the state. With a significant financial and human capital commitment to the


43

product, a study of the CSCOPE curriculum management system’s effect on

standardized student test scores was warranted.

Latent Growth Modeling

The present study examined the relationship between curriculum

implementation and student performance as measured by TAKS mathematics scores

using the latent growth modeling of slope and intercept over time. A latent growth

structural equation model uses the growth factors of random slope and intercept as the

latent variables in measuring student growth in academic performance over time

(Muthen & Muthen, 1998-2010, p. 115). Latent growth modeling was used to

examine the relationship between CSCOPE and student performance on TAKS

mathematics exams. Covariates associated with students’ demographic characteristics

including gender, race/ ethnicity, student LEP status, student economically

disadvantaged (EcoD) status were explored.

Mplus v6 was used for the growth modeling of student performance. Mplus

uses a multivariate approach to latent growth modeling. A multivariate approach

provides for flexibility in modeling outcomes. This multivariate approach allows for

the examination of “residual variances over time, correlated residuals over time, and

regressions among the outcomes over time” (Muthen & Muthen, 1998-2010, p. 97).

Latent growth models use random effects to capture individual differences in

development. Working within a “latent model framework, random effects are

reconceptualized as continuous latent variables, that is, growth factors” (Muthen &


44

Muthen, 1998-2010, p. 97). Piecewise growth models capture phases of development

using slope as a growth factor (Muthen & Muthen, 1998-2010, p. 115).

The present study used maximum likelihood (ML) estimation for model fitting.

Maximum likelihood is a standard approach to estimating parameters and is

sufficiently robust for inference estimation statistics (Myung, 2003, p. 90). It is worth

noting that while ML parameter estimates are robust against non-normality, the results

of significance tests tend to lead rejecting the null hypothesis when the data do not

support such decisions. Concerns with severly non-normal data must be considered to

prevent type I error in accepting a model (Kline, 1998, pp. 125-127).

Goodness-Of-Fit

Goodness-of-fit indices describe how well a model fits a set of observations.

Statistical measurements of goodness-of-fit typically rely on measures of observed

value versus the expected values of a model. Fit indexes are better characterized as

“what does not constitute evidence of good fit?” (Kline, 1998, p. 130). Multiple

indices of model fit were used and reported because a specific index reflects only one

particular facet of the overall model fit (Kline, 1998, p. 130).

When considering available model fit indices and related empirical

considerations, Hooper, Coughlan, and Mullen (2008) advised including the chi-

square statistic, Root Mean Square Error of Approximation (RMSEA), Standardized

Root Mean Square Residual (SRMR), Comparative Fit Index (CFI), and a parsimony

fit index. “These indices have been chosen over other indices as they have been found

to be the most insensitive to sample size, model misspecification and parameter


45

estimates" (Hooper et al., 2008, p. 56). The present study used the Akaike

Information Criteria (AIC) to examine parsimony fit due to the single level (non-

nested) multivariate approach in growth modeling used by Mplus 6.1.

The chi-square (χ2) value is the traditional measure for evaluating overall

model fit, and “assesses the magnitude of discrepancy between the sample and fitted

covariances matrices" (Hu & Bentler, 1999, p. 2). The chi-square test indicates the

difference between the sample and covariance matrices. A chi-square value close to

zero indicates little difference between expected and observed matrices. Reporting of

the chi-square value should be accompanied by the p-value or probability of obtaining

a test statistic at least as extreme as the one observed. Traditionally the p-value should

be reported at either the .01 or .05 level (Hooper et al., 2008, p. 53). For the present

study, the significance level of p ≤ .05 was applied for the chi-square test.

Root Mean Square Error of Approximation (RMSEA) is currently the most

popular measure of model fit. RMSEA is an absolute measure of fit based upon the

non-centrality parameter. Thus, estimates closest to zero represent the best fitting

model. Recommended cut offs for model fit include 0.01, to indicate excellent fit;

0.05, to indicate good fit; and 0.08 to indicate mediocre fit (MacCallum, Browne, &

Sugawara, 1996, pp. 142-146). The RMSEA estimate is usually reported with a

confidence interval. The lower value of the 90% confidence interval should be near

zero, or no worse than 0.05, and the upper limit value should be less than .07 or .08

(Hooper et al., 2008, p. 54).


46

The Standardized Root Mean Square Residual (SRMR) is the average

difference between the predicted and observed variances and covariances (residuals)

in the model based upon standardized residuals. Standardized residuals are fitted

residuals divided by the standard error of the residual. The statistic’s values range

from zero to one. A value less than .05 is considered good fit, and a value below .08 is

considered adequate (Hooper et al., 2008, p. 55).

Comparative Fit Index (CFI), which assumes that all latent variables are

uncorrelated, compares the covariance matrix predicted by the model to the observed

covariance matrix, and compares the null model with the observed covariance matrix

to gauge the percent lack of fit, which is accounted for by going from the null model

to the hypothesized model. CFI statistic values range from 0.0 to 1.0. Statistic values

closest to 1.0 indicate a good fit. Current cut-off criterion recommend CFI ≥ 0.95 (Hu

& Bentler, 1999, p. 27) . The CFI is one of the goodness-of-fit measures least effected

by sample size (Hooper et al., 2008, p. 55).

Akaike Information Criteria (AIC) is a goodness-of-fit measure that adjusts

model chi-square to penalize for model complexity. AIC reflects the discrepancy

between the model-implied and observed covariance matrices. “Therefore, for us the

best model is the one with least complexity, or equivalently, the highest information

gain. In applying AIC, the emphasis is on comparing the goodness-of-fit of various

models with an allowance made for parsimony” (Bozdogan, 1987, p. 356).


47

Modeling

Preliminary analysis of the sample data (N = 468) was performed to determine

descriptive statistics for the means, variances, and correlations of the data using Mplus

6.1. Missing data and missing data patterns were examined. See Tables 4.1 through

4.3 for sample means, covariances, and correlations. Identification of sample

distributions and outliers were examined. No adjustments, elimination of outliers, or

adjustments for non-normal distribution in the sample were made. Estimated means,

covariances, and correlations of the sample data appeared to be within normal ranges.

Table 4.1 Sample Means

Sample Means

Means


0.667 0.971 0.996 0.716 0.726 0.766

Note: N=468

Table 4.2 Sample Covariances

Sample Covariances

Covariances

MATH3SS MATH4SS MATH5SS MATH6SS MATH7SS

MATH3SS 1.303

MATH4SS 0.537 0.837

MATH5SS 0.572 0.655 0.985

MATH6SS 0.487 0.603 0.648 0.848

MATH7SS 0.491 0.629 0.672 0.673 0.812

MATH8SS 0.548 0.658 0.685 0.697 0.734

Covariances (continued)

MATH8SS

MATH8SS 0.934

Note: N=468


48

Table 4.3 Sample Correlations

Sample Correlations

Correlations


MATH3SS 1.000

MATH4SS 0.515 1.000

MATH5SS 0.505 0.721 1.000

MATH6SS 0.463 0.716 0.709 1.000

MATH7SS 0.477 0.763 0.751 0.811 1.000

MATH8SS 0.497 0.745 0.714 0.784 0.842

Correlations (continued)

MATH8SS

MATH8SS 1.000

Note: N=468

The mean curve of the sample data was obtained. The mean curve revealed a marked

increase in the mean scores of students from Grade 3 to Grade 4. The mean score

approaches the upper limit of the scale creating a ceiling effect at Grades 4 and 5. A

marked decline in the mean scores of students from Grades 5 to 6 was observed.

Figure 4.1 illustrates the mean curve. A random sample of 10 individual student

curves in the sample data set was obtained. As can be seen in the random sample of

individual curves there is wide variability in the starting point of student performance

for Grade 3 math. See Figure 4.2 for a an illustration of ten individual curves within

the sample data set.


49

Figure 4.1 Mean Curve

Figure 4.2 Individual Curves

0.5

0.6

0.7

0.8

0.9

1

3rd 4th 5th 6th 7th 8th

Mat

h P

erfo

rman

ce

Grade Level

3 4 5 6 7 8

Grade

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

Mat

h P

erfo

rman

ce

3rd 4th 5th 6th 7th 8th

Grade Level

Mat

h P

erfo

rmance


50

Parameterization of the hypothesized model (LGM1) (see Table 4.4 and Figure

4.1 below) was designed to capture phases of student performance on the TAKS

mathematics exam from grades 3 through 8. The observed variables were z scores

obtained from student TAKS mathematics scores identified as math3ss, math4ss,

math5ss, math6ss math7ss, and math8ss.

Specifications in the model parameters capture different phases of

development by more than one slope growth factor. The first slope factor statement

specifies a growth model for the first phase of student performance capturing three

years of non-CSCOPE curriculum implementation on both districts student

performance. The second slope factor statement specifies a growth model for the

second phase of student performance capturing three years of CSCOPE curriculum

implementation in the CSCOPE district and three additional years of non-CSCOPE

curriculum implementation in the non-CSCOPE district. The intercepts of the

outcome variables at the six time points are fixed at one. The means and variances of

the three growth factors are estimated, and the three growth factors are correlated

because they are independent (exogenous) variables. Maximum likelihood (ML) is

the estimator used in this analysis.

Input and model estimation for the hypothesized latent growth model 1

(LGM1) terminated normally, but the model failed to converge; thus, standard errors

of the model parameter estimates were not computed. See Table 4.4 for a summary of

each model’s fit indices. Respecification of the hypothesized model was needed to

achieve good model fit.


51

I Pre-CSCOPE CSCOPE

Figure 4.3 Hypothesized Model (LGM1)


District Race\Eth EcoD LEP Gender


52

The parameters of LGM1 were respecified to a basic linear growth model involving

fixed time points with no covariates (LGM2). Respecifying a model by trimming the

number of model parameters (covariates) is necessary when a model fails to converge.

This allows for the identifcation and isolation of model parameters that are sources of

or contribute to non-convergence. All other model parameters remained the same.

Figure 4.2 illustrates LGM2 with the covariates removed.

I Pre-CSCOPE CSCOPE

Figure 4.4 LGM2



53

Results indicate LGM2 model fit was poor. The timepoints of models LGM3 and

LGM4 were respecified because the slopes were nonlinear. LGM4 continued using the

previous time points of interest for the study and fixed the covariance between Pre-

CSCOPE implementation, CSCOPE implementation, and the intercept at 0, meaning

that Pre-CSCOPE implementation was not correlated with CSCOPE implementation

and the rate of change in student performance is not related to the students starting

point. All other model parameters remained the same. LGM4 model fit was adequate.

LGM5 through LGM11 include a series of respecifications made to the model starting

with adding the disrict covariate. When the black student covariate was added (LGM8)

the model failed to converge due to the lack of black students in the CSCOPE district.

The black student covariate was removed from models LGM9 through LGM11.

Adding the other covariates tended to improve the overall goodness of fit of the model

but failed to produce significant estimates related to the covariates. LGM12 respecifed

the model to drop all covariates except for district and was accepted as the most

parsimonious explanation of the effect of curriculum implementation on student

mathematics performance when controlling for district. See Figure 4.5 for LGM12, the

final model.


54

I Pre-CSCOPE CSCOPE

Figure 4.5 LGM12 Final Model

.713 .889 .509

.181 .112 .198 .269 .213 .768


District

Note: All 6 intercept

parameters were fixed at 1

0.3 0.4

0.4 0.4 0.4

.260

.270 .259

0

0

0

.206 -.549 .958


55

Table 4.4 LGM Fit Indices

LGM Fit Indices

Model

χ2

df

RMSEA

SRMR

CFI

AIC

LGM1Hypothesized (Linear Growth) Model failed to converge

LGM2 Removed all covariates (Linear Growth) 73.472 12 0.105 .064 .956 4003.632

LGM3 Adjusted time scores (Piecewise Growth) 10.504 11 0.000 0.021 1.000 3942.664

LGM4 Fixed factor

covariance’s to 0 (Piecewise Growth)

13.246 14 0.000 0.023 1.000 3939.406

LGM5 Added district covariate (Piecewise Growth) 36.170 17 0.044 0.027 0.986 3928.384

LGM6 Added gender covariate (Piecewise Growth) 50.103 20 0.057 0.028 0.979 3930.264

LGM7 Added white covariate (Piecewise Growth) 51.226 23 .051 0.025 0.980 3918.530

LGM8 Added black covariates (Piecewise Growth) Model failed to converge

LGM9 Dropped black covariate

and added Hispanic covariate (Piecewise Growth)

53.618 26 .0011 0.024 .981 3922.359

LGM10 Added LEP covariate (Piecewise Growth) 54.740 29 0.044 0.023 0.982 3920.578

LGM11 Added EcoD covariate (Piecewise Growth) 58.779 32 0.042 0.021 0.982 3906.948

LGM12 Final Model Dropped all covariates except

district (Piecewise Growth)

36.170 17 0.0044 0.027 0.986 3928.384

Notes: χ2 Chi-Square

df Degrees of freedom

RMSEA Root Mean Square Error of Approximation

SRMR Standardized Root Mean Square Residual

CFI Comparative Fit Index

AIC Akaike Information Criteria

α p ≤ .05


56

Summary of Findings

The purpose of the study was to analyze and explore the relationships between

two variations of curricular implementation and the resulting student performance on

standardized exams (TAKS mathematics exams). The hypothesized linear LGM was

used to analyze the effects of variations on curricular implementation on student

performance as measured by student TAKS mathemtics scores. The hypothsized

LGM model with all covariates failed to converge. Models’s 2 and 3 revealed that the

growth in student performance over time was not linear.

A piecewise latent growth model was employed to examine the relationships

between student performance and time points of interest for the study. Estimates for

CSCOPE implementation revealed that the CSCOPE district had 0.958 of a standard

deviation difference in growth of student performance during this phase of student

development as compared to the students in the district using the non-CSCOPE

curriculum. Relationships between independent variables or covariates including the

students gender, race/ethnicity, LEP student status, and EcoD student status were

explored through five different model parameterizations. No statistically significant

estimations of effect on sub-populations were discovered during these analyses once

the effect of the district was controlled.

The final model fit the data well. The chi-square test of model fit χ2 = 36.170 ,

df = 17 (p = 0.0044); CFI = 0.986, RMSEA = 0.049 [90% CI = .027, .071] p ≤ .05 =

0.493; SRMR = 0.027. The chi-square test for the baseline model was χ2 = 1436.726,

df = 21 (p = 0.000). The final model revealed CSCOPE implementation had an impact

of .958 of a standard deviation on student mathematics performance. As a point of


57

reference, study parameter information for Texas TAKS Math Scores from 2005 to

2010 are illustrated in Table 4.16.

Table 4.5 State TAKS Math Score Summary

State TAKS Math Score Summary

Year Grade Cut Score SD .958 SD

2005 3 2100 189.87 181.90

2006 4 2100 192.10 184.03

2007 5 2100 231.16 221.45

2008 6 2100 251.56 240.99

2009 7 2100 174.43 167.10

2010 8 700 92.15 88.28

Source (Texas Education Agency, 2005a, 2005b, 2006a, 2006b, 2007a, 2007b, 2008a, 2008b,

2009a, 2009b, 2010b, 2010c)

Summary

Chapter IV discussed the data analysis used in this study. Latent growth

modeling was used to examine the relationships between differing curricula. A

description of how the data were analyzed using latent growth modeling followed.

Identification and explanation of goodness-of-fit statistics advanced the study analysis.

The hypothesized latent growth model was presented. Parameterizations for

additional latent growth models designed to explore relatonships between the latent

and observed variables were presented and discussed. A brief summary of the

analysis was discussed.


58

Chapter V

Conclusions

Introduction

One of the most important factors influencing student achievement is a

guaranteed and viable curriculum. A review of the literature revealed that school and

student success is dependent upon alignment between whatever standards are set forth

by the governing entity. Marzano (2005) has argued that a “guaranteed and viable

curriculum” (p. 22) is the most significant school level factor in determining student

performance outcomes. English and Steffy (2003; 2001) have shown that when the

written, taught, and tested curriculum is tightly aligned, student performance

improves. In the classroom, teacher expertise with classroom curriculum and

instructional methods is the most significant teacher level factor affecting student

academic achievement (Robert .J. Marzano, 2003b). Schmoker (2006) ardently stated

that the quality of curriculum a student receives should not happen to depend on which

teacher a student gets. Schmoker (2006) continues, “If you care about schools, the

curricular chaos within them has to arrest your attention. Remember the premise: the

uglier the problem, the bigger the educational payoff in solving the problem. There’s

one hell of a payoff here” (p. 36).

While a few public school districts in Texas have chosen to remain with locally

developed curriculum or have chosen other commercially available curriculum

products, CSCOPE has emerged as the leading commercially available curriculum


59

product in Texas. Clearly, most students in Texas are receiving curriculum and

instruction based upon CSCOPE. Implementation of the CSCOPE curriculum

management system has not been without critics and conflict. With a significant

financial and human capital commitment to the product across the state, a study of the

curriculum management system’s effect on student standardized test scores was

warranted.

The purpose of the current study was to explore the impact of CSCOPE

implementation on TAKS math scores. Student test scores on the TAKS mathematics

exam in grades 3-8 were used were used as the measure of student performance. A

piecewise latent growth model was used to explore the relationship between the

curricular implementation and the resulting student performance over time. A

piecewise growth model captures phases of growth by examining more than one slope

growth factor at timepoints of interest during the study period.


1. What effect does CSCOPE have on student mathematics performance?

2. What effect does CSCOPE have on student sub-populations mathematics

performance?


60

Summary of findings

A hypothesized latent growth model was used to examine the effects of

curricular implementation within different districts on student performance as

measured by student TAKS mathematics scores. The hypothesized linear latent

growth model failed to converge. Respecification revealed that the student

performance was not linear.

Results revealed that the CSCOPE curriculum had 0.958 of a standard

deviation difference in student performance over the non-CSCOPE curriculum. The

observed increase in the rate of change or growth was not related to the students’

starting point (I) and previous rate performance improvement (Pre-CSCOPE).

Relationships between sub-populations including the students’ gender, race/ethnicity,

LEP student status, and economically disadvantaged student status were explored

through five other parameterizations of latent growth models. When district was

controlled for, no statistically significant estimates of sub-populations were discovered

during these analysis.

The final model fit the data well. The results found that the students in the

district which implemented CSCOPE had .958 of a standard deviation higher

performance on TAKS mathematics scores over a three year period than the district

that did not use CSCOPE.

The effect is significant in terms of student mathematics performance. Because

student scale scores were converted to z scores for study purposes, this represents 96%

of a standard deviation difference in the rate of change of student performance during

the three year period of interest in the study. In practical terms this means that


61

CSCOPE accounted for somewhere between 167 and 241 more horizontal scale score

points, or 88 more vertical scale points, than the non-CSCOPE curriculum during this

period. In terms of an individual student, this would explain a student who had

previously not met standard with a score around 1,935 horizontal, or 615 vertical,

meeting standard and “passing” the TAKS mathematics exam within three years using

the CSCOPE curriculum.

What effect does CSCOPE have on student sub-populations mathematics

performance? When controlling for CSCOPE curriculum implementation, no

statistically significant estimates of relationships between sub-populations and student

performance were discovered. While the sample included ethnic minority and

economically disadvantaged students, these student sub-populations were not

represented in large enough numbers to draw conclusions related to these

sub-populations. There were insufficient numbers of African American (Black), LEP

status, and to a lesser degree, economically disadvantaged students in the sample when

compared to the population. However, implications for closing the achievement gap

with growth rates between 167 and 241 more horizontal scale score points, or 88 more

vertical scale points in a sample that inluded some ethnic minority and economically

disadvantaged students remains appealing for students and stakeholders. Hispanic,

economically disadvantaged, and LEP status students particpated in the study and had

signifcant gains in mathematics performance.


62

Limitations

The results of this study revealed significant differences in student

performance between a district using the CSCOPE curriculum versus a district using a

non-CSOPE curriculum. The demographics of the students sampled in the study were

insufficient in terms of varying demographic characteristics for the study results to

generalize to the study’s population. Sample student demographic characteristics such

as the percent of African American (Black) students, were 13% below the population.

Twenty one percent of the samples students were Hispanic while in Texas 49% of the

students are Hispanic. The study sample included only 3.2% limited English proficient

student status while the poulation includes 16.9%. While the sample included 214

students or 46% economically disadvantaged students the population includes 59%.

Addtionally, prescribed limitations and methodological implications unique to this

study warrant caution. This study did not include a sampling of all curriculum

products locally developed or commercially available for Texas school districts.

While the study does confirm the relationship between CSCOPE and improved student

performance, it does not examine all other curricula.

The growth in student performance in the CSCOPE district was 96% of a

standard deviation more than the growth in student performance in the non-CSCOPE

district; however, the growth was not linear. Respecifying the LGM by fixing the

time scores to improve model fit revealed a positive but non-linear growth relationship

in both districts. It remains unclear if this effect was related to the curricula or other

classroom level factors as possible explanations for this effect. Finally, the relative

level of difficulty of the TAKS test items needed to “meet standard” may be different


63

from one grade level to the next. This is evidenced by the ceiling effect of student

performance seen in grades 3 and 4.

Recommendations

The present study revealed a 96% of a standard deviation difference in growth

of student performance using the CSCOPE curriculum management system over a

non-CSCOPE curriculum over the three year period of interest. The student

performance outcomes as measured on the TAKS mathematics test reveal the positive

effect on student performance associated with CSCOPE curriculum implementation.

In practical terms CSCOPE implementaiton appears to have the abilty to take a

significant portion of individual students from “does not meet” expectations to “meets

expecations” within three years. Stakeholders at all levels should consider this when

working with CSCOPE curriculum implementation. In terms of student performance,

the CSCOPE curriculum management system delivers upon the promise of a

guaranteed and viable curriculum that is tightly aligned to the Texas standards or

Texas Essential Knowledge and Skills (TEKS). The resulting growth in student

performance reveals that the material and human capital invested in the

implementation of the CSCOPE curriculum management system are warranted. This

leaves stakeholders at all levels of the Texas public school system that have

implemented the CSCOPE curriculum management system, or who are considering

implementing the system, to struggle with the dual issues of implementing the

CSCOPE curriculum management system knowing that the system will produce the

type of student performance gains sought, while at times sparking socio political


64

controversy between teachers, administrators, and other stakeholders within the school

community. The curriculum management system produces positive results in math

performance for students who are making their way through public school life.

Teachers, administrators, and other key stakeholders within the school community

may struggle with teacher morale and fatigue associated with CSCOPE currculum

implementation. Implementation plans should be well conceived and supportive of

teachers while putting student academic needs at the forefront of the school’s mission.

Implications for further study

Results of the present study revealed a 96% of a standard deviation difference

in the growth of student performance using the CSCOPE curriculum management

system over a non-CSCOPE curriculum. Results obtained for sub-populations such as

student gender, race/ethnicity, limited English proficient status, and economically

disadvantaged status were not statistically significant and are therefore inconclusive.

Further study is needed regarding the effects of the CSCOPE curriculum management

system on the performance of student sub-populations identified in the Academic

Excellence Indicator System (AEIS). Implications for closing the achievement gap for

economically disadvantaged and minority students beg further study. Changing the

order of entry of covariates in future studies may bring light on this important issue.

Exploring the relationship between student performance using the CSCOPE

curriculum management system and other locally developed or commercially available

curricula is needed. With over 800 Texas school districts implementing the CSCOPE


65

curriculum management system, the question remains, “How does the CSOPE

curriculum management system compare to other curricula?”

Lastly, implications remain for principals, teachers, and other instructional

leaders within schools and districts who implement the CSCOPE curriculum

management system. Implementing the CSCOPE curriculum management system

will likely be viewed as a significant change within most schools. Managing the

resulting conflict, issues with morale, fatigue, communication, trust, and the necessary

competency and capacity building needed to successfully implement and sustain the

system merits consideration and study.

Summary

Chapter V introduced the key findings from the review of the literature: a

tightly aligned, guaranteed and viable curriculum is essential for student success in

education where high stakes exams are used as a central measure of student

performance and school accountability. Instructional leadership from teachers,

principals, and central office administrators is vital for redesigning schools for student

success and academic performance (Elmore, 2009; English & Steffy, 2001; Robert J.

Marzano et al., 2005; Schmoker, 2010 ). Research shows CSCOPE’S claims of a

tightly aligned, guaranteed and viable curriculum are accompanied by significant gains

in student performance over time. Further study is needed regarding effects of

CSCOPE curriclum implementation and the resulting performance of student

sub-populations identified in the AEIS system. Closing the achievement gap remains

a vital goal of schools across Texas and the United States. Further study related to


66

CSCOPE and closing the achievement gap is needed. Research studying the

relationship between CSCOPE and additional locally developed or commercially

available curricular products is needed. Research shows that the CSCOPE curriculum

management system is a viable choice for any school or district focused on meeting

student needs and producing growth in student performance.


67

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77

Appendix A. Sample Descriptive Statistics


78

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 1:34 PM

INPUT INSTRUCTIONS

Title:

Basic run dissertation growth model

filename spinn_diss_7.inp

Data:

File is Spinn_Diss_6b.csv;

Variable:

Names are District LocalID Gender White Black Hispanic Lep EcoD

Math3SS Math4SS Math5SS Math6SS Math7SS Math8SS;

Missing are ALL (999);

usevar = math3ss-math8ss

Analysis:

TYPE = BASIC;

PLOT:

TYPE = PLOT3;

SERIES = math3ss-math8ss(*);

INPUT READING TERMINATED NORMALLY

Basic run preparing for

piecewise dissertation growth model

filename spinn_diss_7.inp

SUMMARY OF ANALYSIS

Number of groups 1

Number of observations 468

Number of dependent variables 6

Number of independent variables 0

Number of continuous latent variables 0

Observed dependent variables

Continuous


Estimator ML

Information matrix OBSERVED

Maximum number of iterations 1000

Convergence criterion 0.500D-04

Maximum number of steepest descent iterations 20

Maximum number of iterations for H1 2000

Convergence criterion for H1 0.100D-03

Input data file(s)

Spinn_Diss_6b.csv

Input data format FREE


79

SUMMARY OF DATA

Number of missing data patterns 35

SUMMARY OF MISSING DATA PATTERNS

MISSING DATA PATTERNS (x = not missing)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

MATH3SS x x x x x x x x x x x x x x x x x x

MATH4SS x x x x x x x x x x x x x

MATH5SS x x x x x x x x x x x



MATH8SS x x x x x x x x x x

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

MATH3SS

MATH4SS x x x

MATH5SS x x x x x x x x



MATH8SS x x x x x x x

MISSING DATA PATTERN FREQUENCIES

Pattern Frequency Pattern Frequency Pattern Frequency

1 193 13 1 25 6

2 7 14 3 26 2

3 3 15 2 27 6

4 6 16 1 28 1

5 2 17 3 29 23

6 1 18 2 30 42

7 4 19 32 31 8

8 5 20 1 32 8

9 2 21 1 33 25

10 1 22 1 34 10

11 1 23 1 35 26

12 3 24 35

COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value 0.100

PROPORTION OF DATA PRESENT

Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

Covariance Coverage

MATH8SS

________

MATH8SS 0.810


80

RESULTS FOR BASIC ANALYSIS

ESTIMATED SAMPLE STATISTICS

Means


________ ________ ________ ________ ________

1 0.667 0.971 0.996 0.716 0.726

Means

MATH8SS

________

1 0.766

Covariances


________ ________ ________ ________ ________

MATH3SS 1.277

MATH4SS 0.513 0.809

MATH5SS 0.547 0.628 0.938

MATH6SS 0.468 0.590 0.633 0.850

MATH7SS 0.475 0.613 0.654 0.671 0.807

MATH8SS 0.539 0.643 0.662 0.699 0.730

Covariances

MATH8SS

________

MATH8SS 0.932

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.505 1.000

MATH5SS 0.500 0.721 1.000

MATH6SS 0.450 0.712 0.709 1.000

MATH7SS 0.468 0.759 0.751 0.810 1.000

MATH8SS 0.494 0.741 0.708 0.785 0.842

Correlations

MATH8SS

________

MATH8SS 1.000

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -1950.080

PLOT INFORMATION

The following plots are available:

Histograms (sample values)

Scatterplots (sample values)

Sample means

Observed individual values


81

Beginning Time: 13:34:45

Ending Time: 13:34:45

Elapsed Time: 00:00:00

MUTHEN & MUTHEN

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Los Angeles, CA 90066

Tel: (310) 391-9971

Fax: (310) 391-8971

Web: www.StatModel.com

Support: [email protected]

Copyright (c) 1998-2010 Muthen & Muthen


82

Appendix B. LGM1 Hypothesized Model


83

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 4:17 PM

INPUT INSTRUCTIONS

Title:

Dissertation Linear Growth Model - Hypothesized Model (SEM1)

filename spinn_diss_7a.inp

Adding covariates

See page 115 of the Mplus user guide

Data:


Variable:



USEVARIABLES ARE District Gender-EcoD Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:

i s1 | math3ss@0 [email protected] [email protected] [email protected] [email protected] [email protected];

i s2 | Math3SS@0 Math4SS@0 Math5SS@0 [email protected] [email protected] [email protected];

i s1 s2 ON District Gender-EcoD;

!s1 WITH s2@0;

!s1 WITH i@0;

!s2 WITH i@0;

PLOT:

TYPE is Plot3;

SERIES = Math3SS (0) Math4SS (1) Math5SS (2) Math6SS (3) Math7SS (4) Math8SS (5);

OUTPUT:

SAMPSTAT;

Tech4;


Dissertation Linear Growth Model - Hypothesized Model (SEM1)

filename spinn_diss_7a.inp

Adding covariates


SUMMARY OF ANALYSIS

Number of groups 1







84

Continuous


Observed independent variables

DISTRICT GENDER WHITE BLACK HISPANIC LEP

ECOD

Continuous latent variables

I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

GENDER 0.513 0.558 0.701 0.778 0.810

WHITE 0.513 0.558 0.701 0.778 0.810

BLACK 0.513 0.558 0.701 0.778 0.810

HISPANIC 0.513 0.558 0.701 0.778 0.810

LEP 0.513 0.558 0.701 0.778 0.810

ECOD 0.513 0.558 0.701 0.778 0.810

Covariance Coverage

MATH8SS DISTRICT GENDER WHITE BLACK

________ ________ ________ ________ ________

MATH8SS 0.810

DISTRICT 0.810 1.000

GENDER 0.810 1.000 1.000

WHITE 0.810 1.000 1.000 1.000

BLACK 0.810 1.000 1.000 1.000 1.000

HISPANIC 0.810 1.000 1.000 1.000 1.000

LEP 0.810 1.000 1.000 1.000 1.000

ECOD 0.810 1.000 1.000 1.000 1.000


85

Covariance Coverage

HISPANIC LEP ECOD

________ ________ ________

HISPANIC 1.000

LEP 1.000 1.000

ECOD 1.000 1.000 1.000

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.670 0.958 0.976 0.716 0.720

Means


________ ________ ________ ________ ________

1 0.760 0.314 0.517 0.759 0.011

Means

HISPANIC LEP ECOD

________ ________ ________

1 0.207 0.032 0.457

Covariances


________ ________ ________ ________ ________

MATH3SS 1.268

MATH4SS 0.517 0.832

MATH5SS 0.543 0.646 0.969

MATH6SS 0.465 0.599 0.640 0.847

MATH7SS 0.476 0.627 0.668 0.673 0.813

MATH8SS 0.531 0.656 0.677 0.698 0.735

DISTRICT 0.043 0.007 -0.005 0.070 0.024

GENDER 0.068 -0.020 0.005 0.022 -0.026

WHITE 0.047 0.072 0.083 0.068 0.058

BLACK -0.002 -0.002 -0.017 0.001 -0.001

HISPANIC -0.040 -0.065 -0.052 -0.058 -0.045

LEP -0.023 -0.038 -0.027 -0.028 -0.023

ECOD -0.114 -0.101 -0.116 -0.081 -0.076

Covariances


________ ________ ________ ________ ________

MATH8SS 0.936


GENDER -0.003 0.000 0.250

WHITE 0.070 -0.005 0.009 0.183

BLACK -0.008 -0.003 -0.001 -0.008 0.011

HISPANIC -0.056 0.003 -0.007 -0.157 -0.002

LEP -0.026 -0.006 0.005 -0.024 0.000

ECOD -0.098 0.019 -0.001 -0.046 -0.001

Covariances

HISPANIC LEP ECOD

________ ________ ________

HISPANIC 0.164


86

LEP 0.025 0.031

ECOD 0.046 0.015 0.248

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.503 1.000

MATH5SS 0.490 0.719 1.000

MATH6SS 0.449 0.714 0.707 1.000

MATH7SS 0.469 0.762 0.752 0.811 1.000

MATH8SS 0.488 0.743 0.711 0.784 0.843

DISTRICT 0.082 0.018 -0.010 0.164 0.057

GENDER 0.120 -0.045 0.010 0.048 -0.057

WHITE 0.098 0.184 0.197 0.172 0.150

BLACK -0.016 -0.018 -0.163 0.012 -0.010

HISPANIC -0.088 -0.175 -0.131 -0.155 -0.124

LEP -0.116 -0.236 -0.156 -0.170 -0.146

ECOD -0.203 -0.223 -0.237 -0.176 -0.170

Correlations


________ ________ ________ ________ ________

MATH8SS 1.000


GENDER -0.006 0.000 1.000

WHITE 0.170 -0.027 0.044 1.000

BLACK -0.079 -0.070 -0.024 -0.184 1.000

HISPANIC -0.144 0.017 -0.033 -0.906 -0.053

LEP -0.154 -0.071 0.054 -0.323 -0.019

ECOD -0.204 0.081 -0.006 -0.214 -0.012

Correlations

HISPANIC LEP ECOD

________ ________ ________

HISPANIC 1.000

LEP 0.356 1.000

ECOD 0.229 0.174 1.000


THE MODEL ESTIMATION TERMINATED NORMALLY

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE

COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.

PROBLEM INVOLVING PARAMETER 20.

THE CONDITION NUMBER IS -0.572D-18.

FACTOR SCORES WILL NOT BE COMPUTED DUE TO NONCONVERGENCE OR

NONIDENTIFIED MODEL.

MODEL RESULTS

Estimate

I |

MATH3SS 1.000

MATH4SS 1.000

MATH5SS 1.000

MATH6SS 1.000


87

MATH7SS 1.000

MATH8SS 1.000

S1 |

MATH3SS 0.000

MATH4SS 0.100

MATH5SS 0.200

MATH6SS 0.200

MATH7SS 0.200

MATH8SS 0.200

S2 |

MATH3SS 0.000

MATH4SS 0.000

MATH5SS 0.000

MATH6SS 0.100

MATH7SS 0.200

MATH8SS 0.300

I ON

DISTRICT 0.129

GENDER 0.091

WHITE 0.143

BLACK -0.356

HISPANIC 0.019

LEP -0.799

ECOD -0.379

S1 ON

DISTRICT -0.326

GENDER -0.376

WHITE 2.659

BLACK 2.016

HISPANIC 2.413

LEP 0.622

ECOD 0.319

S2 ON

DISTRICT 0.851

GENDER -0.199

WHITE -0.723

BLACK -0.321

HISPANIC -0.774

LEP 0.860

ECOD 0.021

S1 WITH

I 0.313

S2 WITH

I 0.020

S1 0.379

Intercepts

MATH3SS 0.000

MATH4SS 0.000

MATH5SS 0.000

MATH6SS 0.000

MATH7SS 0.000

MATH8SS 0.000

I 0.852

S1 -2.207

S2 -0.114

Residual Variances

MATH3SS 0.881

MATH4SS 0.239

MATH5SS 0.298


88

MATH6SS 0.224

MATH7SS 0.115

MATH8SS 0.165

I 0.417

S1 0.866

S2 0.515

MODEL COMMAND WITH FINAL ESTIMATES USED AS STARTING VALUES


i s2 | math3ss@0 math4ss@0 math5ss@0 [email protected] [email protected] [email protected];

i ON district*0.129;

i ON gender*0.091;

i ON white*0.143;

i ON black*-0.356;

i ON hispanic*0.019;

i ON lep*-0.799;

i ON ecod*-0.379;

s1 ON district*-0.326;

s1 ON gender*-0.376;

s1 ON white*2.659;

s1 ON black*2.016;

s1 ON hispanic*2.413;

s1 ON lep*0.622;

s1 ON ecod*0.319;

s2 ON district*0.851;


s2 ON white*-0.723;

s2 ON black*-0.321;

s2 ON hispanic*-0.774;

s2 ON lep*0.860;

s2 ON ecod*0.021;

s1 WITH i*0.313;

s2 WITH i*0.020;

s2 WITH s1*0.379;

[ math3ss@0 ];

[ math4ss@0 ];

[ math5ss@0 ];

[ math6ss@0 ];

[ math7ss@0 ];

[ math8ss@0 ];

[ i*0.852 ];

[ s1*-2.207 ];

[ s2*-0.114 ];

math3ss*0.881;

math4ss*0.239;

math5ss*0.298;

math6ss*0.224;

math7ss*0.115;

math8ss*0.165;

i*0.417;

s1*0.866;

s2*0.515;

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU


89


________ ________ ________ ________ ________

1 0 0 0 0 0

NU


________ ________ ________ ________ ________

1 0 0 0 0 0

NU

HISPANIC LEP ECOD

________ ________ ________

1 0 0 0

LAMBDA

I S1 S2 DISTRICT GENDER

________ ________ ________ ________ ________

MATH3SS 0 0 0 0 0

MATH4SS 0 0 0 0 0

MATH5SS 0 0 0 0 0

MATH6SS 0 0 0 0 0

MATH7SS 0 0 0 0 0

MATH8SS 0 0 0 0 0

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

HISPANIC 0 0 0 0 0

LEP 0 0 0 0 0

ECOD 0 0 0 0 0

LAMBDA

WHITE BLACK HISPANIC LEP ECOD

________ ________ ________ ________ ________

MATH3SS 0 0 0 0 0

MATH4SS 0 0 0 0 0

MATH5SS 0 0 0 0 0

MATH6SS 0 0 0 0 0

MATH7SS 0 0 0 0 0

MATH8SS 0 0 0 0 0

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

HISPANIC 0 0 0 0 0

LEP 0 0 0 0 0

ECOD 0 0 0 0 0

THETA


________ ________ ________ ________ ________

MATH3SS 1

MATH4SS 0 2

MATH5SS 0 0 3

MATH6SS 0 0 0 4

MATH7SS 0 0 0 0 5

MATH8SS 0 0 0 0 0

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

HISPANIC 0 0 0 0 0

LEP 0 0 0 0 0


90

ECOD 0 0 0 0 0

THETA


________ ________ ________ ________ ________

MATH8SS 6

DISTRICT 0 0

GENDER 0 0 0

WHITE 0 0 0 0

BLACK 0 0 0 0 0

HISPANIC 0 0 0 0 0

LEP 0 0 0 0 0

ECOD 0 0 0 0 0

THETA

HISPANIC LEP ECOD

________ ________ ________

HISPANIC 0

LEP 0 0

ECOD 0 0 0

ALPHA


________ ________ ________ ________ ________

1 7 8 9 0 0

ALPHA


________ ________ ________ ________ ________

1 0 0 0 0 0

BETA


________ ________ ________ ________ ________

I 0 0 0 10 11

S1 0 0 0 17 18

S2 0 0 0 24 25

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

HISPANIC 0 0 0 0 0

LEP 0 0 0 0 0

ECOD 0 0 0 0 0

BETA


________ ________ ________ ________ ________

I 12 13 14 15 16

S1 19 20 21 22 23

S2 26 27 28 29 30

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

HISPANIC 0 0 0 0 0

LEP 0 0 0 0 0

ECOD 0 0 0 0 0

PSI



91

________ ________ ________ ________ ________

I 31

S1 32 33

S2 34 35 36

DISTRICT 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

HISPANIC 0 0 0 0 0

LEP 0 0 0 0 0

ECOD 0 0 0 0 0

PSI


________ ________ ________ ________ ________

WHITE 0

BLACK 0 0

HISPANIC 0 0 0

LEP 0 0 0 0

ECOD 0 0 0 0 0

STARTING VALUES

NU


________ ________ ________ ________ ________

1 0.000 0.000 0.000 0.000 0.000

NU


________ ________ ________ ________ ________

1 0.000 0.000 0.000 0.000 0.000

NU

HISPANIC LEP ECOD

________ ________ ________

1 0.000 0.000 0.000

LAMBDA


________ ________ ________ ________ ________

MATH3SS 1.000 0.000 0.000 0.000 0.000

MATH4SS 1.000 0.100 0.000 0.000 0.000

MATH5SS 1.000 0.200 0.000 0.000 0.000

MATH6SS 1.000 0.200 0.100 0.000 0.000

MATH7SS 1.000 0.200 0.200 0.000 0.000

MATH8SS 1.000 0.200 0.300 0.000 0.000

DISTRICT 0.000 0.000 0.000 1.000 0.000

GENDER 0.000 0.000 0.000 0.000 1.000

WHITE 0.000 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

HISPANIC 0.000 0.000 0.000 0.000 0.000

LEP 0.000 0.000 0.000 0.000 0.000

ECOD 0.000 0.000 0.000 0.000 0.000

LAMBDA


________ ________ ________ ________ ________

MATH3SS 0.000 0.000 0.000 0.000 0.000

MATH4SS 0.000 0.000 0.000 0.000 0.000

MATH5SS 0.000 0.000 0.000 0.000 0.000


92

MATH6SS 0.000 0.000 0.000 0.000 0.000

MATH7SS 0.000 0.000 0.000 0.000 0.000

MATH8SS 0.000 0.000 0.000 0.000 0.000

DISTRICT 0.000 0.000 0.000 0.000 0.000

GENDER 0.000 0.000 0.000 0.000 0.000

WHITE 1.000 0.000 0.000 0.000 0.000

BLACK 0.000 1.000 0.000 0.000 0.000

HISPANIC 0.000 0.000 1.000 0.000 0.000

LEP 0.000 0.000 0.000 1.000 0.000

ECOD 0.000 0.000 0.000 0.000 1.000

THETA


________ ________ ________ ________ ________

MATH3SS 0.628

MATH4SS 0.000 0.392

MATH5SS 0.000 0.000 0.457

MATH6SS 0.000 0.000 0.000 0.423

MATH7SS 0.000 0.000 0.000 0.000 0.394

MATH8SS 0.000 0.000 0.000 0.000 0.000

DISTRICT 0.000 0.000 0.000 0.000 0.000

GENDER 0.000 0.000 0.000 0.000 0.000

WHITE 0.000 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

HISPANIC 0.000 0.000 0.000 0.000 0.000

LEP 0.000 0.000 0.000 0.000 0.000

ECOD 0.000 0.000 0.000 0.000 0.000

THETA


________ ________ ________ ________ ________

MATH8SS 0.445


GENDER 0.000 0.000 0.000

WHITE 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

HISPANIC 0.000 0.000 0.000 0.000 0.000

LEP 0.000 0.000 0.000 0.000 0.000

ECOD 0.000 0.000 0.000 0.000 0.000

THETA

HISPANIC LEP ECOD

________ ________ ________

HISPANIC 0.000

LEP 0.000 0.000

ECOD 0.000 0.000 0.000

ALPHA


________ ________ ________ ________ ________

1 0.917 0.589 0.774 0.314 0.517

ALPHA


________ ________ ________ ________ ________

1 0.759 0.011 0.207 0.032 0.457

BETA


________ ________ ________ ________ ________

I 0.000 0.000 0.000 0.000 0.000

S1 0.000 0.000 0.000 0.000 0.000


93

S2 0.000 0.000 0.000 0.000 0.000

DISTRICT 0.000 0.000 0.000 0.000 0.000

GENDER 0.000 0.000 0.000 0.000 0.000

WHITE 0.000 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

HISPANIC 0.000 0.000 0.000 0.000 0.000

LEP 0.000 0.000 0.000 0.000 0.000

ECOD 0.000 0.000 0.000 0.000 0.000

BETA


________ ________ ________ ________ ________

I 0.000 0.000 0.000 0.000 0.000

S1 0.000 0.000 0.000 0.000 0.000

S2 0.000 0.000 0.000 0.000 0.000

DISTRICT 0.000 0.000 0.000 0.000 0.000

GENDER 0.000 0.000 0.000 0.000 0.000

WHITE 0.000 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

HISPANIC 0.000 0.000 0.000 0.000 0.000

LEP 0.000 0.000 0.000 0.000 0.000

ECOD 0.000 0.000 0.000 0.000 0.000

PSI


________ ________ ________ ________ ________

I 1.060

S1 0.000 20.313

S2 0.000 0.000 0.745

DISTRICT 0.000 0.000 0.000 0.215

GENDER 0.000 0.000 0.000 0.000 0.250

WHITE 0.000 0.000 0.000 -0.005 0.009

BLACK 0.000 0.000 0.000 -0.003 -0.001

HISPANIC 0.000 0.000 0.000 0.003 -0.007

LEP 0.000 0.000 0.000 -0.006 0.005

ECOD 0.000 0.000 0.000 0.019 -0.001

PSI


________ ________ ________ ________ ________

WHITE 0.183

BLACK -0.008 0.011

HISPANIC -0.157 -0.002 0.164

LEP -0.024 0.000 0.025 0.031

ECOD -0.046 -0.001 0.046 0.015 0.248

TECHNICAL 4 OUTPUT

ESTIMATES DERIVED FROM THE MODEL

ESTIMATED MEANS FOR THE LATENT VARIABLES


________ ________ ________ ________ ________

1 0.849 0.200 -0.624 0.314 0.517



________ ________ ________ ________ ________

1 0.759 0.011 0.207 0.032 0.457


94

ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES


________ ________ ________ ________ ________

I 1.381

S1 0.527 0.803

S2 0.553 0.602 0.948

DISTRICT 0.554 0.605 0.657 0.895

GENDER 0.554 0.609 0.663 0.684 0.820

WHITE 0.555 0.612 0.670 0.698 0.726

BLACK 0.026 0.018 0.010 0.028 0.046

HISPANIC 0.021 0.013 0.004 -0.001 -0.005

LEP 0.063 0.069 0.075 0.071 0.068

ECOD -0.005 -0.005 -0.006 -0.006 -0.006



________ ________ ________ ________ ________

WHITE 0.919

BLACK 0.064 0.215

HISPANIC -0.010 0.000 0.250

LEP 0.064 -0.005 0.009 0.183

ECOD -0.006 -0.003 -0.001 -0.008 0.011

ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES


________ ________ ________ ________ ________

I 1.000

S1 0.500 1.000

S2 0.483 0.689 1.000

DISTRICT 0.498 0.714 0.713 1.000

GENDER 0.521 0.750 0.752 0.799 1.000

WHITE 0.492 0.713 0.718 0.770 0.836

BLACK 0.047 0.042 0.021 0.063 0.109

HISPANIC 0.036 0.028 0.008 -0.001 -0.012

LEP 0.125 0.180 0.180 0.176 0.175

ECOD -0.041 -0.059 -0.059 -0.059 -0.061



________ ________ ________ ________ ________

WHITE 1.000

BLACK 0.144 1.000

HISPANIC -0.021 0.000 1.000

LEP 0.156 -0.027 0.044 1.000

ECOD -0.056 -0.070 -0.024 -0.184 1.000




MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





95

Appendix C. LGM2 Linear Growth Model


96

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 4:12 PM

INPUT INSTRUCTIONS

Title:

Dissertation Linear Growth Model - SEM2

filename spinn_diss_7b.inp

No covariates


Data:


Variable:



USEVARIABLES ARE Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:


i s2 | Math3SS@0 Math4SS@0 Math5SS@0 [email protected] [email protected] [email protected];

! i s1 s2 ON District Gender-EcoD;

!s1 WITH s2@0;

!s1 WITH i@0;

!s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;


Dissertation Linear Growth Model - SEM2

filename spinn_diss_7b.inp

No covariates


SUMMARY OF ANALYSIS

Number of groups 1







97

Continuous



I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

Covariance Coverage

MATH8SS

________

MATH8SS 0.810

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.667 0.971 0.996 0.716 0.726

Means

MATH8SS

________

1 0.766


98

Covariances


________ ________ ________ ________ ________

MATH3SS 1.277

MATH4SS 0.513 0.809

MATH5SS 0.547 0.628 0.938

MATH6SS 0.468 0.590 0.633 0.850

MATH7SS 0.475 0.613 0.654 0.671 0.807

MATH8SS 0.539 0.643 0.662 0.699 0.730

Covariances

MATH8SS

________

MATH8SS 0.932

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.505 1.000

MATH5SS 0.500 0.721 1.000

MATH6SS 0.450 0.712 0.709 1.000

MATH7SS 0.468 0.759 0.751 0.810 1.000

MATH8SS 0.494 0.741 0.708 0.785 0.842

Correlations

MATH8SS

________

MATH8SS 1.000



MODEL FIT INFORMATION

Number of Free Parameters 15

Loglikelihood

H0 Value -1986.816

H1 Value -1950.080

Information Criteria

Akaike (AIC) 4003.632

Bayesian (BIC) 4065.859

Sample-Size Adjusted BIC 4018.253

(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value 73.472

Degrees of Freedom 12

P-Value 0.0000

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.105

90 Percent C.I. 0.082 0.128


99

Probability RMSEA <= .05 0.000

CFI/TLI

CFI 0.956

TLI 0.944

Chi-Square Test of Model Fit for the Baseline Model

Value 1396.780


P-Value 0.0000

SRMR (Standardized Root Mean Square Residual)

Value 0.064

MODEL RESULTS

Two-Tailed

Estimate S.E. Est./S.E. P-Value

I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.100 0.000 999.000 999.000

MATH5SS 0.200 0.000 999.000 999.000

MATH6SS 0.300 0.000 999.000 999.000

MATH7SS 0.300 0.000 999.000 999.000

MATH8SS 0.300 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.100 0.000 999.000 999.000

MATH7SS 0.200 0.000 999.000 999.000

MATH8SS 0.300 0.000 999.000 999.000

S1 WITH

I -0.082 0.266 -0.308 0.758

S2 WITH

I 0.102 0.173 0.588 0.556

S1 -0.148 0.882 -0.168 0.867

Means

I 0.988 0.056 17.503 0.000

S1 -0.584 0.224 -2.606 0.009

S2 -0.286 0.159 -1.804 0.071

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000


100

Variances

I 0.570 0.086 6.665 0.000

S1 1.593 1.307 1.219 0.223

S2 0.505 0.838 0.602 0.547

Residual Variances

MATH3SS 0.936 0.103 9.109 0.000

MATH4SS 0.213 0.030 7.202 0.000

MATH5SS 0.324 0.032 10.037 0.000

MATH6SS 0.203 0.023 8.904 0.000

MATH7SS 0.109 0.014 7.782 0.000

MATH8SS 0.171 0.025 6.802 0.000

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix 0.590E-04

(ratio of smallest to largest eigenvalue)

TECHNICAL 4 OUTPUT



I S1 S2

________ ________ ________

1 0.988 -0.584 -0.286


I S1 S2

________ ________ ________

I 0.570

S1 -0.082 1.593

S2 0.102 -0.148 0.505


I S1 S2

________ ________ ________

I 1.000

S1 -0.086 1.000

S2 0.190 -0.165 1.000

SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES

SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.988 0.351 -0.584 1.142 -0.286

Means

S2_SE

________

1 0.670

Covariances

I I_SE S1 S1_SE S2


101

________ ________ ________ ________ ________

I 0.443

I_SE -0.013 0.004

S1 0.196 -0.008 0.287

S1_SE -0.012 0.003 -0.007 0.003

S2 0.100 -0.003 0.080 -0.002 0.055

S2_SE -0.003 0.001 -0.001 0.001 -0.001

Covariances

S2_SE

________

S2_SE 0.000

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.310 1.000

S1 0.550 -0.235 1.000

S1_SE -0.349 0.925 -0.250 1.000

S2 0.639 -0.192 0.635 -0.192 1.000

S2_SE -0.289 0.765 -0.192 0.726 -0.177

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION


Histograms (sample values, estimated factor scores, estimated values)

Scatterplots (sample values, estimated factor scores, estimated values)

Sample means

Estimated means

Sample and estimated means


Estimated individual values




MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





102

Appendix D. LGM3 Piecewise Growth Model


103

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 7:06 PM

INPUT INSTRUCTIONS

Title:

Dissertation Piecewise Growth Model - SEM3

filename spinn_diss_7c.inp

No covariates


Data:


Variable:





Analysis:

Processors = 2;

MODEL:


i s2 | Math3SS@0 Math4SS@0 Math5SS@0 [email protected] [email protected] Math8SS*.28;


!s1 WITH s2@0;

!s1 WITH i@0;

!s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7c.inp

No covariates


SUMMARY OF ANALYSIS

Number of groups 1







104

Continuous



I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

Covariance Coverage

MATH8SS

________

MATH8SS 0.810

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.667 0.971 0.996 0.716 0.726

Means

MATH8SS

________

1 0.766


105

Covariances


________ ________ ________ ________ ________

MATH3SS 1.277

MATH4SS 0.513 0.809

MATH5SS 0.547 0.628 0.938

MATH6SS 0.468 0.590 0.633 0.850

MATH7SS 0.475 0.613 0.654 0.671 0.807

MATH8SS 0.539 0.643 0.662 0.699 0.730

Covariances

MATH8SS

________

MATH8SS 0.932

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.505 1.000

MATH5SS 0.500 0.721 1.000

MATH6SS 0.450 0.712 0.709 1.000

MATH7SS 0.468 0.759 0.751 0.810 1.000

MATH8SS 0.494 0.741 0.708 0.785 0.842

Correlations

MATH8SS

________

MATH8SS 1.000



WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE

DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A

LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT

VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES.

CHECK THE TECH4 OUTPUT FOR MORE INFORMATION.

PROBLEM INVOLVING VARIABLE S1.



Loglikelihood

H0 Value -1955.332

H1 Value -1950.080





(n* = (n + 2) / 24)



106

Value 10.504


P-Value 0.4857


Estimate 0.000

90 Percent C.I. 0.000 0.047


CFI/TLI

CFI 1.000

TLI 1.000


Value 1396.780


P-Value 0.0000


Value 0.021

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.225 0.023 9.736 0.000

S1 WITH

I 0.511 0.467 1.095 0.273

S2 WITH

I -0.299 0.183 -1.632 0.103

S1 0.787 0.562 1.401 0.161

Means

I 0.697 0.067 10.402 0.000

S1 0.805 0.173 4.647 0.000

S2 -1.116 0.122 -9.143 0.000


107

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

Variances

I 0.367 0.175 2.097 0.036

S1 -0.758 1.419 -0.534 0.593

S2 0.574 0.468 1.227 0.220

Residual Variances

MATH3SS 0.923 0.182 5.059 0.000

MATH4SS 0.208 0.026 7.847 0.000

MATH5SS 0.300 0.038 7.884 0.000

MATH6SS 0.201 0.020 10.213 0.000

MATH7SS 0.102 0.014 7.453 0.000

MATH8SS 0.187 0.018 10.397 0.000




TECHNICAL 4 OUTPUT



I S1 S2

________ ________ ________

1 0.697 0.805 -1.116


I S1 S2

________ ________ ________

I 0.367

S1 0.511 -0.758

S2 -0.299 0.787 0.574


I S1 S2

________ ________ ________

I 1.000

S1 999.000 999.000

S2 -0.652 999.000 1.000


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.697 0.075 0.805 0.000 -1.116


108

Means

S2_SE

________

1 0.629

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.368

I_SE -0.021 0.012

S1 0.212 -0.016 0.299

S1_SE 0.000 0.000 0.000 0.000

S2 0.046 -0.006 0.064 0.000 0.169

S2_SE -0.020 0.008 -0.013 0.000 -0.004

Covariances

S2_SE

________

S2_SE 0.008

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.309 1.000

S1 0.638 -0.270 1.000

S1_SE 999.000 999.000 999.000 1.000

S2 0.184 -0.125 0.285 999.000 1.000

S2_SE -0.372 0.749 -0.253 999.000 -0.096

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means







MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





109

Appendix E. LGM4 Piecewise Growth Model


110

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 8:07 PM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7d.inp

No covariates, time points of interst, S1 and S2 fixed at 0


Data:


Variable:





Analysis:

Processors = 2;

MODEL:




s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7d.inp

No covariates, time points of interst, S1 and S2 fixed at 0


SUMMARY OF ANALYSIS

Number of groups 1







111

Continuous



I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

Covariance Coverage

MATH8SS

________

MATH8SS 0.810

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.667 0.971 0.996 0.716 0.726

Means

MATH8SS

________

1 0.766


112

Covariances


________ ________ ________ ________ ________

MATH3SS 1.277

MATH4SS 0.513 0.809

MATH5SS 0.547 0.628 0.938

MATH6SS 0.468 0.590 0.633 0.850

MATH7SS 0.475 0.613 0.654 0.671 0.807

MATH8SS 0.539 0.643 0.662 0.699 0.730

Covariances

MATH8SS

________

MATH8SS 0.932

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.505 1.000

MATH5SS 0.500 0.721 1.000

MATH6SS 0.450 0.712 0.709 1.000

MATH7SS 0.468 0.759 0.751 0.810 1.000

MATH8SS 0.494 0.741 0.708 0.785 0.842

Correlations

MATH8SS

________

MATH8SS 1.000





Loglikelihood

H0 Value -1956.703

H1 Value -1950.080





(n* = (n + 2) / 24)


Value 13.246


P-Value 0.5073


Estimate 0.000

90 Percent C.I. 0.000 0.043


113


CFI/TLI

CFI 1.000

TLI 1.001


Value 1396.780


P-Value 0.0000


Value 0.023

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.236 0.022 10.590 0.000

S1 WITH

S2 0.000 0.000 999.000 999.000

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000

Means

I 0.696 0.068 10.295 0.000

S1 0.815 0.177 4.608 0.000

S2 -1.121 0.122 -9.209 0.000

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000


114

Variances

I 0.516 0.062 8.299 0.000

S1 0.833 0.365 2.284 0.022

S2 0.909 0.306 2.975 0.003

Residual Variances

MATH3SS 0.772 0.086 8.979 0.000

MATH4SS 0.212 0.025 8.405 0.000

MATH5SS 0.275 0.029 9.363 0.000

MATH6SS 0.202 0.020 10.234 0.000

MATH7SS 0.103 0.014 7.470 0.000

MATH8SS 0.187 0.018 10.346 0.000




TECHNICAL 4 OUTPUT



I S1 S2

________ ________ ________

1 0.696 0.815 -1.121


I S1 S2

________ ________ ________

I 0.516

S1 0.000 0.833

S2 0.000 0.000 0.909


I S1 S2

________ ________ ________

I 1.000

S1 0.000 1.000

S2 0.000 0.000 1.000


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.696 0.375 0.815 0.811 -1.121

Means

S2_SE

________

1 0.854

Covariances

I I_SE S1 S1_SE S2


115

________ ________ ________ ________ ________

I 0.373

I_SE -0.010 0.003

S1 0.204 -0.006 0.176

S1_SE -0.005 0.001 -0.003 0.001

S2 0.082 -0.003 0.095 -0.001 0.178

S2_SE -0.012 0.002 -0.008 0.001 -0.003

Covariances

S2_SE

________

S2_SE 0.003

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.333 1.000

S1 0.796 -0.309 1.000

S1_SE -0.338 0.932 -0.316 1.000

S2 0.320 -0.146 0.540 -0.127 1.000

S2_SE -0.367 0.915 -0.338 0.854 -0.153

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means







MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





116

Appendix F. LGM5 Piecewise Growth Model


117

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 9:42 PM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7e.inp

Added district covariate, time points of interest, S1 and S2 fixed at 0


Data:


Variable:



USEVARIABLES ARE District Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7e.inp

Added district covariate, time points of interst, S1 and S2 fixed at 0


SUMMARY OF ANALYSIS

Number of groups 1







118

Continuous



DISTRICT


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

Covariance Coverage

MATH8SS DISTRICT

________ ________

MATH8SS 0.810


SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.661 0.964 0.988 0.712 0.722


119

Means

MATH8SS DISTRICT

________ ________

1 0.755 0.314

Covariances


________ ________ ________ ________ ________

MATH3SS 1.278

MATH4SS 0.516 0.814

MATH5SS 0.549 0.635 0.946

MATH6SS 0.472 0.595 0.640 0.854

MATH7SS 0.477 0.618 0.661 0.675 0.811

MATH8SS 0.542 0.651 0.672 0.704 0.736

DISTRICT 0.045 0.006 -0.007 0.071 0.025

Covariances

MATH8SS DISTRICT

________ ________

MATH8SS 0.939


Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.506 1.000

MATH5SS 0.500 0.723 1.000

MATH6SS 0.452 0.714 0.712 1.000

MATH7SS 0.469 0.761 0.754 0.812 1.000

MATH8SS 0.495 0.744 0.713 0.786 0.844

DISTRICT 0.085 0.015 -0.016 0.165 0.059

Correlations

MATH8SS DISTRICT

________ ________

MATH8SS 1.000






Loglikelihood

H0 Value -1948.192

H1 Value -1930.107





(n* = (n + 2) / 24)



120

Value 36.170


P-Value 0.0044


Estimate 0.049

90 Percent C.I. 0.027 0.071


CFI/TLI

CFI 0.986

TLI 0.983


Value 1436.726


P-Value 0.0000


Value 0.027

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.259 0.023 11.166 0.000

I ON

DISTRICT 0.206 0.137 1.498 0.134

S1 ON

DISTRICT -0.549 0.365 -1.505 0.132

S2 ON

DISTRICT 0.958 0.254 3.776 0.000

S1 WITH

S2 0.000 0.000 999.000 999.000


121

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

I 0.629 0.082 7.677 0.000

S1 0.986 0.214 4.600 0.000

S2 -1.396 0.143 -9.795 0.000

Residual Variances

MATH3SS 0.768 0.086 8.964 0.000

MATH4SS 0.213 0.025 8.524 0.000

MATH5SS 0.269 0.029 9.390 0.000

MATH6SS 0.198 0.019 10.213 0.000

MATH7SS 0.112 0.014 7.950 0.000

MATH8SS 0.181 0.018 10.070 0.000

I 0.509 0.062 8.266 0.000

S1 0.889 0.362 2.454 0.014

S2 0.713 0.283 2.521 0.012




TECHNICAL 4 OUTPUT



I S1 S2 DISTRICT

________ ________ ________ ________

1 0.694 0.813 -1.095 0.314


I S1 S2 DISTRICT

________ ________ ________ ________

I 0.518

S1 -0.024 0.954

S2 0.043 -0.113 0.911

DISTRICT 0.044 -0.118 0.206 0.215


I S1 S2 DISTRICT

________ ________ ________ ________

I 1.000

S1 -0.035 1.000

S2 0.062 -0.121 1.000

DISTRICT 0.133 -0.261 0.466 1.000


SAMPLE STATISTICS


122

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.694 0.376 0.813 0.829 -1.095

Means

S2_SE

________

1 0.770

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.374

I_SE -0.010 0.002

S1 0.190 -0.006 0.265

S1_SE -0.005 0.001 -0.003 0.001

S2 0.108 -0.003 -0.030 -0.002 0.316

S2_SE -0.009 0.002 -0.006 0.001 -0.003

Covariances

S2_SE

________

S2_SE 0.002

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.337 1.000

S1 0.604 -0.250 1.000

S1_SE -0.341 0.934 -0.253 1.000

S2 0.315 -0.117 -0.102 -0.108 1.000

S2_SE -0.375 0.907 -0.269 0.853 -0.138

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means


Adjusted estimated means






MUTHEN & MUTHEN


123

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





124

Appendix G. LGM6 Piecewise Growth Model


125

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 10:58 PM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7f.inp

Added district and gender covariates, time points of interst, S1 and S2 fixed at 0


Data:


Variable:



USEVARIABLES ARE District Gender Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District Gender;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7f.inp

Added district and gender covariates, time points of interst, S1 and S2 fixed at 0


SUMMARY OF ANALYSIS

Number of groups 1







126

Continuous



DISTRICT GENDER


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

GENDER 0.513 0.558 0.701 0.778 0.810

Covariance Coverage

MATH8SS DISTRICT GENDER

________ ________ ________

MATH8SS 0.810


GENDER 0.810 1.000 1.000

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.668 0.962 0.988 0.713 0.719


127

Means


________ ________ ________

1 0.754 0.314 0.517

Covariances


________ ________ ________ ________ ________

MATH3SS 1.265

MATH4SS 0.510 0.818

MATH5SS 0.538 0.637 0.945

MATH6SS 0.466 0.596 0.640 0.853

MATH7SS 0.473 0.623 0.663 0.677 0.816

MATH8SS 0.534 0.654 0.672 0.703 0.739

DISTRICT 0.046 0.006 -0.007 0.071 0.025

GENDER 0.070 -0.016 0.003 0.024 -0.024

Covariances


________ ________ ________

MATH8SS 0.940


GENDER -0.003 0.000 0.250

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.502 1.000

MATH5SS 0.492 0.724 1.000

MATH6SS 0.449 0.714 0.712 1.000

MATH7SS 0.465 0.762 0.755 0.812 1.000

MATH8SS 0.489 0.746 0.713 0.786 0.844

DISTRICT 0.088 0.014 -0.016 0.166 0.059

GENDER 0.125 -0.035 0.007 0.053 -0.053

Correlations


________ ________ ________

MATH8SS 1.000


GENDER -0.005 0.000 1.000





Loglikelihood

H0 Value -1946.132

H1 Value -1921.080



128




(n* = (n + 2) / 24)


Value 50.103


P-Value 0.0002


Estimate 0.057

90 Percent C.I. 0.037 0.077


CFI/TLI

CFI 0.979

TLI 0.972


Value 1454.779


P-Value 0.0000


Value 0.028

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.259 0.023 11.179 0.000

I ON

DISTRICT 0.214 0.136 1.574 0.115

GENDER 0.223 0.129 1.724 0.085

S1 ON


129

DISTRICT -0.572 0.362 -1.579 0.114

GENDER -0.660 0.340 -1.939 0.052

S2 ON

DISTRICT 0.962 0.254 3.791 0.000

GENDER 0.078 0.233 0.336 0.737

S1 WITH

S2 0.000 0.000 999.000 999.000

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

I 0.515 0.104 4.938 0.000

S1 1.324 0.275 4.814 0.000

S2 -1.437 0.188 -7.631 0.000

Residual Variances

MATH3SS 0.743 0.084 8.877 0.000

MATH4SS 0.214 0.025 8.529 0.000

MATH5SS 0.271 0.029 9.377 0.000

MATH6SS 0.199 0.019 10.200 0.000

MATH7SS 0.111 0.014 7.883 0.000

MATH8SS 0.181 0.018 10.070 0.000

I 0.502 0.061 8.249 0.000

S1 0.934 0.360 2.597 0.009

S2 0.701 0.283 2.477 0.013




TECHNICAL 4 OUTPUT




________ ________ ________ ________ ________

1 0.698 0.803 -1.095 0.314 0.517



________ ________ ________ ________ ________

I 0.524

S1 -0.063 1.114

S2 0.049 -0.131 0.902

DISTRICT 0.046 -0.123 0.207 0.215

GENDER 0.056 -0.165 0.020 0.000 0.250



________ ________ ________ ________ ________


130

I 1.000

S1 -0.083 1.000

S2 0.071 -0.131 1.000

DISTRICT 0.137 -0.251 0.470 1.000

GENDER 0.154 -0.312 0.041 0.000 1.000


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.698 0.379 0.803 0.844 -1.095

Means

S2_SE

________

1 0.765

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.379

I_SE -0.010 0.002

S1 0.158 -0.007 0.400

S1_SE -0.006 0.001 -0.004 0.001

S2 0.112 -0.003 -0.045 -0.002 0.315

S2_SE -0.009 0.002 -0.006 0.001 -0.003

Covariances

S2_SE

________

S2_SE 0.002

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.323 1.000

S1 0.407 -0.230 1.000

S1_SE -0.329 0.937 -0.226 1.000

S2 0.325 -0.114 -0.127 -0.106 1.000

S2_SE -0.363 0.906 -0.243 0.852 -0.135

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means



131







MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





132

Appendix H. LGM7 Piecewise Growth Model


133

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/29/2012 11:42 PM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7g.inp

Added district, gender, and white covariates, time points of interst, S1 and S2

fixed at


Data:


Variable:



USEVARIABLES ARE District Gender White Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District Gender White;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7g.inp

Added district, gender, and white covariates, time points of interst, S1 and S2 fixed

at


SUMMARY OF ANALYSIS

Number of groups 1






134


Continuous



DISTRICT GENDER WHITE


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

GENDER 0.513 0.558 0.701 0.778 0.810

WHITE 0.513 0.558 0.701 0.778 0.810

Covariance Coverage

MATH8SS DISTRICT GENDER WHITE

________ ________ ________ ________

MATH8SS 0.810


GENDER 0.810 1.000 1.000

WHITE 0.810 1.000 1.000 1.000

SAMPLE STATISTICS



135

Means


________ ________ ________ ________ ________

1 0.667 0.962 0.987 0.713 0.720

Means


________ ________ ________ ________

1 0.755 0.314 0.517 0.759

Covariances


________ ________ ________ ________ ________

MATH3SS 1.266

MATH4SS 0.510 0.817

MATH5SS 0.538 0.636 0.945

MATH6SS 0.467 0.596 0.640 0.854

MATH7SS 0.473 0.622 0.662 0.677 0.816

MATH8SS 0.535 0.654 0.672 0.705 0.740

DISTRICT 0.046 0.006 -0.007 0.072 0.025

GENDER 0.070 -0.016 0.004 0.025 -0.024

WHITE 0.052 0.069 0.078 0.070 0.059

Covariances


________ ________ ________ ________

MATH8SS 0.941


GENDER -0.003 0.000 0.250

WHITE 0.072 -0.005 0.009 0.183

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.501 1.000

MATH5SS 0.492 0.724 1.000

MATH6SS 0.449 0.713 0.713 1.000

MATH7SS 0.465 0.762 0.755 0.812 1.000

MATH8SS 0.490 0.746 0.713 0.786 0.844

DISTRICT 0.088 0.015 -0.014 0.167 0.060

GENDER 0.125 -0.034 0.008 0.053 -0.053

WHITE 0.109 0.177 0.187 0.177 0.153

Correlations


________ ________ ________ ________

MATH8SS 1.000


GENDER -0.006 0.000 1.000

WHITE 0.174 -0.027 0.044 1.000






136

Loglikelihood

H0 Value -1937.265

H1 Value -1911.652





(n* = (n + 2) / 24)


Value 51.226


P-Value 0.0006


Estimate 0.051

90 Percent C.I. 0.032 0.070


CFI/TLI

CFI 0.980

TLI 0.972


Value 1473.637


P-Value 0.0000


Value 0.025

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000


137

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.258 0.023 11.174 0.000

I ON

DISTRICT 0.220 0.135 1.625 0.104

GENDER 0.214 0.129 1.658 0.097

WHITE 0.268 0.153 1.751 0.080

S1 ON

DISTRICT -0.553 0.361 -1.531 0.126

GENDER -0.671 0.340 -1.975 0.048

WHITE 0.394 0.405 0.973 0.331

S2 ON

DISTRICT 0.955 0.255 3.751 0.000

GENDER 0.081 0.234 0.348 0.728

WHITE -0.216 0.281 -0.768 0.443

S1 WITH

S2 0.000 0.000 999.000 999.000

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

I 0.314 0.157 2.001 0.045

S1 1.024 0.416 2.462 0.014

S2 -1.268 0.289 -4.384 0.000

Residual Variances

MATH3SS 0.748 0.084 8.950 0.000

MATH4SS 0.214 0.025 8.532 0.000

MATH5SS 0.269 0.029 9.393 0.000

MATH6SS 0.199 0.019 10.200 0.000

MATH7SS 0.111 0.014 7.874 0.000

MATH8SS 0.181 0.018 10.070 0.000

I 0.482 0.060 8.056 0.000

S1 0.882 0.357 2.472 0.013

S2 0.728 0.284 2.563 0.010




TECHNICAL 4 OUTPUT




________ ________ ________ ________ ________

1 0.697 0.801 -1.089 0.314 0.517


WHITE


138

________

1 0.759



________ ________ ________ ________ ________

I 0.518

S1 -0.043 1.087

S2 0.038 -0.144 0.937

DISTRICT 0.046 -0.121 0.207 0.215

GENDER 0.056 -0.164 0.018 0.000 0.250

WHITE 0.050 0.069 -0.044 -0.005 0.009


WHITE

________

WHITE 0.183



________ ________ ________ ________ ________

I 1.000

S1 -0.058 1.000

S2 0.054 -0.143 1.000

DISTRICT 0.138 -0.251 0.460 1.000

GENDER 0.155 -0.315 0.038 0.000 1.000

WHITE 0.162 0.154 -0.106 -0.027 0.044


WHITE

________

WHITE 1.000


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.697 0.373 0.801 0.824 -1.089

Means

S2_SE

________

1 0.777

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.376

I_SE -0.009 0.002

S1 0.166 -0.007 0.408

S1_SE -0.005 0.001 -0.004 0.001

S2 0.105 -0.003 -0.057 -0.001 0.332

S2_SE -0.009 0.002 -0.006 0.001 -0.003

Covariances


139

S2_SE

________

S2_SE 0.002

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.324 1.000

S1 0.424 -0.233 1.000

S1_SE -0.330 0.938 -0.225 1.000

S2 0.296 -0.102 -0.155 -0.099 1.000

S2_SE -0.363 0.908 -0.246 0.856 -0.121

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means








MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





140

Appendix I. LGM8 Piecewise Growth Model


141

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/30/2012 12:36 AM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7h.inp

Added district, gender, white, and black covariates, time points of interst, S1

and S2 f


Data:


Variable:



USEVARIABLES ARE District Gender White Black

Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District Gender White Black;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;

*** WARNING

Input line exceeded 90 characters. Some input may be truncated.

Added district, gender, white, and black covariates, time points of interst, S1

and S2 fi

1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS


filename spinn_diss_7h.inp

Added district, gender, white, and black covariates, time points of interst, S1 and S2

f


SUMMARY OF ANALYSIS

Number of groups 1



142





Continuous



DISTRICT GENDER WHITE BLACK


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

GENDER 0.513 0.558 0.701 0.778 0.810

WHITE 0.513 0.558 0.701 0.778 0.810

BLACK 0.513 0.558 0.701 0.778 0.810

Covariance Coverage


________ ________ ________ ________ ________

MATH8SS 0.810


GENDER 0.810 1.000 1.000

WHITE 0.810 1.000 1.000 1.000

BLACK 0.810 1.000 1.000 1.000 1.000


143

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.671 0.965 0.980 0.716 0.722

Means


________ ________ ________ ________ ________

1 0.755 0.314 0.517 0.759 0.011

Covariances


________ ________ ________ ________ ________

MATH3SS 1.263

MATH4SS 0.506 0.813

MATH5SS 0.535 0.634 0.961

MATH6SS 0.464 0.593 0.636 0.848

MATH7SS 0.470 0.619 0.661 0.673 0.812

MATH8SS 0.531 0.651 0.677 0.700 0.736

DISTRICT 0.045 0.005 -0.004 0.071 0.024

GENDER 0.070 -0.016 0.006 0.022 -0.026

WHITE 0.049 0.066 0.083 0.067 0.057

BLACK -0.002 -0.002 -0.017 0.001 -0.001

Covariances


________ ________ ________ ________ ________

MATH8SS 0.941


GENDER -0.002 0.000 0.250

WHITE 0.072 -0.005 0.009 0.183

BLACK -0.008 -0.003 -0.001 -0.008 0.011

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.500 1.000

MATH5SS 0.486 0.717 1.000

MATH6SS 0.448 0.713 0.704 1.000

MATH7SS 0.464 0.761 0.749 0.811 1.000

MATH8SS 0.487 0.744 0.712 0.784 0.843

DISTRICT 0.086 0.012 -0.009 0.165 0.058

GENDER 0.125 -0.036 0.011 0.048 -0.057

WHITE 0.102 0.170 0.197 0.171 0.148

BLACK -0.017 -0.019 -0.166 0.013 -0.008

Correlations


________ ________ ________ ________ ________

MATH8SS 1.000


GENDER -0.005 0.000 1.000

WHITE 0.174 -0.027 0.044 1.000

BLACK -0.082 -0.070 -0.024 -0.184 1.000


144



THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE

COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.

PROBLEM INVOLVING PARAMETER 18.

THE CONDITION NUMBER IS 0.712D-18.

FACTOR SCORES WILL NOT BE COMPUTED DUE TO NONCONVERGENCE OR

NONIDENTIFIED MODEL.

MODEL RESULTS

Estimate

I |

MATH3SS 1.000

MATH4SS 1.000

MATH5SS 1.000

MATH6SS 1.000

MATH7SS 1.000

MATH8SS 1.000

S1 |

MATH3SS 0.000

MATH4SS 0.300

MATH5SS 0.400

MATH6SS 0.400

MATH7SS 0.400

MATH8SS 0.400

S2 |

MATH3SS 0.000

MATH4SS 0.000

MATH5SS 0.000

MATH6SS 0.260

MATH7SS 0.270

MATH8SS 0.244

I ON

DISTRICT 0.216

GENDER 0.209

WHITE 0.266

BLACK 0.437

S1 ON

DISTRICT -0.544

GENDER -0.655

WHITE 0.334

BLACK -4.530

S2 ON

DISTRICT 0.952

GENDER 0.054

WHITE -0.139

BLACK 5.678

S1 WITH

S2 0.000

I 0.000

S2 WITH


145

I 0.000

Intercepts

MATH3SS 0.000

MATH4SS 0.000

MATH5SS 0.000

MATH6SS 0.000

MATH7SS 0.000

MATH8SS 0.000

I 0.319

S1 1.073

S2 -1.347

Residual Variances

MATH3SS 0.747

MATH4SS 0.215

MATH5SS 0.265

MATH6SS 0.197

MATH7SS 0.110

MATH8SS 0.184

I 0.480

S1 0.896

S2 0.705

MODEL COMMAND WITH FINAL ESTIMATES USED AS STARTING VALUES


i s2 | math3ss@0 math4ss@0 math5ss@0 [email protected] [email protected] math8ss*.28;

s2 BY math8ss*0.244;

i ON district*0.216;

i ON gender*0.209;

i ON white*0.266;

i ON black*0.437;

s1 ON district*-0.544;


s1 ON white*0.334;

s1 ON black*-4.530;

s2 ON district*0.952;

s2 ON gender*0.054;

s2 ON white*-0.139;

s2 ON black*5.678;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

[ math3ss@0 ];

[ math4ss@0 ];

[ math5ss@0 ];

[ math6ss@0 ];

[ math7ss@0 ];

[ math8ss@0 ];

[ i*0.319 ];

[ s1*1.073 ];

[ s2*-1.347 ];

math3ss*0.747;

math4ss*0.215;

math5ss*0.265;

math6ss*0.197;

math7ss*0.110;

math8ss*0.184;

i*0.480;

s1*0.896;

s2*0.705;


146

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU


________ ________ ________ ________ ________

1 0 0 0 0 0

NU


________ ________ ________ ________ ________

1 0 0 0 0 0

LAMBDA


________ ________ ________ ________ ________

MATH3SS 0 0 0 0 0

MATH4SS 0 0 0 0 0

MATH5SS 0 0 0 0 0

MATH6SS 0 0 0 0 0

MATH7SS 0 0 0 0 0

MATH8SS 0 0 1 0 0

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

LAMBDA

WHITE BLACK

________ ________

MATH3SS 0 0

MATH4SS 0 0

MATH5SS 0 0

MATH6SS 0 0

MATH7SS 0 0

MATH8SS 0 0

DISTRICT 0 0

GENDER 0 0

WHITE 0 0

BLACK 0 0

THETA


________ ________ ________ ________ ________

MATH3SS 2

MATH4SS 0 3

MATH5SS 0 0 4

MATH6SS 0 0 0 5

MATH7SS 0 0 0 0 6

MATH8SS 0 0 0 0 0

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

THETA



147

________ ________ ________ ________ ________

MATH8SS 7

DISTRICT 0 0

GENDER 0 0 0

WHITE 0 0 0 0

BLACK 0 0 0 0 0

ALPHA


________ ________ ________ ________ ________

1 8 9 10 0 0

ALPHA

WHITE BLACK

________ ________

1 0 0

BETA


________ ________ ________ ________ ________

I 0 0 0 11 12

S1 0 0 0 15 16

S2 0 0 0 19 20

DISTRICT 0 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

BETA

WHITE BLACK

________ ________

I 13 14

S1 17 18

S2 21 22

DISTRICT 0 0

GENDER 0 0

WHITE 0 0

BLACK 0 0

PSI


________ ________ ________ ________ ________

I 23

S1 0 24

S2 0 0 25

DISTRICT 0 0 0 0

GENDER 0 0 0 0 0

WHITE 0 0 0 0 0

BLACK 0 0 0 0 0

PSI

WHITE BLACK

________ ________

WHITE 0

BLACK 0 0

STARTING VALUES

NU



148

________ ________ ________ ________ ________

1 0.000 0.000 0.000 0.000 0.000

NU


________ ________ ________ ________ ________

1 0.000 0.000 0.000 0.000 0.000

LAMBDA


________ ________ ________ ________ ________

MATH3SS 1.000 0.000 0.000 0.000 0.000

MATH4SS 1.000 0.300 0.000 0.000 0.000

MATH5SS 1.000 0.400 0.000 0.000 0.000

MATH6SS 1.000 0.400 0.260 0.000 0.000

MATH7SS 1.000 0.400 0.270 0.000 0.000

MATH8SS 1.000 0.400 0.280 0.000 0.000

DISTRICT 0.000 0.000 0.000 1.000 0.000

GENDER 0.000 0.000 0.000 0.000 1.000

WHITE 0.000 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

LAMBDA

WHITE BLACK

________ ________

MATH3SS 0.000 0.000

MATH4SS 0.000 0.000

MATH5SS 0.000 0.000

MATH6SS 0.000 0.000

MATH7SS 0.000 0.000

MATH8SS 0.000 0.000


GENDER 0.000 0.000

WHITE 1.000 0.000

BLACK 0.000 1.000

THETA


________ ________ ________ ________ ________

MATH3SS 0.628

MATH4SS 0.000 0.392

MATH5SS 0.000 0.000 0.457

MATH6SS 0.000 0.000 0.000 0.423

MATH7SS 0.000 0.000 0.000 0.000 0.394

MATH8SS 0.000 0.000 0.000 0.000 0.000

DISTRICT 0.000 0.000 0.000 0.000 0.000

GENDER 0.000 0.000 0.000 0.000 0.000

WHITE 0.000 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

THETA


________ ________ ________ ________ ________

MATH8SS 0.445


GENDER 0.000 0.000 0.000

WHITE 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

ALPHA


________ ________ ________ ________ ________


149

1 0.858 0.438 0.774 0.314 0.517

ALPHA

WHITE BLACK

________ ________

1 0.759 0.011

BETA


________ ________ ________ ________ ________

I 0.000 0.000 0.000 0.000 0.000

S1 0.000 0.000 0.000 0.000 0.000

S2 0.000 0.000 0.000 0.000 0.000

DISTRICT 0.000 0.000 0.000 0.000 0.000

GENDER 0.000 0.000 0.000 0.000 0.000

WHITE 0.000 0.000 0.000 0.000 0.000

BLACK 0.000 0.000 0.000 0.000 0.000

BETA

WHITE BLACK

________ ________

I 0.000 0.000

S1 0.000 0.000

S2 0.000 0.000


GENDER 0.000 0.000

WHITE 0.000 0.000

BLACK 0.000 0.000

PSI


________ ________ ________ ________ ________

I 1.222

S1 0.000 6.113

S2 0.000 0.000 0.745

DISTRICT 0.000 0.000 0.000 0.215

GENDER 0.000 0.000 0.000 0.000 0.250

WHITE 0.000 0.000 0.000 -0.005 0.009

BLACK 0.000 0.000 0.000 -0.003 -0.001

PSI

WHITE BLACK

________ ________

WHITE 0.183

BLACK -0.008 0.011

TECHNICAL 4 OUTPUT




________ ________ ________ ________ ________

1 0.702 0.768 -1.064 0.314 0.517


WHITE BLACK

________ ________

1 0.759 0.011


150



________ ________ ________ ________ ________

I 1.261

S1 0.498 0.815

S2 0.493 0.634 0.946

DISTRICT 0.505 0.616 0.653 0.903

GENDER 0.506 0.615 0.652 0.709 0.821

WHITE 0.505 0.617 0.654 0.703 0.705

BLACK 0.044 0.013 0.002 0.051 0.053


WHITE BLACK

________ ________

WHITE 0.884

BLACK 0.048 0.215



________ ________ ________ ________ ________

I 1.000

S1 0.492 1.000

S2 0.452 0.722 1.000

DISTRICT 0.473 0.718 0.706 1.000

GENDER 0.497 0.752 0.739 0.823 1.000

WHITE 0.478 0.727 0.716 0.787 0.828

BLACK 0.084 0.030 0.005 0.115 0.125


WHITE BLACK

________ ________

WHITE 1.000

BLACK 0.109 1.000




MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





151

Appendix J. LGM9 Piecewise Growth Model


152

Mplus VERSION 6.1

MUTHEN & MUTHEN

01/30/2012 12:41 AM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7i.inp

Added district, gender, white, and Hispanic covariates (dropped black),

time points of interst, S1 and S2 fixed at 0


Data:


Variable:



USEVARIABLES ARE District Gender White Hispanic

Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District Gender White Hispanic;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7i.inp

Added district, gender, white, and Hispanic covariates (dropped black),



SUMMARY OF ANALYSIS

Number of groups 1






153


Continuous



DISTRICT GENDER WHITE HISPANIC


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

GENDER 0.513 0.558 0.701 0.778 0.810

WHITE 0.513 0.558 0.701 0.778 0.810

HISPANIC 0.513 0.558 0.701 0.778 0.810

Covariance Coverage

MATH8SS DISTRICT GENDER WHITE HISPANIC

________ ________ ________ ________ ________

MATH8SS 0.810


GENDER 0.810 1.000 1.000

WHITE 0.810 1.000 1.000 1.000

HISPANIC 0.810 1.000 1.000 1.000 1.000

SAMPLE STATISTICS


154


Means


________ ________ ________ ________ ________

1 0.667 0.964 0.986 0.713 0.720

Means


________ ________ ________ ________ ________

1 0.755 0.314 0.517 0.759 0.207

Covariances


________ ________ ________ ________ ________

MATH3SS 1.266

MATH4SS 0.508 0.816

MATH5SS 0.538 0.634 0.947

MATH6SS 0.466 0.594 0.639 0.852

MATH7SS 0.472 0.621 0.662 0.676 0.815

MATH8SS 0.534 0.653 0.671 0.703 0.738

DISTRICT 0.046 0.006 -0.007 0.072 0.025

GENDER 0.070 -0.016 0.005 0.024 -0.024

WHITE 0.052 0.067 0.079 0.070 0.059

HISPANIC -0.040 -0.057 -0.053 -0.057 -0.044

Covariances


________ ________ ________ ________ ________

MATH8SS 0.939


GENDER -0.003 0.000 0.250

WHITE 0.072 -0.005 0.009 0.183

HISPANIC -0.057 0.003 -0.007 -0.157 0.164

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.500 1.000

MATH5SS 0.491 0.721 1.000

MATH6SS 0.449 0.713 0.711 1.000

MATH7SS 0.465 0.762 0.754 0.811 1.000

MATH8SS 0.489 0.746 0.711 0.786 0.844

DISTRICT 0.088 0.014 -0.015 0.167 0.059

GENDER 0.125 -0.036 0.010 0.053 -0.053

WHITE 0.108 0.173 0.190 0.176 0.153

HISPANIC -0.088 -0.156 -0.134 -0.152 -0.121

Correlations


________ ________ ________ ________ ________

MATH8SS 1.000


GENDER -0.006 0.000 1.000

WHITE 0.173 -0.027 0.044 1.000

HISPANIC -0.145 0.017 -0.033 -0.906 1.000



155




Loglikelihood

H0 Value -1936.180

H1 Value -1909.371





(n* = (n + 2) / 24)


Value 53.618


P-Value 0.0011


Estimate 0.048

90 Percent C.I. 0.029 0.066


CFI/TLI

CFI 0.981

TLI 0.971


Value 1478.199


P-Value 0.0000


Value 0.024

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000


156

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.258 0.023 11.245 0.000

I ON

DISTRICT 0.223 0.136 1.644 0.100

GENDER 0.213 0.129 1.652 0.099

WHITE 0.141 0.477 0.296 0.767

HISPANIC -0.128 0.492 -0.260 0.795

S1 ON

DISTRICT -0.558 0.361 -1.544 0.123

GENDER -0.667 0.340 -1.964 0.050

WHITE 1.555 1.262 1.232 0.218

HISPANIC 1.284 1.302 0.987 0.324

S2 ON

DISTRICT 0.953 0.254 3.750 0.000

GENDER 0.074 0.234 0.317 0.752

WHITE -0.885 0.763 -1.161 0.246

HISPANIC -0.750 0.796 -0.943 0.346

S1 WITH

S2 0.000 0.000 999.000 999.000

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

I 0.440 0.478 0.921 0.357

S1 -0.137 1.265 -0.109 0.914

S2 -0.593 0.770 -0.771 0.441

Residual Variances

MATH3SS 0.750 0.084 8.948 0.000

MATH4SS 0.214 0.025 8.533 0.000

MATH5SS 0.267 0.028 9.377 0.000

MATH6SS 0.198 0.019 10.197 0.000

MATH7SS 0.111 0.014 7.875 0.000

MATH8SS 0.181 0.018 10.067 0.000

I 0.482 0.060 8.060 0.000

S1 0.869 0.356 2.444 0.015

S2 0.736 0.284 2.594 0.009




TECHNICAL 4 OUTPUT



157



________ ________ ________ ________ ________

1 0.701 0.788 -1.082 0.314 0.517


WHITE HISPANIC

________ ________

1 0.759 0.207



________ ________ ________ ________ ________

I 0.516

S1 -0.047 1.130

S2 0.040 -0.178 0.964

DISTRICT 0.047 -0.124 0.208 0.215

GENDER 0.055 -0.160 0.015 0.000 0.250

WHITE 0.047 0.080 -0.049 -0.005 0.009

HISPANIC -0.044 -0.031 0.019 0.003 -0.007


WHITE HISPANIC

________ ________

WHITE 0.183

HISPANIC -0.157 0.164



________ ________ ________ ________ ________

I 1.000

S1 -0.061 1.000

S2 0.057 -0.170 1.000

DISTRICT 0.140 -0.252 0.455 1.000

GENDER 0.154 -0.302 0.031 0.000 1.000

WHITE 0.152 0.175 -0.116 -0.027 0.044

HISPANIC -0.151 -0.071 0.047 0.017 -0.033


WHITE HISPANIC

________ ________

WHITE 1.000

HISPANIC -0.906 1.000


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.701 0.372 0.788 0.819 -1.082

Means

S2_SE

________

1 0.780


158

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.376

I_SE -0.009 0.002

S1 0.160 -0.008 0.459

S1_SE -0.005 0.001 -0.004 0.001

S2 0.108 -0.002 -0.091 -0.001 0.354

S2_SE -0.009 0.002 -0.007 0.001 -0.003

Covariances

S2_SE

________

S2_SE 0.002

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.316 1.000

S1 0.386 -0.253 1.000

S1_SE -0.323 0.938 -0.240 1.000

S2 0.297 -0.074 -0.226 -0.075 1.000

S2_SE -0.358 0.909 -0.252 0.856 -0.102

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means








MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





159

Appendix K. LGM10 Piecewise Growth Model


160

Mplus VERSION 6.1

MUTHEN & MUTHEN

03/03/2012 8:27 PM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7j.inp

Added district, gender, white, Hispanic and LEP covariates (dropped black),



Data:


Variable:



USEVARIABLES ARE District Gender White Hispanic LEP

Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District Gender White Hispanic LEP;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7j.inp

Added district, gender, white, Hispanic and LEP covariates (dropped black),



SUMMARY OF ANALYSIS

Number of groups 1






161


Continuous



DISTRICT GENDER WHITE HISPANIC LEP


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

GENDER 0.513 0.558 0.701 0.778 0.810

WHITE 0.513 0.558 0.701 0.778 0.810

HISPANIC 0.513 0.558 0.701 0.778 0.810

LEP 0.513 0.558 0.701 0.778 0.810

Covariance Coverage


________ ________ ________ ________ ________

MATH8SS 0.810


GENDER 0.810 1.000 1.000

WHITE 0.810 1.000 1.000 1.000

HISPANIC 0.810 1.000 1.000 1.000 1.000

LEP 0.810 1.000 1.000 1.000 1.000

Covariance Coverage


162

LEP

________

LEP 1.000

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.662 0.955 0.982 0.713 0.720

Means


________ ________ ________ ________ ________

1 0.755 0.314 0.517 0.759 0.207

Means

LEP

________

1 0.032

Covariances


________ ________ ________ ________ ________

MATH3SS 1.272

MATH4SS 0.519 0.834

MATH5SS 0.546 0.647 0.955

MATH6SS 0.470 0.603 0.644 0.853

MATH7SS 0.476 0.628 0.666 0.676 0.815

MATH8SS 0.538 0.660 0.675 0.703 0.738

DISTRICT 0.047 0.009 -0.006 0.071 0.025

GENDER 0.069 -0.020 0.004 0.024 -0.024

WHITE 0.056 0.075 0.082 0.070 0.059

HISPANIC -0.044 -0.066 -0.056 -0.057 -0.045

LEP -0.023 -0.038 -0.028 -0.027 -0.023

Covariances


________ ________ ________ ________ ________

MATH8SS 0.939


GENDER -0.003 0.000 0.250

WHITE 0.072 -0.005 0.009 0.183

HISPANIC -0.057 0.003 -0.007 -0.157 0.164

LEP -0.026 -0.006 0.005 -0.024 0.025

Covariances

LEP

________

LEP 0.031

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.504 1.000

MATH5SS 0.495 0.725 1.000


163

MATH6SS 0.452 0.715 0.714 1.000

MATH7SS 0.468 0.761 0.755 0.811 1.000

MATH8SS 0.492 0.746 0.713 0.786 0.844

DISTRICT 0.090 0.021 -0.013 0.167 0.059

GENDER 0.122 -0.043 0.008 0.052 -0.053

WHITE 0.116 0.192 0.196 0.177 0.154

HISPANIC -0.097 -0.177 -0.141 -0.153 -0.122

LEP -0.117 -0.236 -0.161 -0.169 -0.146

Correlations


________ ________ ________ ________ ________

MATH8SS 1.000


GENDER -0.006 0.000 1.000

WHITE 0.173 -0.027 0.044 1.000

HISPANIC -0.145 0.017 -0.033 -0.906 1.000

LEP -0.153 -0.071 0.054 -0.323 0.356

Correlations

LEP

________

LEP 1.000





Loglikelihood

H0 Value -1932.289

H1 Value -1904.919





(n* = (n + 2) / 24)


Value 54.740


P-Value 0.0027


Estimate 0.044

90 Percent C.I. 0.025 0.061


CFI/TLI

CFI 0.982

TLI 0.972



164

Value 1487.102


P-Value 0.0000


Value 0.023

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.258 0.023 11.141 0.000

I ON

DISTRICT 0.213 0.135 1.575 0.115

GENDER 0.220 0.129 1.710 0.087

WHITE 0.139 0.476 0.291 0.771

HISPANIC -0.054 0.493 -0.111 0.912

LEP -0.786 0.652 -1.205 0.228

S1 ON

DISTRICT -0.573 0.361 -1.584 0.113

GENDER -0.655 0.340 -1.929 0.054

WHITE 1.557 1.262 1.233 0.217

HISPANIC 1.346 1.305 1.032 0.302

LEP -0.075 1.762 -0.043 0.966

S2 ON

DISTRICT 0.948 0.254 3.729 0.000

GENDER 0.079 0.234 0.337 0.736

WHITE -0.891 0.762 -1.168 0.243

HISPANIC -0.798 0.799 -0.999 0.318

LEP 0.922 0.965 0.955 0.339

S1 WITH

S2 0.000 0.000 999.000 999.000

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000


165

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

I 0.443 0.477 0.929 0.353

S1 -0.144 1.265 -0.114 0.909

S2 -0.591 0.769 -0.768 0.443

Residual Variances

MATH3SS 0.751 0.084 8.975 0.000

MATH4SS 0.213 0.025 8.512 0.000

MATH5SS 0.267 0.028 9.388 0.000

MATH6SS 0.198 0.019 10.201 0.000

MATH7SS 0.111 0.014 7.874 0.000

MATH8SS 0.182 0.018 10.081 0.000

I 0.473 0.059 8.007 0.000

S1 0.870 0.353 2.465 0.014

S2 0.735 0.282 2.604 0.009




TECHNICAL 4 OUTPUT




________ ________ ________ ________ ________

1 0.693 0.795 -1.063 0.314 0.517


WHITE HISPANIC LEP

________ ________ ________

1 0.759 0.207 0.032



________ ________ ________ ________ ________

I 0.528

S1 -0.046 1.128

S2 0.017 -0.184 0.980

DISTRICT 0.050 -0.127 0.201 0.215

GENDER 0.053 -0.158 0.021 0.000 0.250

WHITE 0.054 0.072 -0.064 -0.005 0.009

HISPANIC -0.052 -0.023 0.035 0.003 -0.007

LEP -0.029 -0.006 0.025 -0.006 0.005


WHITE HISPANIC LEP

________ ________ ________

WHITE 0.183

HISPANIC -0.157 0.164

LEP -0.024 0.025 0.031


166



________ ________ ________ ________ ________

I 1.000

S1 -0.060 1.000

S2 0.024 -0.175 1.000

DISTRICT 0.147 -0.257 0.438 1.000

GENDER 0.145 -0.298 0.042 0.000 1.000

WHITE 0.174 0.159 -0.152 -0.027 0.044

HISPANIC -0.175 -0.053 0.087 0.017 -0.033

LEP -0.229 -0.031 0.142 -0.071 0.054


WHITE HISPANIC LEP

________ ________ ________

WHITE 1.000

HISPANIC -0.906 1.000

LEP -0.323 0.356 1.000


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.693 0.371 0.795 0.818 -1.063

Means

S2_SE

________

1 0.779

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.389

I_SE -0.009 0.002

S1 0.160 -0.008 0.458

S1_SE -0.005 0.001 -0.004 0.001

S2 0.085 -0.001 -0.097 -0.001 0.371

S2_SE -0.009 0.002 -0.007 0.001 -0.002

Covariances

S2_SE

________

S2_SE 0.002

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.322 1.000

S1 0.379 -0.249 1.000

S1_SE -0.329 0.939 -0.236 1.000

S2 0.223 -0.039 -0.235 -0.039 1.000

S2_SE -0.362 0.909 -0.248 0.857 -0.068

Correlations


167

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means








MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





168

Appendix L. LGM11 Piecewise Growth Model


169

Mplus VERSION 6.1

MUTHEN & MUTHEN

03/03/2012 8:45 PM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7k.inp

Added district, gender, white, Hispanic, LEP

and Eco covariates (dropped black),



Data:


Variable:



USEVARIABLES ARE District Gender White Hispanic LEP EcoD

Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District Gender White Hispanic LEP EcoD;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7l.inp

Added district, gender, white, Hispanic, LEP

and Eco covariates (dropped black),



SUMMARY OF ANALYSIS

Number of groups 1




170




Continuous



DISTRICT GENDER WHITE HISPANIC LEP ECOD


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

GENDER 0.513 0.558 0.701 0.778 0.810

WHITE 0.513 0.558 0.701 0.778 0.810

HISPANIC 0.513 0.558 0.701 0.778 0.810

LEP 0.513 0.558 0.701 0.778 0.810

ECOD 0.513 0.558 0.701 0.778 0.810

Covariance Coverage


________ ________ ________ ________ ________

MATH8SS 0.810


GENDER 0.810 1.000 1.000

WHITE 0.810 1.000 1.000 1.000

HISPANIC 0.810 1.000 1.000 1.000 1.000

LEP 0.810 1.000 1.000 1.000 1.000


171

ECOD 0.810 1.000 1.000 1.000 1.000

Covariance Coverage

LEP ECOD

________ ________

LEP 1.000

ECOD 1.000 1.000

SAMPLE STATISTICS


Means


________ ________ ________ ________ ________

1 0.666 0.957 0.981 0.713 0.718

Means


________ ________ ________ ________ ________

1 0.760 0.314 0.517 0.759 0.207

Means

LEP ECOD

________ ________

1 0.032 0.457

Covariances


________ ________ ________ ________ ________

MATH3SS 1.270

MATH4SS 0.518 0.833

MATH5SS 0.546 0.646 0.956

MATH6SS 0.468 0.602 0.644 0.852

MATH7SS 0.478 0.629 0.669 0.677 0.817

MATH8SS 0.533 0.657 0.672 0.701 0.738

DISTRICT 0.044 0.008 -0.007 0.071 0.025

GENDER 0.068 -0.020 0.004 0.024 -0.024

WHITE 0.050 0.073 0.080 0.070 0.060

HISPANIC -0.039 -0.064 -0.053 -0.057 -0.045

LEP -0.023 -0.038 -0.027 -0.027 -0.023

ECOD -0.114 -0.100 -0.116 -0.079 -0.075

Covariances


________ ________ ________ ________ ________

MATH8SS 0.935


GENDER -0.003 0.000 0.250

WHITE 0.070 -0.005 0.009 0.183

HISPANIC -0.056 0.003 -0.007 -0.157 0.164

LEP -0.026 -0.006 0.005 -0.024 0.025

ECOD -0.098 0.019 -0.001 -0.046 0.046

Covariances

LEP ECOD

________ ________

LEP 0.031

ECOD 0.015 0.248


172

Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.504 1.000

MATH5SS 0.496 0.724 1.000

MATH6SS 0.450 0.714 0.714 1.000

MATH7SS 0.469 0.762 0.757 0.812 1.000

MATH8SS 0.489 0.744 0.711 0.785 0.844

DISTRICT 0.084 0.018 -0.015 0.166 0.059

GENDER 0.121 -0.043 0.008 0.053 -0.053

WHITE 0.105 0.187 0.190 0.177 0.155

HISPANIC -0.086 -0.174 -0.134 -0.153 -0.123

LEP -0.115 -0.236 -0.158 -0.169 -0.145

ECOD -0.203 -0.221 -0.239 -0.171 -0.166

Correlations


________ ________ ________ ________ ________

MATH8SS 1.000


GENDER -0.007 0.000 1.000

WHITE 0.170 -0.027 0.044 1.000

HISPANIC -0.144 0.017 -0.033 -0.906 1.000

LEP -0.154 -0.071 0.054 -0.323 0.356

ECOD -0.204 0.081 -0.006 -0.214 0.229

Correlations

LEP ECOD

________ ________

LEP 1.000

ECOD 0.174 1.000





Loglikelihood

H0 Value -1922.474

H1 Value -1893.085





(n* = (n + 2) / 24)


Value 58.779


P-Value 0.0027



173

Estimate 0.042

90 Percent C.I. 0.025 0.059


CFI/TLI

CFI 0.982

TLI 0.971


Value 1510.771


P-Value 0.0000


Value 0.021

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.253 0.023 10.805 0.000

I ON

DISTRICT 0.232 0.134 1.732 0.083

GENDER 0.216 0.127 1.700 0.089

WHITE 0.097 0.473 0.204 0.838

HISPANIC 0.022 0.489 0.046 0.963

LEP -0.681 0.649 -1.050 0.294

ECOD -0.386 0.135 -2.866 0.004

S1 ON

DISTRICT -0.543 0.361 -1.506 0.132

GENDER -0.651 0.338 -1.926 0.054

WHITE 1.606 1.258 1.277 0.202

HISPANIC 1.340 1.302 1.030 0.303

LEP -0.040 1.756 -0.023 0.982

ECOD 0.043 0.361 0.119 0.905

S2 ON


174

DISTRICT 0.923 0.256 3.606 0.000

GENDER 0.083 0.234 0.355 0.723

WHITE -0.869 0.764 -1.138 0.255

HISPANIC -0.891 0.801 -1.112 0.266

LEP 0.822 0.967 0.850 0.395

ECOD 0.306 0.249 1.231 0.218

S1 WITH

S2 0.000 0.000 999.000 999.000

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

I 0.633 0.478 1.324 0.185

S1 -0.225 1.272 -0.177 0.860

S2 -0.719 0.781 -0.921 0.357

Residual Variances

MATH3SS 0.741 0.082 8.989 0.000

MATH4SS 0.215 0.025 8.558 0.000

MATH5SS 0.263 0.028 9.331 0.000

MATH6SS 0.197 0.019 10.182 0.000

MATH7SS 0.111 0.014 7.811 0.000

MATH8SS 0.183 0.018 10.120 0.000

I 0.443 0.057 7.777 0.000

S1 0.916 0.346 2.647 0.008

S2 0.739 0.283 2.607 0.009




TECHNICAL 4 OUTPUT




________ ________ ________ ________ ________

1 0.697 0.782 -1.064 0.314 0.517


WHITE HISPANIC LEP ECOD

________ ________ ________ ________

1 0.759 0.207 0.032 0.457



________ ________ ________ ________ ________

I 0.529

S1 -0.047 1.171

S2 -0.010 -0.175 1.003

DISTRICT 0.046 -0.120 0.202 0.215


175

GENDER 0.052 -0.157 0.022 0.000 0.250

WHITE 0.049 0.079 -0.057 -0.005 0.009

HISPANIC -0.047 -0.029 0.028 0.003 -0.007

LEP -0.029 -0.006 0.024 -0.006 0.005

ECOD -0.106 -0.010 0.104 0.019 -0.001



________ ________ ________ ________

WHITE 0.183

HISPANIC -0.157 0.164

LEP -0.024 0.025 0.031

ECOD -0.046 0.046 0.015 0.248



________ ________ ________ ________ ________

I 1.000

S1 -0.060 1.000

S2 -0.013 -0.161 1.000

DISTRICT 0.137 -0.239 0.434 1.000

GENDER 0.143 -0.290 0.044 0.000 1.000

WHITE 0.158 0.171 -0.133 -0.027 0.044

HISPANIC -0.161 -0.065 0.068 0.017 -0.033

LEP -0.227 -0.029 0.134 -0.071 0.054

ECOD -0.291 -0.019 0.209 0.081 -0.006



________ ________ ________ ________

WHITE 1.000

HISPANIC -0.906 1.000

LEP -0.323 0.356 1.000

ECOD -0.214 0.229 0.174 1.000


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.697 0.370 0.782 0.830 -1.064

Means

S2_SE

________

1 0.781

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.390

I_SE -0.009 0.002

S1 0.163 -0.008 0.482

S1_SE -0.005 0.001 -0.005 0.001

S2 0.057 -0.001 -0.082 -0.001 0.391

S2_SE -0.009 0.002 -0.008 0.001 -0.002


176

Covariances

S2_SE

________

S2_SE 0.002

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.310 1.000

S1 0.377 -0.267 1.000

S1_SE -0.320 0.945 -0.249 1.000

S2 0.145 -0.045 -0.188 -0.035 1.000

S2_SE -0.344 0.908 -0.269 0.860 -0.076

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means








MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





177

Appendix M. LGM12 Piecewise Growth Model


178

Mplus VERSION 6.1

MUTHEN & MUTHEN

03/03/2012 8:45 PM

INPUT INSTRUCTIONS

Title:


filename spinn_diss_7l.inp

Added district covariate, (Deleted gender, white, Black,

Hispanic, LEP, and EcoD covariates)



Data:


Variable:



USEVARIABLES ARE District Math3SS-Math8SS;


Analysis:

Processors = 2;

MODEL:



i s1 s2 ON District;

s1 WITH s2@0;

s1 WITH i@0;

s2 WITH i@0;

PLOT:

TYPE is Plot3;


OUTPUT:

SAMPSTAT;

Tech4;



filename spinn_diss_7m.inp

Added district covariate, (Deleted gender, white, Black,

Hispanic, LEP, and EcoD covariates)



SUMMARY OF ANALYSIS

Number of groups 1





179



Continuous



DISTRICT


I S1 S2

Estimator ML







Input data file(s)

Spinn_Diss_6b.csv


SUMMARY OF DATA





Covariance Coverage


________ ________ ________ ________ ________

MATH3SS 0.513

MATH4SS 0.481 0.558

MATH5SS 0.470 0.536 0.701

MATH6SS 0.476 0.530 0.628 0.778

MATH7SS 0.468 0.519 0.600 0.718 0.810

MATH8SS 0.459 0.511 0.583 0.679 0.735

DISTRICT 0.513 0.558 0.701 0.778 0.810

Covariance Coverage

MATH8SS DISTRICT

________ ________

MATH8SS 0.810


SAMPLE STATISTICS


Means



180

________ ________ ________ ________ ________

1 0.661 0.964 0.988 0.712 0.722

Means

MATH8SS DISTRICT

________ ________

1 0.755 0.314

Covariances


________ ________ ________ ________ ________

MATH3SS 1.278

MATH4SS 0.516 0.814

MATH5SS 0.549 0.635 0.946

MATH6SS 0.472 0.595 0.640 0.854

MATH7SS 0.477 0.618 0.661 0.675 0.811

MATH8SS 0.542 0.651 0.672 0.704 0.736

DISTRICT 0.045 0.006 -0.007 0.071 0.025

Covariances

MATH8SS DISTRICT

________ ________

MATH8SS 0.939


Correlations


________ ________ ________ ________ ________

MATH3SS 1.000

MATH4SS 0.506 1.000

MATH5SS 0.500 0.723 1.000

MATH6SS 0.452 0.714 0.712 1.000

MATH7SS 0.469 0.761 0.754 0.812 1.000

MATH8SS 0.495 0.744 0.713 0.786 0.844

DISTRICT 0.085 0.015 -0.016 0.165 0.059

Correlations

MATH8SS DISTRICT

________ ________

MATH8SS 1.000






Loglikelihood

H0 Value -1948.192

H1 Value -1930.107





181


(n* = (n + 2) / 24)


Value 36.170


P-Value 0.0044


Estimate 0.049

90 Percent C.I. 0.027 0.071


CFI/TLI

CFI 0.986

TLI 0.983


Value 1436.726


P-Value 0.0000


Value 0.027

MODEL RESULTS

Two-Tailed


I |

MATH3SS 1.000 0.000 999.000 999.000

MATH4SS 1.000 0.000 999.000 999.000

MATH5SS 1.000 0.000 999.000 999.000

MATH6SS 1.000 0.000 999.000 999.000

MATH7SS 1.000 0.000 999.000 999.000

MATH8SS 1.000 0.000 999.000 999.000

S1 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.300 0.000 999.000 999.000

MATH5SS 0.400 0.000 999.000 999.000

MATH6SS 0.400 0.000 999.000 999.000

MATH7SS 0.400 0.000 999.000 999.000

MATH8SS 0.400 0.000 999.000 999.000

S2 |

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.260 0.000 999.000 999.000

MATH7SS 0.270 0.000 999.000 999.000

MATH8SS 0.259 0.023 11.166 0.000

I ON

DISTRICT 0.206 0.137 1.498 0.134

S1 ON

DISTRICT -0.549 0.365 -1.505 0.132

S2 ON


182

DISTRICT 0.958 0.254 3.776 0.000

S1 WITH

S2 0.000 0.000 999.000 999.000

I 0.000 0.000 999.000 999.000

S2 WITH

I 0.000 0.000 999.000 999.000

Intercepts

MATH3SS 0.000 0.000 999.000 999.000

MATH4SS 0.000 0.000 999.000 999.000

MATH5SS 0.000 0.000 999.000 999.000

MATH6SS 0.000 0.000 999.000 999.000

MATH7SS 0.000 0.000 999.000 999.000

MATH8SS 0.000 0.000 999.000 999.000

I 0.629 0.082 7.677 0.000

S1 0.986 0.214 4.600 0.000

S2 -1.396 0.143 -9.795 0.000

Residual Variances

MATH3SS 0.768 0.086 8.964 0.000

MATH4SS 0.213 0.025 8.524 0.000

MATH5SS 0.269 0.029 9.390 0.000

MATH6SS 0.198 0.019 10.213 0.000

MATH7SS 0.112 0.014 7.950 0.000

MATH8SS 0.181 0.018 10.070 0.000

I 0.509 0.062 8.266 0.000

S1 0.889 0.362 2.454 0.014

S2 0.713 0.283 2.521 0.012




TECHNICAL 4 OUTPUT



I S1 S2 DISTRICT

________ ________ ________ ________

1 0.694 0.813 -1.095 0.314


I S1 S2 DISTRICT

________ ________ ________ ________

I 0.518

S1 -0.024 0.954

S2 0.043 -0.113 0.911

DISTRICT 0.044 -0.118 0.206 0.215


I S1 S2 DISTRICT

________ ________ ________ ________

I 1.000

S1 -0.035 1.000

S2 0.062 -0.121 1.000

DISTRICT 0.133 -0.261 0.466 1.000


183


SAMPLE STATISTICS

Means

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

1 0.694 0.376 0.813 0.829 -1.095

Means

S2_SE

________

1 0.770

Covariances

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 0.374

I_SE -0.010 0.002

S1 0.190 -0.006 0.265

S1_SE -0.005 0.001 -0.003 0.001

S2 0.108 -0.003 -0.030 -0.002 0.316

S2_SE -0.009 0.002 -0.006 0.001 -0.003

Covariances

S2_SE

________

S2_SE 0.002

Correlations

I I_SE S1 S1_SE S2

________ ________ ________ ________ ________

I 1.000

I_SE -0.337 1.000

S1 0.604 -0.250 1.000

S1_SE -0.341 0.934 -0.253 1.000

S2 0.315 -0.117 -0.102 -0.108 1.000

S2_SE -0.375 0.907 -0.269 0.853 -0.138

Correlations

S2_SE

________

S2_SE 1.000

PLOT INFORMATION




Sample means

Estimated means









184

MUTHEN & MUTHEN

3463 Stoner Ave.


Tel: (310) 391-9971

Fax: (310) 391-8971





185

Appendix N. Institutional Review Board Approval Letter


186


187

Appendix O. TESCCC Confidentiality Oath


188

Craig Spinn


189

Appendix P. TESCCC Agreement to Submit Final Research

Findings


190

Craig Spinn


191

Vitae

Name: Gaylon Craig Spinn

Address: 300 Park Road 4 South

Burnet, Texas 78611

Email Address: [email protected]

Education: B.S. Angelo State University

San Angelo, Texas. Physical Education. 1986

M.Ed. Texas State University

San Marcos, Texas. Educational Leadership. 1994

Ed.D. Texas Tech University

Educational Leadership. 2012

Professional Principal, Burnet High School, Burnet, TX 2001-Present

Experience:

Assistant Principal, Burnet High School, Burnet, TX 1998-2001

Assistant Principal, Burnet Middle School, Burnet, TX 1995-

1998

Biology and Anatomy and Physiology Teacher, Wm. B. Travis

High School, Austin, TX 1989-1995

Biology and Physical Science Teacher, Ballinger High School,

Ballinger, TX 1986-1989