Mathematics Teachers' Perceptions of Self-efficacy ... · And in loving memory of my sister, Kaetia...

Mathematics Teachers' Perceptions of

Self-efficacy:

Effects of Teacher Characteristics

and Supervisory Behaviors

Prosperanta B. Calhoun

Dissertation submitted to the faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Doctor of Education

in

Educational Leadership and Policy Studies

Walt D. Mallory, Chair

Carol S. Cash

William J. Glenn

Anita S. Wynn

June 13, 2019

Falls Church, Virginia

Keywords: (Self-efficacy, Supervisory behaviors, Mathematics Teachers, Perceptions of Self-

efficacy, Teacher Characteristics)

ABSTRACT (ACADEMIC)

Mathematics Teachers' Perceptions of Self-efficacy:

Effects of Teacher Characteristics and Supervisory Behaviors


ABSTRACT

This research is a descriptive, correlational study investigating mathematics teachers' perceptions

of their self-efficacy and the effects of teacher characteristics and supervisory behaviors on

teachers’ self-efficacy. Teachers who teach mathematics from an urban school district in the

southern part of the United States were asked to report on their self-efficacy in teaching

mathematics and their perception of the supervisory behaviors that support the development of

their self-efficacy. The study sought to determine the relationship between teachers of

mathematics self-efficacy and the characteristics and supervisory behaviors that foster the

development of their self-efficacy. Gender, ethnicity, years of mathematics teaching, level of

education, and years at current school are used as control variables. The study findings suggest

instructional leaders need to use a variety of strategies to enhance teacher efficacy. Strategies

that were reported to be particularly useful included those that foster teacher collaboration,

autonomy, and empowerment. Ensuring appropriate systems, services, and support for teacher

collaboration should be a priority for those in leadership positions. An important practical

implication emerging from this research is the need for feedback. It is expected that the results of

this research may benefit educational supervisors when they consider which type of supervision

and supportive actions to adopt to foster the development of mathematics self-efficacy in their

teachers.

Keywords: Self-efficacy, Supervisory behaviors, Mathematics Teachers, Perceptions of Self-

efficacy, Teacher Characteristics

ABSTRACT (GENERAL AUDIENCE)

Mathematics Teachers' Perceptions of Self-efficacy:

Effects of Teacher Characteristics and Supervisory Behaviors


GENERAL AUDIENCE ABSTRACT

This research is designed to investigate mathematics teachers' perceptions of their self-efficacy

and the effects of teacher characteristics and supervisory behaviors on teachers’ self-efficacy.

The study is threefold: (a) to explore the self-efficacy of teachers who teach mathematics, (b) to

identify teacher characteristics and supervisory behaviors that teachers perceived affect teacher

self-efficacy, and (c) to determine whether there is a relationship between the mathematics

supervisory behaviors and teacher self-efficacy as seen by the teachers, while controlling for

gender, ethnicity, years of mathematics teaching, level of education, and years at current school.

Teachers who teach mathematics from an urban school district in the southern part of the United

States were asked to report on their self-efficacy in teaching mathematics and their perception of

the supervisory behaviors that support the development of their self-efficacy. The study findings

suggest instructional leaders need to use a variety of strategies to enhance teacher efficacy.

Strategies that were reported to be particularly useful included those that foster teacher

collaboration, autonomy, and empowerment. Ensuring appropriate systems, services, and support

for teacher collaboration should be a priority for those in leadership positions. An important

practical implication emerging from this research is the need for feedback. It is expected that the

results of this research may benefit educational supervisors when they consider which type of

supervision and supportive actions to adopt to foster the development of mathematics self-

efficacy in their teachers. Keywords: Self-efficacy, Supervisory behaviors, Mathematics

Teachers, Perceptions of Self-efficacy, Teacher Characteristics

[Type here]

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DEDICATION

This dissertation is dedicated to my children, Jameelah, Nora, and Kenyah, who always

inspire and encourage me.

You continue to teach me and help me grow every day. I am so proud of each of you.

Love always! Mommy

And in loving memory of my sister, Kaetia Beneus, and my dearest friends who are not

here to see me graduate: Carmen Boatwright-Bacon and Linda Crawford.

v

ACKNOWLEDGMENTS

I would like to acknowledge everyone who contributed to this academic accomplishment.

My family has had the most impactful effect on this milestone. My parents, who made it all

possible by affording me an education, which is a privilege and a commodity with immeasurable

value. You supported and loved me through the best and the worst of time. I could not have

made it here without you. My children

My deepest gratitude to my dissertation committee, Dr. Cash, Dr. Glenn, Dr. Mallory,

and Dr. Wynn, who guided and encouraged me through this process, without your guidance and

persistent help I could not have completed this project. You exemplified patience, kindness, and

leadership and your guidance and useful feedback enabled me to learn, grow, and develop

exponentially through the process of completing this work. Dr. Mallory, you provided personal

and professional leadership; and Dr. Glenn, thank you for your assistance with the analysis and

your timely feedback. Dr. Patricio, thank you for getting me started early on the literature review

and for the article protocol that you provided.

I thank my “Board of Directors” and my friends, composed of the many leaders who

believed in me and who are always willing to provide candid and supportive feedback along with

a great dose of encouragement when needed. You know who you are, and I sincerely thank you

for inspiring, uplifting, and encouraging me.

Specials thanks to Judy who gave me insightful comments and suggestions and assisted

me with editing this work.

To all my students over the last three decades, the current ones and those that I have yet

to meet, you are the best part of the journey. Thank you for educating me! I am still learning.

vi

I am most appreciative to the school district who gave approval for this research and to

all the teachers who took time to complete the survey and made it possible for me to complete

this project. Many thanks for your time, effort, and candidness.

Finally, to any contributor that I failed to mention, you know who you are, and indeed,

your contribution is greatly appreciated, and you do matter.

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TABLE OF CONTENTS

ABSTRACT (ACADEMIC) ........................................................................................................... ii

ABSTRACT (GENERAL AUDIENCE) ....................................................................................... iii

DEDICATION ............................................................................................................................... iv

ACKNOWLEDGMENTS .............................................................................................................. v

LIST OF FIGURES ....................................................................................................................... xi

LIST OF TABLES ........................................................................................................................ xii

CHAPTER 1 INTRODUCTION .................................................................................................... 1

Teacher Self-Efficacy ..................................................................................................................... 1

Instructional Leader Behaviors ....................................................................................................... 2

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

Purpose of the Study ....................................................................................................................... 3

Research Questions ......................................................................................................................... 3

Research Methodology ................................................................................................................... 4

Delimitations and Limitation .......................................................................................................... 4

Delimitation ............................................................................................................................ 4

Limitation ................................................................................................................................ 5

Definitions....................................................................................................................................... 5

Self-Efficacy ........................................................................................................................... 5

Supervisory Leaders Behaviors .............................................................................................. 6

Teaching Efficacy ................................................................................................................... 7

Significance of the Study ................................................................................................................ 7

Overview of the Study .................................................................................................................... 8

CHAPTER 2 REVIEW OF THE LITERATURE .......................................................................... 9

Self-Efficacy ................................................................................................................................. 10

Effective Teachers ........................................................................................................................ 12

viii

Teacher Self-Efficacy ................................................................................................................... 13

The Development of Teacher Efficacy Beliefs ............................................................................. 13

Enactive Experiences ............................................................................................................ 14

Vicarious Experiences .......................................................................................................... 15

Social Persuasion .................................................................................................................. 15

Emotional/Physiological Arousal ......................................................................................... 16

Experience and the Development of Teacher Self-Efficacy ......................................................... 16

Theoretical Model of Teacher Self-Efficacy ................................................................................ 17

Measuring Teacher Self-Efficacy ................................................................................................. 18

Self-Efficacy and Educational Practices ............................................................................... 20

Self-Efficacy and Adversity .................................................................................................. 22

Self-Efficacy and Group Effectiveness ................................................................................. 24

Self-Efficacy and Teacher Attrition/Burnout ........................................................................ 24

Supporting the Development of Teacher Self-Efficacy ................................................................ 27

The Role of School Leaders .......................................................................................................... 28

Conceptual Model of Leader Effect on Teacher Self-Efficacy .................................................... 31

Summary ....................................................................................................................................... 33

CHAPTER 3 RESEARCH DESIGN AND METHODOLOGY .................................................. 35

Research Questions ....................................................................................................................... 35

Research Design............................................................................................................................ 35

Sample........................................................................................................................................... 36

Instrumentation ............................................................................................................................. 36

Mathematics Teaching Efficacy Beliefs Instrument ............................................................. 37

Leaders Support of Teacher Efficacy Development Inventory ............................................ 39

Data Collection ............................................................................................................................. 41

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

Summary ....................................................................................................................................... 44

ix

CHAPTER 4 FINDINGS .............................................................................................................. 46

Participants .................................................................................................................................... 46

Research Questions ....................................................................................................................... 50

Research Question One ......................................................................................................... 50

Research Question Two ........................................................................................................ 57

Research Question Three ...................................................................................................... 63

Research Question Four ........................................................................................................ 69

Summary ....................................................................................................................................... 78

Chapter 5 DISCUSSION .............................................................................................................. 80

Discussion of Study Findings ....................................................................................................... 80

Demographics ....................................................................................................................... 81

Research Question One ......................................................................................................... 82

Research Question Two ........................................................................................................ 84

Research Question Four ........................................................................................................ 86

Recommendations ......................................................................................................................... 88

Implications................................................................................................................................... 89

Conclusion .................................................................................................................................... 90

Reflections .................................................................................................................................... 91

REFERENCES ............................................................................................................................. 95

Appendix A Demographic/Background Questions .................................................................... 115

Appendix B Comparison of Item Revisions from the Mathematics Teacher Efficacy Beliefs

Instrument (MTEBI) ................................................................................................................ 116

Appendix C Items on Revised MTEBI by Subscale ................................................................... 118

Appendix D Permission to Use MTEBI ..................................................................................... 119

Appendix E the Leaders Support Of Teacher Efficacy Development Inventory (LSTEDI) ...... 120

Appendix F School District Approval Letter .............................................................................. 123

Appendix G Introductory Recruitment Email............................................................................. 124

Appendix H Institutional Review Approval Letter ..................................................................... 126

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Appendix I Summary Statistics of MTEBI and LSEDI.............................................................. 128

Appendix J Complete MTEBI ANOVA by Years of Teaching ................................................. 130

Appendix K Complete MTEBI ANOVA Subgroups by Years of Teaching .............................. 132

Appendix L Complete MTEBI ANOVA by Years at Current School ....................................... 134

Appendix M Complete MTEBI ANOVA Subgroups by Years at Current SCHOOL ............... 136

Appendix N Complete MTEBI ANOVA by Ethnicity ............................................................... 140

Appendix O Complete MTEBI ANOVA Subgroups by Ethnicity ............................................. 142

Appendix P Complete LSTEDI ANOVA by Years of Teaching ............................................... 144

Appendix Q Complete LSTEDI ANOVA Subgroups by Years of Teaching ............................ 146

Appendix R Complete LSTEDI ANOVA by Years at Current School ...................................... 148

Appendix S Complete LSTEDI ANOVA Subgroups by Years at Current SCHOOL ............... 150

Appendix T Complete LSTEDI ANOVA by Ethnicity .............................................................. 153

Appendix U Complete LSTEDI ANOVA Subgroups by Ethnicity ........................................... 155

Appendix V Complete LSTEDI Effectiveness ANOVA by Years of Teaching ........................ 157

Appendix W Complete LSTEDI Effectiveness ANOVA Subgroups by Years of Teaching ..... 159

Appendix X Complete LSTEDI Effectiveness ANOVA by Years at Current School ............... 161

Appendix Y Complete LSTEDI Effectiveness ANOVA Subgroups by Years at Current School

.................................................................................................................................................. 163

Appendix Z Complete LSTEDI Effectiveness ANOVA by Ethnicity ....................................... 166

Appendix AA Complete LSTEDI Effectiveness ANOVA Subgroups by Ethnicity .................. 168

Appendix BB Complete Correlation Matrix of All Values of LSTEDI AND MTEBI .............. 170

xi

LIST OF FIGURES

FIGURE 1. Theoretical Model of Teacher Self-Efficacy. ............................................................... 18

FIGURE 2. Conceptual Model of Leader Effect on Teacher Self-Efficacy. ................................... 33

xii

LIST OF TABLES

TABLE 1. Cronbach Alpha Reliability Coefficients from Two Previous Studies ....................... 39

TABLE 2. Supervisor Strategies Related Sources of Teacher Efficacy....................................... 41

TABLE 3. Study Variables ........................................................................................................... 43

TABLE 4. Summary of Analyses ................................................................................................. 44

TABLE 5. Participants’ Years of Teaching .................................................................................. 47

TABLE 6. Participants’ Years at Current School ......................................................................... 48

TABLE 7. Participants’ Highest Level of Education ................................................................... 49

TABLE 8. Participants’ Ethnicity ................................................................................................ 49

TABLE 9. ANOVA Results: MTEBI by Years of Teaching, ...................................................... 53

TABLE 10. ANOVA Results: MTEBI by Years at Current School ............................................ 54

TABLE 11. ANOVA Results: MTEBI by Race and Ethnicity .................................................... 57

TABLE 12. ANOVA Results: LSTEDI by Years at Current School ........................................... 61

TABLE 13. ANOVA Results: LSTEDI by Race and Ethnicity ................................................... 62

TABLE 14. ANOVA Results: LSTEDI Effectiveness by Years of Teaching ............................. 64

TABLE 15. ANOVA Results: LSTEDI Effectiveness by Years at Current School .................... 68

TABLE 16. Correlation Matrix of LSTEDI and MTEBI Questions ............................................ 70

1

CHAPTER 1 INTRODUCTION

Improving the quality of mathematics instruction has continued to be a focus of many

studies over the past decades (Even & Ball, 2010; Franke, Kazemi, & Battey, 2007). As such,

school leaders face increasing pressures to improve student learning opportunities in

mathematics (Even & Ball, 2010). Studies show that student achievement in mathematics can be

improved by enhancing teacher capacity (Bennett, 2003; Curry, 2008; DuFour, 2004, 2011;

Harris, 2009; Murphy & Lick, 2005). A large body of research suggests teachers are the keys to

improving student achievement in mathematics and identifies teacher self-efficacy as an essential

factor at the core of teaching and learning.

Teacher self-efficacy has been related to ensuring student success regardless of the school

and the challenges that the community may encounter (Armor et al., 1976; Ashton & Webb,

1986; Moore & Esselman, 1992; Ross, 1992). These findings suggest that supervisors can

improve student mathematics learning by mediating teachers’ sense of self-efficacy. Therefore, it

is important to study the supervisory actions that positively influence the development of self-

efficacy in teachers who teach students mathematics.

Teacher Self-Efficacy

Teacher self-efficacy, defined as teachers’ perceived ability to successfully execute

teaching tasks, such as instructional delivery and classroom management, may have crucial

implications in the classroom (Ashton & Webb, 1986; Guskey & Passaro, 1994; Hoy &

Woolfolk, 1993; Wheatley, 2002). Guskey and Passaro (1994) defined teacher self-efficacy as,

“The extent to which a teacher considers he/she can affect a student’s performance,” or “the

expectation a teacher has of his/her ability to promote desirable results of involvement and

learning in students, even those who are conflictive or who lack motivation” (p. 9)

2

Research has identified a relationship among teacher self-efficacy, teacher classroom

behaviors, and student outcomes (Anderson, Greene, & Loewen, 1988; Ashton & Webb, 1986;

Midgley, Feldlaufer, & Eccles, 1989; Ross, 1992). These findings are consistent with the

perception of Bandura (1977) which suggests a correlation between teachers’ self-efficacy and

the investment that teachers put into their teaching, their goals, and their resilience when faced

with stressful situations. These findings indicate a link exists between teacher self-efficacy and

student learning. Therefore, school leaders must find ways to mediate teacher self-efficacy in

order to improve student learning, particularly in mathematics.

Instructional Leader Behaviors

Numerous studies have identified the role of instructional leaders as a critical component

of teacher development (Glickman; 1985, Pajak; 1989). Ross and Gray (2006) identified the

indirect influence that school leaders could have on student achievement by improving teaching

and learning; they also contribute to teachers’ commitment to the profession by adopting certain

leadership behaviors. Glickman (1985) identified direct assistance to teachers as one of the

primary tasks of instructional leaders. Additionally, the identification of leadership behaviors

that support the development of teachers’ self-efficacy is an important approach to improve

student achievement, particularly in math. Blase and Blase (1999) identified leadership behaviors

that positively influence teacher self-efficacy (i.e., giving feedback, giving praise, modeling, and

supporting collaboration among teachers).

Statement of the Problem

Teachers with instructional self-efficacy are more effective in their teaching tasks that

lead to students’ academic success (Ross & Gray, 2006; Klassen et al., 2011). Previous studies

have documented that instructional leaders can affect teacher self-efficacy, thereby affecting

3

instruction and learning (Tschannen-Moran, Woolfolk-Hoy & Hoy, 1998). Some studies have

analyzed the influence of leadership on teachers’ self-efficacy beliefs (Goddard, Hoy, &

Woolfolk-Hoy, 2000; Pajares, 1996; Ross, 1992, 1994, 1998; Tschannen-Moran et al., 1998);

however, there is a void in research that assesses the association between leadership behaviors

and mathematics teachers’ self-efficacy.

Purpose of the Study

This research is designed to investigate mathematics teachers' perceptions of their self-

efficacy and the effects of teacher characteristics and supervisory behaviors on teachers’ self-

efficacy. The purpose of this study is threefold: (a) to explore the self-efficacy of teachers who

teach mathematics, (b) to identify teacher characteristics and supervisory behaviors that teachers

perceived affect teacher self-efficacy, and (c) to determine whether there is a relationship

between the mathematics supervisory behaviors and teacher self-efficacy as seen by the teachers,

while controlling for gender, ethnicity, years of mathematics teaching, level of education, and

years at current school.

Research Questions

The following four research questions are addressed in this study:

1. What are teachers’ perceptions of their math teaching self-efficacy?

2. What strategies do teachers perceive supervisors use to enhance teacher self-efficacy?

3. To what degree do teachers perceive those strategies as effective?

4. What is the relationship between teachers’ perceptions of the strategies used by their

supervisors’ and teachers’ self-efficacy?

4

Research Methodology

This study is a descriptive correlational study that explores teachers’ perceptions of their

self-efficacy in math teaching and the supervisory behaviors that support the development of

their self-efficacy. Teachers reported their perception of the strategies’ mathematics supervisory

leaders use to mediate their self-efficacy and their effectiveness. Demographic statistics (gender,

ethnicity, years of teaching experience, years at current school, and level of education) were used

as controls for the study.

The researcher used two instruments in this quantitative study. Mathematics Teaching

Efficacy Beliefs Instrument (MTEBI) was used to measure participants’ perceptions of their

personal mathematics teaching self-efficacy. Leaders Support of Teacher Efficacy Development

Inventory (LSTEDI), developed by the researcher, was used to measure teachers’ views of

instructional leader behaviors. Descriptive statistics were used to encapsulate the data.

Regression analysis was used to determine the relationship between the teachers’ perceptions of

leader behavior and teacher self-efficacy.

Delimitations and Limitation

Delimitation

The study has the following delimitations:

• A small sample of teachers was asked to participate in the study (specifically

mathematics teachers in a southern United States school district). Some of the

teachers teach math as part of the overall program, are not certified in math, and

may not have a strong background in math.

• No control group was used for comparison purposes.

5

• The study included a self-designed instrument which had not been tested across

subjects in different settings.

• There was no t-test to analyze the effect of teacher mathematics endorsement on

teacher self-efficacy. Although there was not a question relating to teacher

endorsement, I was able to backtrack and identify the endorsement of 52

respondents. Of the 52 respondents, eight had an endorsement in mathematics,

about 15%. The percentage of teachers endorsed in mathematics (15%) correlates

to the ratio of eligible secondary vs. elementary teachers who received the survey,

of 315 teachers: 39 secondary and 276 elementary teachers, a ratio of 14%. Based

on this breakdown, I was not able to run a t-test.

Limitation

There is one limitation to the study. It used a self-reporting tool. As with all self-report,

there is a heavy reliance on the honesty and the candidness of participants. Thus, this represents

an important limitation to the study.

Definitions

Self-Efficacy

Self-efficacy can be described as a set of beliefs that affects an individual’s ability to see

a particular task to completion. These beliefs also have an environmental impact as individuals

often choose to spend their time in an area where they experience success. People with high self-

efficacy are more prone to approach adversity with a can-do attitude and are less likely to give

up without completing a task (Jackson, 2002). Bandura (1977) suggests that self-efficacy can be

heightened in four ways: “(1) by personal accomplishment, (2) by seeing others perform the task

6

(if he/she can do it, so can I), (3) by receiving praise and encouragement, and (4) by emotional

urging” (p. 195-199).

Supervisory Leaders Behaviors

Empirical research indicates that school leaders have the unique ability to impact

instruction by providing feedback to teachers (Sergiovanni & Starrat, 2002; Garza, 2001; Texas

Education Agency, 1997). School leaders can affect student learning by influencing teachers’

self-efficacy. This occurs when leaders acknowledge strengths, identify areas of development,

praise extra professional efforts, ask questions for later reflection, and provide suggestions

(Ovando, 2003. Research affirmed that mathematics supervisors can improve instruction and

raise student achievement by observing teachers and providing feedback (Cobb & Jackson, 2011;

Gamage, Adams, & McCormack, 2009) and helping them become better classroom practitioners

(Louis, Dretzke & Whalstrom, 2010; Leithwood et al., 2004; Waters, Marzano, & McNulty,

2003). Ross and Gray (2006) found that leaders can mediate teacher self-efficacy by giving clear

and viable expectations and connecting student performance to direct instruction. Instructional

leaders can also affect teachers’ self-efficacy by accentuating success, giving constant feedback

(Buck, Lee, & Midgley, 1992; Chester & Beaudin, 1996), and concentrating on academic

achievement (Hoy & Woolfolk, 1993). School leaders also contribute to teacher self-efficacy by

reducing teacher stress and providing opportunities for teachers to observe other educators (Ross

& Gray, 2006).

Ross and Regan (1993), Ross, Hogaboam-Gray, & Bruce (2006), and Mascall (2003)

defined teacher efficacy as a group of expectations that contribute to student achievement. Thus,

by helping to support the development of teachers’ self-efficacy, mathematics supervisory

leaders can have an indirect effect on improving learning outcome for students.

7

Teaching Efficacy

Teacher self-efficacy is a teacher’s judgment on their own ability to mediate student

learning (Amor et al., 1976). Teacher self-efficacy can also be defined as teachers’ perceived

ability to successfully execute teaching tasks, such as instructional delivery, classroom

management, etc. (Ashton & Webb, 1986; Guskey & Passaro, 1994; Hoy & Woolfolk, 1993;

Wheatley, 2002). Teacher efficacy has significant implications in the classroom. Guskey and

Passaro (1994) defined teacher self-efficacy as, The extent to which a teacher considers he/she

has the ability to affect a student’s performance, or the teacher’s expectation of his/her ability to

promote desirable results of involvement and learning in students, even those who are conflictive

or who lack motivation.

Significance of the Study

Across subjects and other factors, teachers play a critical role in the teaching and learning

of mathematics. Furthermore, studies show that teachers with higher self-efficacy levels are

better equipped to teach mathematics and to use various strategies to support their students’

learning (Ford, 2012). Thus, helping teachers become more efficacious leads to better

mathematics learning outcomes for students. Mathematics supervisors who effectively build

teachers’ capacity and support the development of teachers’ self-efficacy indirectly impact

student learning. It is important, therefore, that mathematics supervisors identify strategies that

cultivate the development of teachers’ self-efficacy. This study was designed to identify key

supervisory behaviors that can help increase teachers’ self-efficacy. Consequently, study findings

can inform mathematics supervisors of the practices that foster mathematics teachers’ self-

efficacy and, thereby, improve student achievement.

8

Overview of the Study

This research focused on the relationships between teachers’ self-efficacy and their

perceptions of the supervisory behaviors that mathematics leaders use to influence their self-

efficacy. Teachers teaching mathematics in an urban school district were given surveys regarding

their mathematics self-efficacy Math Teacher Efficacy Beliefs Instrument (MTEBI) and the

supervisory practices they perceived impacted their self-efficacy the Leaders Support of Teacher

Efficacy Development Inventory (LSTEDI). The information gathered from the surveys were

analyzed to determine whether there was a relationship between teachers’ perceptions of

supervisors’ behavior and teachers’ self-efficacy. The researcher calculated descriptive statistics

of the two scales and the demographic data and performed ANOVA and multiple regression

analyses using the results of the two surveys and demographic variables. The results identified

the supervisory practices that teachers perceived influenced their self-efficacy and indicate the

effective practices mathematics supervisors can use to impact student learning outcomes in

mathematics.

9

CHAPTER 2 REVIEW OF THE LITERATURE

Many factors affect student achievement, including teachers, school environment,

adequate resources, and demographics (Leithwood, Seashore, Anderson, & Wahlstrom, 2004).

However, empirical research suggests that good instruction may have a stronger mediating effect

than other factors. Many researchers, such as Whitaker (2004, 2012), have a simple answer to

school improvement. Whitaker stated that it’s people, not programs, and posits a two-step

process for school improvement: “get better teachers, and improve the teachers you have” (p. 5).

Similarly, Sanders, Wright, and Horn (1997) asserted that an effective teacher is more

important than any other element in ensuring student success. They stated:

We have been able to get a very fair measure of the school district, the school, and the

individual classroom. And we’ve been able to demonstrate that ethnicity, poverty, and

affluence can no longer be used as justification for the failure [of students] to make

academic progress. The single biggest factor affecting academic growth of any

population of youngsters is the effectiveness of the individual classroom teacher….

[Furthermore,] the teacher’s effect on academic growth dwarfs and nearly renders trivial

all these other factors that people have historically worried about. (Sanders & Horn 1998,

p. 252)

More recently, Hattie (2009) expanded on the prior research and summarized what works

in schools. Hattie identified six main factors that impact student achievement: student, home,

school, curricula, teacher, and teaching strategies. This extensive research identified the teacher

as the primary contributor influencing student achievement. According to Hattie (2003), “It is

what teachers know, do, and care about which is very powerful in this learning equation…as

such excellence in teaching is the single most powerful influence on achievement” (p. 4). As

10

teachers are the most critical component of a strong educational system; the question remains:

What makes an effective teacher?

Self-Efficacy

Empirical research found a strong correlation between student learning and teacher

efficacy beliefs, i.e., the teacher’s confidence in his/her skill (Goddard, Hoy, & Wolfolk Hoy,

2000; Pajares, 1996; Ross, 1992, 1994, 1998; Tschannen-Moran et al., 1998). Self-efficacy, a

primary focus of Bandura’s cognitive theory, is a construct wherein individuals assess their

ability to plan and perform a particular action. People with high self-efficacy are more likely to

approach adversity with optimism and are less likely to give up without completing a task

(Bembenutty & Chen 2005). Bandura (1997) maintained that teachers’ sense of self-efficacy

impacts their ability to perform teaching tasks and to deal with challenging students. According

to Bandura, teachers with high efficacy beliefs are more likely to put forth greater effort to

ensure student learning. Additionally, they are more apt to try alternative methods to reach a

larger sector of their student population. On the other hand, teachers with lower beliefs in their

ability to perform usually blame students’ low performance on the students’ backgrounds and the

students’ own inability to learn (Bandura, 1997).

Tschannen-Moran et al. (1998) suggested that “teacher efficacy affects teachers’

classroom behaviors, their openness to new ideas, and their attitudes toward teaching. Teacher

efficacy also influences students’ achievement, attitude, and affective growth” (p. 215).

Furthermore, teacher efficacy is also task-specific and cyclical. Tschannen-Moran et al. (1998)

contended that, “Greater efficacy leads to greater effort and persistence, which leads to better

performance, which in turn leads to greater efficacy. The reverse is also true” (p. 234). Thus, a

teacher performance that was accomplished with a level of effort and persistence influenced by

11

the performers' sense of efficacy, when completed, becomes the past and a source of future

efficacy beliefs. Over time, their process stabilizes into a relatively enduring set of efficacy

beliefs.

Teachers’ sense of efficacy is also associated with teacher burnout, commitment to

teaching, and the amount of time spent on subject preparations (Bandura, 1997; Milner, 2002). A

body of research identified teacher efficacy as a predictor of a teacher’s interaction with students

and student achievement (see for review Ross, 1998 and Woolfolk Hoy, Hoy, & Davis, 2009).

Teachers' level of effort, the extent to which they persist, and their thoughts and emotional

reaction regarding teaching are all closely aligned with teachers’ sense of self-efficacy (Ashton

& Webb, 1986; Bandura, 1997; Guskey, 1998).

Anderson, Greene, and Loewen (1988) emphasized that a teacher's self-empowerment

influences students’ confidence in their abilities that in turn, supports their learning. Teacher

efficacy has repeatedly been shown to influence how well students learn, even those who may be

difficult or unmotivated (Guskey & Passaro, 1994). Bandura (1997) hypothesized that a teacher’s

sense of self-efficacy affected young children's beliefs regarding themselves and their aptitudes,

particularly among the low achievers. Teachers with high self-efficacy are more capable of

motivating and giving their students’ the confidence to succeed. Thus, finding and developing

teachers with a strong belief in their efficacy can have a significant impact on teacher

effectiveness in the classroom and can serve as an indicator of teacher quality.

Protheroe (2008) identified two critical questions that are at the center of the theoretical

construct of teacher efficacy and address teaching methods, a component of teacher quality:

• “How does a teacher’s sense of efficacy affect his or her teaching? and

12

• Can a teacher’s sense of efficacy, through its impact on teaching, affect student

achievement?” (Protheroe, 2008, p. 43)

Jerald (2007) identified a strong correlation between teachers’ sense of efficacy and their

classroom teaching methods. For example, teachers with a greater sense of efficacy beliefs

displayed greater levels of planning and organization. They were more willing to explore new

ideas and to try new teaching methodologies to meet students’ learning needs. They showed

more resilience and perseverance in the face of adversity. These teachers were also less

pejorative of students mistakes, and less likely to refer a challenging student for special

education (Jerald, 2007).

The studies described in this introduction demonstrate the importance of teachers'

personal efficacy beliefs as part of any platform to improve schools. This literature review

continues with the current research on teacher self-efficacy. The review begins with a description

of the theoretical framework for efficacy beliefs, or self-efficacy, and then discusses

management practices for supporting the development of self-efficacy within teachers.

Effective Teachers

Being an effective teacher requires instructors to master a myriad of skills, including

classroom management, task mastery, and the ability to motivate students (Stronge, 2007). Reed

& Bergemann (1992) and Segal & Wilson (1998) identified knowledge, self-confidence,

enthusiasm, strong communication and management skills clear instruction, and high

expectations, as characteristics of effective teachers. Studies completed by Dembo (2001) and

Randi (2004) suggested self-regulation also plays a central role in defining a teacher's

effectiveness. Self-regulation, as defined by Zimmerman (2000), is the process of maintaining

cognition and motivation to see a task or a set of goals to completion. Teachers with high self-

13

efficacy are better equipped to possess self-regulation, which makes them more likely to give

greater effort and maintain composure in the classroom.

Teacher Self-Efficacy

Nunn and Jantz (2009) characterized self-efficacy as teachers’ perception of their ability

to impact student learning in a positive way. Guskey and Passro (1994) expanded this definition,

stating that teacher efficacy was:

the extent to which a teacher considers he/she has the ability to affect a student’s

performance, [or] the expectation of a teacher of his/her ability to promote desirable

results of involvement and learning in students, even those who are conflictive or who

lack motivation. (p. 636)

Several researchers have attested to the power of teachers’ self-efficacy and its influence

on learning and motivation (Bandura, 1997). Bembenutty (2007) proposed that teachers’ views

of their self-efficacy create a self-fulfilling prophecy of their ability to influence positive student-

learning outcomes.

The Development of Teacher Efficacy Beliefs

Because teachers’ self-efficacy has been related to their effectiveness in the classroom,

researchers, such as Bandura, have sought to explain how one develops these beliefs. Enactive

experiences, i.e., personal achievements, are built on the premise that success breeds success,

while vicarious experiences are obtained by observing others perform a task and learning via

others’ experiences (Hoy & Spero, 2005). Social persuasion is defined as the self-efficacy

garnered from feedback given by valued supervisors, colleagues, and significant others

(Bandura, 1997). Gurvitch and Metzler (2009) denoted social persuasion as a specific type of

encouragement an individual receives before the accomplishment of a task. By receiving

14

reassurances of his/her capabilities, the individual is more likely to exert additional efforts to see

the task to completion. Hoy and Spero (2005) rated social persuasion as limited in its scope with

a temporary effect on a teacher’s self-efficacy. However, social persuasion can serve as an

impetus that leads to the initiation of a task, the attempt of a new strategy, or the additional

pursuit of accomplishment. Physiological and emotional arousal stems from the feelings that

occur after a successful experience. Gurvitch and Metzler (2009) found an individual’s

performance is affected by anxiety level and excitement. The individual garners more self-

efficacy from a feeling of excitement regarding the task; conversely, feelings of anxiety, and

stress negatively affect his/her performance.

Enactive Experiences

Enactive experiences, also referred to as mastery experiences, provide the most effective

foundation for efficacy development. When teachers perceive success in teaching, their belief in

future success significantly increases (Tschannen-Moran et al., 1998). Teachers automatically

raise the bar and set higher expectations for themselves. Perceived failure in teaching is more

likely to lead to further experiences of unsuccessful teaching, except in instances where the

teacher views failure as a learning experience and identifies steps for future improvements

(Bandura, 1993; Tschannen-Moran et al., 1998). Mulholland and Wallace (2001) found that

positive mastery learning is of particular importance for new teachers in the early stages of

developing their self-efficacy. Further, it is important that teachers attribute their positive

outcomes to their abilities and talents.

Pintrich (2000) and Schunk (2001) suggested that teachers who ascribe their success to

external factors outside of their control do not increase their self-efficacy from that particular

experience. Of the sources of efficacy, Ross and Gray (2006) identify mastery experience as the

15

most significant factor in collective teacher efficacy. Teachers who have experienced success as

a group persevere when they encounter similar obstacles in future tasks.

Vicarious Experiences

Teachers can also garner efficacy from vicarious experiences. In these instances, the

learner-teacher is the observer and recipient of the benefit of the other instructor’s experience.

The effectiveness of this method is contingent on the learner teacher's perception of the model

teacher (Bandura, 1997). The self-efficacy of learner teachers increased when they observed a

master teacher, whom they deemed credible. In contrast, self-efficacy of the learner-teacher was

negatively affected when the master teacher's performance was poor. Further, learner teachers

were particularly vulnerable to the performances of master teachers whom the learner teachers

perceived as similar to themselves (Bandura, 1997). As with enactive experiences, vicarious

experiences were particularly crucial for the development of both future teachers and teachers in

their primary years.

Social Persuasion

Social persuasion can be a source of self-efficacy when an individual received feedback

from a valued person, including a teacher, mentor, or principal (Bandura, 1997). The feedback

was influential in direct proportion to the reliability of the giver. As learner teachers received

positive feedback from a valued mentor, they developed a higher level of self-efficacy in their

ability to deliver effective instruction, manage student behavior, and motivate students. Social

persuasion also acted as a short-term boost that balances occasional setbacks. Mulholland and

Wallace (2001) suggested verbal persuasion received from students in the form of engagement

and enthusiasm can be especially powerful for beginning teachers. These findings imply that

self-efficacy of new teachers could be enhanced by placing them in a classroom where they are

16

likely to receive encouragement from their students rather than placing them in challenging

classrooms, which is a common practice.

Emotional/Physiological Arousal

The last source of efficacy is physiological and emotional arousal, which is defined as the

sensation of relaxation and positive feelings (Bandura, 1997). The difference between

emotional/physiological arousal and enactive experience is somewhat difficult to articulate. The

former can be perceived as a byproduct of the enactive experience. Little research, beyond

Bandura’s initial assertions, has been dedicated to this source of self-efficacy. The idea of

arousal is based on the sense of accomplishment after a successful teaching experience which

can motivate and promote future success. Teachers’ self-efficacy is affected by perceived anxiety

and stress. Bandura (1997) suggested that teacher’s physiological states influence their perceived

capability to complete their teaching tasks and affect job performance. Therefore, minimizing

stress and negative influences within the school environment may lead to higher teacher efficacy.

Experience and the Development of Teacher Self-Efficacy

Studies in Canada, the United States, and Korea found that the development of self-

efficacy in prospective teachers is critical since efficacy is minimally malleable once established

(Gorrell & Hwang, 1995; Housego, 1992; Wenner, 2001). The sense of teacher efficacy appears

to increase during both the preparation for teaching and early teaching (Hoy & Woolfolk, 1990;

Spector, 1990). Findings of research conducted in Israel by Romi and Daniel (1999) and in

Taiwan by Lin and Gorrell (2001) found efficacy unchanged or declining based on the number of

years of service beyond the initial 5 years.

Tschannen-Moran and Hoy (2007) analyzed two of the four sources of teacher efficacy:

verbal persuasion and mastery experiences. Verbal persuasion consists of the support and

17

feedback received from administrators, colleagues, parents, and the community; whereas,

mastery experiences stem from prior successful teaching experiences. Tschannen-Moran and

Hoy (2007) found that other factors that might facilitate the task of teaching include the school

level and setting, teachers’ perception of the availability of resources, and the quality of the

school building.

Theoretical Model of Teacher Self-Efficacy

Figure 1 shows a model that graphically displays the relationship among the four sources

of teacher efficacy and the impact of teacher efficacy on the classroom practices of teachers. The

four sources of teacher efficacy are enactive or mastery experiences, physiological and emotional

states, vicarious experiences, and social persuasion (Bandura, 1977, 1997). The strongest of

these four sources is mastery experiences. When teachers perceive their performance to be

successful, their efficacy level increases. Teachers also acquire a sense of efficacy from

observing other teachers’ successful experiences, which is referred to as vicarious experience.

Teachers can also benefit from the accomplishment of their students, which brings about a form

of social arousal. Social persuasion, in the form of verbal feedback, is also another source of self-

efficacy. As teachers are exposed to one of the four sources of self-efficacy, their self-efficacy

increases. Increased self-efficacy leads to improvement in the teachers’ practices.

18

Figure 1. Theoretical model of teacher self-efficacy. The model depicts the relationship between

the four sources of teacher efficacy and teacher practices.

Measuring Teacher Self-Efficacy

The metrics and methods used to assess teacher self-efficacy have continually evolved

and include questionnaires, Likert-type scales, and interviews. The most enduring measure of

teacher self-efficacy stemmed from two Rand Corporation assessments of inventive educational

programs funded by the Federal Elementary and Secondary Education Act (Armor et al., 1976;

Berman, McLaughlin, Bass, Pauly, & Zellman, 1977). Initially, teacher efficacy in the Rand

Corporation research was measured utilizing a two-item scale. Teachers were asked to provide

their level of agreement with two statements. The first statement was: “When it comes down to it,

a teacher really can’t do much because most of a student’s motivation and performance depends

on his or her home environment.” Teachers who identified with this statement believed that

external factors overwhelm the teacher’s ability to produce student learning. General teaching

efficacy is based on this assertion, and it identifies the many factors the teacher perceives as

having a stronger influence on student learning than a teacher. Such factors can include the

student's home, economic status, and gender (Tschannen-Moran & Hoy, 2001).

Enactive Experiences

Vicarious Experiences

Persuasion

Emotional Arousal

Self-Efficacy Teaching Practices

Theoretical Model of Teacher Self-Efficacy

19

The second item on the Rand assessment stated: “If I really try hard, I can get through to

even the most difficult of unmotivated students.” Teachers who aligned themselves to this

statement acknowledged their ability to motivate and engage students in their learning. They

took ownership of the effectiveness of their own teaching in reaching students. These teachers

suggested they have the amount of training and preparation needed to meet the challenge posed

by their students (Tschannen-Moran & Hoy, 2001).

A second Rand Corporation study (Berman et al., 1977) used Rotter’s (1966) learning

theory, which proposed that, when positive results reinforce a behavior, the individual is likely to

repeat the behavior. The study measured teacher efficacy by deriving a total score using two 5-

point Likert scales. Hoy and Spero (2005) maintained the second factor was inconsistent with

Bandura’s (1986) theory. Researchers suggested the second element, teaching efficacy, described

teacher attitudes toward teaching and learning rather than their personal self-efficacy

(Tschannen-Moran et al., 1998; Hoy & Woolfolk, 1990; Woolfolk & Hoy, 1990). In 1984,

Gibson and Dembo expanded on the Rand scale by developing a 30-item measure that yielded

two factors—self-efficacy and teaching efficacy (Gibson and Dembo, 1984). Bandura (1997)

later developed a 30-item instrument that provided a multi-faceted, non-specific depiction of

teacher self-efficacy. Nunn and Jantz (2009) used the Teacher Efficacy Beliefs and Behaviors

Scale (TEBBS) to measure teacher self-efficacy.

The development of scales to measure teacher self-efficacy beliefs (TEB) has

progressively evolved. While Bandura (1997) established a scale consisting of 30 items rating

seven areas of efficacy, Tschannen-Moran and Hoy (2001) created a 24-item measure named the

Teachers’ Self-Efficacy Scale (TSES). Charalambous et al. (2008) translated the TSES

instrument, modified the scale to measure the mathematics teaching self-efficacy, and used it to

20

gauge the development of efficacy in pre-service teachers. They recorded interviews and

determined that the TSES is useful for measuring a teacher’s perceived self-efficacy in

mathematics. Measuring self-efficacy is an abstract construct that many researchers continue to

investigate to gain a better understanding of the impact of individual and collective beliefs on

learning and teaching, task completion, and overall performance. Each of the scales mentioned

above expanded the research on measuring efficacy.

Skaalvik & Skaalvik(2007) created a scale consisting of the following six subscales: “(a)

instruction, (b) adapting education to individual students’ needs, (c) motivating students, (d)

keeping discipline, (e) cooperating with colleagues and parents, and (f) coping with changes and

challenges.” The researchers included four items in each subscale and attempted to determine if

the dimensions of self-efficacy could be separated from both external control and collective

teacher efficacy. Collective efficacy can be defined as the belief that a group of teachers holds in

their capacity to bring about positive changes in their students’ academic performance (Hattie,

2009). The research confirmed that teacher self-efficacy is a multi-dimensional construct. Six

separate but correlated dimensions of efficacy were identified. The strongest correlation was

between teacher self-efficacy and teacher burnout.

Self-Efficacy and Educational Practices

Self-efficacy also influences teachers’ educational practices. Teachers with higher self-

efficacy approach teaching and learning differently (Gibson & Dembo, 1984). Self-efficacy impacts

several areas of teaching, including academic decision making, goal attainment, and

perseverance to task completion. These areas can have significant implications for teachers’

long-term classroom effectiveness (Bandura, 1993). Allinder (1994) demonstrated that teachers

with high efficacy beliefs spend more time than others developing and organizing lessons that

21

engage and motivate students. These teachers are likely to invest more effort into their teaching

methods and career advancement than others. Teachers’ perceptions also influence their

receptiveness to using a variety of materials and strategies to meet their students’ learning needs

(Ghaith & Yaghi, 1997; Wertheim & Leyser, 2002).

Collective efficacy fosters the willingness to assist other teachers which results in teacher

collaborations that lead to innovative teaching methods. Collective efficacy focuses on the ability

to accomplish organizational goals despite setbacks. Goddard, Hoy, & Woolfolk Hoy (2000)

defined collective efficacy as “the perceptions of teachers in a school that the efforts of the

faculty as a whole have a positive effect on students” (p. 480). Jex & Bliesse, (1999), Koh et al.

(1995) and Park (2004) ascertained that teachers who are involved in these efficacious

connections and are faithful to the values of their organizations tend to adopt instructional

practices proposed by their organization. In addition to being open to innovative practices,

teachers with strong efficacy beliefs are more likely to set high objectives for their students and

for themselves, to display lower propensity for dropping out, and to be less likely to experience

burnout (Bandura 1997; Brouwers, Evers, & Tomic 2001; Gordon et al., 1998; Henson, 2002).

While there have been prior studies that demonstrate a correlation between teacher self-

efficacy and student successful learning outcomes, the research of Nunn and Jantz (2009)

explicitly considered teacher efficacy in the context of response-to-intervention programs. The

study revealed that teacher efficacy beliefs were closely aligned with teachers’ propensity to

become involved in collaborative teamwork and their knowledge of implementation practices.

There was a higher level of involvement among teachers who were more confident in their

intervention and motivational skills than other teachers.

22

Self-Efficacy and Adversity

Teachers with greater confidence in their abilities are more resilient in the face of

adversity (Tschannen-Moran et al., 1998). This partially explains their willingness to use new

approaches. It also may have broader implications ranging from the teachers’ ability to complete

training programs for dealing with discipline and race issues.

Bembenutty (2007) found that self-efficacy impacts teacher training completion. Results

from the study identified a strong link between teachers' motivational beliefs and their use of

monitoring strategies to guide their preparation studies. Bembenutty’s (2007) study showed that

using the four sources of motivation to empower pre-service teachers with self-efficacy could

reduce attrition from teacher certification programs. The research suggests that teacher training

programs should include both firsthand and secondhand instructional experiences designed to

increase their self-efficacy.

Milner and Hoy (2003) found a correlation between teacher self-efficacy and resilience.

The researchers studied a teacher who was the sole female African American teacher among a

staff of 126 members working in an affluent school with 86% European American students. The

study is rather unique because teacher self-efficacy and persistence as they pertain to teaching

minority groups have been minimally explored. This research is anchored in both the theory of

stereotype threat and teacher self-efficacy. Stereotype threat represents "the self-imposed

pressure felt by individuals who fear that they may feed or add credence to negative perceptions

that exist regarding their ethnic group" (Steele, 1997, p. 614).

Milner and Hoy (2003) noted that, unlike the mostly quantitative work done in the field,

their study used a qualitative approach that incorporated context observations and interviews

over 5-months. Milner and Hoy (2003) conducted numerous interviews with the study

23

participant exploring how the participant’s self-efficacy progressed over the years. The subject

was an experienced, well-educated teacher who had earned a doctoral degree and two master’s

degrees. She reported she felt a compelling need to do well as an instructor in order to positively

represent her ethnic group. She also embraced the need to impart knowledge on race issues to her

students to refute negative stereotypical beliefs. In addition, the subject assumed the duty of

educating the other teachers regarding the needs of African American students.

The study revealed that the teacher felt that she had been ostracized in the educational

system from the start because of her ethnicity and education. The teacher also carried the weight

of stereotype threat because she did not want to contribute to any negative perceptions that the

other staff members may have already had about her ethnic group. She placed great emphasis on

the respect that she received from her students and her parents. The teacher also took pride in her

ability to work with the students whom other teachers had difficulty handling. Despite these

successes and the respect that the teacher had earned from her students and parents, she still felt

the rejection of her colleagues. This teacher took comfort in her education and the resilience that

helped her earn a Ph.D. among White students. She persisted in spite of the strain of feeling

isolated. She set out on the momentous task of fighting negative perceptions that eroded her self-

efficacy. However, she used prior success in a similar setting to overcome her current challenges.

The importance of using mastery experiences to develop self-efficacy is significant in keeping

teachers motivated and more focused on achieving expectations.

Hoy and Spero, (2005) found that teachers who were rated highly in self-efficacy also

were more likely to feel that they were supported by their community and colleagues and to be

more satisfied in their roles. These researchers studied 53 prospective teachers enrolled in the

master’s education program for initial certification. The participants were from diverse

24

demographic backgrounds. The researchers collected data in three phases: (a) during the first

quarter of the teacher preparation, (b) at the end of the teacher training, and (c) at the end of the

first year of teaching. The participants used a code to identify themselves to ensure anonymity.

The researchers gathered information regarding the quality of available teaching resources and

the support they received from colleagues and community. Hoy and Spero (2005) found a

correlation between changes in efficacy during teachers’ early years of teaching. The study

participants reported higher their efficacy score at the end of the first year which correlated to

success and satisfaction with their teaching assignment, and a positive relationship between the

change in efficacy and the teachers’ perceived level of support.

Self-Efficacy and Group Effectiveness

Other studies have documented the role of self-efficacy on group effectiveness. Baker

and Campbell (2005) analyzed the dynamics of group study tasks and the attributes required for

team success. The theories of the effectiveness of groups are based, in part, on the assumption

that individuals are willing to work harder for the benefit of the group. However, each member

of the group must feel they contribute a valuable part to the group’s success. These group study

exercises highlighted the increased self-confidence and feelings of efficacy for group members

(Baker and Campbell, 2005). Several studies (Hoy & Spero, 2005; Milner & Hoy, 2003; Baker &

Campbell, 2005) demonstrated how efficacy feelings can mitigate adverse situations. Self-

efficacy can be an important tool for dealing with the many tough situations that teachers face.

Confidence and perseverance are both related to a teacher’s ultimate success.

Self-Efficacy and Teacher Attrition/Burnout

The ability to face hardships has direct implications for teacher retention. Betoret (2006)

found teachers with lower self-efficacy had more difficulties in teaching and experienced higher

25

job-related stress levels. Klassen et al. (2009) identified that these teachers also had less job

satisfaction. Bakker & Schaufeli (2000) and Vandenberghe & Huberman (1999) proposed that

the level of stress experienced by teachers over the course of their careers can, at times, lead to

depression, exhaustion, poor performance, or attitude and personality changes. This stress also

may lead to illness and premature retirement. Chwalisz, Altmaier, and Russell (1992) suggested

a relationship between teacher self-efficacy and teacher burnout. Teachers with higher self-

efficacy experienced lower levels of burnout and were more competent classroom management

and discipline than teachers with lower self-efficacy.

Santoro (2011) stated that teacher attrition is affected by a teacher's perspective related to

the reward of the teaching task rather than to deficiencies in preparedness, commitment, or

competence. Empirical research suggests teachers in the United States, despite the lack of

material rewards and status, attract individuals with a sense of mission and altruism (Crocco &

Costigan 2007; Freedman & Appleman, 2008, 2009; Margolis & Deuel, 2009; Ng & Peter, 2010;

Stotko, Ingram, & Beaty-O’Ferral, 2007). Other researchers also have found that the essence of

teaching encompasses morals, values, and principles (Buchmann, 1986; Campbell, 2008; Carr,

2006; de Ruyter & Kole, 2010; Goodlad, Soder, & Sirotinik, 1990; Jackson, 1992; Jackson &

Bedford, 1965; Lortie, 1975; Margolis & Deuel, 2009; Pring, 2001; Richardson &

Fenstermacher, 2005). Teachers become disengaged and, at times, depressed about the

profession when the teaching task no longer yields altruistic value for them. Over time, a

constant feeling of exhaustion is referred to as teacher burnout (Schwarzer & Hallum, 2008). The

loss of a sense of altruistic value can be related to decreasing efficacy feelings personally or

about the profession in general.

26

Skaalvik and Skaalvik (2010) suggested: “external control or teachers' beliefs that

factors external to their teaching puts limitations to what they can accomplish was negatively

related to both teacher self-efficacy and collective teacher efficacy” (p. 1060). Many external

factors affect teachers’ ability to be effective in the classroom, including teacher preparedness,

available resources, school environment, and student readiness. Valli, Croninger, Chambliss,

Graeber, and Buesi (2008) found that high-stakes accountability had a destructive effect on

teaching and learning, resulting in a visible decline in good teaching from 2002 to 2005.

Research suggests that the No Child Left Behind Act (NCLB) negatively affected efforts to

improve the number of quality teachers as a result of pedagogical constraints, constricted

curriculum, and the disadvantage of working in schools labeled as "needing improvements."

Fenstermacher and Richardson (2005) maintained that “Quality teaching is often presumed to be

simply successful teaching, wherein the learner learns what the teacher teaches. Yet we have

seen that when successful teaching is disconnected from good teaching, the results are seldom

favorable for either the student or the subject matter under study” (p. 192).

Santoro (2011) revealed that teachers know the essence of good teaching. They are,

however, restrained from enacting good teaching by restrictive pedagogical policies. Calhoun

(2003) determined that burnout in high-needs schools transpires because the enormity of the

teaching task in these settings exceeds the capability of a single person. Many situations, such as

increasing external pressures, the loss of autonomy, and the loss of feeling that you can have an

altruistic impact on the community, may decrease feelings of self-efficacy (Johnson & Birkeland,

2003; Johnson, 2004). As these environmental factors grow, the likelihood of teacher burnout

and attrition also increases (Goddard & O’Brien, 2003). Finding ways to decrease these

27

environmental factors which lead to a decrease in teachers’ self-efficacy is, therefore, vitally

important.

Supporting the Development of Teacher Self-Efficacy

School leaders play a critical role in the development of teachers and teacher self-

efficacy. Tschannen-Moran and Hoy (2007) conducted a study with 255 teachers attending

graduate school at Ohio and Virginia state universities. The study also included volunteer

teachers from two elementary schools and one high school in the same states. Teaching

experience ranged from one to 29 years. Demographic data included the work setting (suburban,

urban, or rural), the grade level taught, gender, and ethnic background. The teachers also rated

their perceived level of support, available resources, and level of satisfaction with their

professional performance.

The researchers found that self-efficacy of novice teachers was lower than that of

experienced teachers, although they did not identify significant differences in the self-efficacy

area of student engagement (Tschannen-Moran & Hoy, 2007). The authors hypothesized that

student engagement was still a new focus in education that had not been well researched. They

also postulated that student engagement was related to personality and character. This study

found that race, gender, and school setting did not affect efficacy in either novice or experienced

teachers. Tschannen-Moran and Hoy (2007) identified teaching resources and interpersonal

support as contributory factors in novice teachers’ self-efficacy. The study found that the self-

efficacy of both novice and experienced teachers was, to some degree, the result of mastery or

enactment. The study also suggested verbal persuasion played a progressively less significant

role in maintaining teachers’ self-efficacy.

28

Studies in Canada, the United States, and Korea found that the development of self-

efficacy in prospective teachers is critical, as efficacy is minimally malleable once established

(Gorrell & Hwang, 1995; Housego, 1992; Wenner, 2001). The sense of teacher efficacy appears

to increase during teacher preparation and early teaching (Hoy & Woolfolk, 1990; Spector,

1990). Research conducted in Israel by Romi and Daniel (1999) and in Taiwan by Lin and

Gorrell (2001) found efficacy unchanged or declining based on the number of years of service

beyond the initial 5 years.

The Role of School Leaders

Empirical research demonstrated that school leaders have the unique ability to impact

instruction by providing authentic feedback to teachers (Garza, 2001; Sergiovanni & Starrat,

2002; Schultz & Weinstein, 1990; Texas Education Agency, 1997). School leaders encourage

teacher effectiveness by providing authentic feedback that supports teacher development. School

leaders also can use the knowledge of social persuasion to influence teachers’ self-confidence

and, thereby, student learning. For this reason, school districts seek comprehensive, student-

centered evaluative methods to provide teachers feedback and professional development

(Ovando, 2001).

Ovando (2005) ascertained the need for formative feedback to teachers to guide

instructional practices and for principals use classroom observations to assess teaching and

learning. Further, Stronge (2005) identified accountability and professional development as two

important constructs of teacher evaluation. The Texas Principal Leadership Initiative (1999)

argued that data should be methodically collected, analyzed, and given to teachers and students.

Glickman, Gordon, & Ross-Gordon (2001) found that teacher development occurred at differing

stages of consciousness and concern. They recognized the need for feedback to be

29

developmentally appropriate to the teacher’s functional stages of cognitive, conceptual, and

moral development. Glickman and Gordon (1987) proposed that “Teachers with lower

developmental levels need more structure and direction; teachers at higher developmental levels

need less structure and more active role in decision making” (p. 64).

Ross and Gray (2006) focused on the principal’s role in mediating student achievement

via teacher development. While school districts continue to hold principals accountable for

student learning, research has found that the direct impact of principals on student achievement

is null (Hallinger & Heck, 1996; Leithwood, Jantzi, & Steinbach, 1999; Witziers, Bosker, &

Kruger, 2003). However, studies suggest principals can indirectly impact student learning by

fostering a positive learning environment and empowering teachers (Hallinger, Bickman, &

Davis, 1996).

Ross and Gray (2006) studied the influence of principals’ indirect leadership on student

achievement. Principals who empowered teachers and fostered a professional commitment to

organizational values had a small impact on student achievement. Ross and Gray (2006)

suggested that teachers’ collective efficacy mitigates principals’ minimal impact on student

achievement. Ross and Gray’s (2006) study suggests principals' transformational leadership

positively affects teachers’ collective efficacy that, in turn, contributes minimally to student

achievement. Ross and Gray (2006) proposed the strongest effect on achievement stemmed from

teacher commitment to the learning community and the collaborative partnership.

Empirical research identified transformational leadership as a stronger precursor for

teacher beliefs than transactional leadership. Transformational leadership encompasses the use of

charisma, intellectual stimulation, and individual consideration to improve a system by

motivating the group and solidifying core values. The research model suggests transformational

30

leadership impacts teachers’ commitment to organizational values (Koh et al., 1995; Ngumi,

Sleegers, & Denessen, 2006).

Ross and Gray (2006) proposed that transformational leadership adds to collective

teacher efficacy via the constructs of efficacy identified by Bandura (1986). Principals impact

collective efficacy by setting attainable goals and clear expectations as well as by connecting

student achievement to teacher actions (Lee, Buck, & Midgley, 1992). Principals can also impact

self-efficacy by developing an academic culture (Hoy & Woolfolk, 1993), by giving consistent

feedback (Chester & Beaudin, 1996) and through persuasion, vicarious experience, and reduction

of stress factors in the school.

Drago (2011) suggested nurturing enduring growth and development; leaders need to

move away from informational learning and focus on transformational learning. Drago defined

transformational learning as a construct that alters the way one makes meaning of experiences.

Drago posited that to gain an understanding of transformational learning, adults must first

identify the way they learn, which is referred to as ways of knowing. Ways of knowing affect the

way adults make meaning. School leaders who use different models of support and challenges

promote the development of adult learners and their internal capacities.

Ways of knowing also influences the adults’ perception, expectations, and requirements

of leaders, facilitators, and mentors. The constructive-developmental theory of Drago (2004)

identified school leaders’ need to understand and use the core elements of care, respect, trust,

collaboration, and intentionality to build their teachers’ capacity to affect student learning.

Ensuring transformational learning requires a high level of trust. Administrators need to develop

their own capacities to support the d\development of both students and adults. Understanding

31

ways of knowing helps leaders differentiate their approaches in order to meet the diverse

learning needs of teachers (Drago, 2004).

Conceptual Model of Leader Effect on Teacher Self-Efficacy

Figure 2 displays the conceptual framework of teachers’ development of self-efficacy as

mediated by administrative feedback\k, peer observation, positive experiences, and

encouragement. A body of research demonstrates that school leaders (i.e., principals,

administrators, department heads, and peers) play an essential role in the development of teacher

efficacy (Garza, 2001; Sergiovanni & Starrat, 2002; Schultz & Weinstein, 1990; Texas

Education Agency [TEA], 1997). When teachers receive positive feedback from school leaders,

their self-efficacy increases as they experience emotional arousal, social persuasion, and enactive

experiences. Teacher’s efficacy is also mediated vicariously when administrators provide the

time observation and collaboration among peers.

32

Enactive

Experiences

Vicarious

Experiences

Emotional Arousal

Persuasion

Development

of

Self-Efficacy

Strengthened

Teaching

Practices

Conceptual Model of Leader Effect on Teacher Self-Efficacy

A

D

M

I

N

I

S

T

R

A

T

O

R

Sources of Self-Efficacy Strategies

Modeling

Supporting Coaching

Supporting Collaboration

Promoting Professional

growth

Protecting Instructional

Time

Fostering Autonomy

Emphasizing Teaching and

learning

Giving Feedback

33

Figure 2. Conceptual model of leader effect on teacher self-efficacy. The model displays the

relationship between the principal leadership, the four sources of teacher efficacy and teacher

practices.

Summary

A wealth of literature in the education field confirms the relationship between teacher

self-efficacy attitudes and student achievement. Self-efficacy describes teachers’ belief in their

ability to impact student learning, while collective efficacy refers to the teachers’ belief that they

can have an impact as a faculty or professional group in meeting goals at the organizational

level. In fact, a teacher’s belief in his/her own ability to have an impact can become a self-

fulfilling prophecy (Schilling & Schilling, 1999). Research suggests that teacher efficacy is more

pliable within the first few years of teaching (Bandura, 1997; Mulholland & Wallace, 2001).

Thus, it is imperative for training programs and school leaders to instill these positive beliefs

early in a teacher’s tenure. Bandura (1997) found that self-efficacy can be developed through

four primary methods—first-hand experiences, observations of others, feedback, and emotional

responses to positive experiences.

Teacher self-efficacy has several potential influences on student achievement. Teachers

with high self-efficacy set high expectations for themselves and their students and are more open

to innovative practice. Further, they are more resilient to hardships and less prone to burnout.

Given the importance of teacher self-efficacy on student outcomes and the school

environment, leaders must find positive ways to impact its development through their teachers.

Many studies have suggested that leaders can have an indirect influence on student achievement

by providing teachers constructive feedback that builds their confidence. Also, researchers

emphasized a transformational leadership approach based on charismatic leadership and a

positive environment that helps teachers buy into organizational values. More research is needed

34

for in-depth analyses of leaders’ ability to develop teacher self-efficacy that influences student

achievement.

While teacher efficacy is still difficult to measure, a teacher’s mindset is just as important

as their skill set and certifications. This mindset can change over time if new leadership or other

hardships reduce their belief in their impact and talents. Thus, it is important for leaders to

remain steadfast in their commitment to supporting teachers and creating an organizational

environment that promotes growth.

35

CHAPTER 3 RESEARCH DESIGN AND METHODOLOGY

This chapter includes a description of the methods and procedures I used to gather and

analyze the data collected in this study. This research, a descriptive, correlational study, focuses

on teachers who teach math’ self-efficacy. In this research, I investigated mathematics teachers'

perceptions of their self-efficacy and the effects of teacher characteristics and supervisory

behaviors on teachers’ self-efficacy. This chapter describes the research questions, design,

scales, and metrics and includes a description of the sample and instruments. It also contains the

procedures for data collection and analysis. The results of this research may benefit educational

supervisors when they consider the type of supervision and supportive actions to adopt to foster

the development of mathematics teachers’ self-efficacy.

Research Questions

The following research questions are addressed:

1. What are teachers’ perceptions of their mathematics teaching self-efficacy?





Research Design

This research is a descriptive, correlational study focused on mathematics teachers'

perceptions of their self-efficacy and the effects of teacher characteristics and supervisory

behaviors on teachers’ self-efficacy. I used the correlational design to identify trends and patterns

in the data that can help determine the extent of the relationship between teachers’ perceptions of

36

self-efficacy and supervisors’ behaviors (Johnson & Christensen, 2008). I also identified and

evaluated strategies which teachers reported their supervisors use to enhance teacher self-

efficacy. Additionally, this study sought to determine the relationship between teachers’

descriptions of supervisors’ behaviors and teacher’s perceptions of self-efficacy.

Sample

The study included all teachers who teach mathematics in 13 elementary schools and all

secondary mathematics teachers in three middle and three high schools. All schools were in one

urban school system in the southern area of the United States. The study participants were

teachers who were, at the time, teaching mathematics. These teachers were chosen because they

taught mathematics, which affects school accreditation and graduation requirements.

Choosing teachers at both the secondary and elementary levels for this survey provided a

robust and diversified group of educators. A letter from the math supervisor of the participating

school district invited all teachers who were teaching mathematics in the district to participate in

the research. Teachers at the schools who opted to participate and complete the survey formed

the sample. It was expected that the sample would be comprised of approximately 70 teachers.

Instrumentation

The study collected and compared responses of participants to a demographic survey and

two mathematics scales. The following teacher demographic data were collected: years in

education, years at the current school, gender, and ethnicity. These demographic variables were

collected because several studies found a relationship between teachers’ gender and their beliefs,

job satisfaction, and stress level and self-efficacy (Chaplain, 2008; Klassen & Chiu, 2010; Liu

&Ramsey, 2008). Milner and Hoy (2003) identified a link between teacher self-efficacy,

37

ethnicity, and stereotype threat. The demographic data were used as covariates in the analyses.

The demographic questionnaire is included in Appendix A.

Additionally, teachers were asked to complete two instruments. The Mathematics

Teacher Efficacy Beliefs Instrument (MTEBI) was used to measure teachers’ perceptions of math

teaching self-efficacy, which addressed the first research question. I developed the Leaders

Support of Teacher Efficacy Development Inventory (LSTEDI), an instrument for teachers to

report their perceptions of mathematics supervisors’ behaviors. I used this instrument to address

the second research question. I used teachers’ responses to the LSTEDI and the MTEBI to

examine the relationship between teachers’ math efficacy and their perception of the behaviors

of their math supervisors (the third research question). Teachers responded to the scales online.

Each instrument is described in detail in the following sections.

Mathematics Teaching Efficacy Beliefs Instrument

According to Ernest’s theories (1989), teachers’ beliefs about mathematics are reflected

in their models of teaching. McGee & Wang (2014) suggested that a teacher’s belief system is

affected by the nature of mathematics teaching and his or her ideas about mathematical concepts.

The MTEBI was used to measure participants’ perceptions of their personal mathematics

teaching efficacy and their mathematics teaching outcome expectancy.

The MTEBI instrument stemmed from a revision of the Science Teaching Efficacy Beliefs

Instrument (STEBI) created by Riggs and Enochs (1990). Enochs, Smith, and Huinker (2000)

revised the instrument to measure teachers’ mathematics efficacy in two constructs: their

personal mathematics teaching efficacy and their mathematics teaching outcome expectancy

(McGee & Wang, 2014). The MTEBI is anchored in Bandura’s theory of measuring teacher

efficacy.

38

The MTEBI is comprised of Likert-type items. It includes 21 questions with two

subscales: the Personal Mathematics Teaching Efficacy (PMTE), a 13-item subscale with scores

ranging from 13 to 65 and the Mathematics Teaching Outcome Expectancy (MTOE) which has

eight items with scores from 8 to 40 (Enochs & Riggs, 1990; Riggs & Enochs, 1989). The

response set spans from strongly agree (5) to strongly disagree (1). The PMTE measures a

teacher’s belief in his or her ability to teach mathematics effectively, and the MTOE deals with a

teacher’s belief that effective mathematics teaching leads to student learning. A higher score on

the PMTE indicates a teacher has a stronger belief in his/her ability to teach mathematics

effectively; a higher score on the MTOE signifies a strong belief that students can learn

mathematics from good teaching (Enochs, Smith, & Huinker, 2000). Appendix B includes a

comparison of revised survey items; Appendix C includes a list of final items on the revised

MTEBI subdivided by the two subscales, Personal Self-Efficacy, and Outcome Expectancy.

Documentation of permission to use the MTEBI is displayed in Appendix D.

The MTEBI measures two distinct constructs, personal mathematics teaching efficacy

(PMTE) and mathematics teaching outcome expectancy (MTOE). Since the creation of the

MTEBI, the instrument has been used in numerous studies and has been deemed a valid and

reliable instrument for measuring personal mathematics teacher self-efficacy beliefs and

mathematics teaching outcome expectancy. Enochs, Smith, and Huinker (2000) found that the

MTEBI has a reliability factor similar to the STEBI, with an alpha coefficient of 0.76. Cronbach

Alpha coefficients for the MTEBI can be found in two studies described in Table 1. In each of

these studies, the PMTE and the MTOE subscales were found to have very strong internal

consistency as measured by Cronbach’s alpha. More than 200 articles have cited it (Alkhateeb,

2004; Bleicher, 2004; Briley, 2012; Brown, Westenskow, & Moyer-Packenham, 2011; Bursal &

39

Paznokas, 2006; Mulholland, Dorman, & Odgers, 2004; Newton, Leonard, Evans, & Eastburn,

2012). In the present study, a slightly modified version of the MTEBI was used. I adapted the

instrument for practicing math teachers as opposed to preservice teachers. The analysis of the

results identified math-teaching efficacy of the participating teachers. To check if modifications

affected the reliability of the instrument, I used Cronbach’s alpha and compared the results to

previous studies as found in Table 1.

Table 1

Cronbach Alpha Reliability Coefficients from Two Previous Studies

Study Participants Inventory Items Subscales

PMTE MTOE

Alkhateeb (2004) 144 Jordanians

undergraduate students

MTEBI 21 items in

original scale

.84 .75

Enochs et al. (2000) 324 Elementary

preservice teachers

MTEBI 21 items in

original scale

.88 .77

Leaders Support of Teacher Efficacy Development Inventory

I used the Leaders Support of Teacher Efficacy Development Inventory (LSTEDI) to

identify teacher perceptions of supervisory behaviors that may affect teacher self-efficacy. Math

specialists reviewed the instrument for face validity. Cronbach’s alpha was computed to

determine reliability. The test is important to assess the level of covariance in the items on the

test (Goforth, 2015). Although I employed a statistical software called JMP (pronounced "jump")

to calculate the Cronbach’s alpha, it can be calculated utilizing the following formula:

𝛼 = (𝑘

𝑘 − 1) (1 −

∑ 𝜎𝑦𝑖

2𝑘𝑖=1

𝜎𝑥2

)

Where k represents the number of scale items

𝜎𝑦𝑖

2 represents the variance associated with item i

𝜎𝑥2 represents the variance associated with the observed total scores

40

Bandura’s (1977) theories suggest a correlation between teachers’ self-efficacy and the

investment that teachers put in their teaching, their goals, and their resilience when faced with

difficult situations. The LSTEDI instrument was based on Bandura’s (1997) four sources of

efficacy development for teachers: mastery experiences, vicarious experiences, social

persuasions, and physiological arousal. The instrument yielded four sub-scores, which I

employed in regression analysis of math supervisors’ behaviors and the perception of teacher

self-efficacy.

An additional source of items for the LSTEDI is the symbolic interaction theory (Blumer,

1969; Mead, 1934). Blase and Blase (1999) analyzed teachers’ perspectives on effective

instructional leadership. The symbolic interaction theory identifies meanings that are constructed

by individuals in social settings (Blase & Blase, 1999). The researchers created an open-ended

questionnaire to analyze the characteristics of school leaders that positively influence teaching

and learning. Based on the collective responses, Blase and Blase pinpointed a model of effective

instructional leadership. Several of the LSTEDI questions were constructed utilizing the

identified traits that effective supervisors used to influence teachers positively (Blase & Blase,

1999).

The LSTEDI instrument was created with the support of professors and other

professional practitioners. The LSTEDI is comprised of Likert-type items. The instrument uses a

five-point Likert response set ranging from strongly agree (5) to strongly disagree (1).

Respondents also rate the effectiveness of the strategy on a scale from extremely effective (5) to

not effective (1). The LSTEDI was used to measure teachers’ perceptions of their supervisors’

strategies to improve teacher math teaching efficacy and the effectiveness of these strategies.

Once developed, the questions were correlated and clustered using the four sources of teacher

41

efficacy (Bandura, 1999). Listed below are the overarching strategies (Blase & Blase, 1999) that

partially guided the development of these questions. In Table 2, these strategies are categorized

by the source of efficacy. A draft of the instrument can be found in Appendix E.

Table 2

Supervisor Strategies Related Sources of Teacher Efficacy

Sources of Efficacy Supervisor Strategies

Enactive Experiences Promoting professional growth

Encouraging and supporting the redesign of programs

Applying the principles of adult learning, growth, and development to staff

development

Implementing action research to inform instructional decisions making

Vicarious Experiences Modeling Teaching Skills

Emphasizing the study of teaching and learning

Supporting collaboration among teachers

Providing time and opportunities for peer connections among teachers

Supporting the development of coaching relationships among teachers

Verbal Persuasion Giving feedback, serving as “another set of eyes” and “critical friends.”

Making Suggestions

Giving Praise

Emotional Arousal Talking frequently and openly to teachers about instruction

Using inquiry and soliciting advice and opinions from teachers about

classroom instruction

Data Collection

After obtaining permission from the district, I informed the leadership of each school of

the survey and asked them to invite their math teachers to participate in the study. Appendix F

includes a copy of the school district research approval letter. The teachers were then contacted

via e-mail for informative purposes and invited to participate. A copy of the content of the email

sent to teachers is provided in Appendix G. Teachers were also advised of the expected date of

the survey. They received an e-mail detailing the purpose of the study and a link to access the

42

study. I attempted to correct e-mails that came back as undeliverable. Each teacher was advised

of the Institutional Review Board regulations regarding human subjects and their rights as a

research participant. Teachers denoted informed consent by responding to the survey. Appendix

H contains a full copy of the Institutional Review Board Approval. A two-week window was

allocated for teachers to respond to the surveys. At the end of the two-week period, a reminder e-

mail was sent to encourage teachers to complete the survey within a week. Teachers who

completed the surveys had an opportunity to win one of three $25 gift certificates for Walmart.

All teachers who received the initial invitation to participate received a note expressing gratitude

for their participation.

Data Analysis

Data were collected from all teachers who teach mathematics from the participating

school district who elected to respond to the surveys. Teacher responses were collected with

Qualtics software, which was also used to provide descriptive statistics. I conducted a one-way

ANOVA (analysis of variance) to compare group means by ethnicity, highest degree, years of

teaching, and years at the current school on the two scales, the MTEBI, and the LSTEDI. The

ANOVA allowed me to test for statistical significance. Table 3 lists the variables used in this

study.

43

Table 3

Study Variables

Demographic Variables Dependent Variables

Years of experience MTEBI Personal efficacy (PMTE)

Math teaching efficacy (MTOE)

Years at current school

Gender LSTEDI Personal efficacy (PMTE)

Level of education Math teaching efficacy (MTOE)

Ethnicity Enactive

Vicarious

Verbal persuasion

Emotional arousal

The LSTEDI scale is subdivided into four subscales that are based on the four sources of

teacher efficacy: enactive, vicarious, verbal persuasion, and emotional arousal. For each of these

variables, I calculated the reliability coefficient (α) and Pearson Product-Moment coefficient

correlations and performed an ANOVA for the two instruments using the demographics as

controls. I used the Pearson Product Moment correlation coefficient (r) and ANOVA to

determine whether an association existed between teacher beliefs and the demographic data. I

also determined the nature of the association and the magnitude of the relation. Because the

demographic data resulted in more than two groups, I conducted an ANOVA to compare the

group means to identify any statistically significant differences.

Using multiple regression analyses, teacher perceptions about the strategies’ supervisors

use to improve teacher efficacy were analyzed to determine their relationship with teacher

perceptions of self-efficacy. Responses to both the MTEBI and LSTEDI were disaggregated by

categories of years of teaching, years at current school, gender, level of education, and ethnicity.

I analyzed mean differences for the demographic variables. After checking for normality,

linearity, and homoscedasticity, I computed the p-value and F ratio, and determine whether the

44

relationship occurred by chance or whether a viable statistical relation existed. I also compared

the group means using ANOVA to compare the actual variation of the group averages and the

predicted average, and the degrees of freedom. Table 4 includes a summary of the analyses.

Table 4

Summary of Analyses

Research Questions Variables Analysis

1.Perceptions of math self-

efficacy

MTEBI

Gender, ethnicity, education

level,

years of experience,

years at current school

Descriptive statistics,

Cronbach’s alpha, T-tests,

ANOVAs, and Tuky-Kramer

2. Perceptions of leaders’

strategies

LSTEDI


level,






3. Perceived Effectiveness of

Leaders’ strategies

LSTEDI


level,






4. Self-efficacy and

supervisors’ behaviors

MTEBI, LSTEDI Regression analysis MTEBI

by LSTEDI

Pearson Correlation

Summary

In this chapter, I explained the methodology and procedures that I used to determine the

relationships between teachers’ self-efficacy and their perception of the supervisory behaviors

that mathematics leaders used to influence their self-efficacy. The study participants were

teachers who, at the time of the study, were responsible for teaching mathematics in a school

district in the southern part of the United States. I used two instruments, the Math Teacher

Efficacy Beliefs Instrument (MTEBI) and the Leaders Support of Teacher Efficacy Development

Inventory (LSTEDI). The data were collected for this descriptive and correlational study using

45

the online software Qualtrics. After calculating the descriptive statistics of two scales and the

demographic data, I conducted a t-test and determined the Pearson coefficients and an ANOVA

for each scale. The effectiveness of the strategies used to mediate teacher efficacy was

determined using multiple regression analyses.

46

CHAPTER 4 FINDINGS

The purposes of this research were to study mathematics teachers' perceptions of their

self-efficacy and the effects of teacher characteristics and supervisory behaviors on teachers’

self-efficacy. The study is threefold: (a) to explore the self-efficacy of teachers who teach

mathematics, (b) to identify teacher characteristics and supervisory behaviors that teachers

perceived affect teacher self-efficacy, and (c) to determine whether there is a relationship

between the mathematics supervisory behaviors and teacher self-efficacy as seen by the teachers,

while controlling for gender, ethnicity, years of mathematics teaching, level of education, and

years at current school.

I surveyed elementary teachers and secondary school mathematics teachers from an

urban school system in the southern area of the United States. I assessed the data collected from

the respondents to answer the four research questions:






Participants

I sent an email to all elementary teachers in 13 elementary schools and all secondary

mathematics teachers in three middle and three high schools describing the study and containing

a link to the surveys in Qualtrics. I sent the email to approximately 400 elementary teachers and

60 secondary mathematics teachers. However, some of the elementary teachers were not eligible

to complete the survey because they were not teaching mathematics. Many of the elementary

47

schools used cluster grouping with specific teachers assigned to math instruction. Based on that

model, I determined the number of eligible teachers to be 315 teachers: 39 secondary and 276

elementary teachers. Seventy-three teachers responded to the survey for a response rate of 23%.

Although I did not ask whether the teachers taught elementary or secondary school or whether

the teachers were certified in mathematics or general education, I was able to backtrack and

identify the endorsement of 52 respondents. Of the 52 respondents, eight had an endorsement in

mathematics, about 15%. The percentage of teachers endorsed in mathematics (15%) correlates

to the ratio of eligible secondary vs. elementary teachers who received the survey, of 315

teachers: 39 secondary and 276 elementary teachers, a ratio of 14%. However, based on this

breakdown, I was not able to run a t-test.

Table 5 presents the number of participants by years of teaching as reported by the

respondents. Initially, the survey asked teachers to communicate their years of teaching in four

categories: zero to 3 years, 3 plus to 5 years, 5 plus to 10 years, and more than 10 years.

However, because the number of respondents in the 3-plus to 5 and 5 plus to 10 years were few,

I combined the two subgroups into one group of 3 plus to 10 years for the analysis.

Table 5

Participants’ Years of Teaching

Years of Teaching Number Percent

0 to 3 Years 17 23.29

3 + to 10 Years 17 23.29

More than 10 Years 39 53.42

Total 73 100

Survey participants also shared the number of years they had worked at their current

school. Survey participants had four choices to respond to the question relating to the number

48

years at the current school: zero to 2 years, 2 plus years to 5 years, more than 5 years to 10 years,

and 10 years or more. Table 6 displays participants’ responses regarding their years at their

current school.

Table 6

Participants’ Years at Current School

Years at Current School Number Percentage

Zero to Two Years 26 35.61

Two+ to Five Years 12 16.44

Five+ to Ten Years 10 13.70

More than Ten Years 25 34.25

Total 73 100

Four of the 73 survey participants reported their gender as males, which represents only

5% of the respondents. Therefore, I did not conduct an analysis based on gender. Respondents

were asked to report their highest level of education, subdivided into four groups: BA or BS,

BA+30, MEd or masters, and EdD or doctorate. Due to the low number of respondents indicating

holding BA+30 and EdD or doctorate, I condensed the data into two groups, graduate degree,

and bachelor’s degree. I listed the responses for teachers who held BA +30, BA or BS as

bachelor’s degrees, and I grouped MEd or masters and EdD or doctorate as graduate degrees.

Table 7 lists the degrees as reported by the study participants.

49

Table 7

Participants’ Highest Level of Education

Degrees Number Percent

Bachelors 26 35.62

Graduate 47 64.38

Total 73 100

Question number 5 asked about the participants’ ethnicity. The survey participants had

five options to code as their ethnicity. However, the ethnic background clustered primarily into

two groups, Caucasians and African Americans. Few respondents identified themselves in the

other three categories. I combined the responses for Asian, Latino or Hispanic Origin, and other

into one group. Hence, in the study analysis, “other” represented Asian, Latino or Hispanic, and

other. One person did not answer the question related to ethnicity. The ethnicity of the

participants are displayed in Table 8.

Table 8

Participants’ Ethnicity

Race and Ethnicity Number Percent

Caucasian 32 44.44

African American 33 45.84

Other 7 9.72

Total 72 100

Although there was not a question relating to teacher endorsement, I was able to

backtrack and identify the endorsement of 52 respondents. I was able to ascertain that eight of

the 52 respondents had an endorsement in mathematics, about 15%. The percentage of teachers

endorsed in mathematics (15%) correlates to the ratio of eligible secondary vs. elementary

50

teachers who received the survey, of 315 teachers: 39 secondary and 276 elementary teachers, a

ratio of 14%. Based on this breakdown, I was not able to run a t-test.

I calculated descriptive statistics for each question of the MTEBI and the LSTEDI

surveys. The MTEBI is subdivided into two sets of questions: questions that relate to teachers’

personal self-efficacy and outcome self-efficacy. The personal self-efficacy questions measure

the teachers’ belief in their ability to teach, while the outcome self-efficacy assess teachers’

belief in affecting student performance. The MTEBI is comprised of 20 questions. Twelve

MTEBI questions focus on teachers’ personal self-efficacy, while eight MTEBI questions

measure outcome self-efficacy. The descriptive statistics and Cronbach's alpha for the two

subscales along with the number of responses for each question, mean, standard deviation, and

standard error mean are displayed in Appendix I.

Research Questions

Research Question One

Research Question One is: What are teachers’ perceptions of their math teaching self-

efficacy? An analysis of variance (ANOVA) test was conducted to explore whether, as reported

by teachers, teachers’ self-efficacy varies based on the years of teaching, years at the current

school, ethnicity, and gender. The significant ANOVA results are reported in the sections below

and displayed in Tables 9, 10, and 11. The complete results of the ANOVA are found in

Appendices J through O.

Years of teaching and teachers’ self-efficacy. The comparison based on years of

teacher yielded significant results on questions 2.6, 2.14, and 2.15. The overall analysis of

variance for MTEBI question 2.6 revealed significant differences in teachers’ overall self-

efficacy [F (2, 69) = 3.68, p = 0.0315]. Using η2 as a correlation-based measure of effect showed

51

that differences in years of teaching contributed 9.54% of the overall variability in teachers’ self-

efficacy. Individual group comparison using the Tukey-Kramer test demonstrated significant

differences between the self-efficacy measures for question Q 2.6. Teachers with more than 10

years reported an average of 4.385, while teachers with 0 to 3 years had a mean of 3.941. These

measures were statistically significant at (p = 0.0309), with an effect size of d = 0.73 indicating

that teachers with more than 10 years of teaching were 0.73 standard deviations more efficacious

than teachers within their first 3 years of teaching about having the skills needed to monitor

student understanding. The 95% confidence level for the mean difference of 0.443 was

0.034 ≤ µ ≤ 0.853. This finding is in line with expectations as teachers tend to hone their skills

over time and to add more instructional tools as they refine their craft.

A significant difference arose relating to teachers feeling more efficacious in their ability

to impact student performance. The overall analysis of variance showed significant differences in

teachers’ overall self-efficacy [F (2, 70) = 3.641, p = 0.313]. Using η2 as a correlation-based

measure of effect showed that differences contributed to 9.42% of the overall variability in

teachers’ self-efficacy. Individual group comparison using Tukey-Kramer test demonstrated

significant differences between the self-efficacy measures for question Q 2.14, which revealed

that teachers with 3 plus to 10 years had a mean score of 3.765 and teachers with more than 10

years recorded a mean score of 3.026. These results were statistically significant (p = 0.0321),

with an effect size d = 0.722 suggesting that teachers with 3 plus to 10 years were 0.722 standard

deviations more likely to feel efficacious about their ability to impact student performance

compared to teachers with 10 plus years of teaching. Additionally, the 95% confidence level for

the mean difference 0.739 was 0.051 ≤ µ ≤ 1.426. The results showed that teachers with 3 plus to

52

10 years had significantly higher confidence in their ability to impact student outcome compared

to teachers with 10 plus years of teaching.

Finally, regarding years of teaching and finding real-life examples to help students

conceptualize some of the lessons, the analysis of responses to Question Q 2.15 showed

statistical significance on two comparisons. The groups were 3 plus to 10 years of teaching

compared to 0 to 3 years of teaching and between 10 plus years as compared to 0 to 3 years.

There were significant differences in teachers’ overall self-efficacy [F (2, 70) = 4.894, p =

0.0102]; η2 = 12.26% overall variability in teachers’ self-efficacy.

Individual group comparison using the Tukey-Kramer test demonstrated significant

differences between the self-efficacy measures for questions Q 2.15. These results illustrated that

teachers with 3 plus to 10 years reported a mean score of 4.235 and teachers 0 to 3 years of

teaching had a mean score of 3.471, which was statistically significant (p = 0.0146), with an

effect size d = 0.938, This highlights that teachers with 3 plus to 10 years scored 0.938 deviations

higher than teachers 0 to 3 years. Also, the 95% confidence interval for the mean difference of

0.765 was 0.128 ≤ µ ≤ 1.401. The mean score for teachers with 10 plus years was 4.077 and the

mean for 0 to 3 teaching years was 3.471, which was statistically significant (p = 0.0239), with

an effect size d = 0.743, indicating that teachers with 10 plus years scored 0.743 deviations

higher than teachers within their first 3 years of teaching. Also, the 95% confidence interval for

the mean difference of 0.606 was 0.067 ≤ µ ≤ 1.146. It can be inferred from these results that

teachers are generally less efficacious during their first 3 teaching years. Table 9 displays the

significant results of the MTEBI ANOVAs by years of teaching. The complete findings are

provided in Appendices J and K.

53

Table 9

ANOVA Results: MTEBI by Years of Teaching,

Years of Teaching M

(Overall) SD Subgroups

M

(subgroup)

Mean

Diff p

Q 2.6 I have the skills needed

to monitor student

understanding.

4.28 0.610

More than 10

years 4.385

0.443 0.0309 First 3 years

3.941

Q 2.14 If students show more

interest in mathematics, it is

probably due to the

performance of the students'

teacher.

3.30 1.023

Three +to 10

years 3.765

0.739

0.0321 More than 10

years 3.026

Q 2.15 I find it difficult to

find real-life examples to help

my students conceptualize

some of the lessons.

3.97 0.816

Three + to 10

years 4.235

0.765 0.0146

First 3 years 3.471

More than 10

years 4.077

0.606 0.0239

First 3 years 3.471

Note: M = Mean, SD = Standard Deviation, p = p-value

Years at current school and teachers’ self-efficacy. The data were also analyzed for the

impact of years at the current school on teachers’ self-efficacy. The analysis revealed that like

the dimension of years of teaching, subgroups exhibited differences in “monitor student

understanding” and “teacher’s ability to impact student performance in mathematics.” Table 10

below displays these results. Regarding monitoring student understanding, overall differences in

teachers’ self-efficacy was located at (F (3, 71) = 3.378, p < 0.0232. Group differences η2

indicated 12.96 % overall changeability in teachers’ self-efficacy. The recoded means for

teachers with 5 plus to 10 years was 4.70 and 4.04 for teachers with 2 years or fewer (p < 0.0177,

with an effect size of d = 1.082). The confidence interval for the mean difference of 0.660 is

found at 0.867 ≤ µ ≤ 1.233, indicating that teachers with 5 plus years to 10 years at their current

54

school exhibit higher self-efficacy in their ability to monitor student understanding compared to

teachers with 2 or fewer years at their current school.

Responses to teachers’ ability to exercise control over student performance outcome

revealed that teachers with 2 plus to 5 years at their current school are 13.90% more likely to feel

efficacious compared to teachers with more than 10 years of teaching. The significance was

determined at F (3, 69) = 6.713, p < 0.0155. The mean of responses of teachers with 2 plus to 5

years was 4.00, while the more experienced teachers with 10 plus years were 2.88 (p < 0.0084)

with a strong effect size of 1.095, highlighting that the less experienced teachers scored 1.095

standard deviations higher than their more experienced counterparts. The confidence interval for

the mean difference of 1.120 was found at 0.223 ≤ µ ≤ 2.017. Thus, these results suggest that

teachers during the 2 plus to 10 years at the current school have a greater sense of self-efficacy

and are more willing to take ownership of their students’ academic performance and possibly

less jaded about the outcomes. Table 10 displays the results of the MTEBI ANOVAs by years at

current school. The complete findings are provided in Appendices L and M.

Table 10

ANOVA Results: MTEBI by Years at Current School

Years at Current School M


M

(Subgroup)

Mean

Diff p

Q 2.6 I have the skills needed to

monitor student understanding. 4.28 0.610

Five+ to 10 Years 4.70

0.660 0.0177 Two years or

fewer 4.04

Q 2.14 If students show more

interest in mathematics, it is

probably due to the

performance of the students'

teacher.

3.30 1.023

Two + to 5 Years 4

1.120 0.0084

Ten + Years 2.88


Race and Ethnicity and teachers’ self-efficacy. I also considered the influence of race

ethnicity on teachers’ self-efficacy. The ANOVA revealed statistical significance within some

55

groups for teachers’ mathematical knowledge (Q 2.3), skills needed to monitor student

understanding (Q 2.6), ability to provide effective instructional opportunities (Q 2.11), and

ability to answer students’ questions (Q 2.16). These significant results of race and ethnicity and

teachers’ self-efficacy are listed below in table 11.

The effect of race and ethnicity on teachers’ knowledge of mathematics was pegged at (F

(2, 69) = 5.548, p < 0.0058). Groups differences could explain a η2 = 13.85% of overall

mutability. The mean response for Caucasian participants was 4.67, while the mean response for

African American was 4.16, which was statistically significant at (p < 0.0045). With a mean

difference of 0.510, there was a moderate effect size d = 0.772 within a confidence interval of

0.139 ≤ µ ≤ 0.882, implying that Caucasian participants felt slightly more self-confident of their

mathematical knowledge than others.

The results for race and ethnicity on teachers’ self- efficacy of skills needed to monitor

student understanding also illustrated significant differences [F (2, 68) = 4.468, p < 0.0150].

Caucasian participants had a mean score of 4.50 and African American a mean score of 4.06,

which was statistically significant (p < 0.0107) with an effect size d = 0.718, intimating that

Caucasian scored 0.718 standard deviations higher than African American. The mean difference

was 0.488 within 0.087 ≤ µ ≤ 0.788 confidence interval. These results also highlight that

Caucasian participants felt more efficacious regarding the skills needed to monitor student

understanding.

Also, Caucasian teachers also appeared to evince more self-confidence in their ability to

provide effective instructional opportunities. The analysis manifested notable differences [(F (2,

69) = 3.457, p = < 0.0371] with differences among the groups accounting for η2 = 9.10% of the

56

disparity. Caucasian teachers had a mean score of 4.42 compared to 4.0 for African American.

The difference of 0.42 was significant (p < 0.0291, with d = 0.631, within 0.036 ≤ µ ≤ 0.813).

Finally, both the Caucasian and African American groups displayed significant

differences regarding their ability to answer students’ questions compared to those in the other

group. There was also a significant effect of race and ethnicity on self-efficacy [p < 0.0016; (F

(2, 68) = 7.115]. Post hoc comparisons revealed the mean scores for Caucasians (4.40) and

African Americans (4.25) differed from the mean score for those in the other group (3.17).

However, there was no significant difference between the mean scores for the Caucasian and

African American groups. When taken together, these results suggest that Caucasians and

African Americans denoted a greater sense of self-efficacy (effect d = 1.55 within 0.446 ≤ µ ≤

2.009) with a mean difference of 1.227, compared to the other group (d = 1.369 within 0.300 ≤ µ

≤ 1.867) with a mean difference of 1.083. Table 11 displays the ANOVAs for MTEBI on race

and ethnicity. The complete findings are located in Appendices N and O.

57

Table 11

ANOVA Results: MTEBI by Race and Ethnicity

Race and Ethnicity

Questions

M


M

(Subgroup)

Mean

Diff p

Q 2.3 I understand

mathematics concepts well

enough to be effective in my

teaching of the content.

4.40 0.661

Caucasian 4.67

0.510 0.0045 African

American 4.16

Q 2.6 I have the skills

needed to monitor student

understanding

4.28 0.610

Caucasian 4.50

0.438 0.0107 African

American 4.06

Q 2.11 I have sufficient

mastery of my subject

matter to provide effective

instructional opportunities

in my classroom

4.22 0.672

Caucasian 4.42

0.424 0.0291 African

American 4

Q 2.16 I have the

knowledge needed to

answer my students’

questions.

4.22 0.791

Caucasian 4.40 1.227 0.0010

Other 3.17

African

American 4.25

1.083 0.0042 Other 3.17


Academic degrees and teachers’ self-efficacy. To determine the impact of academic

degrees on teachers’ self-efficacy, I performed pooled t-test analyses. The results showed no

statistical significance for the impact of degrees on mathematics teachers’ self-efficacy. Based on

these results, the degrees held by teachers did not appear to impact their self-efficacy.

Research Question Two

Question Two is: What strategies do teachers perceive supervisors use to enhance teacher

self-efficacy? This question addresses the strategies that teachers’ feel their supervisors use to

mediate their self-efficacy. The impact of gender, ethnicity, years of teaching experience, years

at current school, and level of education on the LSTEDI are analyzed in this section, and the

significant results are reported in tables 12. 13, and 14. The complete findings are provided in

Appendices P through U.

58

Responses to LSTEDI by years of teaching. Interestingly, the number of years of

teaching appeared to have no impact on LSTEDI responses. There was no significant result in

this section. The complete findings for years of teaching are provided in Appendices P and Q.

Responses to LSTEDI by years at current school. The impact of years at current

school on LSTEDI responses exhibited significant differences for some groups. Differences

existed for the following six questions: My instructional leader provides instructional feedback

(Q 3 1.1); My instructional leader models teaching strategies that I can use in my class (Q 3

1.2); My administrator provides me the opportunity to visit and/or observe other colleagues at

my school (Q 3 1.5); My instructional leader encourages me to take instructional risks (Q 3

1.10); My instructional leader fosters reflective practices (Q 3 1.11); My instructional leader

encourages the redesign of programs (Q 3 1.13); and My instructional leader regularly provides

opportunities to learn new strategies at staff development meetings (Q 3 1.17). I reported the

statistically significant differences in Table 13. The complete results are provided in Appendices

R and S.

The analysis pinpointed notable differences in responses to My instructional leader

provides instructional feedback (Q 3 1.1) [F (3, 67) = 2.427 p < 0.0731]. Group differences could

explain 9.8% of the overall changeability in the LSTEDI responses. Statistical significance was

found for differences between teachers with 2 plus years to 5 years (Mean = 3.272) and teachers

with 10 plus years (Mean = 2.440) (p = 0.0486 and an effect d = 0.93). The confidence interval

for the means difference (0.883) was 0.004 ≤ µ ≤ 1.662. The differences may be because teachers

receive more feedback within the earlier years of teaching compared to teachers who are in their

tenth or later years of teaching.

59

Two subgroups displayed differences in response to whether their instructional leader

models teaching strategies that they can use in my class (Q 3 1.2). The difference was significant

[(F (3, 67) = 5.326, p < 0.0024], with and an overall variability of 19.26% in years at current

school. The results revealed differences in means for 2 plus to 5 years at current school (3.272)

compared to 10 plus years (2.12) and less than 2 years (1.923). Statistical significance was found

between 2 plus to 5 years and 10 plus years (p < 0.0017 with an effect size d = 1.29, with means

difference of 1.350 within 0.417 ≤ µ ≤ 2.282) and 2 plus to 5 years and 2 years or less (p <

0.0099, with effect size d = 1.10, with differences in means of 1.153 within 0.215 ≤ µ ≤ 2.090).

These responses suggest teachers with 2 to 5 years at their current school noted their

instructional leader modeling teaching strategies that they can use in their class. These teachers

may have a certain level of comfort and may be more open to receiving these supervisory

strategies as compared to these other groups.

A marginal difference [(F (3, 67) = 2.821, at p < 0.0454] was isolated in responses for My

administrator provides me the opportunity to visit and/or observe other colleagues at my school

(Q 3 1.5). Using a correlation-based measure of effect, η2 accounted for 11.22% of the

variability. However, a post-hoc test did not reveal any differences between groups.

Responses to the question, My instructional leader encourages me to take instructional

risks (Q 3 1.10), illustrated major differences in teachers’ overall perception of their instructional

leaders’ support of instructional risk-taking [F (3, 61) = 3.9845, p = .0117] and η2- based

differences accounted for 2.55% of the variance. A post hoc test determined important

dissimilarities for teachers within two groups. Teachers with 2 plus to 5 years had a mean score

of 3.272 compared to teachers with 10 or more years who had a mean score of 2.190. The

difference was significant (p < 0.0102, and an effect size of d = 1.10, with mean differences of

60

1.231, within 0.228 ≤ µ ≤ 2.234). Teachers with 2 plus to 5 years had scores that averaged 3.272

versus teachers with 2 years or fewer who had scores that averaged 2.042. These results were

significant (p < 0.347, d = 0.97, with mean differences of 1.082, within 0.056 ≤ µ ≤ 2.107).

These results suggest teachers with 2 to 5 years at their current school have developed a comfort

level that allows them to take instructional risk within a supportive environment in contrast to the

novice teachers or the more experienced teachers.

Responses to the question, My instructional leader fosters reflective practices (Q 3 1.11)

were also noteworthy for overall teachers’ self-efficacy at [F (3, 62) = 3.712, p < 0.0160]. Means

differences of 1.023 accounted for 15.23% of the variability. Tukey-Kramer test revealed

differences between 2 plus to 5 years (mean = 3.272) and 2 years or fewer (mean = 2.25) (p <

0.0108, d = 1.10, within 0.186 ≤ µ ≤ 1.862). Novice teachers who are still learning the craft may

find it difficult to reflect on their practices versus teachers with 2 to 5 years of experience.

The analyses also uncovered statistical differences between two groups responses to My

instructional leader encourages the redesign of programs (Q 3 1.13). Two plus to 5 years group

scored a mean of 3.00, and the 2 years or fewer scored a mean of 1.92, which was significant [F

(3, 64) = 3.671, p < 0.0166, with an effect size d = 1.12, within 0.209 ≤ µ ≤ 1.951]. This may be

due to teachers’ perception of the freedom afforded them as they develop their skills. One

speculation from these responses is that teachers with more years at their current school may

have a better understanding of the school culture, and these teachers may be more apt to

proposing programmatic changes.

Also, a marginal difference was found for responses to My instructional leader regularly

provides opportunities to learn new strategies at staff development meetings (Q 3 1.17) [(F (3,

65) = 2.915, at p < 0.0408]. Using a correlation-based measure of effect, t η2 accounted for

61

11.85% of the variability. Nonetheless, a post hoc test did not disclose any significant differences

between groups. Table 13 displays the ANOVAs for LSTEDI and years at current school.

Table 12

ANOVA Results: LSTEDI by Years at Current School



M

(Subgroup)

Mean

Diff p

Q 3 1.1 My instructional

leader provides instructional

feedback.

2.65 0.896

Two + to 5

Years 3.27 0.833 0.0486

Ten + Years 2.44


leader models teaching

strategies that I can use in my

class.

2.98 1.072

Two + to 5

Years 3.27 1.350 0.0017

Ten + Years 2.12

Two + to 5

Years 3.27

1.153 0.0099 Two years or

fewer 1.92

Q 3 1.5 My administrator

provides me the opportunity

to visit and/or observe other

colleagues at my school.

1.89 1.049

Two + to 5

Years 2.45

1.121 0.0744


Q 3 1.10 My Instructional leader

encourages me to take

instructional risks. 2.28 1.114

Two + to 5 Years 3.27 1.231 0..0102 Ten + Years 2.19

Two + to 5 Years 3.27 1.082 0.0347 Two Years or

fewer 2.04

Q 3 1.11 My instructional leader

fosters reflective practices. 2.61 0.926


fewer 2.25


encourages the redesign of

programs. 2.19 0.966

Two + to 5 Years 3 1.080 0.0092 Two Years or

fewer 1.92


regularly provides opportunities

to learn new strategies at staff

development meetings.

2.75 0.961

Two + to 5 Years 3.272 0.873 0.0529



LSTEDI responses by race and ethnicity. I investigated the impact of ethnicity on the

strategies that leaders used to augment teachers’ self-efficacy and reported the significant results

in Table 14. Question (3 1.6), My administrator affords me the opportunity to visit or/observe

colleagues at another school, resulted in significant differences in teachers’ overall perception of

62

the use of that strategy [F (2, 67) = 4.23, p < 0.0046]. The mean differences accounted for

14.86% of the overall variability in teachers’ self-efficacy. Comparison of individual groups

using the Tukey-Kramer test demonstrated significant differences between the self-efficacy

measures for question 3 1.6. Responses for the group, other, resulted in a mean of 2.143, the

African American group had a mean of 1.839, and the Caucasian group had a mean of 1.219.

The difference in means (0.924) for responses of participants in the other and Caucasian groups

was statistically significant (p = .0302, with an effect size of d = 1.35, within 0.073 ≤ µ ≤ 1.775).

The results for the African American group compared the results for the Caucasian groups was

statistically significant (p = .0141, d = 1.19, with means difference of (0.620), within confidence

intervals 0.106 ≤ µ ≤ 1.134). Table 14 displays the ANOVA results for LSTEDI responses on

ethnicity. The complete results are provided in Appendices T and U.

Table 13

ANOVA Results: LSTEDI by Race and Ethnicity

Race and Ethnicity M


M

(Subgroup)

Mean

Diff p

Q 3 1.6 My administrator

affords me the opportunity to

visit or/observe colleagues at

another school.

1.59 0.909

Other 2.14 0.924 0.0302 Caucasian 1.22

African American 1.84 0.620 0.0141


LSTEDI responses by academic degree. I performed pooled t-test analyses to

determine the impact of academic degrees on teachers’ perception of the strategies used by

63

instructional leaders. The results indicated no statistical significance for the impact of degrees on

strategies teachers perceived the leaders used to foster their self-efficacy.

Research Question Three

Research Question Three is: To what degree do teachers perceive those strategies as

effective? This section addresses years of teaching and years at the current school.

Effectiveness of Supervisory Behaviors by Years of Teaching. Instructional leaders

use a variety of strategies to augment teachers’ self-efficacy. Analysis of the variables regarding

the effectiveness of the supervisory behaviors revealed statistical significance in two of the 18

LSTEDI items: The instructional leaders encouraging the sharing of teaching strategies (Q 3

2.3) and The fostering of reflective practices (Q3 2.11).

For the instructional leaders encouraging the sharing of teaching strategies (Q 3 2.3), two

groups exhibited a significant difference in the dimension of effectiveness [F (2, 47) = 6.447, p

= .0034]. The Tukey-Kramer test found differences in teachers with 3-plus to 10 years and

teachers with more than 10 years when compared with teachers within their primary years. The

group of teachers in the 3 plus to 10 years had a mean of 3.182, and the group with more than 10

years had a mean of 3.037. In contrast, the teachers within their first 3 years had a mean of 2.167.

The means difference (1.015) between teachers with 3 plus to 10 years versus those with 3 years

or less was statistically significant at (p = 0.0082 with an effect size of d =1.186).

Additionally, teachers with more than 10 years compared to the primary group showed a

significant difference (p = .0062 with an effect size of d = 1.016) with a difference in means of

(0.870). The 95% confidence interval was 0.232 ≤ µ ≤ 1.8 and 0.219 ≤ µ ≤ 1.522 respectively.

As would be expected, the outcome confirmed that teachers with 3 plus to 10 years and more

64

than 10 years of teaching were more frequently solicited by their instructional leaders to share

teaching techniques compared to teachers within their first few years of teaching.

Regarding fostering of reflective practices (Q3 2.11), teachers who taught for more than

10 years rated their math instructional leaders’ behaviors more effective as opposed to teachers

who had taught fewer than 3 years. These two groups differed significantly [F (2, 49) = 2.355, p

= .0473]. The group difference contributed 11.71 % of the overall variability in perception.

Teachers who taught for more than 10 years recorded a mean of 2.963 similar to 2.231 (means

difference of 0.732) for those who had taught for less than 3 years (p = .0367 and d = 0.824) with

a confidence interval of 0.038 ≤ µ ≤ 1.426. More experienced teachers’ perception of their

instructional leaders’ use of reflective practices was 0.824 standard deviations higher than the

perception of new teachers. This may be because more experienced teachers are more skilled at

analyzing their teaching strategies and reflecting on lessons for means to improve. In some

instances, despite reflection, some new teachers may find it difficult to isolate the crux of the

issues at hand and identify solutions that may support growth. Table 15 displays the results of

this ANOVA. The complete results are provided in Appendices V and W.

Table 14

ANOVA Results: LSTEDI Effectiveness by Years of Teaching

Years of Teaching M


M

(Subgroup)

Mean

Diff p


leader encourages me to share

my teaching techniques with

others.

2.86 0.856

Three + to 10

years 3,182 1.015 0.0082

First 3 years 2.167

More than 10

years 3.037 0.870 0.0062

First 3 years 2.167


leader fosters reflective

practices.

2.73 0.888

More than 10

years

2.963 0.732 0.0367

First 3 years 2.231


65

LSTEDI effectiveness responses by years at current school. The following six areas

had significant differences for LSTEDI effectiveness based on years at the current school: My

instructional leader models teaching strategies that I can use in my class (Q 3 2.2); My

instructional leader praises me for my instructional approach (Q 3 2.7); My instructional leader

encourages me to take instructional risks (Q 3 2.10); My instructional leader fosters reflective

practices (Q 3 2.11); My instructional leader allows me to implement action research to inform

instructional decision making (Q 3 2.14); and My instructional leader regularly provides

opportunities to learn new strategies at staff development meetings (Q 3 2.17). I reported the

following results in Table 16.

Analysis of variance was significant for my instructional leader models teaching

strategies that I can use in my class (Q 3 2.2) on years at current school [F (3, 48) = 3.236, p <

0.0302.] indicating 16.82% of the variability was due to differences among groups. Additional

testing unveiled means of 3.56 for responses from teachers with 2 plus to 5 years and 2.50 for

teachers with 10 plus years of experience, which indicated notable significance with p < 0.0261

and an effect d = 1.10 (within the confidence interval 0.095 ≤ µ ≤ 2.016) for the means

difference of (1.056). This finding suggests that teachers with fewer years of teaching may find

the support of their instructional leaders in their classroom more useful than more experienced

teachers.

Responses to My instructional leader praises me for my instructional approach (Q 3 2.7)

were statistically significant [F (3, 49) = 3.411, p < 0.0246, η2 = 17.27% of changeability.

Teachers with 2 plus years to 5 years scored a mean of 3.444 in contrast to a mean of 2.316 for

teachers with 2 years or less; the difference was significant (p < 0.0127, with d = 1.21). The

95 % confidence interval is found within 0.189 ≤ µ ≤ 2.068, for the means difference of (1.129).

66

The more teachers with more years at their current school may have received more praises over

time from their instructional leader when compared to the novice teacher. These teachers are also

more likely to report a greater level of effectiveness for the strategy.

For the question, My Instructional leader encourages me to take instructional risks (Q 3

2.10), there was a significant difference for years at current school [F (3, 43) = 4.915, p <

0.0050]. The results indicated mean scores for the following groups: 3.50 for 2 plus to 5 years,

2.375 for 10 plus years scored, and 2.357 for 2 years or fewer. There was noteworthy

significance between 2-plus to 5 years versus 10 plus years (p < 0.0139) for a difference in

means of 1.184 and 2 plus to 5 years versus 2 years or fewer (p < 0.0126) with means difference

of 1.125. The effect sizes were d = 1.18 within 0.184 ≤ µ ≤ 2.102 and d = 1.16, within 0.191 ≤ µ

≤ 2.059 respectively. These results suggest that teachers with 2-plus years to 5 years of teaching

found this strategy to be effective in augmenting their self-efficacy.

Many teachers reported their instructional leaders’ fostering reflective practices (Q 3

2.11) an effective method for enhancing their self-efficacy. Substantial differences between three

groups based on years at current school were identified [F (3, 48) = 10.607, p < 0.001]. Using η2

as a correlation-based measure found differences among the groups accounted for 39.85% of the

variability. A post hoc test identified a difference in means for the 2 plus to 5 years group (3.40)

and the 2 years or less group (2.00), which was significant (p < 0.001, d = 1.58, within 0.654 ≤ µ

≤ 2.146), the means difference was (1.40). Significant differences were also found for the 10 plus

years group (mean = 3.056) and the 2 years or less group (mean = 2.00) for difference in means

of 1.056 at (p < 0.003, d = 1.19 , 0.420 ≤ µ ≤ 1.698) ; and for the 5 plus to 10 years group (mean

= 2.857) and the 2 year or less group (mean = 2.00) for difference in means of 0.857 at (p <

0.0445, d = 0.97, 0.420 ≤ µ ≤ 1.699).

67

My instructional leader allows me to implement action research to inform instructional

decision making (Q 3 2.14) was moderately effective in helping to develop teacher efficacy

based on years at current school. The analysis revealed significant differences in teachers’

overall assessment of the strategy’ effectiveness [F (3, 41) = 2.946, p = < 0.03440]. Using η2 as a

correlation-based measure of effect indicated that group differences accounted for 17.74% of the

overall variability in effectiveness. Individual group comparison using Tukey-Kramer test

demonstrated significant differences between the effectiveness measures for question Q 3 2.14.

Teachers with 2 plus to 5 years at their current school reported a mean of 3.356 while teachers

with 2 years or less had a mean of 2.438. These measures were statistically significant (p

= .0258), with an effect size of d = 1.15. The results indicate that teachers with 2 to 5 years at

their current school were 1.15 standard deviations more efficacious regarding the implementation

of action research to inform instructional decision making than teachers in their first 2 years at

their current school. The 95% confidence level for the means difference of 1.118 was 0.104 ≤ µ

≤ 2.132. This finding is in line with the expectation that teachers sharpen their skills over time

and add more instructional tools as they refine their craft.

There were significant differences in teachers’ perception regarding the effectiveness of

the use of staff development and meetings to mediate their efficacy. Question (Q 3 2.17), “My

instructional leader regularly provides opportunities to learn new strategies at staff development

meetings” was significant [F (3, 50) = 2.975, p < 0.0403]. Teachers with 2 plus to 5 years of

teaching had means of 3.5 vis-a-vis teachers with 2 years or fewer teaching who had means of

2.526. The means difference of 0.974 was significant (p < 0.0252 within 0.092 ≤ µ ≤ 1.856; with

an effect size d = 1.08). Table 16 displays the ANOVA for LSTEDI effectiveness and years at

current school. Appendices X and Y display the complete results.

68

LSTEDI effectiveness responses by race and ethnicity. I explored the impact of

ethnicity on the effectiveness of the strategies’ leaders used to affect teachers’ self-efficacy.

Based on the responses that I obtained, there were no statistically significant differences among

subgroups. The complete findings are located in Appendices Z and AA.

Table 15

ANOVA Results: LSTEDI Effectiveness by Years at Current School



M

(Subgroup)

Mean

Diff p


models teaching strategies that I

can use in my class. 2.71 0.957

Two + to 5 Years 3.56 1.056 0.0261

Ten + Years 2.50


praises me for my instructional

approach. 2.70 0.932

Two + to 5 Years 3.44 1.129 0.0127

Two Years or

fewer 2.32


encourages me to take

instructional risks. 2.72 0.971


fewer 2.36

Two + to 5 Years 3.50 1.125 0.0126 Ten + Years 2.38


fosters reflective practices. 2.73 0.888

Two + to 5 Years 3.40 1.400 <.0001 Two Years or

fewer 2

Ten + Years 3.059 1.059 0.0003 Two Years or

fewer 2

Five+ to 10 Years 2.86 0.857 0.0445 Two Years or

fewer 2


allows me to implement action

research to inform instructional

decision making.

2.87 0.968

Two + to 5 Years 3.56 1.118 0.0258

Two Years or

fewer 2.44


regularly provides opportunities to

learn new strategies at staff

development meetings.

2.91 0.896

Two + to 5 Years 3.50 0.974 0.0252

Two Years or

fewer 2.53


LSTEDI effectiveness responses by academic degree. The 16 teachers who held

bachelors’ degrees and 28 teachers who had graduate degrees were asked to respond to the

effectiveness of the instructional leaders’ strategies. Specifically, for Q 3 2.11, My instructional

leader fosters reflective practices, the analysis revealed that teachers with bachelor’s degrees

69

scored a mean of 2.40 and teachers with graduate degrees scored a mean of 2.93 for a difference

of 0.53. Teachers with graduate degrees scored a mean of 0.53 points higher on average than the

group of teachers with bachelor’s degrees. The two standard deviations were 1.14 and 0.62,

respectively. A t-test comparing the teachers with the two types of degrees was statistically

significant [(t (50) = 2.20, p = .0323]. The effect size measure based on the graduate versus

bachelor ‘s standard deviation of 0.888 was d = 0.60, indicating that graduate degree holders

scored 0.60 standard deviations higher than teachers with bachelor’s degrees. In addition, the

95 % confidence interval for the difference in means was 0.047 ≤ µ ≤ 1.027.

For question Q 3 2.15, My instructional leader solicits my advice about instructional

matters, the results showed teachers with bachelor’s degrees scored a mean of 2.31 and while

teachers with graduate degrees scored a mean of 3.04 for a difference of 0.72. Teachers with

graduate degrees scored 0.72 points higher on average than the group of teachers with bachelor’s

degrees. The two standard deviations were 1.08 (graduate degrees) and 0.83 (bachelor’s

degrees). A t-test comparing the teachers with the two types of degrees was statistically

significant [(t (42) = 2.48, p = .0173]. The measure of effect size based on the

graduate/bachelor‘s standard deviation of 0.985 was d = 0.73, indicating that graduate degree

holders scored 0.73 standard deviations higher than teachers with bachelor’s degrees. In addition,

the 95 % confidence interval for the difference in means was 0.134 ≤ µ ≤ 1.312.

Research Question Four

Research question four is: What is the relationship between teachers’ perceptions of the

strategies used by their supervisors and teachers’ self-efficacy? I focused on determining whether

there exists a relationship between teachers’ self-efficacy and the strategies used to support their

efficacy. To investigate this statistically, correctional analyses were used to (a) examine the

70

relationship between the perceived strategies used by math supervisors and teachers’ self-

efficacy and (b) test to what extent do leaders’ behaviors affect teachers’ self-efficacy. Results of

the Pearson correlation indicated significant associations between several LSTEDI strategies and

dimensions of the MTEBI. These results are reported in Table 17, which provides the correlation

factor, descriptive statistics N, and p-value with the upper and lower confidence level for each

correlation. The table containing the full correlation is provided in Appendix BB.

Table 16

Correlation Matrix of LSTEDI and MTEBI Questions

LSTEDI MTEBI Correlation N Lower

95%

Upper

95%

Signif

Prob

Q 3 1.1 Q 2.6 0.2951 70 0.0646 0.4957 .0132

Q 3 1.1 Q 2.15 0.3139 71 0.087 0.5099 .0077

Q 3 1.1 Q 2.17 0.3275 71 0.102 0.521 .0053

Q 3 1.1 Q 2.20 0.2436 71 0.0109 0.4513 .0407

Q 3 1.2 Q 2.6 0.3268 70 0.0994 0.5217 .0058

Q 3 1.2 Q 2.14 0.3189 71 0.0925 0.514 .0067

Q 3 1.2 Q 2.16 0.2586 70 0.0251 0.4653 .0307

Q 3 1.2 Q 2.17 0.2964 71 0.0678 0.4954 .0121

Q 3 1.3 Q 2.6 0.4344 70 0.2221 0.6073 .0002

Q 3 1.3 Q 2.15 0.2729 71 0.0423 0.4759 .0213

Q 3 1.3 Q 2.16 0.3037 70 0.074 0.5028 .0106

Q 3 1.3 Q 2.17 0.4265 71 0.2145 0.6001 .0002

Q 3 1.4 Q 2.15 0.2818 71 0.0519 0.4833 .0173

Q 3 1.4 Q 2.17 0.3116 71 0.0844 0.5079 .0082

Q 3 1.5 Q 2.13 0.2589 71 0.0273 0.4642 .0292

Q 3 1.5 Q 2.19 0.2428 71 0.0101 0.4506 .0413

Q 3 1.6 Q 2.13 0.2392 70 0.0045 0.449 .0461

Q 3 1.7 Q 2.17 0.3939 71 0.1768 0.5744 .0007

Q 3 1.8 Q 2.5 0.3426 69 0.0073 0.4541 .0437

Q 3 1.8 Q 2.6 0.3333 68 0.1031 0.5296 .0055

Q 3 1.8 Q 2.7 0.2523 69 0.0166 0.4615 .0365

Q 3 1.8 Q 2.14 0.2887 69 0.0558 0.4918 .0161

Q 3 1.8 Q 2.17 0.3515 69 0.1253 0.543 .0031

Q 3 1.8 Q 2.18 0.3051 68 0.0719 0.5067 .0114

Q 3 1.8 Q 2.19 0.2379 69 0.0013 0.4493 .049

Q 3 1.9 Q 2.3 0.2603 70 0.027 0.4667 .0295

Q 3 1.9 Q 2.6 0.3028 69 0.0712 0.5034 .0115

71

LSTEDI MTEBI Correlation N Lower

95%

Upper

95%

Signif

Prob

Q 3 1.9 Q 2.11 0.2600 70 0.0267 0.4665 .0297

Q 3 1.9 Q 2.16 0.3400 69 0.1123 0.5337 .0043

Q 3 1.9 Q 2.17 0.2942 70 0.0636 0.4949 .0134

Q 3 1.9 Q 2.18 0.2828 69 0.0494 0.4869 .0186

Q 3 1.10 Q 2.17 0.4028 65 0.1762 0.5888 .0009

Q 3 1.11 Q 2.14 0.2541 66 0.0129 0.4674 .0395

Q 3 1.12 Q 2.6 0.2829 69 0.0496 0.487 .0185

Q 3 1.12 Q 2.7 0.2700 70 0.0374 0.4749 .0238

Q 3 1.12 Q 2.10 0.2401 69 0.0036 0.4511 .0469

Q 3 1.12 Q 2.14 0.248 70 0.0138 0.4564 .0385

Q 3 1.12 Q 2.18 0.3192 69 0.0892 0.5168 .0075

Q 3 1.13 Q 2.6 0.3128 67 0.0785 0.5143 0.01

Q 3 1.13 Q 2.16 0.3355 67 0.1036 0.5327 .0055

Q 3 1.13 Q 2.17 0.3898 68 0.1668 0.5748 .001

Q 3 1.13 Q 2.20 0.2634 68 0.0266 0.4722 .03

Q 3 1.14 Q 2.5 0.2623 66 0.0216 0.4742 .0334

Q 3 1.14 Q 2.6 0.2971 65 0.0573 0.5044 .0163

Q 3 1.14 Q 2.7 0.3873 66 0.1603 0.5754 .0013

Q 3 1.14 Q 2.14 0.276 66 0.0364 0.4856 .0249

Q 3 1.14 Q 2.17 0.4179 66 0.1956 0.5993 .0005

Q 3 1.14 Q 2.18 0.3279 65 0.0913 0.5294 .0077

Q 3 1.15 Q 2.6 0.4143 64 0.1876 0.5991 .0007

Q 3 1.15 Q 2.7 0.3046 65 0.0655 0.5105 .0136

Q 3 1.15 Q 2.14 0.2471 65 0.0034 0.4631 .0472

Q 3 1.15 Q 2.17 0.3735 65 0.1426 0.5658 .0022

Q 3 1.16 Q 2.6 0.2593 65 0.0164 0.4733 .037

Q 3 1.16 Q 2.15 0.2768 66 0.0373 0.4863 .0245

Q 3 1.16 Q 2.17 0.3692 66 0.1396 0.5611 .0023

Q 3 1.16 Q 2.18 0.2762 65 0.0346 0.4873 .0259

Q 3 1.16 Q 2.19 0.2538 66 0.0125 0.4671 .0398

Q 3 1.17 Q 2.6 0.3008 68 0.0672 0.5031 .0127

Q 3 1.17 Q 2.16 0.3717 68 0.1462 0.5604 .0018

Q 3 1.17 Q 2.18 0.3257 68 0.0946 0.5234 .0067

Q 3 1.17 Q 2.20 0.2441 69 0.0079 0.4545 .0432

Q 3 1.18 Q 2.17 0.2869 67 0.0501 0.4931 .0186

Note: N = Count

My instructional leader provides instructional feedback (3 1.1). My instructional

leader provides instructional feedback was correlated to four dimensions of the MTEBI: (Q 2.6)

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I have the skills needed to monitor student understanding: (Q 2.15) I find it difficult to find real-

life examples to help my students conceptualize some of the lessons; (Q 2.17) Given a choice, I

would not invite the principal to evaluate my mathematics teaching; and (Q 2.20) I do not know

what to do to turn students on to mathematics.

The results pinpointed a significant relationship between the following pairs of questions:

(Q 3 1.1) and (Q 2.6) [r(69) = 0.30, p = .0132]; (Q 3 1.1) and (Q2.15) [r(70) = 0.31, p = .0077];

(Q 3 1.1) and (Q 2.17) [r(70) = 0.33, p = .0053]; and (Q 3 1.1) and (Q 2.20) [r(70) = 0.24, p

= .0407]. These results suggest receiving feedback had a small association with teachers’ ability

to monitor student understanding, and to know what to do to turn students on to mathematics. A

higher correlation was found between receiving feedback and teachers’ ability to help students

conceptualize lessons with real-life examples and to invite the principal to evaluate their

teaching.

My instructional leader models teaching strategies that I can use in my class (Q 3

1.2). There were small associations between Q 3 1.2 and the following four MTEBI questions:

(Q 2.6) I have the skills needed to monitor student understanding; (Q 2.14) If students show more

interest in mathematics, it is probably due to the performance of the students' teacher; (Q 2.16) I

have the knowledge needed to answer my students’ questions; and (Q 2.17) Given a choice, I

would not invite the principal to evaluate my mathematics teaching. The respective correlation

results are: r(69) = 0.33, p = .0058; r(70) = 0.32, p = .0067; r(69) = 0.26, p = .0307; and r(70) =

0.30, p = .0121. The analysis also revealed a small association between Q 3 1.2 and personal

self-efficacy [r(71) = 0.30, p = .0102].

My instructional leader encourages me to share my teaching techniques with others

(Q 3 1.3). A small positive link existed between (Q 3 1.3) and the following two items: (Q 2.15)

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I find it difficult to find real-life examples to help my students conceptualize some of the lessons

[r(70) = 0.27, p = .0213] and (Q 2.16); I have the knowledge needed to answer my students’

questions [r(69) = 0.30, p = .0106]; Q 3 1.2 had a moderate association with (Q 2.6) I have the

skills needed to monitor student understanding [r(69) = 0.43, p = .0002], and (Q 2.17) Given a

choice, I would not invite the principal to evaluate my mathematics teaching [r(70) = 0.43, p

= .0002]. Moreover, the analysis found a small association with teachers’ personal self-efficacy

[r(71) = 0.35, p = .0028].

My instructional leader fosters the development of coaching relationships among

educators (Q 3 1.4). There was a small positive correlation between (Q 3 1.4) and (Q 2.15) I

find it difficult to find real-life examples to help my students conceptualize some of the lessons

[r(70) = 0.28, p = .0173] and (Q 2.17) Given a choice, I would not invite the principal to evaluate

my mathematics teaching [r(70) = 0.31, p = .0082].

My administrator provides me the opportunity to visit and/or observe other

colleagues at my school (Q 3 1.5). There was a small positive correlation between Q 3 1.5 and

(Q 2.13) Students’ achievement in mathematics is directly related to their teacher’s effectiveness

in mathematics teaching [r(70) = 0.26, p = .0273] and (Q 2.19) When teaching mathematics, I

will usually welcome student questions [r(70) = 0.24, p = .0413].

My administrator affords me the opportunity to visit or/observe colleagues at

another school, (Q 3 1.6). There was a small correlation between Q 3 1.6 and (Q 2.13)

students’ achievement in mathematics is directly related to their teacher’s effectiveness in

mathematics teaching [r(69) = 0.24, p = .0461].

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My Instructional leader praises me for my instructional approach (Q 3 1.7). Q 3 1.7

had a moderate interrelation with Q 2.17 [r(71) = 0.39, p = .0007]. The analysis also indicated a

small link with teachers’ personal self-efficacy [r(71) = 0.25, p = .0367].

My instructional leader allows the use of professional judgment in how I implement

new strategies, (Q 3 1.8). The analysis isolated small positive reciprocal relation between Q 3

1.8 and the following seven questions: (Q 2.5) I know how to teach mathematics concepts

effectively; (Q 2.6), I have the skills needed to monitor student understanding; (Q2.7) I use

effective teaching strategies that support my students learning needs; (Q2.14) If students show

more interest in mathematics, it is probably due to the performance of the students' teacher;

(Q2.17) Given a choice, I would not invite the principal to evaluate my mathematics teaching;

(Q2.18) When a student has difficulty understanding some difficult concepts, I am usually able to

find different instructional techniques to assist them; and (Q2.19) When teaching mathematics, I

will usually welcome student questions. The correlation statistics were: (Q 3 1.8) and (Q2.5)

r(68) = 0.24, p = .0437; (Q 3 1.8) and (Q2.6) r(67) = 0.33, p = .0055; (Q 3 1.8) and (Q2.7) r(68)

= 0.25, p = .0365; (Q 3 1.8) and (Q2.14) r(68) = 0.29, p = .0161; (Q 3 1.8) and (Q2.17) r(68) =

0.35, p = .0031; (Q 3 1.8) and (Q2.18) r(67) = 0.30, p = .0114; and (Q 3 1.8) and (Q2.19); r(68) =

0.23, p = .0490. Furthermore, (Q 3 1.8) displayed a small positive relation to teachers’ personal

self-efficacy, [r(69) = .31, p = .0104].

My instructional leader encourages me to collaborate with other colleagues (Q 3

1.9). Q 3 1.9 was correlated with five dimensions of the MTEBI: (Q 2.3) I understand

mathematics concepts well enough to be effective in my teaching of the content [r(69) = 0.26, p

= .0295]; (Q 2.6) I have the skills needed to monitor student understanding [r(68) = 0.30, p

= .0115]; (Q 2.11) I have sufficient mastery of my subject matter to provide effective

75

instructional opportunities in my classroom [r(69) = 0.26, p = .0297]; (Q 2.16) I have the

knowledge needed to answer my students’ questions [r(68) = 0.34, p = .0043]; (Q 2.17) Given a

choice, I would not invite the principal to evaluate my mathematics teaching [r(68) = 0.29, p

= .0134]; and (Q 2.18) When a student has difficulty understanding some difficult concepts, I am

usually able to find different instructional techniques to assist them [r(68) = 0.28, p = .0186].

Teacher collaboration also had a positive association with teachers’ personal self-efficacy [r(70)

= 0.34, p = .0040].

My Instructional leader encourages me to take instructional risks (Q 3 1.10). Q 3

1.10 had a moderate positive relationship with (Q 2.17) Given a choice, I would not invite the

principal to evaluate my mathematics teaching [r(64) = 0.40, p = .0009]. A small correlation was

detected between Q 3 1.10 and teacher’s personal self-efficacy [r(65) = 0.25, p = .0488].

My instructional leader fosters reflective practices (Q 3 1.11). The results showed a

modicum correlation between Q 3 1.11 (Q 2.14) If students show more interest in mathematics, it

is probably due to the performance of the students' teacher [r(65) = 0.25, p = .0395]. In addition,

the study found a modest relationship with teachers’ outcome expectancy [r(66) = 0.25, p

= .0392].

My instructional leader sends other teachers to visit my classroom (Q 3 1.12). Q 3

1.12 slightly mediated teachers’ self-efficacy in five of the 20 MTEBI dimensions: (Q 2.6) I have

the skills needed to monitor student understanding [r(68) = 0.28, p = .0185]. (Q2.7) I use

effective teaching strategies that support my students learning needs [r(69) = 0.27, p = .0235]; (Q

2.10) “When a low-achieving student makes progress, it is usually due to the extra attention that

I provide” [r(68) = 0.24, p = .0469]. (Q2.14) If students show more interest in mathematics, it is

probably due to the performance of the students' teacher [r(65) = 0.25, p = .0385]. (Q2.18)

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“When a student has difficulty understanding some difficult concepts, I am usually able to find

different instructional techniques to assist them” [r(69) = 0.31, p = .0075]. Moreover, analyses

isolated a meager rapport with teachers’ outcome expectancy [r(70) = 0.27, p = .0215].

My instructional leader encourages the redesign of programs (Q 3 1.13). The

correlation results showed a small association between Q 3 1.13 and (Q 2.6) I have the skills

needed to monitor student understanding [r(66) = 0.31, p = .0100]; (Q 2.16) I have the

knowledge needed to answer my students’ questions [r(66) = 0.34, p = .0055]; (Q 2.20) I do not

know what to do to turn students on to mathematics, and had a stronger [r(67) = 0.26, p

= .0300]; and a slightly stronger association with (Q 2.17) Given a choice, I would not invite the

principal to evaluate my mathematics teaching [r(67) = 0.39, p = .0010]. A correlation was also

present with teacher’s personal self-efficacy [r(68) = 0.33, p = .0053].

My instructional leader allows me to implement action research to inform

instructional decision making (Q 3 1.14). Q 3 1.14 varied positively with six items: (Q2.5) I

know how to teach mathematics concepts effectively; (Q 2.6) I have the skills needed to monitor

student understanding; (Q2.7) I use effective teaching strategies that support my students

learning needs; (Q2.14) If students show more interest in mathematics, it is probably due to the

performance of the students' teacher; (Q2.17) Given a choice, I would not invite the principal to

evaluate my mathematics teaching; and (Q2.18) When a student has difficulty understanding

some difficult concepts, I am usually able to find different instructional techniques to assist them.

The statistics for these six pairs are: (Q 3 1.14) and (Q2.5) r(65) = 0.26, p = .0334; (Q 3 1.14)

and (Q2.6) r(64) = 0.29, p = .0163; (Q 3 1.14) and (Q2.7) r(65) = 0.38, p = .0013; (Q 3 1.14) and

(Q2.14) r(65) = 0.28, p = .0249; (Q 3 1.14) and (Q2.17) r(65) = 0.42, p = .0005; and (Q 3 1.14)

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and (Q2.18) r(64) = 0.33, p = .0077; and (Q 3 1.8). Additionally, the result determined a

moderate relationship with teacher’s personal self-efficacy [r(66) = 0.38, p = .0018].

My instructional leader solicits my advice about instructional matters (Q 3 1.15).

There was a moderate correlation between Q 3 1.15 and (Q 2.6) I have the skills needed to

monitor student understanding [r(63) = 0.41, p = .0007]; (Q 2.17) Given a choice, I would not

invite the principal to evaluate my mathematics teaching [r(64) = 0.37, p = .1426]; and a small

relationship with (Q 2.7) I use effective teaching strategies that support my students learning

needs [r(64) = 0.30, p = .0136]; and (Q 2.14) If students show more interest in mathematics, it is

probably due to the performance of the students' teacher [r(64) = 0.25, p = .0472]. Teacher’s

personal self-efficacy also correlated with question Q 3 1.15 [ r(65) = 0.31, p = .0115].

My instructional leader gives me a lot of autonomy in my teaching (Q 3 1.16). The

investigation found four dimensions of the MTEBI that correlated positively with Q 3 1.16. The

dimensions identified were (Q 2.6) I have the skills needed to monitor student understanding

[r(64) = 0.26, p = .0370]; (Q 2.15) I find it difficult to find real-life examples to help my students

conceptualize some of the lessons [r(65) = 0.28, p = .0245]; (Q2.17) Given a choice, I would not

invite the principal to evaluate my mathematics teaching [r(65) = 0.37, p = .0123]; (Q2.18) When

a student has difficulty understanding some difficult concepts, I am usually able to find different

instructional techniques to assist them [r(64) = 0.28, p = .0259]; and (Q2.19) When teaching

mathematics, I will usually welcome student questions [r(65) = 0.26, p = .0398]. The

investigation also showed a small association with teachers’ personal self-efficacy construct

[r(66) = 0.32, p = .0084].

My instructional leader regularly provides opportunities to learn new strategies at

staff development meetings (Q 3 1.17). Q 3 1.17 had a small affiliation to (Q 2.6) I have the

78

skills needed to monitor student understanding [r(67) = 0.30, p = .0127]; (Q 2.16) I have the

knowledge needed to answer my students’ questions [r(65) = 0.37, p = .0018]; (Q 2.18) When a

student has difficulty understanding some difficult concepts, I am usually able to find different

instructional techniques to assist them [r(67) = 0.33, p = .0067]; and (Q 2.20) I do not know what

to do to turn students on to mathematics, and had a stronger [r(68) = 0.24, p = .0432]. In

addition, Q 3 1.17 had a small positive association with teachers’ personal self-efficacy [(r(69) =

0.30, p = 0 .0127].

My instructional leader gives me the choice to select staff development suited to my

needs (Q 3 1.18). Q 3 1.18 and (Q2.17) Given a choice, I would not invite the principal to

evaluate my mathematics teaching were positively correlated [r(66) = 0.29, p = .0186].

Summary

This study was a descriptive, correlational study focused on teachers who teach

mathematics’ self-efficacy. The research explored teachers’ perceptions of their self-efficacy

using years of experience, years at current school, education, gender, and ethnicity as controls.

The study also analyzed the relationship between teachers’ descriptions of supervisors’ behaviors

and teacher’s perceptions of self-efficacy. Data were collected from 73 teachers (four males and

69 females) using the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) and the

Leaders Support of Teacher Efficacy Development Inventory (LSTEDI) to measure teachers’

self-efficacy.

I calculated descriptive statistics for all variables and conducted an analysis of variance

(ANOVA) tests to investigate the relationship between the responses to MTEBI and the LSTEDI

controlling for years of experience, years at current school, education, gender, and ethnicity. I

79

also used pairwise correlation analyses to determine whether there was a link between specific

instructional leaders behaviors and teachers’ self-efficacy.

Research question four investigated the relationship between teachers’ perceptions of the

strategies used by their supervisors and teachers’ self-efficacy. I found several statistically

significant correlations between the strategies’ leaders used and teachers’ self- efficacy. Of these

relationships, instructional leaders’ behaviors of (a) allowing the use of professional judgment

and (b) implementation of action research, (c) encouraging teacher collaboration, and (d) giving

teachers autonomy in teaching positive correlated to five or more dimensions of teacher self-

efficacy as reported by the teachers in the present study. These findings suggest these strategies

could have a great effect on increasing overall teacher efficacy. The implications of these

findings are discussed in Chapter 5.

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CHAPTER 5 DISCUSSION

Empirical research identifies a relationship between teacher efficacy and student learning

(Anderson, Greene, & Loewen, 1988; Ashton & Webb, 1986; Midgley, Feldlaufer, & Eccles,

1989; Ross, 1992). Teacher self-efficacy has also been associated with teachers’ ability to

maintain a conducive learning environment and uphold a commitment to their professional

responsibilities (Dellinger et al., 2008). Furthermore, research demonstrates that school leaders

have the unique ability to impact instruction by providing feedback to teachers (Garza, 2001;

Sergiovanni & Starrat, 2002; Schultz & Weinstein, 1990; Texas Education Agency [TEA],

1997). Therefore, it is important to understand teachers’ perceptions of their self-efficacy and the

effect of instructional leaders on it.

Discussion of Study Findings

This research focused on mathematics teachers' perceptions of their self-efficacy and the

effects of teacher characteristics and supervisory behaviors on teachers’ self-efficacy. The study

explored the self-efficacy of teachers who teach mathematics, identified teacher characteristics

and supervisory behaviors that teachers perceived affect teacher self-efficacy, and determined

whether there was a relationship between the mathematics supervisory behaviors and teacher

self-efficacy as seen by the teachers, while controlling for gender, ethnicity, years of

mathematics teaching, level of education, and years at current school. The study sought to

answer the following research questions.




81



To answer these four questions, I used the Mathematics Teaching Efficacy Beliefs Instrument

(MTEBI) and the Leaders Support of Teacher Efficacy Development Inventory (LSTEDI)

surveys to gather teachers’ perception.

Demographics

I invited all elementary teachers and secondary mathematics teachers in a school district

in the southern area of the United States to take part in the survey; 73 of the 315 eligible teachers

participated in the survey. From this small sample, key findings emerged. Descriptive statistics

revealed most of the 73 survey participants were women (five males and 68 females). Fifty-three

percent of the survey participants had more than 10 years of teaching, which suggested most of

the teachers in the schools were experienced teachers with many years of teaching. The

remaining participants were divided equally among teachers with 0 to 3 years of teaching and

those with 3 plus to 10 years of teaching.

The number of years at the current school was more equally distributed; teachers with 0

to 3 years and those with more than 10 years accounted, in equal parts, for 70% of the study

respondents. Those with two plus to 5 years and 5 to 10 years accounted for the other 30%. Thus,

the bulk of the participants were either experienced teachers or teachers in their primary years.

Furthermore, most of the teachers held graduate degrees (65%); this finding does not align with

previous research which indicated a shortage of qualified minority teachers, specifically African

American teachers in urban public schools serving mainly primarily minority students (Ingersoll

& May, 2011). Lastly, the study sample was evenly distributed between Caucasians and African

Americans (about 45% each) and 10% in the other category. These findings confirmed previous

82

research indicating the percentage of African American teachers is higher in urban school

systems serving a majority-minority student body. A body of research suggests minority teachers

generally represent a small portion of the teaching staff and there exists a disparity between

percentages of minority teachers vis-a-vis the minority student population (e.g., Foster, 1997;

Haberman, 1996; Ingersoll & May, 2011; Quiocho & Rios, 2000). The following sections

discuss findings related to each of the research questions.

Research Question One

Research question one centered on teachers’ perceptions of their mathematics teaching

self-efficacy. I identified statistically significant differences between teachers based on years of

experience, years at the school, and race/ethnicity.

Years teaching. Based on years of teaching, I found statistical significance in three

categories of the MTEBI. Seasoned teachers with more than 10 years of experience reported

feeling more efficacious in their ability to monitor student understanding compared to teachers in

their primary years. These results seem to be consistent with other research, which found teacher

efficacy appears to increase during both the preparation for teaching and early teaching (Hoy &

Woolfolk, 1990; Spector, 1990). However, teacher efficacy remained unchanged or declining

based on the number of years of service beyond the initial 5 years (Romi & Daniel, 1999; Lin &

Gorrell, 2001). A more recent study by Dolgun and Caner (2011) found minimal differences

between preservice teachers’ efficacy compared to the efficacy of experienced teachers.

However, the research found preservice teachers’ perceived self-efficacy was lower in the area of

instruction classroom management (Dolgun & Caner, 2011).

In addition, teachers within their first 3 years of teaching felt more efficacious about their

ability to improve students’ interest in mathematics compared to teachers with more than 10

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years of teaching. Also, the more seasoned teachers (i.e., teachers with more than 3 years to 10

years and teachers with more than 10 years of experience) reported they had more difficulty

finding real-life examples to help students conceptualize some lessons compared to teachers in

their primary years. These findings suggest that teachers in their primary years of teaching were

more likely to feel self-efficacious and take ownership of student outcome. These results are

inconsistent with research by Romi and Daniel (1999) and Lin and Gorrell (2001) whereas self-

efficacy appears to steadily increase during the first few years of teaching, then level off and

eventually decline with years of teaching beyond the first 5 to 10 years. A more recent study

identified similar levels of self-efficacy among teachers who felt capable, with a high degree of

preparation for classroom and instructional challenges, irrespective of differing experience and

training. (Paz et al., 2012)

Years at current school. For years at current school, teachers with 5 plus to 10 years at

their current school were more likely to convey that they had the skills needed to monitor student

understanding compared to teachers within 2 or fewer years of teaching. Teachers with 5 plus to

10 years at the current school also felt more confident of their ability to increase student interest

in mathematics compared to teachers with more than 10 years at their current school. Thus,

teachers with 5 to 10 years at the current school reported a greater sense of self-efficacy and

more willingness to take ownership of their students’ academic performance. It has been

suggested that teachers’ self-efficacy is minimally malleable once established (Gorrell & Hwang,

1995; Housego, 1992; Wenner, 2001). This does not appear to be the substantiated by this

research.

Race and ethnicity. As it relates to ethnicity, this research showed Caucasian teachers

displayed more self-efficacy than African American teachers when it came to understanding

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mathematics concepts for effective teaching, having the skills needed to monitor student

understanding, and having sufficient mastery of subject matter to provide effective instructional

opportunities in their classrooms. Both Caucasian and African American teachers reported being

more efficacious regarding possessing the knowledge needed to answer students’ questions than

the other group. These results indicate ethnicity may play a role in certain aspects of teachers’

self-efficacy. When taken together, these results suggest that the Caucasian teachers denoted a

greater sense of self-efficacy than either the African American or other teachers. These findings

contrast with previous studies by Tschannen-Moran and Hoy (2007), which found that race,

gender, and school setting did not affect efficacy in either novice or experienced teachers.

Finally, I did not find any statistically significant results for the impact of academic

degrees on self- efficacy which suggests that the teachers who held graduate degrees did not feel

a greater sense of self- efficacy when compared to teachers with bachelor’s degrees. This

outcome is contrary to that of Tschannen-Moran & Johnson (2011) who found significant

positive relations between the highest level of education and teachers' self-efficacy beliefs.

Research Question Two

This question inquired about the strategies that teachers perceived supervisors use to

enhance teacher self-efficacy. I identified statistically significant differences between teachers

based on years at the school and race/ethnicity. These finding are outline below.

Years at current school. The number of years worked by teachers at their school had

greater differences on teachers’ perception of the strategies used by their supervisors compared

to the other dimensions (years of teaching, ethnicity, and level of education). Teachers with 2 to

5 years at their current school reported receiving a variety of strategies from their instructional

supervisors more often than the other groups. The teachers with more than 2 years but fewer than

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5 years at their school were more likely to denote that they: (a) received instructional feedback

and encouragement from supervisors to take instructional risk, (b) had opportunities to visit other

colleagues, (c) learned new strategies at staff development meetings, and (d) received teaching

strategies by their leaders. Teachers’ self-efficacy has been found to be especially malleable

during the early years of teaching (Hoy & Woolfolk, 1990). However, during the first 2 years of

teaching, teachers receive a variety and volume of information that can be overwhelming, which

may not be absorbed and processed during these initial years. By the third year, teachers may

develop a certain level of comfort and may be better able to receive these supervisory strategies.

Race and ethnicity. Differences in ethnicity regarding feedback were found when the

other and African American groups were compared to Caucasian teachers. The other and African

American groups reported higher group means for receiving feedback from their instructional

leaders than the Caucasian group. However, with a small sample size for the group Other,

caution must be applied, as the findings might not be extrapolative and are not well researched.

Research Question Three

Question three focused on the degree to which teachers perceived the leaders’ strategies

to mediate their self-efficacy as effective. In response to this inquiry, teachers with more than 10

years of experience were more likely to report the supervisory efforts to foster reflective

practices and to promote the sharing of teaching techniques as an effective practice. However,

more significant group differences were found regarding the number of years at the current

school. Again, teachers with 2 to 5 years at the current school more often perceived the strategies

used by their instructional leaders more effective than the other groups. I did not find any

significant group responses regarding ethnicity and how teachers perceived the effectiveness of

the strategies used by their leaders.

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Overall, teachers identified receiving instructional feedback and sharing instructional

practices as effective strategies used by their leaders to support them. The analyses revealed that

teachers with 3 plus to 10 years and more than 10 years of teaching reported more frequently

being solicited by their instructional leaders to share teaching techniques compared to teachers

within their primary years of teaching. As would be expected, more experienced teachers were

more likely to be tapped by their instructional leaders to share teaching techniques. These

findings are consistent with prior research which pinpointed a strong correlation between leaders

making suggestions in the form of feedback and encouraging teachers to share their practices,

among others, as powerful strategies that leaders used. Teachers reported receiving feedback as

having a powerful effect on their self-efficacy and motivation. (Blase & Blase, 1999).

Research Question Four

This question focused on the relationship between teachers’ perceptions of the strategies

used by their supervisors and the teachers’ self-efficacy. The analysis found evidence that

teachers’ self-efficacy was related to supervisors’ behaviors. Thirteen of 20 of the MTEBI items

were correlated to LSTEDI items. Further, investigations revealed that nine of the 13 MTEBI

items could be classified as related to teachers’ outcome expectancy and four as teachers’

personal self-efficacy. From these observations, it appears that teachers’ outcome expectancy

(75%) is more related to the strategies used by instructional leaders compared to teachers’

personal self- efficacy (50%). Bandura (1977) defined outcome expectancy as the individuals’

beliefs in an expected outcome based on certain actions. Schunk (1987) proposed that these

beliefs are impacted by observation and experiences. The results of the present study tie well

with previous research in that participants reported they believed their actions would lead to

specific outcomes related to certain behaviors of their leaders. Tschannen-Moran (2009) found

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that principals can generate greater trust among staff by fostering autonomy within learning

teams and allowing teachers to craft their collaborative efforts. Also, Datnow (2011) and

Gallimore et al. (2009) identified leaders’ need to provide collaborative structures and cultures

along with an autonomous environment that foster teacher instructional decisions

It is also worth noting interesting relationships revealed by the correlation results. Three

of the supervisory practices with the greatest number of associations with teachers’ self-efficacy

dealt with fostering teacher autonomy and teacher empowerment. The three practices included:

(a) My instructional leader allows the use of professional judgment in how I implement new

strategies; (b) My instructional leader allows me to implement action research to inform

instructional decision making; and (c) My instructional leader gives me a lot of autonomy in my

teaching. Two additional supervisory behaviors related to teacher collaboration (My instructional

leader sends other teachers to visit my classroom, and My instructional leader encourages me to

collaborate with other colleagues) had strong relationships with five or more teacher self-efficacy

constructs. These findings are consistent with previous research which outlined the importance

of teacher autonomy and empowerment (White, 1992) and collaboration (Hallam, Smith, Hite,

Hite, & Wilcox, 2015). The results of my research found clear support for these previous

findings. I should also point out that four practices with a strong correlation with four additional

teacher self-efficacy items also related to these findings. The four practices included: (a) My

instructional leader models teaching strategies that I can use in my class; (b) My instructional

leader encourages me to share my teaching techniques with others; (c) My instructional leader

solicits my advice about instructional matters; and (d) My instructional leader regularly provides

opportunities to learn new strategies at staff development meetings. These findings suggest

implications for school leaders and future research. These findings are also aligned with

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Tschannen-Moran (2009), which found trust among teachers was increased when the principal

allowed for heightened teacher discretion and professional judgment. Trust and collaboration

among teachers increased as they witnessed one another making student-focused instructional

decisions.

Recommendations

Improving educational outcome for all students continues to be a focus for our schools

and our nation. School leaders explore behaviors that support mathematics teachers to improve

student learning outcome (Even & Ball, 2010; Franke, Kazemi, & Battey, 2007); increasing

teacher self-efficacy is one factor that can bolster these efforts (Swackhamer et al., 2009). The

results of this study support the idea that teacher self-efficacy is related to supervisory behaviors.

Furthermore, instructional leaders need to use a variety of strategies to enhance teacher

efficacy. Strategies that were reported to be particularly useful included those that foster teacher

collaboration, autonomy, and empowerment. Ensuring appropriate systems, services, and support

for teacher collaboration should be a priority for those in leadership positions.

Mathematics supervisors should encourage teachers to practice action research in their

classrooms. They should also foster peer observations to promote self-efficacy through enactive

and vicarious experiences. Mathematics teachers can experience increased self-efficacy, not only

by experiencing success in their observable practices but also by seeing the successful actions of

their peers (Datnow, 2011; Gallimore et al., 2009; Tschannen-Moran, 2009).

Mathematics supervisors should regularly provide teachers’ opportunities to learn new

strategies at staff development meetings. They also need to model good teaching strategies that

can be used in the classroom. Moreover, teacher choice is crucial to fostering teacher

89

empowerment and increasing mathematics teachers’ self-efficacy (Datnow, 2011; Gallimore et

al., 2009; Tschannen-Moran, 2009).

This research was conducted with a small sample of teachers in a school district in the

southern United States. The sample had limited gender diversity. Some participating teachers

taught math as part of the overall program, were not certified in math, and may not have had a

strong background in math. Furthermore, the author used a self-designed instrument which had

not been tested across subjects in different settings. Finally, the study used self-reporting tools,

which rely heavily on the honesty and the candidness of the participants.

More research using controlled trials in a variety of setting is needed to confirm the

results of this research. I would also recommend additional studies using a diverse pool of

teachers with greater gender diversity to confirm the results across gender lines, I also

recommend an exploration of the differences among elementary, middle, and high school

mathematics teachers regarding teacher perceptions of supervisory behaviors and their impact on

self-efficacy. Using teacher certification as one of the controls in the study is also warranted.

Implications

The findings of this study have a few important implications for future practice.

Mathematics supervisory leaders should become familiar with the vital role teacher self-efficacy

plays. It plays a role in teacher instructional practices, teacher retention, and teachers’ ability to

maintain a conducive learning environment (Betoret, 2006; Klassen et al., 2009). Mathematics

instructional leaders should take note of this study’s findings, especially the strategies

participants reported and the effectiveness of these practices.

Another important practical implication emerging from this research is the need for

feedback. Teachers reported receiving feedback was vitally important to enhancing their

90

efficacy. When teachers received positive feedback, they experienced a combination of verbal

persuasion through encouragement and emotional arousal from the positive feedback. Both of

these supportive actions promote increased self-efficacy and advance teachers’ impact on student

learning (Ovando, 2001, 2003, 2005). This information can be used to develop targeted

interventions aimed at increasing mathematics teachers’ self-efficacy and, thereby, improve

student learning outcome.

Although the Cronbach’s alpha reliability scale reported above 96% for each of the

LSTEDI and MTEBI items, a reliability study would strengthen the results of this study and

increase the generalizability of the results. Finally, conducting research using a comparative

group of teachers and supervisors would enhance understanding of teachers’ self-efficacy and

mathematics supervisory behaviors.

Conclusion

This study was an exploration of mathematics teachers’ self-efficacy, the strategies

teachers perceived leaders used to enhance teacher self-efficacy, and the correlation between the

leaders’ behaviors and teacher self-efficacy as perceived by the teachers. Years of experience,

years at the current school, education, gender, and ethnicity were used as controls. The findings

from this study are consistent with previous research and make several contributions to the

current literature. The instrument used to identify the supervisory behaviors can be used in future

studies to explore supervisory behaviors further. The need to increase students’ learning

outcomes will continue to drive further research. Gaining a greater understanding of the impact

of teacher self-efficacy on student learning and the factors that promote a greater sense of self-

efficacy is vital to ensuring successful outcomes in our schools and, ultimately, in society.

91

Reflections

It is said that “Success is a journey, not a destination.” This quote truly encapsulates my

experience through the doctoral program. The journey, the lessons learned along the way, will

guide me for many years to come. I will start from the beginning. A dear friend, as she was

completing the program, suggested that I consider joining the new cohort that was starting

through Virginia Tech. We had worked together during her journey through the process. I had

seen her stressed out at times. However, overall, she had always talked positively about the

process. My friend encouraged me to attend the next cohort orientation; I agreed to attend.

Nonetheless, on the day of that orientation, I decided to go home. I was a few miles from home

when this friend called and told me to turn the car around. I did. And so, it all started.

During the orientation, I asked a few questions. I thought I had gained a good

understanding of what would be expected of me. So, I thought. I applied and was granted

admission to the doctoral cohort. I started classes in August 2013; I met some wonderful

colleagues. Within days, we had all bonded on one level or another. We were going to make it.

We all had various reasons why we had started this journey. In my case, I saw this experience as

an opportunity to hone my leadership skills and to strengthen my understanding of educational

leadership.

I had very high expectations. I felt certain that I could complete the program by May

2017. That was the goal that I had set for myself. Well, it is also said that life is what happens

while we are busy making plans. Indeed, several things would happen to alter the course that I

had undertaken. But ultimately, I kept my focus on completing the journey.

During the first semester, we had an overwhelming amount of work. That, coupled with a

stressful position, stretched me to the limit. However, one of the tasks that we completed the first

92

semester was to identify a research problem and to write a literature review about the topic. I

thought for sure that this was going to be an insurmountable obstacle. How was I going to write a

25-page literature review in one semester? Well, I recently shared the process that led to my

reaching this milestone with one of my colleagues who is just starting her journey. I had

mentioned to her that I had to read two to six articles per week and pull relevant information

needed for the weekly review according to a protocol. As I relayed the process, I realize that the

protocol helped me complete the literature review with minimal stress. Having students get a

head start on the literature review during their first semester is a good way to ensure that a

critical part of the work is accomplished from the get-go.

Although this part was behind me, the journey was not a straight line; I encountered

many curvy roads, mountains, and valleys. Through it all, I could always count on the support of

my cohort members and the understanding and support of my professors. I must say they granted

me privacy, for the most part, when I needed it, tough love when required, and a good dose of

encouragement along the way. Although there were times when I did not communicate, my

professors were always there ready to help when I reached out. With a hefty dose of patience,

they encouraged and challenged me along the way.

I chose the topic of mathematics teachers’ self-efficacy because I have always felt that

my strong self-efficacy has guided and supported me through the most difficult tasks and

experiences. I personally value grit and perseverance, and I have a strong belief that if you

believe you can, then you will. As a mathematics teacher, I made it my goal to help every

student, and I truly believed I could. I found myself accomplishing exactly that goal. Hence, I

decided to delve into that topic and learn more about the research surrounding self-efficacy. At

93

one point in time, I explored another topic but soon found my way back to pondering about self-

efficacy and its impact on teachers and their practices.

I had some personal and professional setbacks along the way; I lost a dear friend and

cohort member during my second year of the program. We sat next to each other for over a year.

During the summer of 2014, she was instrumental in my staying in the program despite some

serious challenges I was facing at the time. She was stern with me and made me promise never to

quit. So, I was committed to completing the program.

I previously mentioned my timeline for completing the process in May 2017. I

approached the process with a certain level of naivety when I requested permission to complete

my survey in a previous school district. I assume that all school leaders would be interested in

learning more about supporting teachers. I was crushed when my request was denied, and I

would not be able to conduct my surveys in the district. Meanwhile, life happened. I transitioned

into a new school district, and I had to focus more on the job at hand.

One of the most important things I learned through the process is that you have to select

your board of directors carefully. You must also share with them the goals you hope to

accomplish. I say this because many times, when I wanted to keep the dissertation process out of

my mind, one of them would ask about my progress and when I anticipated completing the task.

Some invited themselves to graduation and checked regularly on my expected graduation date.

My village, my board of directors, continued to encourage me and push me toward the finishing

line.

As I researched and explored behaviors and strategies that foster teachers’ self-efficacy, I

did not notice that I was also developing my own self-efficacy in many facets through the

process. I could have missed the forest for the trees, as it is said at times. Only at the very end did

94

I realize that I had acquired increased self-efficacy related to writing in my third language. With

a mathematics background, numbers have always appealed more to me than letters. Additionally,

English is the fourth or possibly fifth language in my line of language acquisition. I feel

empowered by the research process; I have come so very far to have come to this point. I take

pride in this work. I am truly humbled and feel a tremendous sense of accomplishment. One

more cliché, “A journey of a thousand miles starts with the first step.” As I conclude this

journey, I see new beginnings are beckoning on ahead of me. I am fully aware that the road is

steep but having shared some vicarious experiences with others, I am equipped with my enactive

experiences, a dose of verbal persuasion, and some emotional arousal. I forge on to the next

chapter in my life. Special thanks to all who have contributed to this accomplishment.

95

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Appendix A Demographic/Background Questions

1. How many years have taught mathematics?

• 0 – 3 _______ years

• >3 – 5 _______years

• >5 – 10 _______years

• 10+ _______years

•

2. How many years have you taught at your current school? ______ years

• 0 – 2 _______ years

• >2 – 5 _______years

• >5 – 10 _______years

• 10+ _______years

3. What is your gender? ______Male ______Female

4. What is your highest level of education?

_______BA or BS

_______BA+30

_______MEd or Masters

_______Ed.D or Doctorate

5. What is your ethnic background?

1. Caucasian

2. African American

3. Asian

4. Latino or Hispanic Origin

5. Other

116

Appendix B Comparison of Item Revisions from the Mathematics Teacher Efficacy Beliefs

Instrument (MTEBI)

Wording from MTEBI Revised Wording

1 When a student does better than usual in

Mathematics, it is often because the teacher

exerted a little extra effort.

When a student does better than usual in

Mathematics, it is often because I exerted a

little extra effort.

2 I continually find better ways to teach

mathematics.

I continually find better ways to relate the

curriculum to the students in a meaningful

manner by using age appropriate topics in my

lessons.

3 Even if I try very hard, I not teach

mathematics as well as I most subjects. I understand mathematics concepts well

enough to be effective in my teaching of

the subject level.

I have a clear understanding of the subject

matter and work hard to make it

meaningful for my students.

4 When the mathematics grades of students

improve, it is often due to their teacher

having found a more effective teaching

approach.

When the grades of students improve, it is

often because I found a more effective

teaching approach.

5 I know how to teach mathematics concepts

effectively.

I am confident in my understanding and

teaching of mathematics concepts.

6 I not be very effective in monitoring

mathematics activities.

I have the training and skills needed to

monitor student understanding and make

adaptation and modifications to the lesson as

needed to meet students varied learning

needs.

7 If students are underachieving in

mathematics, it is most likely due to

ineffective mathematics teaching.

I generally use effective teaching strategies in

to encourage the academic curiosity and

critical thinking skills of students.

8 I generally teach mathematics ineffectively.

9 The inadequacy of a student’s mathematics

background can be overcome by good

teaching.

The inadequacy of a student’s mathematics

background can be overcome by good

teaching.

10 When a low-achieving child progresses in

mathematics, it is usually due to extra

attention given by the teacher.

When a student makes progress in their

achievement, it is usually due to the extra

attention and explantion that I provide.

11 I understand mathematics concepts well

enough to be effective in teaching

elementary mathematics.

Utilizing my strong knowledge of

mathematics, I use a variety of strategies

to reach my students learning needs.

117

Wording from MTEBI Revised Wording

WORDING FROM MTEBI REVISED WORDING

12 The teacher is generally responsible for the

achievement of students in mathematics.

The teacher is generally responsible for the

achievement of students in mathematics.

13 Students’ achievement in mathematics is

directly related to their teacher’s

effectiveness in mathematics teaching.

Students’ achievement in mathematics is

directly related to their teacher’s effectiveness

in mathematics teaching.

14 If parents comment that their child is

showing more interest in mathematics at

school, it is probably due to the

performance of the child’s teacher.

If students show more interest in mathematics

at school, it is probably due to the

performance of the student’s teacher.

15 I find it difficult to use manipulatives to

explain to students why mathematics works.

I find it difficult to find real-life examples to

help my students conceptualize some of the

lessons.

I relate the curriculum to students in a

meaningful manner using real world

examples.

16 I typically be able to answer students’

mathematics questions.

I have the knowledge and skills needed to

answer my students’ questions.

18 Given a choice, I not invite the principal to

evaluate my mathematics teaching.

Given a choice, I would not invite the

principal to evaluate my mathematics

teaching.

19 When a student has difficulty understanding

a mathematics concept, I usually be at a loss

as to how to help the student understand it

better.

When a student has difficulty understanding

some difficult concepts, I am usually able to

find different instructional techniques to assist

them.

20 When teaching mathematics, I usually

welcome student questions.

I enable students to participate actively in the

lessons while providing continuous and

meaningful feedback.

I solicit comments, questions, and other

contributions from students throughout

the lesson.

21 I do not know what to do to turn students on

to mathematics.

A teacher is very limited in his/her efforts to

influence students’ interest in mathematics.

I generally infuse the lessons with real-

world examples to capture students'

interest in the subject matter.

118

Appendix C Items on Revised MTEBI by Subscale

Item Revised Wording

Outcome Expectancy Subscale

1 When a student does better than usual in Mathematics, it is often because the teacher

exerted a little extra effort.

4 When the mathematics grades of students improve, it is often due to their teacher

having found a more effective teaching approach.

7 If students are underachieving in mathematics, it is most likely due to ineffective

mathematics teaching.

9 The inadequacy of a student’s mathematics background can be overcome by good

teaching.

10 When a low-achieving child progresses in mathematics, it is usually due to extra

attention given by the teacher.

12 The teacher is generally responsible for the achievement of students in mathematics.

13 Students’ achievement in mathematics is directly related to their teacher’s

effectiveness in mathematics teaching.

14 If students show more interest in mathematics at school, it is probably due to the

performance of the student’s teacher.

Personal Self-Efficacy Subscale

2 I continually find better ways to teach mathematics.

3 Even if I try very hard, I do not teach math as well as I teach other subjects.

5 I know how to teach mathematics concepts effectively.

6 I am not very effective in monitoring mathematics activities.

8 I generally teach math ineffectively.

11 I have a strong enough knowledge of mathematics concepts to be an effective math

teacher.

15 I find it difficult to use manipulative to explain math concepts to students.

16 I typically am able to answer students’ mathematics questions.

18 Given a choice, I not invite the principal to evaluate my mathematics teaching.

19 When a student has difficulty understanding some math concepts, I am usually at a loss

as to how to help the student understand it better.

20 When teaching mathematics, I usually welcome student questions.

21 I do not know what to do to turn students on to math.

119

Appendix D Permission to Use MTEBI

120

Appendix E the Leaders Support Of Teacher Efficacy Development Inventory

(LSTEDI)

Thank you very much for agreeing to take part in this important survey measuring

teachers’ teaching and learning beliefs, math teacher efficacy beliefs, and strategies that

math leaders use to influence teacher efficacy. When responding to the LSTEDI survey,

please consider the leader that works most closely with the math teaching teams, such as

the department chair, instructional coach, or assistant principal. The survey helps us gather

valuable information that may inform supervisory efforts and the strategies that leaders use

to influence teacher efficacy. Please respond honestly to each question. Be assured that the

responses that you provide be kept in the strictest confidence. Please fill out once choice

per statement and respond to all three survey instruments and the demographic data.

Strategy Agreement Effectiveness

Always. Most of the time, about half

the time, sometimes, never.

Seldom, Sometimes, Often, and Very

Often.

Sel

do

m

Ag

ree

Dis

ag

ree

Str

on

gly

Dis

ag

ree

Ex

trem

ely

Eff

ecti

ve

Ver

y E

ffec

tiv

e

Mo

der

ate

ly e

ffec

tiv

e

So

mew

ha

t E

ffec

tiv

e

No

t E

ffec

tiv

e

SA A D SD EE VE ME SE NE

1 My instructional leader provides

instructional feedback.

(Verbal Persuasion)

2 My instructional leader models teaching

strategies that I can use in my class.

(Vicarious) Experience

3 My instructional leader encourages me

to share my teaching techniques with

others. (Verbal Persuasion) Experience

4 My instructional leader fosters the

development of coaching relationships

among educators.

(Enactive) Collaboration

5 My administrator provides me the

opportunity to visit and/or observe other

colleagues at my school.

(Vicarious) Experience

6 My administrator affords me the

opportunity to visit or/observe

colleagues at another school.

(Vicarious) collaboration

121





Often.

Sel

do

m

Ag

ree

Dis

ag

ree

Str

on

gly

Dis

ag

ree

Ex

trem

ely

Eff

ecti

ve

Ver

y E

ffec

tiv

e

Mo

der

ate

ly e

ffec

tiv

e

So

mew

ha

t E

ffec

tiv

e

No

t E

ffec

tiv

e



7 My Instructional leader praises me for

my instructional approach

(Emotional Arousal) Feedback

8 My instructional leader allows the use of

professional judgment in how I

implement new strategies.

(Enactive) Motivation

9 My instructional leader encourages me

to collaborate with other colleagues.

(Vicarious) collaboration

10 My Instructional leader encourages me

to take instructional risks.

(Verbal Persuasion) Motivation

11 My instructional leader fosters reflective

practices.

(Enactive) Feedback

12 My instructional leader sends other

teachers to visit my classroom.

(Emotional Arousal) Collaboration

13 My instructional leader encourages the

redesign of programs

(Verbal Persuasion) Motivation

14 My instructional leader allows me to

implement action research to inform

instructional decision making.

(Enactive) Experience

15 My instructional leader solicits my

advice about instructional matters.

(Emotional Arousal) Feedback

16 My instructional leader gives me a lot of

autonomy in my teaching

(Emotional Arousal) Motivation

122





Often.

Sel

do

m

Ag

ree

Dis

ag

ree

Str

on

gly

Dis

ag

ree

Ex

trem

ely

Eff

ecti

ve

Ver

y E

ffec

tiv

e

Mo

der

ate

ly e

ffec

tiv

e

So

mew

ha

t E

ffec

tiv

e

No

t E

ffec

tiv

e


17 My instructional leader regularly

provides opportunities to learn new

strategies at staff development meetings.

Experience

18 My instructional leader gives me the

choice to select staff development suited

to my needs.

123

Appendix F School District Approval Letter

Portsmouth Public Schools

Office of Research and Evaluation

3651 Hartford Street • Portsmouth, Virginia 23707

(757) 393-8840 • FAX (757) 393-8233

January 24, 2019

Prosperanta Calhoun

[email protected]

Dear Ms. Calhoun:

I am pleased to inform you that your request to conduct the study entitled “Effect of Supervisory

Behaviors on Mathematics Teachers’ Self-efficacy” has been given conditional approval. This

study should be conducted on a voluntary basis and administered to elementary and middle

school math teachers only via email.

A copy of the results of your interview must be forwarded to the Office of Research and

Evaluation, Portsmouth Public Schools upon completion.

Best wishes for continued success.

Sincerely,

Derrick Nottingham, Director

xc: Dr. Anita Wynn

124

Appendix G Introductory Recruitment Email

Good morning,

My name is Prosperanta Calhoun. I am a graduate student at Virginia Tech in the Educational Leadership

Program. I am conducting research on the Effects of Leadership Behaviors on Math Teachers Efficacy,

and I am inviting you to participate because you currently teach mathematics at the elementary, middle, or

high school level.

The research is designed to identify the types of supervision and supportive actions that instructional

leaders who supervise mathematics instruction can adopt to foster the development of teacher efficacy.

Participation in this study includes taking a survey about your perceptions of your self-efficacy in math

teaching and the supervisory behaviors that support the development of your self-efficacy. You will also

be asked your assessment of the effectiveness of those strategies.

Should you agree to participate, as a mathematics teacher practitioner, you will fill out two surveys: the

Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), which measures math teaching self-efficacy

and the Leaders Support of Teacher Efficacy Development Inventory (LSTEDI), which will identify

strategies that teachers perceive as effectively supporting teacher efficacy. You will also need to provide

some demographic data (gender, ethnicity, years of teaching experience, years at current school, and level

of education). The survey will take approximately 15 minutes.

Below is a link to the survey. Your responses to the survey will be collected using a data collection

software, called Qualtrics, which enables online data collection. At the conclusion of the study period, the

information will be exported into Excel for analytical purposes. When responding to the LSTEDI survey,

please consider the leader that works most closely with the mathematics teams, such as the department

chair, instructional coach, or assistant principal. Please respond honestly to each question. Be assured that

the responses that you provide will be kept in the strictest confidence.

This study will be used for dissertation research and publication. The survey findings will be shared with

the Assistant Superintendent of Curriculum. When possible, it will be broken down by subject, by school,

and demographics (gender, ethnicity, years of teaching experience, years at current school, and level of

education). However, no data will be shared when the population is less than three individuals.

Every effort will be made to maintain the anonymity of the participants.

Please click on this link to access the survey:

https://virginiatech.qualtrics.com/SE/?SID=SV_bf1jRvQ7M7sMbTn

The submit button at the end of this survey redirects to a brief survey where you can elect to provide your

name and email if you would like to be considered for a drawing for three $25 dollars gift certificate for

Walmart. Participation in the drawing is also voluntary. The two surveys are not linked, and your

responses will not be associated with your name. All participants will be entered into the drawing

regardless of whether you complete the survey in its entirety. The odds of winning a gift certificate is 1 in

67 if all 200 eligible teachers participate.

It is important for you to note that you are free to withdraw from this study at any time without penalty.

You are free not to answer any questions that you choose or respond to what is being asked of you

without penalty.

https://virginiatech.qualtrics.com/SE/?SID=SV_bf1jRvQ7M7sMbTn

125

Should you have any questions about this study, you may contact one of the research investigators:

Prosperanta Calhoun 571-334-2697 or [email protected]; Walt Mallory,

[email protected].

Should you have any questions or concerns about the study’s conductor your rights as a research subject

or need to report a research-related injury or event, you may contact The Virginia Tech Institutional

Review Board at [email protected] or (540)231-3732.

mailto:[email protected]

mailto:[email protected]

126

Appendix H Institutional Review Approval Letter

127

IRB Number 17-062 page 2 of 2 Virginia Tech Institutional

Review Board

Date* OSP Number Sponsor Grant Comparison Conducted?

* Date this proposal number was compared, assessed as not requiring comparison, or comparison information was revised.

If this IRB protocol is to cover any other grant proposals, please contact the IRB office ([email protected]) immediately.

128

Appendix I Summary Statistics of MTEBI and LSEDI

Groups Count Sum Average Variance M SD SE α

Q 2.1 72 259 3.60

0.920 3.60 0.959 0.113

0.960

Q 2.2 72 313

4.35

0.343 4.35 0.585 0.069

0.958

Q 2.3 73 321 4.40 0.437 4.40 0.661 0.077 0.958

Q 2.4 73 292 4.00 0.639 4 0.799 0.094 0.959

Q 2.5 73 303 4.15 0.602 4.15 0.776 0.091 0.958

Q 2.6 72 308 4.28 0.372 4.28 0.610 0.072 0.958

Q 2.7 73 321 4.40 0.354 4.40 0.595 0.070 0.958

Q 2.8 73 307 4.21 0.860 4.21 0.927 0.109 0.959

Q 2.9 73 272 3.73 0.896 2.73 0.947 0.111 0.959

Q 2.10 72 295 4.10 0.427 4.10 0.653 0.077 0.958

Q 2.11 73 308 4.22 0.451 4.22 0.672 0.079 0.958

Q 2.12 73 270 3.70 0.741 3.70 0.861 0.100 0.959

Q 2.13 73 267 3.66 0.951 3.66 0.975 0.114 0.959

Q 2.14 73 241 3.30 1.047 3.30 1.023 0.120 0.958

Q 2.15 73 290 3.97 0.666 3.97 0.816 0.100 0.959

Q 2.16 72 304 4.22 0.626 4.22 0.791 0.093 0.959

Q 2.17 73 286 3.92 1.104 3.92 1.051 0.123 0.958

Q 2.18 72 300 4.17 0.451 4.17 0.671 0.079 0.958

Q 2.19 73 341 4.67 0.224 4.67 0.473 0.055 0.958

Q 2.20 73 272 3.73 1.063 3.73 1.031 0.121 0.959

Q 3 1.1 71 188 2.65 0.803 2.65 0.896 0.106 0.956

Q 3 1.2 71 162 2.28 1.148 2.38 1.0715 0.127 0.957

Q 3 1.3 71 185 2.61 1.185 2.61 1.089 0.13 0.957

Q 3 1.4 71 195 2.75 1.021 2.75 1.010 0.120 0.958

Q 3 1.5 71 134 1.89 1.101 1.89 1.049 0.125 0.957

Q 3 1.6 70 111 1.59 0.826 1.59 0.909 0.109 0.958

Q 3 1.7 71 168 2.37 0.921 2.37 0.960 0.114 0.957

Q 3 1.8 69 197 2.86 1.126 2.86 1.061 0.128 0.957

Q 3 1.9 70 222 3.17 0.840 3.17 0.916 0.109 0.957

Q 3 1.10 65 155 2.38 1.240 2.28 1.114 2.661 0.957

Q 3 1.11 66 172 2.61 0.858 2.61 0.926 0.114 0.957

Q 3 1.12 70 122 1.74 1.005 1.74 1.003 0.120 0.958

Q 3 1.13 68 149 2.19 0.933 2.19 0.966 0.117 0.957

Q 3 1.14 66 157 2.38 1.162 2.38 1.078 0.133 0.957

Q 3 1.15 65 151 2.32 1.097 2.32 1.047 0.130 0.957

Q 3 1.16 66 167 2.53 0.991 2.53 0.996 0.123 0.958

129

APPENDIX I Summary Statistics of MTEBI and LSTEDI (Cont.)

Groups Count Sum Average Variance M SD SE α

Q 3 1.17 69 190 2.75 0.924 2.75 0.961 0.115 0.957

Q 3 1.18 67 132 1.97 1.060 1.97 1.029 0.126 0.958

Q 3 2.1 59 158 2.68 0.739 2.68 0.860 0.112 0.957

Q 3 2.2 52 141 2.71 0.915 2.71 0.957 0.133 0.957

Q 3 2.3 50 143 2.86 0.735 2.86 0.856 0.121 0.957

Q 3 2.4 57 159 2.79 0.776 2.79 0.881 0.117 0.958

Q 3 2.5 37 97 2.62 1.075 2.62 1.037 0.170 0.957

Q 3 2.6 27 69 2.56 1.333 2.56 1.155 0.222 0.957

Q 3 2.7 53 143 2.70 0.869 2.70 0.932 0.128 0.957

Q 3 2.8 56 167 2.98 0.927 2.98 0.963 0.129 0.957

Q 3 2.9 59 185 3.14 0.740 3.14 0.860 0.112 0.958

Q 3 2.10 47 128 2.72 0.944 2.72 0.971 0.142 0.958

Q 3 2.11 52 142 2.73 0.789 2.73 0.888 0.123 0.957

Q 3 2.12 29 77 2.66 1.091 2.66 1.044 0.194 0.956

Q 3 2.13 45 120 2.67 1.000 2.67 1 0.149 0.957

Q 3 2.14 45 129 2.87 0.936 2.87 0.968 0.144 0.957

Q 3 2.15 44 122 2.77 0.970 2.77 0.985 0.149 0.957

Q 3 2.16 51 146 2.86 0.801 2.86 0.895 0.125 0.957

Q 3 2.17 54 157 2.91 0.803 2.91 0.896 0.122 0.957

Q 3 2.18 43 111 2.58 1.106 2.58 1.051 0.160 0.957

SE 73 308.55 4.23 0.230 4.23 0.480 0.056

OE 73 274.18 3.76 0.255 3.73 0.505 0.059

Note: M = Mean, SD = Standard Deviation, SE = Standard Error, α = Cronbach's alpha

130

Appendix J Complete MTEBI ANOVA by Years of Teaching

Source df SS MS F p

Q 2.1 Teaching Years 2 1.96 0.982 1.07 0.35

Error 69 63.36 0.918

C. Total 71 65.32

Q 2.2 Teaching Years 2 1.24 0.620 1.85 0.16

Error 69 23.08 0.334

C. Total 71 24.32

Q 2.3 Teaching Years 2 1.15 0.574 1.32 0.27

Error 70 30.33 0.433

C. Total 72 31.48

Q 2.4 Teaching Years 2 0.08 0.042 0.06 0.94

Error 70 45.92 0.656

C. Total 72 46.00

Q 2.5 Teaching Years 2 2.79 1.397 2.41 0.10

Error 70 40.55 0.579

C. Total 72 43.34

Q 2.6 Teaching Years 2 2.52 1.261 3.64 0.03

Error 69 23.92 0.347

C. Total 71 26.44

Q 2.7 Teaching Years 2 0.24 0.121 0.34 0.72

Error 70 25.24 0.361

C. Total 72 25.48

Q 2.8 Teaching Years 2 0.49 0.244 0.28 0.76

Error 70 61.43 0.878

C. Total 72 61.92

Q 2.9 Teaching Years 2 0.50 0.248 0.27 0.76

Error 70 64.02 0.915

C. Total 72 64.52

Q 2.10 Teaching Years 2 0.03 0.013 0.03 0.97

Error 69 30.29 0.439

C. Total 71 30.32

Q 2.11 Teaching Years 2 1.71 0.857 1.95 0.15

Error 70 30.78 0.440

C. Total 72 32.49

Q 2.12 Teaching Years 2 0.29 0.143 0.19 0.83

Error 70 53.08 0.758

C. Total 72 53.37

Q 2.13 Teaching Years 2 0.48 0.239 0.25 0.78

Error 70 67.96 0.971

C. Total 72 68.44

131

Appendix J Complete MTEBI ANOVA by Years of Teaching (Cont.)

Source df SS MS F p Q 2.14 Teaching Years 2 7.10 3.551 3.64 0.03

Error 70 68.27 0.975

C. Total 72 75.37

Q 2.15 Teaching Years 2 5.88 2.941 4.89 0.01

Error 70 42.06 0.601

C. Total 72 47.95

Q 2.16 Teaching Years 2 3.08 1.538 2.57 0.08

Error 69 41.37 0.600

C. Total 71 44.44

Q 2.17 Teaching Years 2 1.44 0.722 0.65 0.53

Error 70 78.06 1.115

C. Total 72 79.51

Q 2.18 Teaching Years 2 1.16 0.578 1.29 0.28

Error 69 30.84 0.447

C. Total 71 32.00

Q 2.19 Teaching Years 2 0.45 0.224 1.00 0.37

Error 70 15.66 0.224

C. Total 72 16.11

Q 2.20 Teaching Years 2 2.28 1.140 1.07 0.35

Error 70 74.24 1.061

C. Total 72 76.52

SE Teaching Years 2 0.67 0.335 1.48 0.24

Error 70 15.91 0.227

C. Total 72 16.58

OE Teaching Years 2 0.33 0.163 0.63 0.53

Error 70 18.04 0.258

C. Total 72 18.36

132

Appendix K Complete MTEBI ANOVA Subgroups by Years of Teaching

MTEBI Subgroups Subgroups Diff Std

Diff

Lower

CL

Upper

CL

p-

Value

Q 2.1 Zero to Three Years More than Ten Years 0.409 0.280 -0.261 1.078 0.316

Q 2.1 Zero to Three Years Three + to Ten Years 0.294 0.329 -0.493 1.081 0.645

Q 2.1 Three + to Ten Years More than Ten Years 0.115 0.280 -0.555 0.784 0.912


Q 2.2 More than Ten Years Three + to Ten Years 0.277 0.169 -0.127 0.681 0.235


Q 2.3 More than Ten Years Zero to Three Years 0.278 0.191 -0.181 0.736 0.321


Q 2.3 Three + to Ten Years Zero to Three Years 0.059 0.226 -0.482 0.599 0.963







Q 2.6 More than Ten Years Zero to Three Years 0.443 0.171 0.034 0.853 0.031





















133

Appendix K Complete MTEBI ANOVA Subgroups by Years of Teaching (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value




Q 2.14 Three + to Ten Years More than Ten Years 0.739 0.287 0.052 1.426 0.032



Q 2.15 Three + to Ten Years Zero to Three Years 0.765 0.266 0.128 1.401 0.015

Q 2.15 More than Ten Years Zero to Three Years 0.606 0.225 0.067 1.146 0.024

















SE More than Ten Years Zero to Three Years 0.236 0.139 -0.096 0.568 0.211

SE Three + to Ten Years Zero to Three Years 0.192 0.164 -0.200 0.584 0.472

SE More than Ten Years Three + to Ten Years 0.044 0.139 -0.288 0.376 0.946

OE Three + to Ten Years Zero to Three Years 0.176 0.174 -0.240 0.593 0.571

OE Three + to Ten Years More than Ten Years 0.146 0.148 -0.207 0.499 0.586

OE More than Ten Years Zero to Three Years 0.030 0.148 -0.323 0.384 0.977

134

Appendix L Complete MTEBI ANOVA by Years at Current School

Source df SS MS F p

Q 2.1 School Years 3 1.50 0.501 0.53 0.66

Error 68 63.82 0.938

C. Total 71 65.32

Q 2.2 School Years 3 0.58 0.194 0.56 0.65

Error 68 23.74 0.349

C. Total 71 24.32

Q 2.3 School Years 3 1.24 0.415 0.95 0.42

Error 69 30.23 0.438

C. Total 72 31.48

Q 2.4 School Years 3 0.12 0.041 0.06 0.98

Error 69 45.88 0.665

C. Total 72 46.00

Q 2.5 School Years 3 1.75 0.585 0.97 0.41

Error 69 41.59 0.603

C. Total 72 43.34

Q 2.6 School Years 3 3.43 1.143 3.38 0.02

Error 68 23.02 0.338

C. Total 71 26.44

Q 2.7 School Years 3 1.76 0.588 1.71 0.17

Error 69 23.72 0.344

C. Total 72 25.48

Q 2.8 School Years 3 1.42 0.475 0.54 0.66

Error 69 60.49 0.877

C. Total 72 61.92

Q 2.9 School Years 3 1.21 0.403 0.44 0.73

Error 69 63.31 0.918

C. Total 72 64.52

Q 2.10 School Years 3 0.85 0.283 0.65 0.58

Error 68 29.47 0.433

C. Total 71 30.32

Q 2.11 School Years 3 2.29 0.763 1.74 0.17

Error 69 30.20 0.438

C. Total 72 32.49

Q 2.12 School Years 3 2.28 0.761 1.03 0.39

Error 69 51.09 0.740

C. Total 72 53.37

Q 2.13 School Years 3 1.11 0.371 0.38 0.77

Error 69 67.33 0.976

C. Total 72 68.44

135

Appendix L Complete MTEBI ANOVA by Years at Current School (Cont.)

Source df SS MS F p

Q 2.14 School Years 3 10.48 3.492 3.71 0.02

Error 69 64.89 0.940

C. Total 72 75.37

Q 2.15 School Years 3 1.45 0.483 0.72 0.55

Error 69 46.50 0.674

C. Total 72 47.95

Q 2.16 School Years 3 1.75 0.583 0.93 0.43

Error 68 42.70 0.628

C. Total 71 44.44

Q 2.17 School Years 3 3.06 1.019 0.92 0.44

Error 69 76.45 1.108

C. Total 72 79.51

Q 2.18 School Years 3 0.16 0.052 0.11 0.95

Error 68 31.84 0.468

C. Total 71 32.00

Q 2.19 School Years 3 0.84 0.280 1.27 0.29

Error 69 15.27 0.221

C. Total 72 16.11

Q 2.20 School Years 3 4.17 1.391 1.33 0.27

Error 69 72.35 1.048

C. Total 72 76.52

SE School Years 3 1.06 0.353 1.57 0.20 SE Error 69 15.53 0.225 SE C. Total 72 16.58 OE School Years 3 0.50 0.166 0.64 0.59 OE Error 69 17.87 0.259 OE C. Total 72 18.36

136

Appendix M Complete MTEBI ANOVA Subgroups by Years at Current SCHOOL


Diff

Lower

CL

Upper

CL

p-

Value

Q 2.1 Two+ to Five Years Five+ to Ten Years 0.417 0.415 -0.676 1.509 0.747

Q 2.1 Two+ to Five Years Zero to Two Years 0.397 0.340 -0.499 1.293 0.650

Q 2.1 Two+ to Five Years More than Ten Years 0.357 0.340 -0.539 1.253 0.722

Q 2.1 More than Ten Years Five+ to Ten Years 0.060 0.362 -0.895 1.015 0.998

Q 2.1 More than Ten Years Zero to Two Years 0.040 0.274 -0.682 0.762 0.999

Q 2.1 Zero to Two Years Five+ to Ten Years 0.020 0.362 -0.935 0.975 1.000

Q 2.2 Five+ to Ten Years Zero to Two Years 0.260 0.221 -0.322 0.842 0.644


Q 2.2 Five+ to Ten Years More than Ten Years 0.140 0.221 -0.442 0.722 0.921


Q 2.2 Five+ to Ten Years Two+ to Five Years 0.083 0.253 -0.583 0.750 0.988





Q 2.3 More than Ten Years Two+ to Five Years 0.150 0.232 -0.462 0.762 0.917

Q 2.3 Zero to Two Years Two+ to Five Years 0.096 0.231 -0.512 0.704 0.976














Q 2.6 Five+ to Ten Years Zero to Two Years 0.660 0.218 0.087 1.233 0.018






137

Appendix M Complete MTEBI ANOVA Subgroups by Years at Current School (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value















Q 2.9 Zero to Two Years More than Ten Years 0.206 0.268 -0.500 0.913 0.868






















138



Diff

Lower

CL

Upper

CL

p-

Value







Q 2.14 Two+ to Five Years More than Ten Years 1.120 0.341 0.223 2.017 0.008






























139



Diff

Lower

CL

Upper

CL

p-

Value













SE Five+ to Ten Years Zero to Two Years 0.368 0.177 -0.097 0.833 0.169

SE Five+ to Ten Years More than Ten Years 0.218 0.177 -0.249 0.685 0.611

SE Two+ to Five Years Zero to Two Years 0.191 0.166 -0.245 0.627 0.657

SE Five+ to Ten Years Two+ to Five Years 0.177 0.203 -0.358 0.711 0.820

SE More than Ten Years Zero to Two Years 0.150 0.133 -0.200 0.500 0.674

SE Two+ to Five Years More than Ten Years 0.041 0.167 -0.397 0.480 0.995

OE Two+ to Five Years Zero to Two Years 0.234 0.178 -0.234 0.701 0.557

OE Two+ to Five Years More than Ten Years 0.218 0.179 -0.253 0.688 0.618

OE Two+ to Five Years Five+ to Ten Years 0.175 0.218 -0.399 0.749 0.853

OE Five+ to Ten Years Zero to Two Years 0.059 0.189 -0.440 0.557 0.990

OE Five+ to Ten Years More than Ten Years 0.043 0.190 -0.459 0.544 0.996

OE More than Ten Years Zero to Two Years 0.016 0.143 -0.359 0.391 1.000

140

Appendix N Complete MTEBI ANOVA by Ethnicity

Source df SS MS F p

Ethnicity 2 1.29 0.644 0.69 0.51

Q 2.1 Error 68 63.87 0.939

C. Total 70 65.15

Ethnicity 2 1.01 0.506 1.48 0.23

Q 2.2 Error 68 23.18 0.341

C. Total 70 24.20

Ethnicity 2 4.34 2.169 5.55 0.01

Q 2.3 Error 69 26.98 0.391

C. Total 71 31.32

Ethnicity 2 1.57 0.783 1.22 0.30

Q 2.4 Error 69 44.43 0.644

C. Total 71 46.00

Ethnicity 2 2.54 1.269 2.22 0.12

Q 2.5 Error 69 39.46 0.572

C. Total 71 42.00

Ethnicity 2 3.06 1.531 4.47 0.02

Q 2.6 Error 68 23.30 0.343

C. Total 70 26.37

Ethnicity 2 0.89 0.447 1.26 0.29

Q 2.7 Error 69 24.43 0.354

C. Total 71 25.32

Ethnicity 2 0.40 0.200 0.23 0.80

Q 2.8 Error 69 61.47 0.891

C. Total 71 61.88

Ethnicity 2 2.23 1.113 1.30 0.28

Q 2.9 Error 69 59.27 0.859

C. Total 71 61.50

Ethnicity 2 1.29 0.646 1.56 0.22

Q 2.10 Error 68 28.20 0.415

C. Total 70 29.49

Ethnicity 2 2.96 1.478 3.46 0.04

Q 2.11 Error 69 29.49 0.427

C. Total 71 32.44

Ethnicity 2 0.00 0.002 0.00 1.00

Q 2.12 Error 69 53.27 0.772

C. Total 71 53.28

Ethnicity 2 0.47 0.235 0.24 0.79

Q 2.13 Error 69 67.85 0.983

C. Total 71 68.32

141

Appendix N Complete MTEBI ANOVA by Ethnicity (Cont.)

Source df SS MS F p

Ethnicity 2 1.42 0.711 0.68 0.51

Q 2.14 Error 69 72.23 1.047

C. Total 71 73.65

Ethnicity 2 0.26 0.128 0.19 0.83

Q 2.15 Error 69 47.69 0.691

C. Total 71 47.94

Ethnicity 2 7.68 3.841 7.11 0.00

Q 2.16 Error 68 36.71 0.540

C. Total 70 44.39

Ethnicity 2 2.84 1.420 1.28 0.29

Q 2.17 Error 69 76.66 1.111

C. Total 71 79.50

Ethnicity 2 0.15 0.075 0.16 0.85

Q 2.18 Error 68 31.82 0.468

C. Total 70 31.97

Ethnicity 2 0.86 0.430 2.01 0.14

Q 2.19 Error 69 14.79 0.214

C. Total 71 15.65

Ethnicity 2 2.28 1.141 1.06 0.35

Q 2.20 Error 69 74.16 1.075

C. Total 71 76.44

Ethnicity 2 1.14529 0.572645 2.5755 0.0834

SE Error 69 15.34197 0.222347

C. Total 71 16.48726

Ethnicity 2 0.617299 0.30865 1.2012 0.307

OE Error 69 17.72953 0.25695

C. Total 71 18.34683

142

Appendix O Complete MTEBI ANOVA Subgroups by Ethnicity


Diff

Lower

CL

Upper

CL

p-

Value

Q 2.1 Other African American 0.406 0.406 -0.566 1.377 0.579

Q 2.1 Caucasian African American 0.215 0.242 -0.366 0.796 0.650

Q 2.1 Other Caucasian 0.190 0.403 -0.776 1.157 0.885

Q 2.2 African American Other 0.419 0.244 -0.166 1.005 0.207

Q 2.2 Caucasian Other 0.364 0.243 -0.219 0.946 0.299

Q 2.2 African American Caucasian 0.056 0.146 -0.294 0.406 0.923

Q 2.3 Caucasian African American 0.510 0.155 0.139 0.882 0.005






























143

Appendix O Complete MTEBI ANOVA Subgroups by Ethnicity (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value










Q 2.16 Caucasian Other 1.227 0.326 0.446 2.009 0.001

Q 2.16 African American Other 1.083 0.327 0.300 1.867 0.004














SE Caucasian Other 0.2842 0.1962 -0.186 0.7542 0.3221

SE Caucasian African American 0.2451 0.117 -0.035 0.5254 0.0982

SE African American Other 0.0391 0.1968 -0.432 0.5104 0.9785

OE Other African American 0.3086 0.2115 -0.198 0.8152 0.3169

OE Other Caucasian 0.1905 0.2109 -0.315 0.6957 0.6403

OE Caucasian African American 0.1181 0.1258 -0.183 0.4194 0.6175

144

Appendix P Complete LSTEDI ANOVA by Years of Teaching

Source df SS MS F p

Q 3 1.1

Teaching Years 2 2.300 1.150 1.45 0.24

Error 68 53.897 0.793

C. Total 70 56.197

Q 3 1.2

Teaching Years 2 2.645 1.323 1.16 0.32

Error 68 77.721 1.143

C. Total 70 80.366

Q 3 1.3

Teaching Years 2 6.851 3.425 3.06 0.05

Error 68 76.107 1.119

C. Total 70 82.958

Q 3 1.4

Teaching Years 2 2.539 1.270 1.25 0.29

Error 68 68.897 1.013

C. Total 70 71.437

Q 3 1.5

Teaching Years 2 4.187 2.094 1.95 0.15

Error 68 72.911 1.072

C. Total 70 77.099

Q 3 1.6

Teaching Years 2 2.571 1.285 1.58 0.21

Error 67 54.415 0.812

C. Total 69 56.986

Q 3 1.7

Teaching Years 2 0.170 0.085 0.09 0.91

Error 68 64.309 0.946

C. Total 70 64.479

Q 3 1.8

Teaching Years 2 0.465 0.232 0.20 0.82

Error 66 76.086 1.153

C. Total 68 76.551

Q 3 1.9

Teaching Years 2 0.810 0.405 0.47 0.62

Error 67 57.133 0.853

C. Total 69 57.943

Q 3 1.10

Teaching Years 2 0.906 0.453 0.36 0.70

Error 62 78.479 1.266

C. Total 64 79.385

Q 3 1.11

Teaching Years 2 2.034 1.017 1.19 0.31

Error 63 53.723 0.853

C. Total 65 55.758

Q 3 1.12

Teaching Years 2 1.692 0.846 0.84 0.44

Error 67 67.679 1.010

C. Total 69 69.371

Q 3 1.13

Teaching Years 2 0.618 0.309 0.32 0.72

Error 65 61.897 0.952

C. Total 67 62.515

145

Appendix P Complete LSTEDI ANOVA by Years of Teaching (Cont.)

Source df SS MS F p

Q 3 1.14

Teaching Years 2 0.630 0.315 0.27 0.77

Error 63 74.900 1.189

C. Total 65 75.530

Q 3 1.15

Teaching Years 2 3.392 1.696 1.57 0.22

Error 62 66.824 1.078

C. Total 64 70.215

Q 3 1.16

Teaching Years 2 1.657 0.829 0.83 0.44

Error 63 62.782 0.997

C. Total 65 64.439

Q 3 1.17

Teaching Years 2 2.486 1.243 1.36 0.26

Error 66 60.325 0.914

C. Total 68 62.812

Q 3 1.18

Teaching Years 2 0.996 0.498 0.46 0.63

Error 64 68.945 1.077

C. Total 66 69.940

146

Appendix Q Complete LSTEDI ANOVA Subgroups by Years of Teaching

LSTEDI Subgroups Subgroups Diff Std

Diff

Lower

CL

Upper

CL

p-

Value

Q 3 1.1 Three + to Ten Years Zero to Three Years 0.526 0.310 -0.217 1.269 0.214

Q 3 1.1 Three + to Ten Years More than Ten Years 0.306 0.265 -0.330 0.942 0.485

Q 3 1.1 More than Ten Years Zero to Three Years 0.220 0.260 -0.403 0.842 0.676




Q 3 1.3 More than Ten Years Zero to Three Years 0.751 0.309 0.011 1.490 0.046


Q 3 1.3 More than Ten Years Three + to Ten Years 0.368 0.315 -0.387 1.124 0.476





Q 3 1.5 Zero to Three Years Three + to Ten Years 0.563 0.361 -0.302 1.427 0.270























147

Appendix Q Complete LSTEDI ANOVA Subgroups by Years of Teaching (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value



















148

Appendix R Complete LSTEDI ANOVA by Years at Current School

Source df SS MS F p

Q 3 1.1

School Years 3 5.51 1.836 2.43 0.07

Error 67 50.69 0.757

C. Total 70 56.20

Q 3 1.2

School Years 3 15.48 5.159 5.33 0.00

Error 67 64.89 0.969

C. Total 70 80.37

Q 3 1.3

School Years 3 2.70 0.900 0.75 0.53

Error 67 80.26 1.198

C. Total 70 82.96

Q 3 1.4

School Years 3 4.57 1.524 1.53 0.22

Error 67 66.87 0.998

C. Total 70 71.44

Q 3 1.5

School Years 3 8.65 2.882 2.82 0.05

Error 67 68.45 1.022

C. Total 70 77.10

Q 3 1.6

School Years 3 3.62 1.206 1.49 0.22

Error 66 53.37 0.809

C. Total 69 56.99

Q 3 1.7

School Years 3 5.93 1.976 2.26 0.09

Error 67 58.55 0.874

C. Total 70 64.48

Q 3 1.8

School Years 3 6.73 2.243 2.09 0.11

Error 65 69.82 1.074

C. Total 68 76.55

Q 3 1.9

School Years 3 4.11 1.370 1.68 0.18

Error 66 53.83 0.816

C. Total 69 57.94

Q 3 1.10

School Years 3 13.01 4.335 3.98 0.01

Error 61 66.38 1.088

C. Total 64 79.38

Q 3 1.11

School Years 3 8.49 2.830 3.71 0.02

Error 62 47.27 0.762

C. Total 65 55.76

Q 3 1.12

School Years 3 0.30 0.100 0.10 0.96

Error 66 69.07 1.047

C. Total 69 69.37

149

Appendix R Complete LSTEDI ANOVA By Years at Current School (Cont.)

Source df SS MS F p

Q 3 1.13

School Years 3 9.18 3.059 3.67 0.02

Error 64 53.34 0.833

C. Total 67 62.51

Q 3 1.14

School Years 3 7.67 2.556 2.34 0.08

Error 62 67.86 1.095

C. Total 65 75.53

Q 3 1.15

School Years 3 6.42 2.139 2.05 0.12

Error 61 63.80 1.046

C. Total 64 70.22

Q 3 1.16

School Years 3 1.32 0.441 0.43 0.73

Error 62 63.12 1.018

C. Total 65 64.44

Q 3 1.17

School Years 3 7.45 2.483 2.92 0.04

Error 65 55.36 0.852

C. Total 68 62.81

Q 3 1.18

School Years 3 2.24 0.748 0.70 0.56

Error 63 67.70 1.075

C. Total 66 69.94

150

Appendix S Complete LSTEDI ANOVA Subgroups by Years at Current SCHOOL


Diff

Lower

CL

Upper

CL

p-

Value

Q 3 1.1 Two+ to Five Years More than Ten Years 0.833 0.315 0.004 1.662 0.049

Q 3 1.1 Two+ to Five Years Zero to Two Years 0.696 0.313 -0.128 1.520 0.127

Q 3 1.1 Two+ to Five Years Five+ to Ten Years 0.606 0.391 -0.424 1.636 0.414

Q 3 1.1 Five+ to Ten Years More than Ten Years 0.227 0.338 -0.664 1.117 0.908

Q 3 1.1 Zero to Two Years More than Ten Years 0.137 0.244 -0.505 0.779 0.943

Q 3 1.1 Five+ to Ten Years Zero to Two Years 0.090 0.336 -0.797 0.976 0.993

Q 3 1.2 Two+ to Five Years Zero to Two Years 1.350 0.354 0.417 2.282 0.002





Q 3 1.2 More than Ten Years Zero to Two Years 0.197 0.276 -0.529 0.923 0.891


Q 3 1.3 Two+ to Five Years More than Ten Years 0.480 0.396 -0.563 1.523 0.621









Q 3 1.4 More than Ten Years Five+ to Ten Years 0.244 0.388 -0.779 1.268 0.922







Q 3 1.5 Zero to Two Years Five+ to Ten Years 0.321 0.391 -0.709 1.350 0.845



Q 3 1.6 More than Ten Years Two+ to Five Years 0.335 0.325 -0.523 1.192 0.734




151

Appendix S Complete LSTEDI ANOVA Subgroups by Years at Current School (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value
































Q 3 1.12 Five+ to Ten Years Two+ to Five Years 0.162 0.460 -1.050 1.374 0.985





152

Appendix S Complete LSTEDI ANOVA Subgroups by Years at Current School (Cont.)




































153

Appendix T Complete LSTEDI ANOVA by Ethnicity

Source df SS MS F p Q 3 1.2 Ethnicity 2 1.54 0.770 0.66 0.52

Error 68 78.83 1.159

C. Total 70 80.37

Q 3 1.3 Ethnicity 2 0.02 0.012 0.01 0.99

Error 68 82.93 1.220

C. Total 70 82.96

Q 3 1.4 Ethnicity 2 0.24 0.118 0.11 0.89

Error 68 71.20 1.047

C. Total 70 71.44

Q 3 1.5 Ethnicity 2 2.80 1.398 1.28 0.28

Error 68 74.30 1.093

C. Total 70 77.10

Q 3 1.6 Ethnicity 2 8.47 4.233 5.85 0.00

Error 67 48.52 0.724

C. Total 69 56.99

Q 3 1.7 Ethnicity 2 1.87 0.936 1.02 0.37

Error 68 62.61 0.921

C. Total 70 64.48

Q 3 1.8 Ethnicity 2 4.00 1.999 1.82 0.17

Error 66 72.55 1.099

C. Total 68 76.55

Q 3 1.9 Ethnicity 2 0.64 0.322 0.38 0.69

Error 67 57.30 0.855

C. Total 69 57.94

Q 3 1.10 Ethnicity 2 0.09 0.045 0.04 0.97

Error 62 79.29 1.279

C. Total 64 79.38

Q 3 1.11 Ethnicity 2 0.02 0.012 0.01 0.99

Error 63 55.73 0.885

C. Total 65 55.76

Q 3 1.12 Ethnicity 2 1.46 0.730 0.72 0.49

Error 67 67.91 1.014

C. Total 69 69.37

Q 3 1.13 Ethnicity 2 0.29 0.144 0.15 0.86

Error 65 62.23 0.957

C. Total 67 62.51

Q 3 1.14 Ethnicity 2 2.83 1.417 1.23 0.30

Error 63 72.70 1.154

C. Total 65 75.53

154

Appendix T Complete LSTEDI ANOVA By Ethnicity (Cont.)

Source df SS MS F p

Q 3 1.15 Ethnicity 2 0.91 0.457 0.41 0.67

Error 62 69.30 1.118

C. Total 64 70.22

Q 3 1.16 Ethnicity 2 0.12 0.059 0.06 0.94

Error 63 64.32 1.021

C. Total 65 64.44

Q 3 1.17 Ethnicity 2 0.57 0.285 0.30 0.74

Error 66 62.24 0.943

C. Total 68 62.81

Q 3 1.18 Ethnicity 2 0.07 0.035 0.03 0.97

Error 64 69.87 1.092

C. Total 66 69.94

155

Appendix U Complete LSTEDI ANOVA Subgroups by Ethnicity


Diff

Lower

CL

Upper

CL

p-

Value

Q 3 1.1 Other African American 0.232 0.378 -0.674 1.138 0.813

Q 3 1.1 Other Caucasian 0.232 0.378 -0.674 1.138 0.813

Q 3 1.1 Caucasian African American 0.000 0.227 -0.543 0.543 1.000

Q 3 1.2 Caucasian Other 0.518 0.449 -0.559 1.594 0.485

Q 3 1.2 African American Other 0.424 0.449 -0.652 1.501 0.615



Q 3 1.3 African American Caucasian 0.031 0.276 -0.63 0.693 0.993








Q 3 1.6 Other Caucasian 0.924 0.355 0.073 1.775 0.030

Q 3 1.6 African American Caucasian 0.620 0.214 0.1059 1.134 0.014






















156

Appendix U Complete LSTEDI ANOVA Subgroups by Ethnicity (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value

















157

Appendix V Complete LSTEDI Effectiveness ANOVA by Years of Teaching

Source df SS MS F p

Q 3 2.1 Teaching Years 2 1.70 0.850 1.16 0.32

Error 56 41.18 0.735

C. Total 58 42.88

Q 3 2.2 Teaching Years 2 1.51 0.753 0.82 0.45

Error 49 45.17 0.922

C. Total 51 46.67

Q 3 2.3 Teaching Years 2 7.75 3.877 6.45 0.00

Error 47 28.27 0.601

C. Total 49 36.02

Q 3 2.4 Teaching Years 2 4.25 2.124 2.92 0.06

Error 54 39.23 0.726

C. Total 56 43.47

Q 3 2.5 Teaching Years 2 0.38 0.189 0.17 0.85

Error 34 38.33 1.127

C. Total 36 38.70

Q 3 2.6 Teaching Years 2 0.17 0.083 0.06 0.94

Error 24 34.50 1.438

C. Total 26 34.67

Q 3 2.7 Teaching Years 2 1.32 0.659 0.75 0.48

Error 50 43.85 0.877

C. Total 52 45.17

Q 3 2.8 Teaching Years 2 0.88 0.439 0.46 0.63

Error 53 50.10 0.945

C. Total 55 50.98

Q 3 2.9 Teaching Years 2 2.45 1.224 1.69 0.19

Error 56 40.47 0.723

C. Total 58 42.92

Q 3 2.10 Teaching Years 2 0.86 0.429 0.44 0.64

Error 44 42.55 0.967

C. Total 46 43.40

Q 3 2.11 Teaching Years 2 4.71 2.355 3.25 0.05

Error 49 35.52 0.725

C. Total 51 40.23

Q 3 2.12 Teaching Years 2 1.09 0.544 0.48 0.62

Error 26 29.46 1.133

C. Total 28 30.55

158

Appendix V Complete LSTEDI Effectiveness ANOVA By Years of Teaching (Cont.)

Source df SS MS F p

Q 3 2.13 Teaching Years 2 1.55 0.774 0.77 0.47

Error 42 42.45 1.011

C. Total 44 44.00

Q 3 2.14 Teaching Years 2 0.58 0.288 0.30 0.74

Error 42 40.63 0.967

C. Total 44 41.20

Q 3 2.15 Teaching Years 2 3.83 1.913 2.07 0.14

Error 41 37.90 0.924

C. Total 43 41.73

Q 3 2.16 Teaching Years 2 1.26 0.631 0.78 0.46

Error 48 38.78 0.808

C. Total 50 40.04

Q 3 2.17 Teaching Years 2 1.33 0.665 0.82 0.44

Error 51 41.21 0.808

C. Total 53 42.54

Q 3 2.18 Teaching Years 2 2.31 1.153 1.04 0.36

Error 40 44.16 1.104

C. Total 42 46.47

159

Appendix W Complete LSTEDI Effectiveness ANOVA Subgroups by Years of Teaching


Diff

Lower

CL

Upper

CL

p-

Value







Q 3 2.3 Three + to Ten Years Zero to Three Years 1.015 0.324 0.232 1.799 0.008








Q 3 2.5 Zero to Three Years More than Ten Years 0.125 0.433 -0.937 1.187 0.955






















160

Appendix W Complete LSTEDI Effectiveness ANOVA Subgroups by Years of Teaching (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value



















161

Appendix X Complete LSTEDI Effectiveness ANOVA by Years at Current School

Source df SS MS F p

Q 3 2.1 School Years 3 3.37 1.123 1.56 0.21

Error 55 39.51 0.718

C. Total 58 42.88

Q 3 2.2 School Years 3 7.85 2.617 3.24 0.03

Error 48 38.82 0.809

C. Total 51 46.67

Q 3 2.3 School Years 3 2.72 0.908 1.25 0.30

Error 46 33.30 0.724

C. Total 49 36.02

Q 3 2.4 School Years 3 4.18 1.393 1.88 0.14

Error 53 39.30 0.741

C. Total 56 43.47

Q 3 2.5 School Years 3 1.55 0.518 0.46 0.71

Error 33 37.15 1.126

C. Total 36 38.70

Q 3 2.6 School Years 3 1.49 0.498 0.35 0.79

Error 23 33.17 1.442

C. Total 26 34.67

Q 3 2.7 School Years 3 7.80 2.601 3.41 0.02

Error 49 37.37 0.763

C. Total 52 45.17

Q 3 2.8 School Years 3 4.66 1.552 1.74 0.17

Error 52 46.33 0.891

C. Total 55 50.98

Q 3 2.9 School Years 3 3.22 1.073 1.49 0.23

Error 55 39.70 0.722

C. Total 58 42.92

Q 3 2.10 School Years 3 11.08 3.694 4.91 0.01

Error 43 32.32 0.752

C. Total 46 43.40

Q 3 2.11 School Years 3 16.03 5.344 10.60 <.0001

Error 48 24.20 0.504

C. Total 51 40.23

Q 3 2.12 School Years 3 2.00 0.667 0.58 0.63

Error 25 28.55 1.142

C. Total 28 30.55

162

Appendix X Complete LSTEDI Effectiveness ANOVA by Years at Current School (Cont.)

Source df SS MS F p

Q 3 2.13 School Years 3 6.01 2.005 2.16 0.11

Error 41 37.99 0.926

C. Total 44 44.00

Q 3 2.14 School Years 3 7.31 2.436 2.95 0.04

Error 41 33.89 0.827

C. Total 44 41.20

Q 3 2.15 School Years 3 6.97 2.322 2.67 0.06

Error 40 34.76 0.869

C. Total 43 41.73

Q 3 2.16 School Years 3 3.64 1.214 1.57 0.21

Error 47 36.40 0.774

C. Total 50 40.04

Q 3 2.17 School Years 3 6.44 2.148 2.98 0.04

Error 50 36.09 0.722

C. Total 53 42.54

Q 3 2.18 School Years 3 4.06 1.353 1.24 0.31

Error 39 42.41 1.087

C. Total 42 46.47

163

Appendix Y Complete LSTEDI Effectiveness ANOVA Subgroups by Years at Current

School


Diff

Lower

CL

Upper

CL

p-

Value



































164

Appendix Y Complete LSTEDI Effectiveness ANOVA Subgroups by Years at Current

School (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value



























Q 3 2.11 Two+ to Five Years Zero to Two Years 1.400 0.280 0.655 2.145 <.0001

Q 3 2.11 More than Ten Years Zero to Two Years 1.059 0.240 0.420 1.698 0.000

Q 3 2.11 Five+ to Ten Years Zero to Two Years 0.857 0.316 0.015 1.699 0.045










165

Appendix Y Complete LSTEDI Effectiveness ANOVA Subgroups by Years at Current School

(Cont.)


Diff

Lower

CL

Upper

CL

p-

Value





































166

Appendix Z Complete LSTEDI Effectiveness ANOVA by Ethnicity

Source df SS MS F p

Q 3 2.1 Ethnicity 2 0.42 0.211 0.28 0.76

Error 56 42.46 0.758

C. Total 58 42.88

Q 3 2.2 Ethnicity 2 2.60 1.298 1.44 0.25

Error 49 44.08 0.900

C. Total 51 46.67

Q 3 2.3 Ethnicity 2 0.86 0.430 0.57 0.57

Error 47 35.16 0.748

C. Total 49 36.02

Q 3 2.4 Ethnicity 2 0.23 0.113 0.14 0.87

Error 54 43.25 0.801

C. Total 56 43.47

Q 3 2.5 Ethnicity 2 1.39 0.693 0.63 0.54

Error 34 37.32 1.098

C. Total 36 38.70

Q 3 2.6 Ethnicity 2 1.45 0.727 0.53 0.60

Error 24 33.21 1.384

C. Total 26 34.67

Q 3 2.7 Ethnicity 2 2.25 1.127 1.31 0.28

Error 50 42.92 0.858

C. Total 52 45.17

Q 3 2.8 Ethnicity 2 1.86 0.929 1.00 0.37

Error 53 49.12 0.927

C. Total 55 50.98

Q 3 2.9 Ethnicity 2 0.93 0.464 0.62 0.54

Error 56 41.99 0.750

C. Total 58 42.92

Q 3 2.10 Ethnicity 2 1.44 0.719 0.75 0.48

Error 44 41.97 0.954

C. Total 46 43.40

Q 3 2.11 Ethnicity 2 0.68 0.340 0.42 0.66

Error 49 39.55 0.807

C. Total 51 40.23

Q 3 2.12 Ethnicity 2 0.42 0.210 0.18 0.84

Error 26 30.13 1.159

C. Total 28 30.55

167

Appendix Z Complete LSTEDI Effectiveness ANOVA by Ethnicity (Cont.)

Source df SS MS F p

Q 3 2.13 Ethnicity 2 1.60 0.799 0.79 0.46

Error 42 42.40 1.010

C. Total 44 44.00

Q 3 2.14 Ethnicity 2 1.32 0.658 0.69 0.51

Error 42 39.88 0.950

C. Total 44 41.20

Q 3 2.15 Ethnicity 2 0.02 0.010 0.01 0.99

Error 41 41.71 1.017

C. Total 43 41.73

Q 3 2.16 Ethnicity 2 0.34 0.171 0.21 0.81

Error 48 39.70 0.827

C. Total 50 40.04

Q 3 2.17 Ethnicity 2 2.16 1.082 1.37 0.26

Error 51 40.37 0.792

C. Total 53 42.54

Q 3 2.18 Ethnicity 2 0.30 0.149 0.13 0.88

Error 40 46.17 1.154

C. Total 42 46.47

168

Appendix AA Complete LSTEDI Effectiveness ANOVA Subgroups by Ethnicity


Diff

Lower

CL

Upper

CL

p-

Value








































169

Appendix AA Complete LSTEDI Effectiveness ANOVA Subgroups by Ethnicity (Cont.)


Diff

Lower

CL

Upper

CL

p-

Value















Q 3 2.18 Other African Amerian 0.000 0.594 -1.445 1.445 1.000

170

Appendix BB Complete Correlation Matrix of All Values of LSTEDI AND MTEBI

Q

2.1 Q 2.2

Q

2.3

Q

2.4

Q

2.5

Q

2.6

Q

2.7

Q

2.8

Q

2.9

Q

2.10

Q

2.11

Q

2.12

Q

2.13

Q

2.14

Q

2.15

Q

2.16

Q

2.17

Q

2.18

Q

2.19

Q

2.20

Q 2.1 --

Q 2.2

-

.023 -- "**

Q 2.3

-

.105 .374 --

Q 2.4 .328 .060 .000 --

Q 2.5

-

.113 .358 .694 .134 --

Q 2.6

-

.094 .292 .624 .115 .648 --

Q 2.7

-

.067 .497 .441 .146 .621 .707 --

Q 2.8 .295 .159 .295 .094 .342 .177 .354 --

Q 2.9

-

.054 .084 .088 .441 .133 .110 .147 .033 --

Q 2.10 .305 .295 .237 .485 .246 .190 .331 .270 .405 --

Q 2.11

-

.021 .280 .802 .052 .735 .668 .544 .417 .074 .205 --

Q 2.12 .104 .046 .042 .242 .027 .092 .074 .061 .136 .151 .116 --

Q 2.13 .114 .100 .042 .410 .032 .148 .118 .002 .424 .272 .095 .703 --

Q 2.14 .007 .204 .087 .340 .029 .261 .325 .007 .273 .249 .105 .341 .439 --

Q 2.15

-

.229 .167 .278 .043 .248 .365 .223 .173 .134 .136 .264 .047 .075 .093 --

Q 2.16 .040 .245 .505 .050 .363 .493 .203 .170 .069 .104 .496 .169 .106 .098 .190 --

Q 2.17

-

.025 .285 .407 -.033 .441 .394 .297 .345 -.009 .260 .439 .003 -.028 .088 .402 .365 --

Q 2.18 .007 .303 .479 .127 .515 .484 .435 .218 .135 .185 .569 .283 .193 .194 .391 .416 .403 --

Q 2.19 .086 .461 .379 .147 .364 .275 .372 .219 -.049 .106 .186 .060 -.007 .150 .084 .163 .280 .309 --

Q 2.20

-

.133 .242 .264 .017 .348 .243 .293 .190 .107 .165 .309 .031 .057 .106 .371 .306 .299 .186 .098 --

171

Appendix BB Complete Correlation Matrix of All Values of LSTEDI and MTEBI (Cont.)

172


173


Mathematics Teachers' Perceptions of Self-efficacy ... · And in loving memory of my sister, Kaetia...

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Transcript of Mathematics Teachers' Perceptions of Self-efficacy ... · And in loving memory of my sister, Kaetia...