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The path to math: leadership matters: effective practices of principals that improve student achievement in secondary mathematics

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Content Running head: THE PATH TO MATH: LEADERSHIP MATTERS

1

THE PATH TO MATH: LEADERSHIP MATTERS
EFFECTIVE PRACTICES OF PRINCIPALS THAT IMPROVE STUDENT ACHIEVEMENT
IN SECONDARY MATHEMATICS

by

Michelle Hyo Jung Pyo

________________________________________________________________________

A Dissertation Presented to the
FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION

August 2013

Copyright 2013 Michelle Hyo Jung Pyo

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DEDICATION
This dissertation is dedicated to my parents, Kwang and Kristy Pyo, and my brother,
Daniel Pyo, for inspiring me to take this journey. From a young age, my parents have instilled a
love of learning and a desire to constantly evolve, develop, and be a better version of myself. As
a family, we have embraced happy moments and persevered through tougher times. Through
this, I have learned to endure, be present, and to give 110% of my energy into all that I set out to
do. Without the unwavering support and guidance of my family, I would not be where I am or
who I am today – Dr. Michelle Pyo.

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ACKNOWLEDGEMENTS
First and foremost, I want to thank Dr. Rudy Castruita, the chairman of my committee.
His insight and expertise in the world of education has been invaluable to me during this journey.
Dr. C has mentored me and encouraged me to grow not only as a student but as an educator as
well. I am very fortunate to have an advisor who is offered constant support and guidance to
complete this dissertation. I am thankful for his persistence, patience, and for believing in me.
Appreciation is also expressed to Dr. Pedro Garcia and Dr. Laila Hasan, the other two
members of my committee. Both individuals possess a great deal of knowledge about education
and it was greatly beneficial to have them both as resources.
I am particularly grateful for my family and friends. They offered their endless love and
were always readily available to offer words of encouragement. My family and friends were
patient and understanding whenever I was “missing in action” at various functions. I greatly
appreciate their belief in me.
I would also like to acknowledge Jeffrey “Chip” Naeyaert for being there for me without
fail and always believing in me. Thank you for your gentle nudging and support throughout this
journey.
Lastly, none of this would be possible without the guidance, expertise, and teachings of
all of my educators at every level of schooling. Thank you for inspiring me to become an
educator and for inspiring me to always grow and learn.

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TABLE OF CONTENTS
Dedication 2
Acknowledgements 3
List of Tables 5
List of Figures 7
Abstract 8
Chapter 1: Overview of the Study 9
Chapter 2: Literature Review 16
Chapter 3: Methodology 48
Chapter 4: Findings 60
Chapter 5: Conclusions 110
References 122
Appendices 130
Appendix A: IRB Approval 130
Appendix B: Recruitment Letters 131
Appendix C: Letters of Permission from Philip Hallinger 135
Appendix D: Principal Instructional Management Rating Scale 137
Appendix E: PIMRS Survey 144

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LIST OF TABLES
Table 3.1: Research Design Chart 53
Table 4.1: Frequency of Principals’ Gender, Ethnicity, and Highest Education 63
Table 4.2: Frequency of Years Served as a Classroom Teacher and Primary 64
Subject Taught
Table 4.3: Frequency of Years Served as Principal of Current School Site and 66
Years Served as an Administrator
Table 4.4: Statistics of Instructional Leadership Delegated 67
Table 4.5: Descriptive Statistics for Job Function I: Frame the School Goals 69
Table 4.6: Descriptive Statistics for Job Function II: Communicate the School Goals 70
Table 4.7: Descriptive Statistics for Job Function III: Supervise and Evaluate 71
Instruction
Table 4.8: Descriptive Statistics for Job Function IV. Coordinate the Curriculum 72
Table 4.9: Descriptive Statistics for Job Function V: Monitor Student Progress 73
Table 4.10: Descriptive Statistics for Job Function VI: Protect Instructional Time 74
Table 4.11: Descriptive Statistics for Job Function VII: Maintain High Visibility 75
Table 4.12: Descriptive Statistics for Job Function VIII: Provide Incentives 76
for Teachers
Table 4.13: Descriptive Statistics for Job Function IX: Promote Professional 77
Development
Table 4.14: Descriptive Statistics for Job Function X: Provide Incentives for Learning 78
Table 4.15: Descriptive Statistics for the Principal Instructional Leadership Job 79
Functions
Table 4.16: Percent of Students at Penny High School Testing at Proficient 94
Level or Higher
Table 4.17: Percent of Students at Weston High School Testing at Proficient 94
Level or Higher
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Table 4.18: Percent of Students at Arthur High School Testing at Proficient 95
Level or Higher
Table 4.19: Frequency of Principals’ Gender, Ethnicity, and Highest Education 96
Table 4.20: Frequency of Years Served as a Classroom Teacher and Primary 97
Subject Taught
Table 4.21: Frequency of Years Served as Principal of Current School Site and Years 98
Served as an Administrator
Table 4.22: Statistics of Instructional Leadership Delegated 99
Table 4.23: Descriptive Statistics for the Principal Instructional Leadership Job 100
Functions

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LIST OF FIGURES
Figure 3.1. Data analysis methods 55
Figure 3.2. Creswell’s model for qualitative data analysis 56

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ABSTRACT
The quality of school leadership is linked to student academic achievement (Leithwood et al.,
2004; Thompson & Barnes, 2007; Glatthorn & Jailall, 1997; Lezotte, 1991; Edmonds, 1979;
Hallinger & Heck, 1996; Crum & Sherman, 2008). The purpose of this study was to examine the
instructional leadership (IL) of high school principals and its impact on student achievement,
particularly in mathematics. This study sought to determine the: (1) self-perceived IL behaviors
of high school principals; (2) IL strategies that influenced positive outcomes of academic
achievement; and (3) relationship between the IL behaviors of principals and student
mathematics achievement. Using a mixed methods approach, quantitative data was drawn from
26 principals who completed the Principal Instructional Management Rating Scale (PIMRS)
survey (Hallinger, 1999) and qualitative data was gathered from three of these principals through
an interview. Triangulation of data emphasized principal’s impact on student achievement.
Surveyed principals frame the school goals as well as supervise and evaluate instruction.
Interviewed principals expressed the importance of: (1) shared IL functions; (2) teacher
empowerment; (3) professional learning communities and other professional developments; (4)
creating opportunities for all students to be successful; and (5) evolving the school culture. A
positive correlation was found between principals’ IL and student performance in secondary
mathematics. Students have exhibited improved test scores in mathematics since the current
instructional leader and principal began his or her tenure. This study begins to bridge the gap
between principals’ IL abilities and student learning outcomes, particularly in secondary
mathematics.

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CHAPTER 1
OVERVIEW OF THE STUDY
Introduction
Despite the critical importance of a strong understanding of mathematics, students
throughout the United States are struggling to succeed in mathematics. Math is more than
simply plugging numbers into formulas and calculating values. Math is a way of thinking that
enables people to solve complex problems by using reasoning and logic skills. Nearly every
career requires at least a basic knowledge of math skills.
A student’s performance on national math exams is a strong predictor of their potential
educational attainment. Murnane (1995) found the average scores of students who graduated
college were nearly double of their classmates who only received a high school diploma.
Furthermore, the level of schooling a student completes is highly correlated with the amount of
money earned (Murnane et al., 1995). Students who are Latino, African American, Native
American and from poverty-ridden communities have less access to higher-level math courses
and perform worse than white middle-class students (Tate, 1997; Kitchen, 2003; Allexsaht-
Snider, 2001). Despite the importance of developing critical thinking skills, schools that serve
students from low-income areas generally enact the “pedagogy of poverty” and focus on rote
instruction of basic skills (Haberman, 1991). Action must be taken to eliminate the pedagogy of
poverty and ultimately, increase the math proficiencies of those students who traditionally have
failed to excel in mathematics.
It is important to consider what currently is being done to improve student achievement
in mathematics. Some teachers structure their classrooms so all students, regardless of
background, have the opportunity to excel and advance in mathematics. However, the efforts of
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these teachers are individualized for their own classrooms and disconnected from other teachers.
All students attaining educational equity in mathematics and other subject areas (Quinn, 2002)
must be a shared goal that all teachers collaboratively work towards. For this to happen, school
administrators must get involved.
In particular, principals are highly influential in determining the success of a school and
the types of experiences that students receive. The procedures, curriculum, and programs they
enact directly impact teaching practices. In turn, this affects the types of learning experiences
students engage in. Principals must take responsibility for their school’s performance and strive
to build a strong school community where learning takes place. To facilitate this, principals
must serve as powerful instructional leaders for the excellent teachers they hire, develop and
retain. A principal’s ownership of his or her role as an instructional leader has a direct
relationship to improved student performance (Quinn, 2002, p. 447). Schools that excel
academically have principals who are effective instructional leaders. Similarly, principals of
low-achieving schools are not effective instructional leaders (p. 449). The key relationship
between effective leadership and student performance is undeniable, particularly in the area of
reading and math (Quinn, 2002; Andrews, 1987).
Considering the indispensible importance of math for all students, principals must
commit to taking action against the pedagogy of poverty and work towards equity for all students.
Using their roles as instructional leaders, principals can guide the school community and
classroom environment to improve teacher instruction and improve student outcomes.
Statement of the Problem
As a highly visible leader, an effective principal is able to facilitate meaningful change
within their school. An emphatic principal can motivate and drive the staff and students to work
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towards meeting school-wide goals to improve academic achievement, particularly in
mathematics. Along the same lines, an ineffective principal can have the opposite effects and
drive their school to failure.
The principal plays a pivotal role in setting the direction of a school. As the instructional
leader of a school, the principal can impact teachers’ instructional practices to students’
academic performance (Quinn, 2002, p. 447). The uncertainty lies in identifying the specific
actions principals have taken that has led to improved academic achievement in secondary
mathematics. Current and dated literature affirms the importance of a principal and their abilities
to move a school in a particular direction. Research also indicates that a student’s performance
in high school mathematics is a strong beacon for a student’s ability to complete college and how
much money they will earn in their future careers. Current research is missing the connection
between high school principals’ practices and student performance in secondary mathematics.
Purpose of the Study
The purpose of this study was to uncover the practices of high school principals who
have successfully used their role as the instructional leader to improve student learning and
achievement in mathematics. This study sought to uncover instructional leadership traits,
behaviors, practices, and actions.
Research Questions
The following research questions will be explored and answered through this study:
(1) What are the self-perceived instructional leadership behaviors of high school
principals?
(2) What instructional leadership strategies do principals employ that influence positive
outcomes of academic achievement?
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(3) What is the relationship between the instructional leadership behaviors of principals
and student achievement in mathematics?
Importance of the Study
There is a national and economic importance for students to develop a strong foundation
in mathematical skills. An article in The Wall Street Journal states that America is losing critical
ground in math and science skills, which are the “scientific and technical building blocks of our
economy” (Mullich, 2009). As a result, the international economic playing field is no longer
skewed in favor of the United States. According to the Committee on Prospering in the Global
Economy of the 21
st
Century, the global playing field is flattening out which results in countless
American companies are outsourcing job to other countries as these countries have gained
“easier access to information technology and rising technical competences” (2007).
According to the Trends in Mathematics and Science Study (TIMSS), 4
th
- and 8
th
-graders
in the United States performed worse than students taking the same exam in several leading
Asian and European countries such as South Korea, Japan and England (2007). To remain a
competitive force on the global level, it is imperative that our students are high skilled in the
areas of math and science. It is evident that students in the United States are not fluent in these
areas.
For the first time ever in 2008, more patents were issued abroad than to Americans by the
U.S. Patent and Trademark Office (Mullich, 2009). Math and science are the foundation for
innovation. Intel’s Dunkle states that, “fluency in math is needed to understand science, and
science creates the innovations that will help solve the challenges we face” (Mullich, 2009).
Because math and science play such a significant role globally, it is crucial that math and science
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education are reexamined and remediated such that all students are able to learn effectively. The
United States needs highly skilled mathematicians to compete and thrive on a global level.
This study will be useful to principals in practice. Current principals can use the
strategies their colleagues used successfully to improve math achievement within their own
schools. Principals can also use the information found in this study as the basis for their own
professional development and work towards improving their own schools academic performance
in mathematics.
Furthermore, this study will be useful to principal leadership programs and other
programs that award individuals with the administrative services credential. The leadership traits
and practices that this study reveals would be useful tools for principals to be equipped with.
Training programs can teach future administrators what has worked for other principals in the
past in various settings in moving the school towards excelling in mathematics.
Limitations, Delimitations, Assumptions
The main limitations for the scope of this study relate to the observed events of the
researcher and those being interviewed. Principals, teachers and students will be interviewed
and their answers are assumed to be true. However, it is impossible to know for certain if
everything people say in their interviews is accurate. Also, this research examines five years’
worth of data ranging from the 2006-2007 to 2010-2011 school years. Because the quantitative
data collection began prior to this year, it is impossible to go back in time and know for certain
what happened in the past qualitatively.
The delimitation of this study was the criteria used to select principals asked to
participate in this study. All selected principals met the following selection criteria:
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(1) lead a comprehensive public high school serving grades nine through twelve;
(2) located in large urban areas (i.e., Los Angeles county);
(3) minimum of 45% free and reduced lunch;
(4) minimum of 1100 students; and
(5) minimum of two years as the principal at their current school site.
Schools with predominantly minority and low-income student populations were chosen
because research has shown that these are the groups of students that typically perform poorly in
secondary math courses and exams. Furthermore, schools with marked improvement in
mathematics were chosen to examine what principals of these schools have done to boost student
achievement. Lastly, principals who have been in their position since the 2006-2007 school year
were chosen to track the specific tactics and actions they chose to enact in their schools that have
led to improved student academic achievement.
Definition of Terms
The following terms and acronyms will be used throughout the study:
API: Academic Performance Indicator: All California K-12 schools receive an API score
based on overall performance and progress. Scores range from 200 to 1000; the latter being the
highest score possible.
AYP: Annual Yearly Progress: Similar to the API, schools receive an AYP score based
on performance and progress but this score is used federally and stems from the No Child Left
Behind Act.
CST: California Standards Test: All students from grades two to eleven take the CSTs
every spring in the areas of math, writing, reading, science and history. The CST gauges student
learning based on state learning standards specific to each subject area.
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Equity: All students will learn regardless of their background (Allexsaht-Snider, 2001).
As it pertains to mathematics, all students will be able to receive a quality mathematics education
and there will be equitable outcomes for all students.
IL: Instructional leadership: This is the administrator’s behaviors that affect a teacher’s
practice, which in turn leads to effective instruction and improved student learning (Quinn, 2001,
p. 447).
PI: Performance Improvement: This is the idea that you can measure the outcome of a
process or procedure, in this case schools, and then work to improve their effectiveness and
efficiency.
Organization of the Dissertation
Chapter 1 presents an overview of the study including background information, the
statement of problem and the purpose and importance of this study. This chapter also outlines
research questions, definitions of key terms and the limitations, delimitations and assumptions
associated with this study. Chapter 2 is a review of related literature and research and presents
the theoretical framework that is the basis for this study. Chapter 3 states the methodology used
to conduct this study and includes detailed information on the sampling criteria, instrumentation,
data collection and data analysis. Results and findings of the study are reported in Chapter 4.
The final chapter summarizes the findings and discusses limitations of the study, implications for
practice and concludes with recommendations for future research.

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CHAPTER 2
LITERATURE REVIEW
The importance of developing a strong understanding of mathematics is undeniable. In
2002, No Child Left Behind (NCLB) mandated that all students to be proficient in mathematics
by the end of the 2013-14 school year. Despite this quickly approaching deadline, many students
across the nation still struggle to succeed in secondary mathematics.
Presented in this chapter is a brief history of education in the United States leading up to
the current era of educational accountability. The significance of an education in mathematics
will be discussed. Previous literature on effective schools research will be synthesized. In
particular, the impact and role of the principal will be discussed in great detail along with
prevailing educational leadership theories. Connections will be made between the role of the
principal, student learning outcomes, and mathematics education. This literature review will
serve as a theoretical framework to answer the research questions presented in this study.
Era of Educational Accountability
Current education mandates hold schools accountable for student learning outcomes.
Outcomes are measured by student achievement on assessments linked to explicit learning
standards and performance targets (Marsh, 1999). Leading up to the era of educational
accountability, the U.S. Department of Education published a report in 1983 entitled “A Nation
at Risk: The Imperative for Educational Reform”. The report stated that the performance of U.S.
students was far worse than that of students in other industrialized countries. American students
produced the lowest scores on seven out of nineteen academic tests and were never first or
second on any test (Gardner, 1983). Based on the recommendations made by “A Nation at Risk”,
schools enacted varied reforms but these failed to produce an increase in achievement. To make
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matters worse, public schools in the U.S. had the third-highest expenditures compared to other
economically advanced countries but produced among the lowest levels of academic
achievement (Walberg, 2001).
The Elementary and Secondary Education Act (ESEA) was enacted in 1965 to create
equitable education opportunities to disadvantaged students, particularly those who came from
low-income families (Thomas & Brady, 2005). However, no accountability measures were in
place to ensure that the Title I funds were used properly and not abused. Over time, provisions
were added to make certain funds were used to provide supplemental services to students in need
and that these students demonstrated improved academic achievement (Thomas & Brady, 2005).
In 2002, President Bush signed the No Child Left Behind (NCLB) Act as a
reauthorization of the Elementary and Secondary Education Act (ESEA). No Child Left Behind
is based on four pillars: (1) stronger accountability for results; (2) more freedom for states and
communities; (3) proven education methods; and (4) more choices for parents (Department of
Education, 2004). Accountability mandates of NCLB hold states and schools accountable for
student academic achievement and progress. Under NCLB, states must develop math and
science programs that are more rigorous, aligned with academic content standards and “standards
expected for postsecondary study in engineering, mathematics, and science” (Department of
Education, 2004).
Furthermore, NCLB requires all students demonstrate proficiency in mathematics on an
annual assessment by the end of the 2013-14 school year. These mandates have increased the
pressure for enhanced performance and achievement of satisfactory learning results by schools
and students (Ruebling, Stow, & Kayona, 2008). The United States Department of Education
(2009) reported that more than three-quarters of all fourth- and eighth-graders performed below
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the proficient level in 2000. High school seniors have not exhibited any improvement in
mathematics since 1996. Schools serving students in low-income areas have failed to improve
low levels of achievement and achievement has remained stagnant from 1988 to 1996 (Walberg,
2001). Furthermore, students who are of low socio-economic status and students who are of
ethnic minorities have consistently exhibited lower levels of academic achievement than students
who come from wealthy homes and are Caucasian (Kortez & Kim, 2007). Rather than
improving, performance has deteriorated even more for these students at the lower levels of
achievement (Department of Education, 2009).
The deadline set by NCLB for mathematics proficiency is fast approaching but
performance remains stagnant and students across the nation are not showing signs of
improvement. According the United States Department of Education (2009), students are not
exhibiting the excellence necessary for “global economic leadership and homeland security in
the 21
st
century.”
Importance of Mathematics Education
Students must exhibit a strong understanding of mathematics to meet federal
accountability mandates but possessing math skills is of national and economic importance as
well. Mathematical ability is an essential and critical skill that our students must possess to
thrive in the technological age of today. The U.S. Department of Education (2009) warns that
the current state of math performance “shortchanges our students’ future and endangers our
prosperity and our nation’s security.”
Math and science skills are the “scientific and technical building blocks of our economy”
(Mullich, 2009) as well as the foundation for innovation. Intel’s Dunkle states that, “fluency in
math is needed to understand science, and science creates the innovations that will help solve the
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19
challenges we face” (Mullich, 2009). Alas, students across the nation are struggling to succeed
in these subjects. The Committee on Prospering in the Global Economy of the 21
st
Century
(2007) states that countless American companies even outsource jobs to other countries that have
gained better and “easier access to information technology and rising technical competencies”.
Unfortunately, more patents were issued abroad than to Americans by the U.S. Patent and
Trademark Office for the first time since 2008 (Mullich, 2009).
Excellence in math and science is essential and indicate a student’s readiness for success
in engineering, medicine, and careers in the “high-tech, fast-growing, competitive sectors of
modern economies” (Walberg, 2001, p. 56). The United States needs highly skilled
mathematicians to compete and thrive on a global level. Despite this fact, American students are
struggling to excel in mathematics.
A report released by the Organization for Economic Cooperation and Development
(OECD) showed that students in the U.S. made the smallest value-added achievement gains in
mathematics compared to other countries surveyed. “Value-added gains” is defined as the
amount of improvement in academic achievement over a given time period (Walberg, 2001).
Compared to students in other economically advanced countries, American students perform
worse in mathematics and also exhibit the least amount of improvement in academic
achievement. The achievement gap between students in the United States and other
industrialized countries must be closed to remain competitive in the global market and for
innovation to flourish.
An achievement gap also exists among students within the United States. White middle
class students outperform students who are African-Americans, Latinos, Native Americans and
students who are of low socioeconomic status (Allexsaht-Snider & Hart, 2001; Weber, Radu,
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Mueller, Powell, & Maher, 2010). White middle class students exhibit higher scores in
mathematics and also reach higher levels of mathematics. Countless studies and reports attest to
the fact that students of low socioeconomic status perform below the national average on
standardized mathematics assessments and are more likely to drop out of school early (Weber,
Radu, Mueller, Powell, & Maher, 2010).
The National Council of Teachers of Mathematics (NCTM) was founded in 1920 and
works to “ensure equitable mathematics learning of the highest quality for all students through
vision, leadership, professional development and research”. Providing students equitable
learning opportunities that are free from any biases can close the achievement gap in
mathematics. This includes both intentional and unintentional biases based on race, gender,
socioeconomic status, language, or any other factor. NCTM (2012) states that well-qualified
teachers must hold high expectations for all students, challenge them to achieve at high levels,
and engage students using instructional practices that are tied to both content and students’ needs.
Mathematics is a “critical filter” and a student’s mathematics coursework is considered
the gateway to technological literacy and higher education (Schoenfeld, 2002). Success in
mathematics is an indicator for future success beyond schooling. Murnane, Willet, and Levy
(1995) found that the math scores of students who went on to graduate school from college was
nearly double that of students whose highest level of education was completing high school.
Society views education as a democratic vehicle for advancement (Schoenfeld, 2002) and this is
especially true when considering math education. All students must be given access to a high-
quality mathematics education.
In its simplest form, Edmond (1979) defines equity to be a “sense of fairness in the
distribution of primary goods and services that characterize our social order” (p. 15) while
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maintaining the assumption that some will have or need more than others. Allexsaht-Snider and
Hart (2001) states that math educational equity requires the following: (1) equitable distribution
of resources; (2) equitable quality of instruction; and (3) equitable learning outcomes. Once
differences between sub-groups of students disappear, equity has been achieved. Learning
outcomes must be improved for all students but achieving equity in mathematics education is a
process that is easier said than done. Student outcomes linked to equity include student
achievement as well as course enrollment, interest and motivation in pursuing mathematics, and
valuing of mathematics (Allexsaht-Snider & Hart, 2001). Equity must be inherent in school
culture to maximize the learning potential of all students (NCTM, 2010). In addition to
determining the math courses that students should take, educational leaders need to ensure that
all students are given the opportunity and access to learn mathematics (Schoenfeld, 2005).
Effective Schools Research
As a result of the accountability era, researchers searched for ways that schools
effectively fulfilled their core responsibility of teaching and learning of students. The need for
improved learning outcomes is undeniable, particularly in the area of mathematics. Students in
the U.S. scored lower than the OECD average on the mathematics literacy scale. Of the students
who failed to achieve basic levels of mathematics literacy, most were of minority or low-
socioeconomic status. Effective schools research uncovers the collective efforts, behaviors,
practices, and procedures of schools – by both teachers and leaders – that have led to improved
student learning outcomes for all students. The focus of effective schools research is on
collective efforts rather than what just individual teachers do to improve outcomes.
The Search for Effective Schools project sought to identify schools that effectively taught
poor children and minority children (Edmonds, 1979). The project stated that “all children are
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22
eminently educable and that the behavior of the school is critical in determining the quality of
that education” (p. 20). Administrative behaviors, policies, practices and other factors under the
school’s control were found to have the greatest impact on school effectiveness (p. 16). Through
his research, Edmonds (1979) found the six most tangible and crucial elements of effective
schools to be the following:
(a) They have strong administrative leadership without which the disparate elements of
good schooling can neither be brought together nor kept together; (b) Schools that are
instructionally effective for poor children have a climate of expectation in which no
children are permitted to fall below minimum but efficacious levels of achievement; (c)
The school's atmosphere is orderly without being rigid, quiet without being oppressive,
and generally conducive to the instructional business at hand; (d) Effective schools get
that way partly by making it clear that pupil acquisition of basic school skills takes
precedence over all other school activities; (e) When necessary, school energy and
resources can be diverted from other business in furtherance of the fundamental
objectives; and (f) There must be some means by which pupil progress can be frequently
monitored. (p. 22)
Crum and Sherman (2008) found effective schools that produce high-achievement to
practice the following: (1) develop personnel and facilitating leadership; (2) delegate
responsibilities and empower the team; (3) recognize ultimate accountability; (4) communication
and rapport; (5) facilitate instruction; and lastly, (6) manage change (p. 7).
Lezotte (1991) produced seven correlates of effective schools: (1) safe and orderly
environment; (2) climate of high expectations; (3) instructional leadership; (4) clear and focused
mission; (5) opportunity to learn and student time on task; (6) frequent monitoring of students
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progress; and (7) home-school relations (Lezotte, 1991). The seven correlates of effective
schools parallels Edmonds’ six characteristics of effective schools. A common theme that
emerges from effective schools research is the impact that strong, instructional leadership has on
a school’s ability to be effective and produce positive student academic learning outcomes
(Leithwood et al., 2004; Thompson & Barnes, 2007; Glatthorn & Jailall, 1997; Lezotte, 1991;
Edmonds, 1979; Hallinger & Heck, 1996; Crum & Sherman, 2008).
Through their extensive review of research dating form 1980 to 1995, Hallinger and Heck
(1996) assert the notion that school leadership affects students learning. Effective schools
research has also examined the role of the principal. Crum and Sherman (2008) stated that
outstanding principals have the following six attributes: (1) external awareness and engagement;
(2) a bias towards innovation and action; (3) personal qualities and relationships; (4) vision,
expectations and a culture of success; (5) teacher learning, responsibility and trust; and (6)
student support, common purpose and collaboration (p. 4). In addition to these six attributes,
excellent principals are focused on the students and their learning.
Leithwood et al. (2006) identified three basic categories of leader practices: (1) setting
directions; (2) developing people; and (3) redesigning the organization. Setting directions means
working with the group or organization to develop shared goals that instill a sense of purpose or
a vision. Also, it is important to maintain high performance expectations. By developing people,
the leader is building capacity and motivation for achievement. Instructional leadership skills
plays an indispensible role when developing people in an organization as it involves the ability to
help teachers improve the quality of teaching and learning of students. Lastly, it is important for
leaders to be able to facilitate positive change when improvement and achievement becomes
stagnant. Leaders must be able to strengthen school cultures, modify organizational structures
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and build collaborative practices (p. 8, 23). These elements are essential for ensuring that a
school is successful at fulfilling its mission of producing student learning outcomes.
Considering the colossal impact principals have, they must direct their focus on
facilitating systemic change to improve student academic achievement and learning outcomes.
To be effective, the leader must help the organization “set a defensible set of directions and
influencing members to move in those directions” (Leithwood et al., 2004, p. 6). The idea that
there is not just one simple quick-fix solution is to be stressed. Improving student learning and
student outcomes is a process. School improvement is a never-ending journey and schools
should be working to move closer to learning for all (Lezotte, 1991). Though the process may
appear innately ceaseless, education leaders and educators must take continuous steps towards
creating equitable opportunities and improving learning outcomes for our students.
As a result of effective schools research, the Interstate School Leadership Licensure
Consortium (ISLLC) is part of the Council of Chief State School Officers (CCSSO). The ISLLC
holds that the primary responsibility of a school leader is to improve teaching and learning for all
children. The consortium has identified six school leadership standards: (1) developing a shared
vision for learning; (2) creating a school environment that is conducive to both student learning
and staff professional development; (3) effectively managing school organization, operation and
resources; (4) collaborating with the faculty and community; (5) acting with integrity, fairness
and ethics; and (6) handling political, social, legal and cultural contexts (ISLLC, 2008, p. 6).
State education leadership policies regarding the principalship have used these six standards as a
model. These standards have been used to inform the preparation, licensing, induction, and
professional development of school leaders (p. 4) and are used by various organizations
including education departments at the state level.
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Also through effective schools research, a definition of a highly effective principal (HEP)
was developed. Glatthorn and Jailall (1997) found that the quality of teachers within a school is
linked to the quality of the principal. A HEP can implement reform movements within a school
that lead to improved student academic outcomes. Furthermore, a HEP can sustain this change
over time, produce high student achievement, and turn around a school that is low-performing
(Glatthorn & Jailall, 1997). No Child Left Behind also includes language regarding HEPs. In
addition to meeting state requirements for becoming a principal, a HEP must be able to “produce
improvements in student achievement that are comparable to high-achieving schools made up of
similar children with similar challenges” (Thompson & Barnes, 2007, p. 50). An administrator’s
ability to accomplish this task is indicative of the ability to lead a school effectively.
According to McEwan (2003), a highly effective principal is one who is: (1) a
communicator; (2) an educator; (3) an envisioner; (4) a facilitator; (5) a change master; (6) a
culture builder; (7) an activator; (8) a producer; (9) a character builder; and (10) a contributor.
By possessing and making use of these ten traits, a highly effective principal is able to push a
school towards producing improvements in student academic achievement. The National
Association of Secondary School Principals (NASSP) asserts that highly effective principals are
responsible for implementing school-wide reforms that will ultimately lead to improved teaching,
high levels of academic achievement and improved learning outcomes. Failure to successfully
meet accountability mandates set by state and federal measures will lead to corrective actions for
the school.
Emergent in the effective schools literature is the notion that the quality of leadership in a
school makes a difference in student learning outcomes. Missing from effective schools research
is direct connections to how school leaders have been able to effectively effect improvement in
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student learning in mathematics. Considering the widespread lack of mathematical fluency that
U.S. students exhibit, this issue must be addressed immediately. The principal who is also a
strong instructional leader is best equipped with the skills necessary to facilitate change that will
lead to and sustain improved student learning and academic achievement, particularly in
mathematics.
Evolution of the Principalship
A principal’s primary function has shifted and evolved over time since the development
of the principalship in the education system. When schools were first developed, the primary
role of the principal was as the head teacher of the school. As head teacher, the principal was the
local expert on teaching and learning – both responsible for a large student body and for the
development of teachers (Hill, 2002). As school systems began to expand and develop, there
was a need for principals to shift their focus to school organization, inputs, and processes.
Beck and Murphy (1993) describe the evolution of principalship from the 1920’s to the
1990’s. In the 1920’s and 1930’s, the principal served roles such as the spiritual leader,
scientific manager, dignified leader, and social leader. In the 1940’s, the principal became the
democratic leader and curriculum leader and in the decade following, the principal was the
defender of educational practice. The principal became the accountable, bureaucratic executive
in the 1960’s. In the 1970’s, the principal took on a more personable role as the community
leader and facilitator of positive relationships. The principal as an instructional leader began to
take shape in the 1980’s in response to schools’ need for a visionary and a change agent.
As standards-based accountability pressures emerged with recent education laws, the
focus of the principal shifted back to the school’s main instructional leader who oversees
teaching and learning. Principals began to feel pressure to increase student achievement and
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outcomes with the onset of the era of educational accountability (Timar, 2003). The
accountability mandates as defined by NCLB and state-specific measures include the need to
improve student achievement and preparing students to pass a high school exit examination
while also complying with “class size reductions, high-stakes accountability, and increasing
restrictions on funding” (Timar, 2003, p. 189).
Furthermore, contemporary school leaders are tasked with ensuring the schools they lead
are meeting the needs of an ever-changing “demographic context of education” where student
populations are increasingly diverse and more students are less proficient in English, if at all
(Timar, 2003, p. 189). This is all while consistently improving student achievement and facing
shortages in district funding which lead to shortages in teachers and administrators. Graczweski
(2009) states that there is a great need for instructional leadership in schools to meet the needs of
all students as well as comply with educational accountability mandates.
Darling-Hammond, Meyerson, and La Pointe (2007) discuss the multitude of functions
that contemporary leaders are responsible for. These roles range from “educational visionaries
and change agents to instructional leaders, curriculum and assessment experts, budget analysts,
facility managers, special program administrators, and community builders” (p. 2). Meanwhile,
principals must also create an academically challenging while personally supportive culture in
schools to motivate traditionally underperforming, underserved, and poor students to complete
school (Kaplan & Owens, 2001). To effectively fulfill the diverse set of functions, principals
must possess a wide range of skills and abilities. Principals require a diverse set of skills
“including both the capacity to develop strong instruction and a sophisticated understanding of
organizations and organizational change” (p. 2).
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Principals are assumed to possess sufficient knowledge about teaching and learning to be
effective instructional leaders because they typically enter the field of education as teachers. Yet,
most principals lack deep and current knowledge about teaching and learning (Hill, 2002) and
teachers possess limited knowledge about the functioning of schools. The clash between
“organizationally clueless teachers and educationally uninformed administrators” leads to
schools with poor foundations for success (Beck & Murphy, 1993, p. 5). Experience in the
classroom does not necessarily translate to the ability to be an effective instructional leader.
Principals must be armed with the abilities and knowledge to handle an intricate, ever-changing
environment to properly implement reform movements that will lead to sustained improvement
in student learning outcomes (Fullan, 2002; Hill, 2002). Furthermore, extensive knowledge of
teaching and learning are critical to leveraging change in the classroom. School improvement
must be the priority of the principal and an extensive applied knowledge must be acquired.
Impact of the Principal
Much of the research conducted by leaders in the field of education, including effective
schools research, stresses the crucial and decisive role that principals play in the success of
schools, both improving the quality of education provided as well as the development of a high-
performing school. Studies have consistently asserted the notion that principals who lead high-
performing schools possess the skills and traits necessary to be highly effective (Thompson &
Barnes, 2007). Furthermore, research reinforces the revelation that quality of school leadership
is linked to student performance (Leithwood et al., 2004; Thompson & Barnes, 2007; Glatthorn
& Jailall, 1997; Lezotte, 1991; Edmonds, 1979; Hallinger & Heck, 1996; Crum & Sherman,
2008). Waters, Marzano, and McNulty (2003) found a substantial relationship between the
principal and student achievement. Having a principal with more leadership ability meant higher
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achievement by students of that school. The inverse statement was also found to be true in that
less principal leadership ability meant lower levels of student achievement (p. 3).
Considering the influence of principals on the schools they lead, they must use their
power to effect change as it pertains to student learning of mathematics. Robert Moses argues
“mathematics education is a civil rights issue” as quantitative literacy is an issue that can hold
particular students to “second-class economic status in our increasingly technology society” (as
cited in Schoenfeld, 2002, p. 12). The math learning experience of students of color and students
who are from low-income homes are typically shortchanged when compared to their wealthier,
Caucasian counterparts. Poor, African-American, Latino, and Native American students have a
higher drop out rate and lower scores on standardized math tests (Schoenfeld, 2002).
The Southeast Center for Teaching Quality (SECTQ, 2005) found that the quality of
leadership in a school was “single greatest predictor of AYP status” over any other school-
related factor, including school size and teacher retention (p. 7). In 2002 and 2004, SECTQ
surveyed the opinions of teachers in North Carolina about several factors impacting a teacher’s
decision to remain in a school as well as student learning. The survey sought to find the impact
of working conditions on time. Surveyed topics included time, facilities and resources,
empowerment, leadership and professional development. The analysis of approximately 90
percent of schools in North Carolina and 34,000 responses revealed that teacher working
conditions are critical to increasing student achievement (SECTQ, 2005). Of the major findings
of this comprehensive study, SECTQ determined that leadership played the most critical role in
improving teacher working conditions. Teachers ranked the quality of leadership as the most
important condition for determining student academic success as well as job satisfaction (p. 23).
Research also shows that the quality of a principal also impacts school culture.
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As a result of the research, the SECTQ (2005) recommended that leaders at the state level
invest in high quality school leaders who not only support teaching and learning but also
empower teachers to make decisions about instruction that will help all students succeed.
Principals must be equipped with the necessary knowledge and skills to facilitate school
improvement. Furthermore, the SECTQ (2005) affirms the importance of school leadership that
is “responsive to the need of all teachers and students” (p. 22). A lack of administrative support
is a common cause of teacher job dissatisfaction and one of the top reasons for leaving a school
according to the School and Staffing Survey from the National Center for Education Statistics
(SECTQ, 2005). This includes providing support as an instructional leader as well as facilitating
professional development to encourage and empower teacher to improve their practice. By
continuously and consistently acting in this manner, a principal is effectively able to actualize
improvement in school performance as well as student academic achievement.
Leithwood et al. (2004) found that leadership was the second most influential factor for
student learning, the first being classroom instruction. Leadership accounts for about a fourth of
total school effects (p. 5). Furthermore, leadership is the primary factor that contributes to
differences in schools’ effectiveness in producing student learning outcomes (p. 17). A principal
has a tremendous impact on teachers’ teaching practice, student achievement, and ultimately, the
performance and success of a school.
Research finds that fewer school leaders are involved with mathematics education-related
leadership responsibilities (Spillane, 2005). Considering the impact of the principal, it is
imperative that the principal is involved with the teaching and learning of mathematics and
ensuring that it is high-quality education. Principals must also lead teachers to employ
reformative instructional practices such as inquiry-based instruction. There are four conditions
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that will enable all students to receive a high quality mathematics instruction: (1) high-quality
curriculum; (2) a stable, knowledgeable, and professional teaching community; (3) high quality
assessment that is aligned with curricular goals; and (4) stability and mechanisms for the
evolution of curricula, assessment, and professional development (Schoenfeld, 2005).
In “Beyond NCLB: Fulfilling the promise to our nation’s children”, Thompson and
Barnes (2007) upholds the crucial role held by the principal in a school’s ability to be effective at
producing student learning outcomes. Included are discussions of principals who have turned
around low-performing schools. Simply replacing the principal in a struggling school is a quick
fix solution to the problem. Thompson and Barnes (2007) stated that consistent and quality
leadership were essential for change that lasts over time. These high-quality principals
effectively managed their schools, hired and retained effective teachers, and built a school
culture that was inherently supportive of teachers helping students attain high levels of
achievement (p. 32). Principals must not only set high expectations and goals for the school – of
both teachers and students – but also create support structures and provide resources to ensure
that the school is able to successfully achieve these goals.
Darling-Hammond, Meyerson, and La Pointe’s (2009) examination of Grant Elementary
further reinforced the notion that principals play a central role in shaping a school’s ability to be
effective. Four years prior to being recognized as a National Blue Ribbon School, Grant
Elementary was the lowest performing school in the district and faced constant turnover in both
the administrative and teaching staff. One principal was brought in from New York to improve
student achievement and overall school performance but “shook things up” and was unable to
improve achievement (p. 81). It wasn't until Grant Elementary hired a leader who possessed the
skillset to be effective that they truly began to improve. The new principal kept her staff and
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students accountable, focused on shared leadership, and engaged the teaching staff in ongoing
professional development as she embraced the role of an instructional leader (p. 81). The
principal plays a crucial role in setting the direction that a school moves as well as shaping a
school into “vibrant learning communities”.
Kaplan and Owings (2001) describe how principals can effectively implement strategies
that personalize learning in order to prevent academic failure for traditionally underperforming
students rather than trying to “fix” the students. The first step is to build a positive school
culture with staff members committed to every student’s achievement. Clear and high
expectations must be set and opportunities must be given for teachers to collaborate with one
another. Small, caring, and structured learning communities are found to be effective for at-risk
students. Kaplan and Owings (2001) also describe intervention and prevention methods such as
interdisciplinary teams, school-based assistance teams, continuity of teacher and learner
relationships, extended time with the same teacher, cooperative learning, and academic tutoring.
The curriculum used and methods of instruction must be meaningful for the students. Extra time
and extra help along with effective home-school partnerships also help to better prevent
academic failure for at-risk students.
Leadership is an essential ingredient of effective educational change (Fullan, 2002).
Though replacing leadership may affect short-term progress, Fullan (2002) maintains that
consistent, quality leadership is critical to maintain improvements over time. The principals are
at the forefront of school leadership and principals “matter” for student achievement gains
(Brewer, 1993). The principal plays a pivotal role in steering the direction of a school. The
procedures, curriculum, and programs principals enact have a direct impact on the instructional
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practices of teachers, which in turn has a direct impact on the types of academic learning
experiences students are given the opportunity to engage in.
Successful Leadership Models
The responsibilities and roles of a principal are vast and wide-ranging. The ability of a
principal to effectively fulfill the required functions has a tremendous impact on a school’s
ability to be successful in improving student instruction and learning outcomes. Considering all
that a principal is tasked with, examining research on successful principals will give insight as to
how the daunting task of effective principalship is accomplished.
Leadership is defined as an “influence process that shapes the behavior of individuals and
groups towards the attainment of goals” (as cited in Hallinger & Heck, 2010, p. 656). A report
by the Wallace Foundation identified the three fundamental practices of successful leadership:
(a) setting directions; (b) developing people; and (c) redesigning the organization (as cited in
SECTQ, 2005, p. 22). First, by setting the direction of a school, the principal will be able to
better suit to further the organization towards improvement. Robinson, Lloyd and Rowe (2008)
find that establishing goals and expectations will focus, structure, and coordinate the work of
teachers. These goals must be “embedded in school and classroom routines and procedures” (p.
659). Research also stresses the importance of principals developing a vision and purpose of the
school, creating shared goals, and setting high expectations for teachers and students (Leithwood,
2005). The degree of staff consensus on stated goals impacted the level of achievement in
schools (Robinson, Lloyd, & Rowe, 2008). It is important to consider both the process of
developing goals collectively as a staff as well as the content of the goals.
Second, the principal is the guiding force behind creating professional development
opportunities for teachers to improve their practice and improve student learning as a result
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(Knipe & Speck, 2002). Contexts for teaching learning and development can be both formal and
informal. To develop the teachers on staff, the principal must create opportunities for
professional development that connects specific content-based curriculum with the overarching
school-wide goals and vision (Hill, 2007). Engaging teachers in such learning opportunities has
been found to improve student achievement. Research shows that leaders who are actively
involved as “learning leaders” lead schools with higher student outcomes (Robinson, Lloyd, &
Rowe, 2008, p. 663). “Learning leaders” are involved with the planning and implementation of
professional development and engage with teachers in the learning process. It is also important
for the learning leader to create a culture of ongoing learning within the school.
Last, an effective principal is able to implement reform movements within a school that
lead to improved student academic outcomes. Ideally, a principal is able to facilitate and sustain
this change over time, produce high student achievement, and turn around a school that is low-
performing (Glatthorn & Jailall, 1997). In addition to the three fundamental practices of
successful leadership, it is also important for principals to be visible and accessible to staff,
students, and parents (Leithwood, 2005). The principal also plays a critical role in recruiting,
developing, and retaining excellent teachers.
The Wallace Foundation’s three fundamental practices of successful leadership can be
applied to the leadership practice of principals to improve student math fluency. First, the
principal must embed improved mathematical learning outcomes into the school’s stated goals
and vision. Providing students with high-quality instruction, especially for math, must be a
priority in order to improve student learning and mastery.
Secondly, the principal must work to develop the teaching staff in content-related
professional development opportunities that are connected with the school mission and goals.
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The problem with typical professional development opportunities is that it is “disconnected from
any school-improvement plan or school-wide priority” and “only loosely related to actual
classroom needs” (Elmore, 2002, p. 24). Effective professional development is just the opposite
of that and serves the purpose of building capacity, knowledge and skills. Principals must ensure
that teachers are effectively equipped with the pedagogy and content necessary to help students
develop a deep understanding of concepts. Principals must engage with teachers in professional
development opportunities to ensure they possess a rich, conceptual understanding of
mathematics. As stated by Manouchehri (2000), it is making connections between concepts,
seeing the relationships of ideas, the ability to reason mathematically and problem solve. Novice
teachers need to most support as many exhibit a lack of depth of content knowledge and an
inability to make connections between concepts (Frykholm, 1999; Charalambous, 2011).
Principals must engage teachers in professional development that is ongoing, on-site and focused
on mathematics will enable teachers to build their effectiveness over time (Haycock, 1998, p. 12).
In this manner, the effectiveness of teaching will improve which will in turn, positively impact
student learning.
Lastly, principals must redesign the organization to embrace reform movements that
research has shown to improve student learning outcomes. In math classrooms, NCTM suggests
that teachers employ a student-centered, inquiry-based approach to best facilitate the learning
process. For reform-based instruction to occur and be effective, school leaders and teachers must
believe mathematics to be a way of thinking and problem solving rather than limiting
mathematics to computations and rigid rules (Cross, 2009). This requires a change in the belief
structures and principals must push for this change to occur. Beliefs about mathematics,
mathematics teaching and student learning are central to the way teachers conceptualize and
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actualize their role in the classroom (Frykholm, 1999; Liljedahl, 2009; Cross, 2009). Following
this logic, mathematical expertise cannot be determined solely by a student’s ability to perform
calculations but rather a student’s ability to use their mathematical knowledge to solve problems
(Cross, 2009). Principals equip teachers with the knowledge and tools necessary for them to
provide meaningful learning opportunities for students to mathematically reason, make
connections and problem solve (Frykholm, 1999).
Research consistently and repeatedly shows that the closer school leaders are to the “core
business of teaching and learning,” the more likely they will positively impact student
performance and learning outcomes (Robinson, Lloyd, & Rowe, 2008, p. 664). Hill (2002)
asserted the idea that the principal must place school improvement at the center of focus and the
principal and staff must acquire an extensive knowledge base about teaching and learning.
Studies examining effective leadership have shed light on various models of leadership believed
to be influential in transforming schools by improving teaching and learning for all students.
Instructional and transformational leadership theories have dominated empirical research on
educational leadership for the last quarter century, if not longer (Robinson, Lloyd, & Rowe, 2008,
p. 638; Hallinger, 2007, p. 2). Underlying both theories is the certainty that student learning
outcomes must be improved.
Instructional leadership is focused on improving curriculum and instruction as well as
setting school-wide goals. Under the model of instructional leadership, the principal serves as
the primary agent of change (Elmore, 2000; Williams, 2010). The instructional leader works to
define the school mission, manages the instructional program and promotes a positive school-
learning climate (Hallinger, 2003). In contrast, transformational leadership is focused on
empowering others to enact change and make improvements to the school. The transformational
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leader uses personality and relationships as a tool in the process of creating change. As the
transformational leader, the principal must develop a shared vision and motivate teachers to
achieve and perform (Hallinger, 2007). Marks and Printy (2003) states that instructional
leadership provides “intellectual direction and aims at innovating within the organization, while
empowering and supporting teachers as partners in decision making” (p. 371).
Several other educational leadership theories have been explored but the two prevailing
theories in current literature are instructional leadership and transformational leadership. These
two dominant theories and its deviations will be further explored and connections will be made
to mathematics education.
Instructional Leadership
The era of educational accountability stirred the need for instructional leadership to
improve student teaching and learning outcomes. Instructional leadership theory dictates the
principal serve as an agent of change (Graczweski, 2009). Instructional leaders play a critical
role in improving student academic achievement (Hallinger & Murphy, 1986). This model of
leadership focuses on the technicalities of teaching and learning. Research shows that principals
have facilitated improved school-wide performance by focusing on the academic program, using
assessment data, and engaging in professional development (Ruebling, Stow, & Kayona, 2008).
By taking responsibility for student academic achievement, principals can facilitate change that
would lead to more effective educational practices and improved learning outcomes (Ruebling,
Stow, & Kayona, 2008; Graczweski, 2009).
Mathematics education reform has been led by NCTM and has guided the learning-to-
teach process (Frykholm, 1999; Manouchehri, 2000). The Principles and Standards for School
Mathematics (NCTM, 2011) asserts that curriculum must be “mathematically rich, providing
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students with opportunities to learn important mathematical concepts and procedures with
understanding.” Several studies discuss the importance of mathematics education being focused
on standards-based instruction, a conceptual approach and student-centered learning (Frykholm,
1999; Artzt, 2011; Liljedahl, 2009; Manouchehri, 2000). This form of inquiry-based learning is
reconmmended by the National Commission on Mathematics and Science Teaching (NCMST,
2000) for math and science instruction. In a student-centered learning environment, teachers
serve as facilitators as students work to build knowledge. For this to take place, teachers must
have a deep, conceptual understanding of math, which allows for reasoning and problem solving
(Frykholm, 1999; Manouchehri, 2000).
The role of the principal in this process is as a powerful instructional leader for the
teachers within their school sites. Teachers often develop mathematical content knowledge
independent of pedagogical knowledge. This is not sufficient to teach mathematics, as content
and pedagogy must be connected (as cited in Prediger, 2010, p. 74). Because many teachers may
not have made these explicit connections, principals must take ownership of this missing
connection and provide opportunities for teachers to develop student-centered pedagogical
practices that are connected to their math content knowledge. Quinn (2002) states that a
principal’s ownership of his or her role as an instructional leader has a direct relationship to
improved student performance. Schools that excel academically have principals who are
effective instructional leaders. Similarly, principals of low-achieving schools are not effective
instructional leaders (Quinn, 2002). The key relationship between effective leadership and
student performance is undeniable. Using their roles as instructional leaders, principals can
guide the school community and classroom environment to improve teacher instruction and
improve student outcomes.
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Some criticize that the term “instructional leader” is sloganistic in that it is used widely
and generically without clear definition as to what the term means. Innately, it conveys the
importance of instruction but most leaders and organizations use this term loosely and no
differently than any other cliché term pertaining to improving instruction for students
(Leithwood, Louis, Anderson, & Wahlstrom, 2004, p. 6). Research offers several different
frameworks for the instructional leader with specifically stated leadership practices.
Hallinger (1985) offers a widely researched and used model of instructional leadership,
which includes three main dimensions: (1) defining the school’s mission; (2) managing the
instructional program; and (3) promoting a positive learning climate. Within these three
dimensions are ten specific corresponding leadership practices. Murphy (1990) offered a similar
framework: (1) developing missions and goals; (2) managing the educational production
function; (3) promoting an academic environment based on positive expectations and standards;
and (4) developing a supportive environment (as cited in Hill, 2002).
Hill (2002) also discusses the instructional leadership frameworks developed by
Scheerens and Bosker (1997) as well as that of Hill and Crevola (1999). Scheerens and Bosker’s
model of instructional leadership had the following five dimensions: (1) time devoted to
educational versus administrative tasks; (2) the head teacher as a meta-controller of classroom
processes; (3) the head teacher as a quality controller of classroom teachers; (4) the head teacher
as a facilitator of work-oriented teams; and (5) the head teacher as an initiator and facilitator of
staff professionalization. In contrast, Hill and Crevola only had three dimensions: (1) high
expectations of student achievement; (2) engaged learning time; and (3) focused teaching.
Andrews and Soder (1987) found principals who were effective instructional leaders to
be high performers in four areas: (1) resource providers; (2) instructional resources; (3)
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communicators; and (4) visible presence in the school. As a resource provider, the principal
gathers resources from the building, district, and community. Resources can be anything that
assists in achieving the school’s goals or vision, including materials, information, and
opportunities. Quinn (2002) asserts the notion that principals must inform teachers about new
resources including educational strategies, technologies, and tools that increase the quality of
instruction for students. As an instructional resource, the principal works with teachers to further
develop their teaching practice and to improve school curriculum. Professional development
opportunities are structured to enhance “Active Teaching”. As the communicator, the principal
articulates the vision, school goals, and expectations for instruction. As a visible presence, the
principal is seen throughout the campus by staff, students, and the community. Andrews and
Soder (1987) found that student achievement was significantly higher in schools with strong
instructional leaders than those without.
Heck (1992) researched three domains of instructional leadership as it pertains to the
principal: (a) governing the school; (b) developing school climate; and (c) organizing and
monitoring the school’s instructional program. From this study, Heck (1992) found found eight
key instructional leadership tasks associated with school achievement: (1) makes regular class
visits; (2) promotes discussion of instructional issues; (3) minimizes class interruptions; (4)
emphasizes test results; (5) participates in discussion about how instruction affects achievement;
(6) ensures systematic monitoring of student progress; (7) communicates instructional goals; and
(8) protects faculty from external pressures.
Quinn (2002) finds that in order to improve student achievement, principals must provide
instructional leadership to “facilitate and promote active learning experiences for all students” (p.
452). Instructional leadership impacts teachers’ instructional practice, which in turn, impacts
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student learning. Several descriptors are used to build an understanding of instructional practice:
active learning/active teaching; teacher-led conversation; teacher-led instruction; student
seatwork/teacher engaged; student seatwork/teacher disengaged; and total disengagement (as
cited in Quinn, 2002, p. 453).
Instructional leadership theory traditionally places the principal as the instructional leader
of a school. Critics state that the instructional leadership model is too prescriptive and too top-
down in that principals assign essential tasks to improve teaching and learning (as cited in
Stewart, 2006). However, instructional leadership responsibilities do not have to be strictly
limited to the principal. Marks and Printy (2003) find that shared instructional leadership is the
“active collaboration of principal and teachers on curriculum, instruction, and assessment” (p.
371). As the name suggests, shared instructional leadership requires the principal and teachers to
share responsibilities that the principal would assume under the traditional model of instructional
leadership. These shared responsibilities include staff development, curriculum and instruction
development, and supervision of instruction (Marks & Printy, 2003). As the leader of
instructional leaders, the principal draws on the expertise of teachers to work towards improving
school performance.
Transformational Leadership
Transformational leadership is often used synonymously with charismatic leadership as
these leaders are focused on charismatic and affective elements of leadership (Northouse, 2007).
Transformational leaders strive to improve morale and increase motivation of the members of the
organization. This type of leadership strives to transform self-interest and unite social systems
around common purposes (Keeley, 1995). Bass and Violio (1994) discuss the four I’s of
transformational leadership: (a) idealized influence; (b) inspirational motivation; (c) intellectual
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stimulation; and (d) individualized consideration. Effective transformational leaders are able to
“forge the strategy culture allow” by integrating “creative insight, persistence and energy,
intuition and sensitivity to the needs of others” (p. 112). They align others around the vision and
empower others to take greater responsibility for achieving the vision.
Leithwood and Jantzi (1999) find that transformational leadership has six dimensions: (1)
building school vision and goals; (2) providing intellectual stimulation; (3) offering
individualized support; (4) symbolizing professional practices and values; (5) demonstrating high
performance expectations; and (6) developing structures to foster participation in school
decisions.
In addition to empowering teachers, transformational leadership “facilitates the
redefinition of a people’s mission and vision, a renewal of their commitment, and the
restructuring of their systems for goal accomplishment” (as cited in Leithwood & Polin, 1992, p.
9). Transformational leaders believe that people in their organizations are trustworthy of
responsibility, purposeful, and contributors to the greater good. The resulting sentiment is a
sense of purpose, family, and long-term commitment (Bass & Avolio, 2003). Principals who are
transformational leaders have personal relationships with teachers and use these relationships to
motivate them into action.
By virtue of the transformational leadership theory, principals who are transformational
leaders should be able to effect change and “performance beyond expectations” (Northouse,
2001) by employing the four I’s of transformational leadership. Research describes principals
who, as transformational leaders, are able to effect change in their schools that lead to improved
student learning outcomes. This particular leadership theory differs from more traditional
leadership theories because it emphasizes emotions and values rather than rational processes
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(Yukl, 1999). The literature does not provide any insight as to how a principal can become a
transformational leader. Many transformational leader traits pertain to personality rather than
specific learned skills and behaviors. For example, an emphasis is placed on using charisma and
building relationships to move the organization.
For principals to effect change in the way that teachers teach and students learn, they
must be more than just influential, amiable, and charming. Leaders must be equipped with the
tools necessary to develop the practice of their teachers in a manner that enables improved
learning outcomes. Specifically for teachers of mathematics, principals must be able to instill the
belief that mathematics is a way of thinking and problem solving rather than just computations
and rigid rules. Additionally, principals must ensure that teachers are equipped with the
expertise necessary to teach in this manner. Without this belief and skillset, educational reform
is not possible. Research shows that many teachers revert back to a traditional way of explaining
mathematics as a hierarchy of facts and procedures despite how strongly a teacher may feel
about mathematics reform. Conversely, teachers with conceptual content knowledge focused
more on incorporating reform-based instructional strategies into their classroom, were less rigid
in their teaching, and taught students to develop their own conceptual understanding of
mathematics (Frykholm, 1999). To develop the believes and tools necessary for this to occur,
school leaders need much more than just charisma and require the abilities of an instructional
leader.
Transformational leadership is effective due to the amount of influence, power, and
control a leader has over their followers to effect change. Critics believe that transformational
leadership theory is unethical and that principals have too much power over their teachers and
staff. Many leaders are pursuing both personal and organizational interests and “self-serving
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leaders could result in deception and exploitation of followers” (as cited in Bass & Steidlmeier,
1999, p. 182). Keely (1995) holds that it is a myth to believe that charisma is an important
aspect of leadership. Rather, charisma is more concerned with impressions than actually running
an organization (p. 90). The dark side of charismatic leadership, or transformational leadership,
is “narcissism, authoritarianism, Machiavellianism, flawed vision, a need for power coupled with
lack of activity inhibition and promotion among followers of dependency, personal identification,
and lack of internalization of values and beliefs” (as cited in Bass & Steidlmeier, 1999, p. 182).
While it is important to recognize that not all transformational leaders fall to the “dark side”, it is
equally as important to address these aspects that could have detrimental effects to school
performance and student learning.
Another problem with transformational leadership is a lack of checks and balances for the
leader in place (Keely, 1995). As a result, there is great potential for the leader to abuse power.
The leader convinces people with diverse needs that they share common goals, regardless of
whether or not they actually do. Organizational goals are often formed at the expense of the
minority. Keely (1995) goes on to refute the claim that transformational leaders need to create a
vision that transcends the need of the individuals in an organization. Rather, “Successful leaders
and acceptable visions reflected the diverse interests of constituents rather than the leader's goals
for the institution” (p. 90). Essentially, the needs of the individuals can be acknowledged by
creating goals and a vision that is inclusive of individuals rather than exclusive.
Leithwood and Jantzi (1999) state that transformational leadership does not include
transactional practices, also referred to as managerial practices, which are fundamental to
organizational stability. While a transformational leader may have the personality to move an
organization forward, this change cannot be sustained if the principal does not possess the ability
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to manage the school. Needless to say, the weaknesses of transformational leadership can be
addressed and strengthened by incorporating other leadership skills and processes.
Leadership for Learning
Considering the strengths of both instructional leadership and transformational leadership,
researchers have proposed that both theories be combined to maximize the impact on schools.
Hallinger and Heck (2010) refer to this blend of leadership as “leadership for learning” whereas
Marks and Printy (2003) refer to this as “integrated leadership”. In any case, the combination of
transformational leadership with instructional leadership has the potential to have substantial
impact on school performance. Integrated leadership strives to build the academic capacity of
schools to improve student learning outcomes. A school-wide focus on learning must be created
and sustained. Learning occurs for both students and teachers and is referred to as capacity
building. School improvement is a dynamic process and principals must work strategically to
develop and improve schools. Furthermore, school leaders must work to increase the teachers’
breadth and density of instructional expertise (Hallinger & Heck, 2010, p. 657). Integrated
leadership is measured by the quality of pedagogy and achievement of students (Marks & Printy,
2003).
Principal Leadership and Mathematics Education
Overall improvement in mathematics achievement is fleeting if it exists at all. As shown
by various published studies, students are struggling to succeed in secondary mathematics. In
particular, students with low socioeconomic status were the lowest performers on national
standardized assessments in mathematics. This same population of students is the most likely to
drop out of high school (Weber et al., 2010). The lack of mathematics fluency of students is a
pressing problem that requires immediate attention and action by principals.
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There is extensive literature on the impact of leadership on learning and the importance
of mathematics. However, there is very limited existing research that explicitly makes
connections between the impact that leadership has on teaching and learning secondary
mathematics. The key relationship between effective leadership and student performance is
undeniable, especially in the area of reading and math (Quinn, 2002; Andrews & Soder, 1987).
Current accountability measures have placed extreme urgency and pressure on improving student
achievement, particularly in mathematics. As the instructional leader, the principal has the
ability to affect classroom instruction. Given the significant impact that a principal can have on
student learning, it is essential to consider the relationship between the principal and math
achievement.
Educational change needs to take place to improve the quality of instruction and student
learning outcomes. To accomplish improved student achievement, school leadership and staff
must work together to improve their own performance. Educational change has three phases: (1)
initiation; (2) implementation; and (3) institutionalization (Hill, 2002). Action must be taken to
uncover the specific traits, behaviors, and actions of principals who have effectively been able to
not only improve but also sustain improved student achievement in mathematics.
Summary
Student learning outcomes in mathematics is in a devastated state and in need of
immediate attention and improvement. The literature shows the evolution of education and what
has led to the current era of educational accountability. There are extreme pressures on
principals to improve the overall performance of their schools, which includes student academic
achievement. In order to meet the requirements set by the accountability mandates, particularly
pertaining to mathematics education, principals must work to change the practices in place to
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improve instruction for students. The existing literature also shows several leadership models
that have been effective at improving student learning. Instructional leadership theory is
prevalent in the literature pertaining to effective schools. Hallinger and Murphy’s (1985)
prevailing three dimensions of instructional leadership were used as a lens for further research:
(a) defining the school’s mission; (b) managing the instructional program; and (c) promoting a
positive school climate. The practices of principals that have effectively improved student
outcomes in secondary mathematics were examined and connections were made between the
theory and the student achievement that results.

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CHAPTER 3
METHODOLOGY
Success in mathematics courses is indispensible as it is considered a critical filter and
indicator for future success. Mathematics is the gateway to technological literacy and higher
education (Schoenfeld, 2002). Research also indicates that a student’s performance in high
school mathematics is a strong beacon for a student’s ability to complete college and how much
money they will earn in their future careers. One study found that the math scores of students
who went on to graduate school from college was nearly double that of students whose highest
level of education was completing high school (Murnane, Willet, & Levy, 1995). Yet, students
across the nation are struggling to succeed in mathematics. Furthermore, principals are
pressured to improve the overall performance of their schools, which includes student academic
achievement. In order to meet the requirements set by the accountability mandates, particularly
pertaining to mathematics education, principals must work to change the practices in place to
improve instruction for students.
Students of color and students from low-income homes are the lowest performers on
national standardized math tests and the most likely to drop out of high school (Schoenfeld,
2002; Weber, 2010). Schoenfeld (2002) found the mathematics learning experience for these
groups of at-risk students is typically shortchanged when compared to their wealthier, Caucasian
counterparts. Principals must ensure that all students are given access to a high-quality
mathematics education. Principals must also take immediate action to tackle the lack of
mathematics fluency that students exhibit.
Literature repeatedly shows the impact that school leadership has on student learning,
particularly in the area of reading and mathematics (Quinn, 2002; Andrews & Soder, 1987). A
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principal’s ownership of his or her role as an instructional leader has a direct relationship to
improved student performance (Quinn, 2002). Schools that excel academically have principals
who are effective instructional leaders. Similarly, principals of low-achieving schools are not
effective instructional leaders (Quinn, 2002). Hallinger and Murphy’s (1985) prevailing three
dimensions of instructional leadership were used as a lens for further research: (a) defining the
school’s mission; (b) managing the instructional program; and (c) promoting a positive school
climate.
Purpose of Study
To date, limited research has explicitly made connections between the principal’s
instructional leadership and students’ achievement in secondary mathematics. Given the
significant impact a principal has on student learning, it was essential to consider this
relationship. The purpose of this research was to bridge this gap in the literature. In the current
climate of educational accountability and high-stakes testing, this study sought to uncover the
effective practices of high school principals who successfully used their role as instructional
leaders to improve student learning and achievement in mathematics. This study attempted to
uncover the traits, behaviors, practices and actions of principals who have improved academic
achievement in mathematics and sustained this improvement over time. In particular, the study
focused on principals leading comprehensive public schools in large urban areas of California
with large groups of minority students and students from low-income households.
Methodology Overview
Chapter 3 describes the research design employed to answer the research questions of this
study. This chapter will describe the sample and population, the instrumentation used, the plan
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for data collection, and lastly, the methods for data analysis. The methodology of this study was
designed to answer the following three research questions:
(1) What are the self-perceived instructional leadership behaviors of high school
principals?
(2) What instructional leadership strategies do principals employ that influence positive
outcomes of academic achievement?
(3) What is the relationship between the instructional leadership behaviors of principals
and student achievement in mathematics?
Research Design
A mixed methods approach was used to complete this investigation. The first phase of
the study used quantitative methods. Principals who met the selection criteria received surveys
with questions about their own educational leadership practices. Principals responded to the 50
survey questions using a Likert scale. On average, the survey took 20 minutes to complete. The
final question on the survey asked if they would be open to a follow-up, in-person interview. The
second phase of the study used qualitative methods. Of the principals who responded to the
survey, four were selected for a follow-up interview. An interview protocol was used with all
four principals to ensure consistency in the questions asked.
Sample and Population
Purposeful sampling was used to gain knowledge about issues that are of central
importance to the purpose of the inquiry (Patton, 2002). By using a purposeful sample, the
investigator was able to examine information-rich cases to yield insights and an in-depth
understanding. Principals who met the selection criteria were sent an initial letter of introduction
and a follow-up email with the link for the survey. The last question of the survey asked if they
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were open to participating in a follow-up interview. Those who continued to phase two of the
study opted to do so.
The data used for this study came from public schools in large urban areas of California.
Principals asked to participate in this study met the following selection criteria:
(1) lead a comprehensive public high school serving grades nine through twelve;
(2) located in large urban areas (i.e., Los Angeles county);
(3) minimum of 45% free and reduced lunch;
(4) minimum of 1100 students; and
(5) minimum of two years as the principal at their current school site.
Several resources were used to locate schools that met the selection criteria for this study.
The California Department of Education (CDE) website, Education Data Partnership (Ed-Data)
website, and Great Schools website were used to gather information about various schools in
large urban areas of California. An emphasis was placed on schools in southern California.
These websites gave information about school demographics, test scores, API, AYP, and other
relevant student and school information. Using these resources, a list of principals was generated
to solicit for the first phase of this study.
Instrumentation
A mixed methods approach was used to complete this study. All principals who
participated in this study were volunteers. An instructional leadership framework was used to
create the survey questions and interview protocol.
Phase one consisted of quantitative methods. Principals who met the selection criteria
and agreed to partake in the study were given a web-based survey that asked questions about
their instructional leadership behaviors and traits. Hard copies were given on request.
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Responses to the 50 questions were on a Likert scale ranging from one to five. A response of
one represented almost never, two represented seldom, three represented sometimes, four
represented frequently, and five represented almost always. On average, the survey took about
20 minutes to complete. Upon completion of the survey, principals were given the option to
potentially continue onto the next phase of the study.
Phase two consisted of one-on-one interviews with principals who opted to participate
beyond phase one. Qualitative data was gathered through interviews with high school principals
who opted to continue to the second phase. The purpose of conducting interviews with
principals was to engage in deep discussions pertaining their role as the instructional leader of
the school and how they used this role to facilitate a change in instructional practice of teacher to
better serve students, particularly in the area of mathematics. An interview protocol was used as
a tool to guide the interview process but was not followed in any specific order. The researcher
kept an open format during the interview but used the protocol as a checklist of questions and
topics to be asked and discussed. Questions were clustered and sequenced based on the flow of
the interview conversation.
Data was drawn from multiple sources. Triangulation of data ensures internal validity
and works to strengthen the results (Patton, 2002). The instruments used in this study included
interviews, surveys, and analysis of information available on the California Department of
Education website and other related websites. The interview protocol was tested with other
principals who were not asked to participate in the study. The initial test was to ensure validity
of the protocol and to ensure that questions were structured in a manner that would capture
responses that would fully answer the research questions of this study.
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Data Collection
The data collection process was separated into two separate phases and guided by the
research questions of this study (see Table 3.1). Data from completed surveys, interviews, and
various documents were used to answer the research questions.

Table 3.1
Research Design Chart
Research Question Data Needed Data Sources Instrumentation
#1: What are the self-
perceived instructional
leadership behaviors of
high school principals?
• Evidence of the
different levels of
instructional
leadership behaviors
and skills that
principals posses
• High school
principals
• Web-based
survey
#2: What instructional
leadership behaviors do
principals employ that
they believe to influence
positive outcomes of
academic achievement?
• Evidence of the
instructional
leadership behaviors
that impact student
achievement
• High school
principals
• Interview
protocol
#3: What is the
relationship between the
instructional leadership
behaviors of principals
and student achievement
in mathematics?
• Evidence of
relationship between
principal’s role as
the instructional
leader and student
achievement in
mathematics
• High school
principals
• Web-based
survey
• Interview
protocol
• Data websites
(such as
California
Department of
Education)

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High school principals who fit the selection criteria were sent a general recruitment letter.
This purpose of this letter was to introduce the researcher, the research, and to invite the
principal to participate in this study. All principals who were a part of this study were volunteers.
The initial letter was followed up with a phone call and an email with a survey link. The last
question of the survey asked if they were open to participating in a follow-up interview. Those
who continued to phase two of the study opted to do so. The principals being interviewed were
provided with an informed consent protocol in advance of their interview as well as at the start of
their interview (Patton, 2002, p. 407). To answer the final research question, school performance
data was collected from the California Department of Education (CDE) website, Education Data
Partnership (Ed-Data) website, and Great Schools website. This information was used along
with data from the surveys and interviews.
Data Analysis
Extensive data was collected through the surveys, interviews and education websites that
gave information about school performance. Data analysis consisted of both quantitative and
qualitative methods (see Figure 3.1).
RQ1 What are the self-perceived instructional leadership behaviors of high school
principals?
Quantitative data was drawn from the answers given by principals on the initial survey.
Principals responded to the 50 survey questions on a Likert scale ranging from one to five. On
average, principals took about 20 minutes to complete the survey. These responses were
examined using a non-parametric test on IBM Statistical Package for the Social Science (SPSS)
software. The data was analyzed and compared in multiple ways to get a better picture of each
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principal and their instructional leadership skills. From here, principals and their instructional
leadership abilities were compared with one another.

Figure 3.1. Data analysis methods

RQ2 What instructional leadership strategies do principals employ that influence
positive outcomes of academic achievement?
Qualitative data was gathered from the interviews conducted with high school principals
who meet the selection criteria. Interviews with principals included deep discussions pertaining
to how they served as the instructional leader of school and how they used this role to facilitate a
change in instructional practice of teaches to better serve students, particularly in the area of
mathematics. Data from this phase of the study was more challenging to analyze than the
quantitative data from the first phase.
Research
Question #1
• Phase 1 -
Surveys
• Analysis:
Quantitiatve
(SPSS)
Research
Question #2
• Phase 2 -
Interviews
• Analysis:
Qualitative
(Creswell &
Patton)
Research
Question #3
• Step 1: Analyze
data from CDE,
Ed-Data, Great
Schools using
quantitative
methods
• Step 2:
Determine
relationships, if
any, between
school
performance
data analysis and
analysis of
Phase 1 & Phase
2
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Data from the interviews were analyzed using both Creswell’s (2009) data analysis steps
and Patton’s (2002) method for coding. Creswell (2009) states the following steps should be
used for data analysis: (1) organize and data for analysis by transcribing interviews and
compiling field notes; (2) determine general tone of data; (3) code data into discernible chunks;
(4) generate categories or themes for the data; (5) determine representation of categories or
themes; and (6) interpret data (see Figure 3.2).

Figure 3.2. Creswell’s model for qualitative data analysis

With the consent of each principal, interviews were recorded. These recordings were
transcribed. The researcher also took copious notes during the interview to capture what the
audio recording did not such as facial expressions and gestures. To make sense of the
“undigested complexity of reality” (Patton, 2002, p. 463), the data was analyzed using an
Step 1
• Organize and data for analysis by transcribing interviews and compiling field
notes
Step 2
• Determine general tone of data
Step 3
• Code data into discernible chunks
Step 4
• Generate categories or themes for the data
Step 5
• Determine representation of categories or themes
Step 6
• Interpret data
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inductive approach. First, the data was color-coded and copied onto an Excel spreadsheet
organized using the same colors used to highlight the data. Then the organized information was
analyzed inductively. Patton (2002) describes this as the process of finding patterns, themes and
categories in the gathered information. Patterns typically are the descriptive data and themes
emerge as a way to categorize the patterns. Aggregating the data in this manner allowed for a
large block of information to be grouped into smaller, more manageable chunks.
The research question that guided the interview was, “What instructional leadership
strategies do principals believe they employ that influence positive outcomes of academic
achievement in mathematics?” To capture the complete picture, the interview protocol was
separated into five main categories of questions: (1) school vision / goals; (2) teachers; (3)
students; (4) math-specific; and (5) leadership. To analyze data gathered from the interview
using this protocol, different colors were used to separate transcribed notes from principals’
responses into topics that the interview questions corresponded with. After doing this, these
responses were recorded onto an excel spreadsheet. The first column was used to match
responses with the corresponding interview transcription notes, using a numerical identification
number. Each question was written in its own column and color-coded using the same colors as
previously used to code the transcription notes. Given the natural flow of the conversation, some
principals answered questions on the protocol without being directly asked them. For example,
one principal discussed department-specific staff development and shared leadership when asked
what he does to develop his staff. As a result, some responses were placed in more than one
column. From here, the aggregated information was used to further code the data by extracting
key information. For each interview, direct quotes were record on the first row and the second
row was the analysis of the quotes as it related to the research question.
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RQ3 What is the relationship between the instructional leadership behaviors of
principals and student achievement in mathematics?
Determining the relationship between the instructional leadership behaviors of principals
and student achievement in mathematics was a two-step process. The first step was to collect
and analyze school performance data from CDE, Ed-Data and Great Schools. The California
Department of Education website offered countless information about schools including scores
from various tests. The Ed-Data website gave reports at multiple levels ranging from state,
county, district, and school. The reports included information about students, staff, finances and
performance rankings at the various levels. The Great Schools website also gave an array of
information about specific schools including demographics, staff information, API and AYP data,
and test scores. For each principal who participated in the study, information about the school
they led was extracted from these websites. The second step of this study was to determine
relationships, if any, between the school performance data analysis and principal instructional
leadership behaviors from both phases of this study.
Summary
This study sought to uncover the instructional leadership behaviors and traits of
principals that have led to improved student outcomes in secondary mathematics. Three main
research questions guided every stage of the study. To answer these questions, a survey and an
interview protocol were developed using Hallinger and Murphy’s (1985) instructional leadership
dimensions as a lens. The three dimensions included: (a) defining the school’s mission; (b)
managing the instructional program; and (c) promoting a positive school climate. A mixed-
methods approach was used to analyze the collected data.
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Principals who participated in this study have led for a minimum of three years at their
current traditional public high school. The reasoning behind looking for principals who have led
for a minimum of three years was the assumption that their instructional leadership skills
impacted student achievement. The schools were located in large urban areas, had a majority
minority and low-income population. The schools also exhibited growth from the 2008-2009
school year to the 2010-2011 school year on the Algebra 1 California Standards Test. Ultimately
this study was looking for connections between principal instructional leadership behaviors and
student achievement in secondary mathematics. The next chapter presents the results of this
study.

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CHAPTER 4
FINDINGS
Introduction
As previously stated, the principal plays a pivotal role in setting the direction of a school
and defining the successes or failures that a school experiences. Serving as the primary and most
visible agent of change, the principal has the power to enact changes within the school site he or
she leads. A principal who embraces the characteristics of an instructional leader – whether it be
intentional or not – has the ability to push his or her teachers and students to improve student
learning and increase academic achievement. An effective instructional leader can have a strong,
positive impact on a teacher’s instructional practice. In turn, this has an affect on student
learning in that particular teacher’s classroom. Considering the current climate of educational
accountability and high-stakes testing, improving student achievement is critical to the survival
of a school.
In addition to meeting educational accountability requirements, student learning and
achievement in secondary mathematics is of particular importance. Research indicates success
in secondary mathematics is a strong predictor for a student’s ability to complete college as well
as how much money they will earn in future careers. The connection between principals’
leadership practices and student performance in secondary mathematics is missing in current
literature.
Principals were purposefully selected to voluntarily participate in this study. Using a
mixed methods approach, this study examined the leadership practices of high school principals
who successfully used their role as instructional leaders to improve student learning and
achievement in mathematics. Through careful analysis of the Principal Instructional
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Management Rating Scale (PIMRS) survey and subsequent interviews, the study uncovered the
traits, behaviors, practices, and actions of principals who have improved academic achievement
in mathematics and sustained this improvement over time. The study focused on principals
leading comprehensive public schools in large urban areas of California with large groups of
minority students and students from low-income households.
This chapter first presents general demographic information of the volunteer participants.
Following is a reporting of findings based on each of the three research questions that this study
was based. The last portion of this chapter is a discussion of findings a well as the researcher’s
reflections on the significance of the findings.
Demographic Information
The web-based survey was created using an internet survey distributor – Qualtrics.com.
The survey was sent to 120 principals across southern California. All selected principals met the
following selection criteria:
(1) lead a comprehensive public high school serving grades nine through twelve;
(2) located in large urban areas (i.e., Los Angeles county);
(3) minimum of 45% free and reduced lunch;
(4) minimum of 1100 students; and
(5) minimum of two years as the principal at their current school site.
The first portion of this survey contained demographic information questions. The
questions asked for the principal’s: (a) gender; (b) ethnicity; (c) highest level of education
obtained; (d) number of years served as a classroom teacher; (e) primary subject(s) taught as a
classroom teacher; (f) number of years serve as the current site principal; (g) total number of
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years as an administrator; and (h) percentage of instructional leadership complete by self and
delegated to others.
The principals’ responses to these eight questions served as the independent variables for
this study. Table 4.1 shows information about the participants’ gender, ethnicity, and highest
level of education obtained. Of the 28 principals who volunteered to participate in this study,
53.6% were male and 46.4% were female. The majority of principals identified themselves as
either Caucasian (46.4%) or Hispanic (42.9%). Principals were given the option to identify with
more than one group, which explains a response frequency total of 29. Of the 28 respondents, all
but one principal had continued their education beyond a bachelor degree. There were 15
principals, or 53.6% of principals, who earned a masters degree. The remaining 12 principals
had earned doctorates and composed 42.8% of the volunteer participant pool.
Principals were asked to report the number of years served as a classroom teacher. As
shown in Table 4.2, responses ranged from a minimum value of 3 years to a maximum value of
25 years. On average, the participants had served 9.2 years in the classroom as a teacher with a
standard deviation value of 5.4. Nearly half of the principals, or 46.4%, had served in the
classroom from 6 to 10 years. The most frequent response was serving a total of 10 years in the
classroom, which 5 principals had done. Nearly a quarter of the participants had been a
classroom teacher for 3 to 5 years. Table 4.2 also shows the frequency and percentages of the
primary subjects that principals taught while in the classroom. Most principals had taught a
variety of subjects, rather than just one. Over two-thirds of the participants taught a core content
course of either Language Arts / English, Mathematics, Science, or Social Science. Other
courses taught included Business English and Computers, Spanish, and Behavioral Science.

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Table 4.1
Frequency of Principals’ Gender, Ethnicity, and Highest Education
Demographic Independent Variable f %
Gender Female 15 53.6
Male 13 46.4
Total 28 100
Ethnicity African-American 2 6.9
Asian 1 3.4
Caucasian 13 44.8
Hispanic 12 41.4
Other 1 3.4
Total 29 100.0
Highest Education B.A./B.S. 1 3.6
M.A./M.Ed 15 53.6
Ph.D/Ed.D. 12 42.8
Ed.S. 0 0.0
Other 0 0.0
Total 28 100

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Table 4.2
Frequency of Years Served as a Classroom Teacher and Primary Subject Taught
Demographic Independent Variable f %
Years Served as a
Classroom Teacher
0-5 years 8 28.6
6-10 years 13 46.4
11-15 years 5 17.9
16-20 years 0 0.0
M = 9.2 >20 years 2 7.1
SD = 5.4 Total 28 100
Primary Subjects
Taught
K-6 5 13.2
Art / Applied Arts 0 0.0
Language Arts / English 8 21.1
Mathematics 6 15.8
Physical Education 3 7.9
Science 5 13.2
Social Science 7 18.4
Special Education 1 2.6
Other: 3 7.9
Total 38 100

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Table 4.3 shows the number of years that the participants have served as the principal of
their current school site and the total number of years as an administrator of any level at any
school site. Of the 28 principals who responded to the survey, respondents had served a
minimum of 1 and a maximum of 12 years as the principal of their current school site. Nearly
half of the respondents had been at their current school site for 3 to 4 years. One-fourth of the
respondents have been the principal of their current school site for over 5 years. The mean value
was 3.5 years served as the principal of their current school site whereas the mean value for the
total number of years served overall as an administrator was 12 years. For overall number of
years served as an administrator, the minimum value was 5 years and the maximum value was 22
years. The most frequent response was having served 8 years as an administrator and 14 years as
an administrator. Eight principals, or 28.6%, have 5 to 8 years of administrative experience.
One-fourth of principals have anywhere from 9 to 12 years of administrative experience. Nine
principals, or 32.1%, have 13 to 16 years experience. Only 14.3%, or 4 participants, have served
as an administrator for over 17 years.

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Table 4.3
Frequency of Years Served as Principal of Current School Site and Years Served as an
Administrator
Demographic Independent Variable f %
Years Served as
Principal of Current
School Site
1-2 years 8 28.6
3-4 years 13 46.4
5-6 years 4 14.3
M = 3.5 >6 years 3 10.7
SD = 2.4 Total 28 100
Years Served as
Administrator Overall
5-8 years 8 28.6
9-12 years 7 25.0
13-16 years 9 32.1
M = 12.0 >17 years 4 14.3
SD = 4.4 Total 28 100

The final part of the demographics section of the web-based survey asked to state how
the instructional leadership responsibilities were delegated between themselves and the assistant
principal(s), curriculum director(s), department chair(s), teacher leader(s) and other key
stakeholders of the school. Principals were given the following description of instructional
leadership:
Instructional leadership can be defined as the leadership behaviors that affect a teacher’s
practice, which in turn leads to effective instruction and improved student learning
(Quinn, 2001, p. 447). A widely researched and used model defines the three main
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dimensions of instructional leadership to be: (1) defining the school’s mission; (2)
managing the instructional program; and (3) promoting a positive learning climate.
(Hallinger, 1985)
Principals’ responses indicated that instructional leadership responsibilities were often
distributed amongst key individuals at the school site. Table 4.4 shows the minimum value,
maximum value, mean, and standard deviation of responses to this question on the survey. One
principal reported that all instructional leadership responsibilities were delegated amongst the
assistant principals, department chairs, and teacher leaders. Another principal reported to take on
85% of the instructional leadership responsibilities and delegating the remaining 15% to the
assistant principal. Aside from these two extreme cases, principals most often listed themselves
for taking on the greatest percentage of instructional leadership responsibility, with a mean of
44.1% of the total responsibilities.

Table 4.4
Statistics of Instructional Leadership Delegated
Stakeholder Minimum Value Maximum Value Mean
Standard
Deviation
Assistant Principal(s) 5.0% 60.0% 25.8% 11.50
Curriculum Director(s) 0.0 50.0% 2.5% 9.57
Department Chair(s) 0.0 50.0% 15.2% 12.87
Teacher Leader(s) 0.0 35.0% 12.3% 9.06
Other 0.0 10.0% 0.5% 2.08
Self 0.0 85.0% 44.1% 17.93

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Principals reported that assistant principals took on the second largest portion of the
instructional leadership responsibilities, with a mean of 25.8%. The majority of instructional
leadership responsibilities were delegated amongst school administrators, namely, the principal
and assistant principal. These two roles took on over two-thirds of the tasks as evidenced by a
combined mean of 69.9%. The remaining third was given to other roles within the school. On
average, department chairs were given the third most responsibilities with a mean of 14.2%.
Teacher leaders came next with a mean of 12.3% of instructional leadership responsibilities.
Principals only reported curriculum leaders to take on an average of 2.5% of the instructional
leadership tasks. However, this may be attributed to some schools not having curriculum
directors. Two principals reported they delegated some responsibilities to other members of the
school staff other than those listed on the survey. These instructional leaders included the “Vice
Principal” and the “Guidance Office”.
Research Question One: What are the Self-Perceived Instructional Leadership Behaviors
of High School Principals?
The first research question was answered through a descriptive statistical analysis of the
responses that principals gave on the PIMRS. Principals responded to instructional leadership
functions that were separated into the following ten main categories: (1) frame the school goals;
(2) communicate the school goals; (3) supervise and evaluate instruction; (4) coordinate the
curriculum; (5) monitor student progress; (6) protect the instructional time; (7) maintain high
visibility; (8) provide incentives for teachers; (9) promote professional development; and (10)
provide incentives for learning (Hallinger, 1990). Each of these ten categories contained five
questions that were answered using a 5-point Likert scale. A response of “1” represented
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“almost never”, “2” represented “seldom”, “3” represented ”sometimes”, “4” represented
“frequently”, and “5” represented “almost always.”
The means and standard deviations for the first job function of framing the school goals
are shown in Table 4.5. Overall, the mean for framing the school goals was 4.58 and standard
deviation was 0.19. Principals strongly connected to this job category and felt they almost always
framed the school goals. Scores on the Likert scale ranged from 2 to 5. Of the five different job
functions in this category, two principals scored themselves as a 2 for the behavior of securing
staff input on goal development using either formal or informal methods. This category received
the lowest mean score of a 4.35. The highest mean score of 4.81 was for the behavior of using
student performance data to develop the school goals.

Table 4.5
Descriptive Statistics for Job Function I: Frame the School Goals
Principal Instructional Leadership Behaviors N Mean Standard Deviation
I. Frame the School Goals 26 4.58 0.19
1. Develop a focused set of annual school-wide goals 26 4.73 0.45
2. Frame the school's goals in terms of staff
responsibilities for meeting them
26 4.46 0.65
3. Use needs assessment or other formal and informal
methods to secure staff input on goal development
26 4.35 0.98
4. Use data on student performance when developing
the school's academic goals
26 4.81 0.40
5. Develop goals that are easily understood and used
by teachers in the school
26 4.54 0.65

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Table 4.6 shows the means and standard deviations for the second job function of
communicating the school goals. The overall mean for communicating the school goals was
4.16 with a standard deviation of 0.42. Scores on the Likert scale ranged from 1 to 5. The
lowest mean score in this category was for the last two questions which was associated with
ensuring that the school’s academic goals are reflected in highly visible displays and referring to
the school’s goals or mission in forums with students. These two particular behaviors received a
mean score of 3.69 and 3.73, respectively. The highest mean score was tied between two
behaviors of discussing the school’s academic goals with teachers and referring to the school’s
academic goals when making curricular decisions with teachers. A mean score of 4.54 for these
behaviors indicates that principals felt they almost always acted in this manner.

Table 4.6
Descriptive Statistics for Job Function II: Communicate the School Goals
Principal Instructional Leadership Behaviors N Mean Standard Deviation
II. Communicate the School Goals 26 4.16 0.42
6. Communicate the school's mission effectively to
members of the school community
26 4.73 0.68
7. Discuss the school's academic goals with teachers at
faculty meetings
26 4.46 0.58
8. Refer to the school's academic goals when making
curricular decisions with teachers
26 4.35 0.86
9. Ensure that the school's academic goals are reflected
in highly visible displays in the school (e.g., posters or
bulletin boards emphasizing academic progress)
26 4.81 1.05
10. Refer to the school's goals or mission in forums with
students (e.g., in assemblies or discussions)
26 4.54 1.12

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Table 4.7 reveals the means and standard deviations for the third job function of
supervising and evaluating instruction. The overall mean for supervising and evaluating
instruction was 4.33 and standard deviation of 0.42. Scores on the Likert scale ranged from 1 to
5. Principals scored themselves the lowest for reviewing student work products when evaluating
classroom instruction. The mean for this particular behavior was 3.81, which is 0.5 lower than
the second lowest mean for pointing out specific weaknesses of instructional practices to
teachers during post-observation feedback. Principals scored themselves the highest for
regularly conducing informal observations and pointing out specific strengths of instructional
practices to teachers during post-observation feedback. Both of these behaviors had a mean of
4.58.

Table 4.7
Descriptive Statistics for Job Function III: Supervise and Evaluate Instruction
Principal Instructional Leadership Behaviors N Mean Standard Deviation
III. Supervise & Evaluate Instruction 26 4.33 0.42
11. Ensure that the classroom priorities of teachers are
consistent with the goals and direction of the school
26 4.35 0.80
12. Review student work products when evaluating
classroom instruction
26 3.81 1.02
13. Conduct informal observations in classrooms on a
regular basis (informal observations are unscheduled,
last at least 5 minutes, and may or may not involve
written feedback or a formal conference)
26 4.58 0.58
14. Point out specific strengths in teacher's
instructional practices in post-observation feedback
(e.g., in conferences or written evaluations)
26 4.58 0.64
15. Point out specific weaknesses in teacher
instructional practices in post-observation feedback
(e.g., in conferences or written evaluations)
26 4.31 0.97
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Table 4.8 displays the means and standard deviations for the fourth job function of
coordinating the curriculum. The overall mean for coordinating the curriculum was 4.14 and the
standard deviation was 0.31. Principals’ responses ranged from 2 to 5 for this particular job
function. The lowest mean score in this category was for participating in the review of curricular
materials with a mean score of 3.62. Scores were highest for making it clear who is responsible
for coordinating the curriculum across grade levels with a mean of 4.38. Close behind is the
behavior of using school-wide testing results when making curricular decisions with a score of
4.35.

Table 4.8
Descriptive Statistics for Job Function IV. Coordinate the Curriculum
Principal Instructional Leadership Behaviors N Mean Standard Deviation
IV. Coordinate the Curriculum 26 4.14 0.31
16. Make clear who is responsible for coordinating the
curriculum across grade levels (e.g., the principal, vice
principal, or teacher-leaders)
26 4.38 0.70
17. Draw upon the results of school-wide testing when
making curricular decisions
26 4.35 0.80
18. Monitor the classroom curriculum to see that it
covers the school's curricular objectives
26 4.27 0.83
19. Assess the overlap between the school's curricular
objectives and the school's achievement tests
26 4.08 0.80
20. Participate actively in the review of curricular
materials
26 3.62 0.80

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Table 4.9 shows the means and standard deviations for the fifth job function of
monitoring student progress. The overall mean for monitoring student progress was 4.17 with a
standard deviation of 0.36. Scores ranged from 2 to 5 for this category. The lowest mean score
of 3.58 was for the behavior of meeting with teachers individually to discuss the academic
progress of students. Principals scored themselves the highest for using tests and other
performance measures to assess progress towards school-wide goals. This particular behavior
had a mean of 4.50.

Table 4.9
Descriptive Statistics for Job Function V: Monitor Student Progress
Principal Instructional Leadership Behaviors N Mean Standard Deviation
V. Monitor Student Progress 26 4.17 0.36
21. Meet individually with teachers to discuss student
progress
26 3.58 0.81
22. Discuss academic performance results with the
faculty to identify curricular strengths and weaknesses
26 4.35 0.75
23. Use tests and other performance measure to assess
progress toward school goals
26 4.50 0.71
24. Inform teachers of the school's performance results
in written form (e.g., in a memo or newsletter)
26 4.31 0.93
25. Inform students of school's academic progress 26 4.12 0.95

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Table 4.10 reveals the means and standard deviations for the sixth job function of
protecting the instructional time. The overall mean for protecting the instructional time was 4.23
with a standard deviation of 0.43. Scores ranged from 1 to 5 on the Likert scale for this job
function. Principals reported that they least commonly ensure that students are not called to the
office during instructional time. This behavior had a mean of 3.69. With a mean of 4.73,
principals felt they most often encouraged teachers to use the instructional time to teach and
practice new skills and concepts.

Table 4.10
Descriptive Statistics for Job Function VI: Protect Instructional Time
Principal Instructional Leadership Behaviors N Mean Standard Deviation
VI. Protect Instructional Time 26 4.23 0.43
26. Limit interruptions of instructional time by public
address announcements
26 4.62 0.50
27. Ensure that students are not called to the office
during instructional time
26 3.69 0.97
28. Ensure that tardy and truant students suffer
specific consequences for missing instructional time
26 4.04 1.34
29. Encourage teachers to use instructional time for
teaching and practicing new skills and concepts
26 4.73 0.45
30. Limit the intrusion of extra- and co-curricular
activities on instructional time
26 4.08 0.93

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Table 4.11 displays the means and standard deviations for the seventh job function of
maintaining high visibility. The overall mean for maintaining high visibility was 3.82 and the
standard deviation was 1.04. Scores ranged from 1 to 5 and this particular job category had the
largest number of 1 scores. The behavior of tutoring students or providing direct instruction to
classes resulted in the lowest mean out of all behaviors for all ten categories. This particular
behavior had a mean score of 2.27. Principals reported that they spoke informally with students
and teachers during recess and breaks. This behavior had a mean score of 4.85.

Table 4.11
Descriptive Statistics for Job Function VII: Maintain High Visibility
Principal Instructional Leadership Behaviors N Mean Standard Deviation
VII. Maintain High Visibility 26 3.82 1.04
31. Take time to talk informally with students and
teachers during recess and breaks
26 4.58 0.58
32. Visit classrooms to discuss school issues with
teachers and students
26 4.04 0.82
33. Attend/participate in extra- and co-curricular
activities
26 4.85 0.37
34. Cover classes for teachers until a late or substitute
teacher arrives
26 3.35 1.29
35. Tutor students or provide direct instruction to
classes
26 2.27 1.28

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Table 4.12 shows the means and standard deviations for the eighth job function of
providing incentives for teachers. The overall mean for providing incentives for teachers fell
was 3.76 with a standard deviation of 0.58. Scores ranged the entire Likert scale. The lowest
mean score in this category of 3.12 was for writing memos in the personnel files of teachers to
acknowledge exceptional performance. The highest mean score of 4.65 was for complimenting
teachers for their efforts or performance in private.

Table 4.12
Descriptive Statistics for Job Function VIII: Provide Incentives for Teachers
Principal Instructional Leadership Behaviors N Mean Standard Deviation
VIII. Provide Incentives for Teachers 26 3.76 0.58
36. Reinforce superior performance by teachers in
staff meetings, newsletters, and/or memos
26 3.88 0.91
37. Compliment teachers privately for their efforts or
performance
26 4.65 0.56
38. Acknowledge teachers' exceptional performance
by writing memos for their personnel files
26 3.12 1.31
39. Reward special efforts by teachers with
opportunities for professional recognition
26 3.73 0.96
40. Create professional growth opportunities for
teachers as a reward for special contributions to the
school
26 3.42 1.10

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Table 4.13 reveals the means and standard deviations for the ninth job function of
promoting professional development. The term “professional development” includes both
formal and informal education-related trainings, conferences, seminars, and other forms of
development. The overall mean for promoting professional development was 4.45 with a
standard deviation of 0.53. Scores mostly ranged from 3 to 5 with only one response of a 2.
The behavior principals least identified with was setting aside time during staff meetings for
teachers to share ideas or information from in-service activities as it received a mean score of
4.27 as well as the only 2 score. The highest mean of 4.62 was for ensuring that staff in-service
activities are consistent with the school’s goals.

Table 4.13
Descriptive Statistics for Job Function IX: Promote Professional Development
Principal Instructional Leadership Behaviors N Mean Standard Deviation
IX. Promote Professional Development 26 4.45 0.53
41. Ensure that in-service activities attended by staff
are consistent with the school's goals
26 4.62 0.64
42. Actively support the use in the classroom of
skills acquired during in-service training
26 4.42 0.70
43. Obtain the participation of the whole staff in
important in-service activities
26 4.46 0.65
44. Lead or attend teacher in-service activities
concerned with instruction
26 4.50 0.71
45. Set aside time at faculty meetings for teachers to
share ideas or information from in-service activities
26 4.27 0.96

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Table 4.14 shows the means and standard deviations for the last job function of providing
incentives for learning. The overall mean for providing incentives for learning was 3.56 and had
a standard deviation of 0.51. Scores ranged the entire Likert scale of 1 to 5. The lowest mean
score of 2.92 in this category was for contacting parents to communicate improved or exemplary
student performance or contributions. Principals scored themselves the highest for recognizing
students who do superior work with formal rewards such as honor role or mention in the
Princpal’s newsletter.

Table 4.14
Descriptive Statistics for Job Function X: Provide Incentives for Learning
Principal Instructional Leadership Behaviors N Mean Standard Deviation
X. Provide Incentives for Learning 26 3.56 0.51
46. Recognize students who do superior work with
formal rewards such as an honor roll or mention in
the Principal's newsletter
26 4.12 0.86
47. Use assemblies to honor students for academic
accomplishments or for behavior or citizenship
26 3.88 1.18
48. Recognize superior student achievement or
improvement by seeing in the office the students
with their work
26 3.15 1.22
49. Contact parents to communicate improved or
exemplary student performance or contributions
26 2.92 1.02
50. Support teachers actively in their recognition
and/or reward of student contributions to and
accomplishments in class
26 3.73 0.87

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The overall means and standard deviations for each of the ten instructional leadership
categories are provided in Table 4.15. The instructional leadership job category that most
principals identified themselves as exhibiting most frequently was framing the school goals, as
evidenced by a mean of 4.58. The second most frequent instructional leadership job function
was promoting professional development, as evidenced by a mean of 4.45. Principals also
scored themselves high in the category of supervising and evaluating instruction with a mean of
4.33. A score of 4 indicates that principals stated that they frequently performed these job
functions. Principals scored themselves the lowest on providing incentives for learning,
providing incentives for teachers and maintaining high visibility with means of 3.56, 3.76, and
3.82, respectively. A score of 3 indicates that they only “sometimes” perform these job functions.
Nevertheless, scores for these particular job categories were within one standard deviation of the
“frequently” classification.

Table 4.15
Descriptive Statistics for the Principal Instructional Leadership Job Functions
Principal Instructional Leadership Behaviors N Mean Standard Deviation
I. Frame the School Goals 26 4.58 0.19
II. Communicate the School Goals 26 4.16 0.42
III. Supervise & Evaluate Instruction 26 4.33 0.31
IV. Coordinate the Curriculum 26 4.14 0.31
V. Monitor Student Progress 26 4.17 0.36
VI. Protect Instructional Time 26 4.23 0.43
VII. Maintain High Visibility 26 3.82 1.04
VIII. Provide Incentives for Teachers 26 3.76 0.58
IX. Promote Professional Development 26 4.45 0.53
X. Provide Incentives for Learning 26 3.56 0.51
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Research Question Two: What Instructional Leadership Strategies Do Principals Employ
that Influence Positive Outcomes of Academic Achievement?
The second research question was answered through careful analysis of interviews with
three high school principals. Mrs. Shore, Ms. Estuary, and Mr. Creek met the selection criteria
and volunteered to be a part of the second phase of this study. Qualitative data gathered from
these interviews were analyzed using Creswell’s (2009) data analysis steps and Patton’s (2002)
method for coding. Each of the hour-long interviews resulted in deep discussions about the role
the principal believed he or she played at their school site in facilitating improvements in student
academic achievement. Analysis of the transcriptions and field notes gave light to the following
five recurring themes: (1) shared instructional leadership functions; (2) teacher empowerment;
(3) professional learning communities (PLCs) and other forms of professional development; (4)
creating opportunities for all students to be successful and college-eligible; and (5) evolving the
school culture. While the personalities of each of the three principals were very different, the
commonalities in reported actions were uncanny.
Shared Instructional Leadership Functions
Each of the three principals interviewed reported that instructional leadership
responsibilities were shared amongst key individuals on the school staff. While each principal
reserved some instructional leadership tasks for themselves, they each delegated the
responsibilities to members of the administration team, the leadership team, and other leaders on
staff.
The administration team for each of the three school sites consisted of three assistant
principals. Each of these assistant principals played a key role in sharing the bulk of the
instructional leadership responsibilities. Additionally, each of the three assistant principals had
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an overarching assignment. As stated by Mr. Roger Creek, “one is generally tasked with what
we would traditionally call curriculum and instruction, one is tasked with managing student
conduct and attendance and one is charged with managing athletics and activities and operations”
(personal communication, January 30, 2013). Ms. Estuary (personal communications, January
29, 2013) went into detail to describe the roles each of these three assistant principals adopted.
The Assistant Principal of Curriculum and Instruction worked with department chairs, course
leads, monitored the activities of the multiple Professional Learning Communities, set up
instructional rounds, and organized professional developments. This assistant principal was also
charged with organizing all testing as well as the budget for instructional and professional
development. The Assistant Principal of Guidance and Student Support Services took care of all
attendance matters, managed the counselors, and was also in charge of discipline and school
security. The Assistant Principal of Business and Activities was in charge of all athletics, band,
cheerleading squad, and the Associated Student Body, as well as all expenditures related to
business and activities.
In addition to the overarching roles, each of the three assistant principals were in charge
of leading multiple academic departments. The assistant principals worked with each of these
departments to develop their goals for growth and development, or “smart goals” as Mr. Creek
referred to them as (personal communication, January 30, 2013). At Penny High School, Ms.
Shore required the administrators at her school site to conduct a minimum of 10 teacher
observations per week because “what gets observed gets measured and what gets measured gets
done” (personal communication, January 24, 2013). Teachers are provided with immediate
positive and constructive feedback to “make sure they are providing the best possible classroom
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environment for all of our students”. In addition to the feedback, the administrators leave room
for discussion and opportunities for further development and growth.
The three principals who were interviewed reported that their assistant principals took on
a large portion of the instructional leadership responsibilities, second to the principal. In addition
to the school administrators, the department chairs also played an important role in fulfilling
instructional leadership duties. All three principals that the department leaders at their school site
were appointed and the position had little turnover. The principals each attributed this sense of
permanence in the role of the department chair position to various bureaucratic reasons including
district rules and teacher contract language. As stated by Mr. Creek, “once you are selected as
the department chair, you basically stay unless you step down or unless the principal writes you
up” (personal communication, January 30, 2013). All three principals expressed a desire to see
this rule change in their district “because it can lead to very stagnant department leadership”
(Roger Creek, personal communication, January 30, 2013).
Teacher Empowerment
To avoid stagnancy, each of the three principals created other roles within their school
sites to give other teachers opportunities to lead. Creating a variety of leadership roles was
beneficial in several ways. First, the roles did not have the permanence that the department chair
position had. Additionally, more teachers were given the opportunity to take advantage of
leadership roles rather than waiting for the current department chair to step down. As stated by
Ms. Estuary, “we just value the turnover of creative ability and a shared leadership, not because
we want to get rid of people but so we can share the responsibilities” (personal communication,
January 29, 2013). Furthermore, Mr. Creek states, “I believe profoundly in the powers, in the
power of teachers to impact student achievement. I was a good English teacher and I could
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maybe help English teachers but the reality is that my experts are out there. Historically, they
really haven't been empowered here to make decisions, to make choices and it showed in our
results” (personal communication, January 30, 2013).
At Penny High School, Ms. Shore has created opportunities for teachers at her school to
lead in a variety of roles. Recently, she implemented the Advancement Via Individual
Determination (AVID) program at her school site. She took several teachers on staff to the
weeklong AVID summer training institute. Some of these teachers have led staff developments
for the entire school site to train them on AVID strategies. The teachers who attended the
institute were given leadership roles as AVID core teachers and one has taken on the role of
being the AVID coordinator of Penny High School. These positions are separate from
department chairs. “I try to give them more opportunities to be in charge because that’s what the
teachers have asked for” (Elizabeth Shore, personal communication, January 24, 2013). Through
a variety of positions, the teachers at Penny High and the other two high schools are sharing the
instructional leadership responsibilities with the administrators.
By allowing faculty members not in typical leadership positions to take charge, Mr.
Creek, Ms. Shore, and Ms. Estuary were effectively empowering their staff. All three principals
expressed the importance of valuing the abilities, expertise, and wealth of knowledge each of
their teachers brought to the table. The principals spoke about the importance of letting go
control and allowing the leaders on staff – both appointed in official positions and volunteers – to
take charge. Of her role as the principal, Ms. Estuary states, “What do you do as principal? You
just empower really good teachers and then you just give them power and the freedom because
you go into teaching because it’s a passion and you care about teaching kids. You know that it’s
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the most important job in the world and you want to help kids learn” (personal communication,
January 29, 2013).
All three principals discussed the importance of not only empowering teachers but giving
them full reign and control in fulfilling given responsibilities. They each admitted that it can be
challenging to let go of power and not micromanage their staff but this step was important in
order for teachers to feel as though their expertise, knowledge, and judgment is trusted and
valued. In turn, teachers begin to take ownership of their responsibilities and their work, which
increases productivity and boosts staff morale. Mr. Creek related the act of “letting go” to
teaching a teenager how to drive for the first time:
There will come a time when you have a child who is learning how to drive. And at
some point, you will sit in the car – terrified – but you will just have to release control.
Eventually that kid turns out to be fine. And in fact, she turns out to more than fine. Its
kind of like that. (personal communication, January 30, 2013)
In addition to typical leadership roles, empowering teachers took on multiple forms at
each of the school sites. Some roles were similar across sites while others were unique to a
particular school. Teachers took on leadership different roles, “not just department chairs but
course leads, intervention specialists, instructional coaches. If you build positions for teachers to
take on roles to give back and work with their peers, they will thrive and grow. Most of our
professional development is just observing and learning from each other and each other’s
classrooms. We have a very empowered, hard-working team of teachers so we just allow them
to lead” (Linda Estuary, personal communication, January 29, 2013). Allowing teachers to “just
lead” is beneficial for the school as a whole. For example, Ms. Estuary believes that “course
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leads are very instrumental; they're just really important in our campus in terms of the
instructional and curriculum piece” (personal communication, January 29, 2013).
Professional Learning Communities and Other Professional Development
Professional Learning Communities (PLC) played an important role at each of the three
school sites. Each of the three principals discussed the impact of PLCs in the way department
functions and its subsequent impact on student achievement. They attribute improved teaching
practices and improved student achievement to the PLC process. In addition to the PLCs,
principals offered their teachers other opportunities for professional development to improve and
deepen their staff’s instructional practices. Ms. Shore believes that “ongoing staff development
is necessary” and that she must ensure that she is “providing opportunities for teachers to make
sure they utilize the best possible strategies within the classroom” (personal communication,
January 24, 2013). The interviewed principals attribute improved student achievement across
subject areas to PLCs and other forms of professional development.
Department leaders were given autonomy in determining how the Professional Learning
Community would be conducted. Administrators frequently attended PLC meetings as an
observer rather than an active participant. The principal and assistant principals limited their
contributions to when their input was solicited and allowed for the department chairs to lead
these meetings. This form of autonomy empowered those teachers leading PLC meetings.
A weekly meeting time for Professional Learning Communities is embedded in the
school schedule with either a later start time or early dismissal time for students. Ms. Estuary
states that the embedded time is not enough and “because our staff is so hard-working, they have
scheduled other times for PLC and during those times, teachers are sharing best practices,
writing and analyzing common assessments, and talking about what is working for student
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learning. The PLC process is district-wide and we use Moodle to share lesson plans across our
district” (personal communication, January 29, 2013).
When Mr. Creek began as the principal of Arthur High, he implemented the use of “the
class Professional Learning Communities program as it was defined and designed by Dufour.
This was something that created a little bit of a challenge was that this school was not a PLC
school. They didn’t know what it was. They hadn’t done anything like that before” (Roger
Creek, personal communication, January 30, 2013). At the beginning of each semester, Mr.
Creek had each department set a professional growth goal that will improve student learning. At
the end of the semester, teachers “evaluate the degree to which they achieved their goal… The
basic process of PLC is, you know, begin by identifying what you need to work on and write a
goal. Spend the next 18 weeks sharing your strategies, your process, your procedures, and
putting together your best lessons. If you're doing a really good job, you’re checking your
progress along the way. And then at the end of the 18 weeks, stop, look at what your data told
you and see if you can figure out what worked or what didn't work and what you need to do next
time” (Roger Creek, personal communication, January 30, 2013). Mr. Creek was pushing the
teachers at his school site to focus on learning and growing as an educator, to work
collaboratively, and to be accountable for results.
In addition to Professional Learning Communities, each of the three principals also
valued other forms of professional development. At Penny High, Ms. Shore believes in the
importance of continuously providing teachers with different opportunities for professional
development. She uses Title I funds to pay teachers for attending voluntary professional
developments held outside of the normal school day. Some training sessions are run by the
school district while others are led by teachers at her school site. “We are implementing AVID
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strategies school-wide so my AVID core teachers help out with staff development” (Elizabeth
Shore, personal communication, January 24, 2013). This school year, Ms. Shore started an
optional “Lunch and Learn” meeting with teachers. Once a month, she invites her teachers to
enjoy a catered lunch and engage in collegial conversations. “I have a focus, usually. This time,
because I went to the Kate Kinsella conference, I gave them a couple of articles that I had
received and read. Sent it to them ahead of time and then we discussed some of the key things
that are happening and related it to the school” (Elizabeth Shore, personal communication,
January 24, 2013).
At Weston High School, teachers who attended professional developments are asked to
present what they learned to the staff so all teachers could benefit from the newly gained
knowledge. This act of sharing knowledge was a way to empower teachers and Ms. Estuary was
ensuring that many teachers would benefit from new instructional strategies, ideas, knowledge,
or approaches. Ms. Estuary values the uniqueness of each member on her faculty and
encourages teachers to apply new skills to their classroom in a way that is authentic and true to
their own teaching style. She says, “if you trusted everybody is a good teacher, they're going to
go to it an in-service and they're going to take it and they're going to pilot, they're going to use it
their way.” Teachers are asked to immediately to put the newly learned skills and strategies into
action. Ms. Estuary asks for demonstration teachers to volunteer their classrooms where their
colleagues conduct instructional rounds. Ms. Estuary spoke in detail about how instructional
rounds are used at her school site:
When we do instructional rounds, we critically look. Peers go and you're welcomed in
the classroom so the teachers say, "come see, I'm doing this". So lets say that we've
decided that we're using thinking maps across all curriculums. There are several things to
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look at – critical reading strategies, all students are reading, thinking maps, Cornell notes,
Jane Schaffer writing strategies… Strategies that our teachers decided to use and think
are effective enough that all teachers should be using it. So then we set up instructional
rounds to go see it in practice. (personal communication, January 29, 2013)
At Arthur High, many teachers participate in a variety of on-going professional
development opportunities. For example, some English teachers are a part of the Pathways
Project through the University of California, Irvine. Algebra teachers are a part of an “intensive
2-year long program that is district directed.” While Mr. Creek finds value in his teachers
participating in professional developments, he believes “the best professional development is
really just a group of teachers working together around their own work and trying to figure out
how to influence student learning and student achievement” (Roger Creek, personal
communication, January 30, 2013).
Struggling teachers are given additional support structures in the form of mentor teachers
and instructional coaches. Each of the three principals interviewed felt it was just as important to
set teachers up for success as it was to set students up for success. At Weston High and Penny
High, teachers who were not meeting expectations were offered an instructional coach to help
improve their teaching practice. “People are in their different levels of practice and our job as
administrators is to be instructional leaders and we have to help people grow. And that's really
hard to tell people, ‘you're not cutting it and we're here to help you grow’ but that's our job”
(Linda Estuary, personal communication, January 29, 2013). An instructional coach’s support
was highly suggested for some teachers but it was ultimately up to the teacher whether or not to
take advantage of the support. Some teachers requested to work with an instructional coach to
further develop their own practice. At Penny High, the English and math departments received
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ongoing support from an instructional coach because improvement in student academic
achievement in these subject areas were a part of the district and school goals. Both Ms. Shore
and Ms. Estuary spoke highly about the positive effects that an instructional coach had on
teaching practices.
Arthur High did not have funding to provide teachers with instructional coaches.
However, Mr. Creek set up structures within his school site for struggling teachers to receive
support from their colleagues who were further developed in their teaching practice. In many
ways, mentor teachers served as instructional coaches for their colleagues.
Creating Opportunities for Students to be Successful and College-Eligible
Each of the three interviewed principals spoke extensively about the importance of
preparing their students for college and ensuring they were competitive candidates for California
State Universities (CSU) and University of California (UC) schools. The schools’ mission and
goals are all to get their students into a university. The majority of students at Weston High,
Penny High, and Arthur High come from families with low socioeconomic status and their first
language is not English. Many of the students “don't have the belief that they can go to college.
We are making sure that we are preparing them for the future and giving them the tools…. and
we have opportunities for all students” (Elizabeth Shore, personal communication, January 24,
2013).
In their own words, each of the principals reinforced the idea that “it starts with climate
and you need to be kind and be caring and be supportive and every student needs to experience
academic success and earn good grades in rigorous classes” (Roger Creek, personal
communication, January 30, 2013). It is important that “we are creating a culture where we
believe all students can learn and all students will excel” (Elizabeth Shore, personal
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communication, January 24, 2013). Providing opportunities for all students to be successful
takes on multiple forms at each of the school sites. Each of the schools offer Advanced
Placement and honors courses as well as college readiness course that helps students develop
more effective study habits.
At Weston High, the counseling department conducts grade level meetings twice a year
and meet with each individual student to help them understand their transcripts and to ensure
they are taking the appropriate coursework to qualify for admission into a 4-year university.
Many of the students at Weston High are the first in their families to attend college. To make
college more realistic and accessible for both students and families, Ms. Estuary and her staff
help students apply for scholarships and hold financial aide fairs where they help parents fill out
the FAFSA application.
In addition to empowering students with the knowledge of what it takes to be successful,
Ms. Estuary found importance in providing all students with opportunities and not limiting
access to classes so that students can make the choice to go to college or not. To further
reinforce this mindset, Weston High only offers college preparatory courses that fulfill
requirements for admission to a CSU and UC. Ms. Estuary says, “we take the standpoint that
every student needs to have access to the most rigorous courses possible and then making it
accessible to them. It’s not about making it hard to get there” (personal communication, January
29, 2013). Ms. Estuary has worked to add an Advanced Placement course every year since
becoming the principal of Weston High. She prides herself in having the largest number of
students in AP and Honors courses in the entire district, despite being a school with the lowest
socio-economic status of students. She states that “80% of the student body is living below the
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poverty line but the largest percentage in the district that are going onto college... it means we've
convinced them that they, too, can do that” (personal communication, January 29, 2013).
To further ensure that students are successful in their academic courses, Weston High
School has built in “embedded support” as the last 20-minutes of each 2-hour block period.
Teachers are given autonomy in determining which students must stay for this intervention time
and how it is structured in their own classroom. Some students stay for additional academic help
or to catch up on work while others serve as peer experts and tutor other students in the class.
The message the embedded support system sends to the kids is that:
It is not okay with us for you to not do well; we are not going to let you fail. So if you're
struggling, or if you don't do your work, that’s our time to work with you because you
have to have a C or better to get out of embedded support. You have to be earning a
passing grade. And a D is not a passing grade because it won't get you into college.
(Linda Estuary, personal communication, January 29, 2013)
Mr. Creek holds his students at Arthur High to the same standard. While a D is technically a
passing grade, he considers both D’s and F’s to be failing grades. His reasoning is that colleges
will not accept D’s and to be competitive, students must earn a C or better. It is the mission of
the educators at Arthur High to keep kids from failing.
It is important that all students “have the opportunity to go to college because in our
culture and in our world today, that's how they will make the best lives for themselves and
contribute to our community” (Linda Estuary, personal communication, January 29, 2013).
Schools are working to create and give all students multiple opportunities to succeed
academically so their futures are not limited by a lack of academic success.
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Evolving the School Culture
Along with preparing students to be college ready and eligible, principals worked to
develop the school culture. Principals strove to foster a sense of community and build
relationships between and amongst all members of the school setting including the
administration, teachers, students, parents, and community at large.
At Arthur High, Mr. Creek stressed the importance of being a “kind, caring, inclusive
school where every student experiences academic success. I place a higher emphasis on climate
because without a safe, kind, caring, and supportive climate, kids mostly can't learn, particularly
if they come from difficult, challenging home environments.” Mr. Creek also emphasizes the
importance of maintaining ongoing and clear communication between all key stakeholders of the
school. The purpose of this is to “act more like a school than a collection of departments and
that's beginning to happen but it takes a long time to completely change things” (personal
communication, January 30, 2013). It was important to the school culture and morale to operate
collaboratively rather than separately.
The results of a Healthy Kids survey at Penny High showed that students did not feel
connected with their teachers and as a result, did not feel comfortable or safe. As a result, Ms.
Shore has challenged and pushed her staff on this issue and has conducted multiple professional
developments to equip teachers with “the skills and tools to be culturally relevant as well as
instructional strategies to get them more involved with their students and collaborating. There is
a strong focus on making sure we are striving for excellence with that student connectedness”
(Elizabeth Shore, personal communication, January 24, 2013). Penny High qualified for a grant
and as a result, was able to hire a Safe and Supportive Schools Coordinator who is “helping us
build a bridge between the teachers, the students, and the community.”
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Research Question 3: What is the Relationship Between the Instructional Leadership
Behaviors of Principals and Student Achievement in Mathematics?
Determining the relationship between the instructional leadership behaviors of principals
and student achievement in secondary mathematics was a two-step process. First, school
performance data was gathered to determine how schools performed on the math portions of the
California High School Exit Examination (CAHSEE) and the Standardized Testing and
Reporting (STAR). Scores on the CAHSEE were reported on the performance of high school
sophomores. Scores for the STAR Program were reported for freshman, sophomore, and junior
students. The STAR Program includes the four exams: the California Standards Tests (CST), the
California Modified Assessment, the California Alternate Performance Assessment, and the
Standards-based Tests in Spanish.
School Performance Data
The school performance data for each the three interviewed principals’ school sites are
highlighted in this section. Further discussion analyzing increases in scores can be found later in
this chapter.

Table 4.16 shows Penny High School’s performance data on the mathematical
portions of the CAHSEE and STAR exams since Ms. Shore became the principal in the 2008 to
2009 school year. There has been a 7.0% increase in the percent of students testing proficient or
higher on the STAR exams. For the CAHSEE exam, sophomore students have exhibited an
overall growth of 1.9% since Ms. Shore first began as the principal of Penny High. The greatest
jump in scores occurred between her second and third year as principal. Scores went from
35.8% to 43.0%, which is a 7.2% increase.

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Table 4.16
Percent of Students at Penny High School Testing at Proficient Level or Higher
2011-2012 2010-2011 2009-2010 2008-2009
STAR 15.0% 11.0% 9.0% 8.0%
CAHSEE 40.0% 43.0% 35.8% 38.1%

Table 4.17 shows the performance data for Weston High School since Ms. Estuary has
been principal. The percent of students scoring proficient or higher has increased since Ms.
Estuary became principal in the 2008 to 2009 school year. There has been an overall increase of
6.0% for students testing proficient and higher on the STAR exams. Similar to Ms. Shore, the
greatest jump in CAHSEE scores occurred between Ms. Estuary’s second and third years serving
as principal with a 6.2% jump. Overall, scores on the CAHSEE have increased by 6.4% since
Ms. Estuary began as principal of Weston High.

Table 4.17
Percent of Students at Weston High School Testing at Proficient Level or Higher
2011-2012 2010-2011 2009-2010 2008-2009
STAR 36.0% 35.0% 33.0% 30.0%
CAHSEE 61.0% 66.0% 59.8% 54.6%

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Table 4.18 shows Arthur High School’s performance data since Mr. Creek was appointed
as principal in 2010. Student scores on the STAR exam have increased by 1.0% in the two most
recent years that Mr. Creek has served as principal. This is similar to the growth exhibited
during Ms. Shore and Ms. Estuary’s first years as principal of their respective high schools. A
10.0% jump occurred in CAHSEE mathematics test scores during Mr. Creek’s first two years as
principal. This is remarkable improvement exhibited by students in only one school year.

Table 4.18
Percent of Students at Arthur High School Testing at Proficient Level or Higher
2011-2012 2010-2011
STAR 17.0% 16.0%
CAHSEE 48.0% 38.0%

Phase I – Survey
Phase I of this study asked principals for their voluntary input on a survey about their
own instructional leadership practices. Table 4.19 gives the demographic information of the
three principals who volunteered and were selected for an interview. Two principals were
female while one was male. Two principals identified themselves to be Caucasian while one
identified as African-American. All three principals completed graduate work. One principal
earned her Masters degree while the other two principals went on to earn their Doctorate degrees.
Table 4.20 shows the number of years that each administrator served as a classroom teacher and
the subjects their primarily taught. On average, the three interviewed principals served 17.3
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years in the classroom with a standard deviation of 6.8. Two of the three served in classroom for
11 to 15 years. The third principal served as a classroom teacher for over 20 years. The subject
areas taught by the principals raged widely and include English Language Arts, Science, and
Special Education.

Table 4.19
Frequency of Principals’ Gender, Ethnicity, and Highest Education
Demographic Independent Variable f %
Gender Female 2 66.7
Male 1 33.3
Total 3 100
Ethnicity African-American 1 33.3
Asian 0 0.0
Caucasian 2 66.7
Hispanic 0 0.0
Other 0 0.0
Total 3 100.0
Highest Education B.A./B.S. 0 0.0
M.A./M.Ed 1 33.3
Ph.D/Ed.D. 2 66.7
Ed.S. 0 0.0
Other 0 0.0
Total 3 100

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Table 4.20
Frequency of Years Served as a Classroom Teacher and Primary Subject Taught
Demographic Independent Variable f %
Years Served as a
Classroom Teacher
0-5 years 0 0
6-10 years 0 0
11-15 years 2 66.7
16-20 years 0 0.0
M = 17.3 >20 years 1 33.3
SD = 6.8 Total 3 100
Primary Subjects
Taught
K-6 0 0.0
Art / Applied Arts 0 0.0
Language Arts / English 1 33.3
Mathematics 0 0.0
Physical Education 0 0.0
Science 1 33.3
Social Science 0 0.0
Special Education 1 33.3
Other: 0 0.0
Total 3 100

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Table 4.21 exhibits the number of years each interviewed principal has served as an
administrator. The mean number of years served as principal of their current school site was 4.3
school years and the standard deviation was 1.2. One interviewed principal has served for 3 to 4
years while the other two principals have served for 5 to 6 years. The average number of overall
years as an administrator is 12.0 with a standard deviation of 3.61. Two of the interviewed
principals have been in an administrative position for 9 to 12 years. The third principal has been
an administrator for 13 to 16 years.

Table 4.21
Frequency of Years Served as Principal of Current School Site and Years Served as an
Administrator
Demographic Independent Variable f %
Years Served as
Principal of Current
School Site
1-2 years 0 0.0
3-4 years 1 33.3
5-6 years 2 66.7
M = 4.3 >6 years 0 0.0
SD = 1.2 Total 3 100
Years Served as
Administrator Overall
5-8 years 0 0.0
9-12 years 2 66.7
13-16 years 1 33.3
M = 12.0 >17 years 0 0.0
SD = 3.61 Total 3 100

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Table 4.22 shows how the three interviewed principals believe they delegate instructional
leadership duties amongst key stakeholders at their school site. The responses indicate that
principals reserve the greatest percentage of instructional leadership tasks for themselves, with a
mean average of 40%. However, the standard deviation for reserving responsibilities for
themselves was 30.0 and responses ranged from 20% to 60%. The second largest percentage of
instructional leadership tasks was delegated to the assistant principals, with a mean of 26.7%.
Department chairs and teacher leaders were last with a mean of 21.7% and 11.7%, respectively.
With a standard deviation of 16.07, the second largest discrepancy in answers was for the
percentage of responsibilities delegated to the department chair. One principal reported 40%
while another reported 10% of tasks delegated to the department chair.

Table 4.22
Statistics of Instructional Leadership Delegated
Stakeholder Minimum Value Maximum Value Mean
Standard
Deviation
Assistant Principal(s) 20.0% 30.0% 26.7% 5.77
Curriculum Director(s) 0.0 0.0 0.0 0.0
Department Chair(s) 10.0% 40.0% 21.7% 16.07
Teacher Leader(s) 10.0% 15.0% 11.7% 2.89
Other 0.0 0.0 0.0 0.0
Self 20.0% 60.0% 40.0% 30.0

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Table 4.23 displays the overall mean and standard deviation for each of the ten principal
instructional leadership job functions. With a mean of 4.93, the three interviewed principals felt
they almost always performed the instructional leadership job function of “Supervise and
Evaluate Instruction.” This particular job function also had the smallest standard deviation of
0.26, which indicates that all three principals scored themselves closely to one another on the ten
questions for this section. Principals who were interviewed scored themselves highly on the job
functions of “Frame the School Goals,” “Promote Professional Development,” and “Coordinate
the Curriculum”, with mean scores of 4.73, 4.60, and 4.40, respectively. Interviewed principals
scored themselves the lowest in the category of “Provide Incentives for Learning” with a mean
score of 3.73. Nevertheless, a score of 3 means the particular job function is sometimes
performed. The job functions of “Provide Incentives for Teachers” and “Protect Instructional
Time” had the second lowest mean of 3.93.

Table 4.23
Descriptive Statistics for the Principal Instructional Leadership Job Functions
Principal Instructional Leadership Behaviors Mean Standard Deviation
I. Frame the School Goals 4.73 0.80
II. Communicate the School Goals 4.00 1.46
III. Supervise & Evaluate Instruction 4.93 0.26
IV. Coordinate the Curriculum 4.40 0.83
V. Monitor Student Progress 4.33 0.98
VI. Protect Instructional Time 3.93 1.39
VII. Maintain High Visibility 4.27 1.33
VIII. Provide Incentives for Teachers 3.93 1.22
IX. Promote Professional Development 4.60 0.59
X. Provide Incentives for Learning 3.73 1.03
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Phase II – Interviews
For Phase II of this study, the researcher purposefully selected 3 principals for an hour-
long in-person interview. Of the 26 principals who completed Phase I of the study, 13 principals
volunteered to continue on with the study. Analyzing data from Phase II gave light to five
common themes across all interviews: (1) shared instructional leadership functions; (2) teacher
empowerment; (3) professional learning communities (PLCs) and other forms of professional
development; (4) creating opportunities for all students to be successful and college-eligible; and
(5) evolving the school culture.
Comparative analysis of the quantitative data from Phase I and qualitative data from
Phase II gave light to the interviewed principals’ beliefs about their own instructional leadership
practices. The survey responses from the three selected principals are consistent with the
information drawn from the interviews. The three principals spoke extensively about
supervising and evaluating instruction. It was no coincidence that the responses on the survey
for this particular instructional job function had an overall mean of 4.93. Along the same lines,
the principals did not speak much to providing incentives for teachers, providing incentives for
learning during the interview, or protecting instructional time. On their survey these were the
two areas the interviewed principals scored the lowest.
Instructional Leadership and Student Achievement in Mathematics
Through a series of questions, principals were indirectly asked about their instructional
leadership behaviors as it relates to secondary mathematics. Comparative analysis was
conducted using the data from Phase I and Phase II of the study as well as the performance data
on the math portions of the CAHSEE and CST. The analysis shows a connection between
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student academic achievement in secondary mathematics and the instructional leadership
behaviors of principals.
Each interviewed principal offered insights based on the context of their school site –
including both teacher and student circumstances. Though there were variances in behaviors, the
importance of strong instructional leadership functions was integral to each principal’s anecdotes.
Nevertheless, the interviews produced common themes of instructional leadership as it pertained
to mathematics, most of which overlapped with the data extracted for Research Question 2: (1)
data-driven decision-making; (2) professional learning communities (PLCs) and other forms of
professional development; and (3) creating opportunities for all students to be successful and
college-eligible.
Data-Driven Decision-Making
Each of three interviewed principals spoke to the importance of data-driven decision-
making, particularly when it comes to making decisions that impacts students. It is important to
examine student achievement data on state exams as well as common assessments provided by
the school or district.
Ms. Shore said, “we support teachers by providing data and helping them disaggregate
their data” (personal communication, January 24, 2013). Once data has been disaggregated,
teachers an administrators brainstorm ways to target specific areas that need improvement.
Furthermore, Ms. Shore and leaders on campus, “support teachers by listening to their issues and
trying to problem-solve and provide additional help.”
Ms. Estuary stated, “we are a very data-driven school and a very data-driven school
district” (personal communication, January 29, 2013). A decade ago, data indicated that students
matriculating to Weston High as freshmen were the lowest performing eighth graders in the
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entire district, particularly in mathematics. This accounted for anywhere from 400 to 500
students per year. Ms. Estuary and her staff have used this data as a challenge and a motivator.
“If that's what we have, we have to be the best math program in the district. It has just become a
mission and I don't know of any other department in the entire district that works so well
together” (Linda Estuary, personal communication, January 29, 2013).
Professional Learning Communities and Other Professional Development
All three interviewed principals spoke highly about PLCs and the effect it had on student
academic achievement. Mr. Creek says, “the PLC system works. PLC works, teacher ownership
of what they wanted to work on, what their goals were, a more open, trusting, inclusive
environment worked” (personal communication, January 30, 2013).
At Arthur High School, Mr. Arthur believes that because of the PLC system:
The best professional development is a team of teachers working together on something
they write down. Math is one of those departments where it’s so just transparently easy
after being in their classrooms all this time; I don't even worry about them anymore.
They're all right where they should be, they're in-step, they all teach physically in the
same area, they eat lunch together. They're very much in-step and I'm not concerned
about them at all. That's because I'm there too. (personal communication, January 30,
2013)
Mr. Creek believes that the math department works well together under the PLC model and has
been successful at helping students be successful in mathematics.
Since Ms. Shore became principal of Penny High School, she has been working closely
with math instructional coaches and the PLC model to push the mathematics department forward
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and deepen their teaching practices to better serve their students. She believes that while change
is difficult, there has been a shift in instruction.
The way that we teach all subjects, but most importantly, the way that we teach math, has
to change. We have to involve the students more. You have to find ways to scaffold the
lesson, find ways to have small group learning. We've implemented AVID tutorials
within our class. So, kids sitting around, working on problems, figuring it out. Before,
there really wasn't an opportunity for students to interact with each other. So the
interaction has been a big part of it. Just having that opportunity is big. So definitely,
there is a change in instruction. (Elizabeth Shore, personal communication, January 24,
2013)
At Penny High, teachers also do “Action Walks” which is similar to the “Instructional
Rounds” conducted by the teachers at Weston High. The purpose is to provide teachers the
opportunity to go through different classes, chosen either with purpose or randomly. By
engaging in action walks, “teachers get a chance to get out of their class and get a glimpse of
what's happening. They see good and bad but they get ideas and that's what I'm excited about.
We've even a few of our math teachers to our school and sent them to another school, just to see
a variety of different classrooms” (Elizabeth Shore, personal communication, January 24, 2013).
Ms. Shore believes in the power of constant communication, constant professional development,
and constant feedback to effect change in student academic performance.
At Weston High, the goal was to build a PLC where teachers are learning from one
another and trying new things every year. “They're analyzing their practices to get better. It's
the best way. And that's their goal” (Linda Estuary, personal communication, January 29, 2013).
Within the math department, and other departments as well, teachers do not teach the same
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course every single year. Ms. Estuary finds importance in ensuring that her staff is constantly
challenged so they are able to stretch and grow.
As it pertains to mathematics, Ms. Estuary believes their collaborative work through
PLCs and instructional rounds have been pivotal to students’ academic growth in the subject.
Their collegial work through instructional rounds at our school made them realize that
sometimes the kids are not the problem, its not the problem, the problem is that the kids
are having problems with the academic language of math. It’s not the process, its that
they don't get the words. And so then they have integrated this whole academic
vocabulary part of their curriculum to make sure that the kids understand the vocabulary.
(Linda Estuary, personal communication, January 29, 2013)
Another way the math department engages in professional development is by holding
“Math Days” after each quarterly common assessment. This practice takes place over the course
of two block days. During each of the six periods, all students taking math during that period are
engaged in a common activity in the auditorium. Meanwhile, math teachers are meeting together
in a separate room to look at data from the common assessment and strategize on how to move
forward with instruction. During these two days, teachers are immersed in collaborative work
while students only miss one block period of math.
Mr. Creek believes that “kids will do better on CSTs, on STAR, on the CAHSEE, if their
teaching is appropriately aligned. Kids will also do better on those assessments if teachers stop,
identify what kids aren't learning, and reteach” (personal communication, January 30, 2012).
Particularly in mathematics, Mr. Creek believes that depth in material is more important than
breadth of material. He stresses to his math teachers the notion that he would “rather see
students maybe learn fewer big topics well then to finish the entire curriculum. I have very
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intentionally given people permission to teach less but to make sure that what we do teach, kids
actually know.” Prior to Mr. Creek’s principalship, teachers were rushing to finish the
curriculum prior to state testing in the spring. Unfortunately, students were not retaining any
information and this method is “unsupportable by any piece of evidence about how the brain
works and about how kids actually learn” (Roger Creek, personal communication, January 30,
2012).
Creating Opportunities for Students to be Successful and College-Eligible
The three interviewed principals each spoke extensively about the importance of
providing students with adequate opportunities to be successful and competitive candidates for
CSU and UC schools. This notion was embedded into the mission of each of their three schools.
Extensive discussion on this notion can be found in the previous section for the second research
question. Principals who were interviewed felt success in mathematics was essential for students
to be successful in college.
At Weston High, the math department is constantly looking critically at how to build
interventions for students who are not passing. To ensure students are successful, math teachers
are developing interventions and making use of “academic mentors who are trained to be tutors
in classes better than any department in the school” (Linda Estuary, personal communication,
January 29, 2013). Ms. Estuary and her staff reinforce the importance of success in academic
courses. On Math Days, students who failed the common assessment report to a different room
rather than the auditorium with the other students to receive individual tutoring and support.
Afterwards, they are given the opportunity to retake either part or all of the common assessment.
Ms. Estuary feels this is important to “matching our mission of getting kids into college.” The
counselors also push students to take 4 years of math courses to be more competitive college
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applicants. Of her math department, Ms. Estuary says, “I don’t have to do anything to inspire the
math department. They inspire me” (personal communication, January 29, 2013). It is clear that
Ms. Estuary has great faith in the abilities and dedication of her math department. The value she
places in her teachers gets paid forward in the work the teachers do with their students.
Summary
The purpose of this study was to ascertain the instructional leadership behaviors and traits
of high school principals and make connections to student achievement in mathematics. Three
main questions guided this study: (1) what are the self-perceived instructional leadership
behaviors of high school principals?; (2) what instructional leadership strategies do principals
employ that influence positive outcomes of academic achievement in mathematics?; and (3) what
is the relationship between the instructional leadership behaviors of principals and student
achievement in mathematics?
Chapter 4 provided a detailed discussion of the findings of this study. Participation was
voluntary for both phases of the study. The start of the chapter provided demographic
information about the principals who chose to complete the survey in Phase I. This included
information about principals’ gender, ethnicity, the highest level of education obtained, the
number of years they served in the classroom, and the subject(s) they primarily taught. The
number of years the served as the principal of their current school site and the total number of
years as an administrator was also reported. The demographics information also included
statistical information about the percentage of instructional leadership delegated to other key
stakeholders of the school including assistant principal(s), curriculum director(s), department
chair(s), teacher leader(s), others, and themselves. The demographic information was used to
guide the data analysis for this study.
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Data from Phase I of this study was used to answer the first research question. Survey
responses were aggregated and disaggregated to apprehend a clear picture of principals’ self-
perceived instructional leadership behaviors. Data from Phase II of this study was used to
answer the second research question. An hour-long interview with three different principals
revealed information about principals’ instructional leadership strategies that raised student
academic achievement. Coding and analyzing Phase II data revealed five common themes
amongst each of the three principals that pertained to the instructional leadership behaviors: (1)
shared instructional leadership functions; (2) teacher empowerment; (3) professional learning
communities (PLCs) and other forms of professional development; (4) creating opportunities for
all students to be successful and college-eligible; and (5) evolving the school culture.
Data from both phases of the study was used to answer the third research question.
Student performance data on the math portions of the CST and CAHSEE was obtained from the
California Department of Education website. Comparative analysis of student performance data
coupled with data from Phase I and Phase II was used to uncover the connection between
instructional leadership and student achievement in secondary mathematics. Three common
themes arose: (1) data-driven decision-making; (2) professional learning communities (PLCs)
and other forms of professional development; and (3) creating opportunities for all students to be
successful and college-eligible. Each of the three principals placed importance in using
instructional leadership to facilitate improved instruction for students across all subjects. The
exact term of “instructional leadership” was only used a couple times across all three interviews
but the behaviors and functions of instructional leadership were stressed throughout each of the
interviews. The focus on instructional leadership ultimately had an impact on student
achievement on secondary mathematics, as evidenced by a steady increase in student
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achievement on the math portions of the CAHSEE and CST exams. The next chapter presents a
summary and discussion of this study.

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CHAPTER 5
CONCLUSIONS
This study sought to identify the instructional leadership behaviors of principals that have
lead to improved student achievement in secondary mathematics. Principals were purposefully
chosen and asked to participate in this study based on specific selection criteria. Selected
principals voluntarily completed a web-based survey for Phase I. Principals who completed the
first phase of the study were given the option to continue onto the next phase of the study. For
Phase II of the study, three principals were selected for an hour-long interview discussing their
instructional leadership behaviors. This study sought to answer the following research questions:
(1) What are the self-perceived instructional leadership behaviors of high school
principals?
(2) What instructional leadership strategies do principals employ that influence positive
outcomes of academic achievement?
(3) What is the relationship between the instructional leadership behaviors of principals
and student achievement in mathematics?
A mixed methods approach was used to gather and critically analyze data as well as draw
conclusions in response to each of the research questions. A detailed description of the data and
results was given in Chapter 4.
This chapter summarizes the background and purpose of this study. The three research
questions that guided this study are reviewed and the findings are summarized in this chapter.
Chapter 5 also includes a discussion on how the findings of this study inform the practice of
professionals in the field of education, in particular for principals and those in leadership roles.
The last part of the chapter gives recommendations for future research by researchers who are
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also interested in learning more about the connection between instructional leadership and
student achievement in mathematics.
Summary of the Study
A high school principal plays a critical role in determining the level of academic success
that students are able to obtain (Waters, Marzano, & McNulty, 2003, p. 3). As the instructional
leader of a school, the principal can impact teachers’ instructional practices to students’
academic performance (Quinn, 2002, p. 447). Missing in the current research is the connection
between high school principals’ instructional leadership behaviors and improved student
achievement in mathematics. Success in secondary mathematics is of critical importance.
Current and dated literature is saturated with research indicating that a student’s performance in
high school mathematics is a strong beacon for a student’s ability to complete college and how
much money they will earn in their future careers (Schoenfeld, 2002).
The purpose of this study was to identify the practices of high school principals who have
successfully used their role as the instructional leader to improve student learning and
achievement in mathematics. This study sought to identify instructional leadership traits,
behaviors, practices, and actions of principals. The sample for this mixed methods study was
selected based on the following criteria: (1) lead a comprehensive public high school serving
grades nine through twelve; (2) school site is located in large urban areas (i.e., Los Angeles
county); (3) minimum of 45% of student population receiving free and reduced lunch; (4)
minimum of 1100 students; and (5) minimum of two years as the principal at their current school
site.
There were two phases of this study. For Phase I, principals who met the selection
criteria were asked to complete the web-based version of the Principal Instructional Management
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Rating Scale (PIMRS) instrument. Quantitative data was gathered from the 50 questions from
the survey, which were answered on a Likert scale ranging from one to five. A response of one
represented almost never, two represented seldom, three represented sometimes, four represented
frequently, and five represented almost always. After completing the survey, principals were
given the option to continue on to the next phase of the study. Of the principals who opted to
continue onto Phase II, three were selected for an hour-long interview based on school
performance data. Since starting their tenure as principal of their current school site, students
have exhibited steady improvement on the mathematics portions of the CST and CAHSEE. An
interview protocol was used as a tool to guide the interview. The purpose of the interviews was
to engage in deeper discussion pertaining to instructional leadership behaviors that have led to
improved student achievement in secondary mathematics.
From here, the quantitative and qualitative data were critically analyzed to answer the
first two research questions. To answer the third research question, the data from both phases of
the study as well as school performance data from the California Department of Education
website were comparatively analyzed to look for connections between principals’ instructional
leadership behaviors and student achievement in mathematics. A mixed methods approach was
used to complete this study. Data was purposefully drawn from multiple sources including
surveys, interviews, and analysis of school performance on the math portion of the CST and
CAHSEE. Triangulation of data ensured internal validity and strengthened the results of this
study (Patton, 2002).

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Conclusions
Findings and conclusions for each research question will be discussed in this section.
Research Question One: What are the Self-Perceived Instructional Leadership Behaviors
of High School Principals?
Phase I data clearly exhibits the self-perceived instructional leadership behaviors of high
school principals. The first portion of the survey asked for demographic information. Of the
principals who volunteered to participate in this study, 96.4% have earned graduate degrees.
Principals served an average of 9.2 years as a classroom teacher. Principals have served an
average of 3.5 years at their current school site and an average of 12.0 overall years as an
administrator. On average, principals reported they reserve 44.1% of instructional leadership
responsibilities for themselves while delegating the majority of tasks to other key leaders on staff.
The assistant principal, department chairs, and teacher leaders were delegated the most
instructional leadership tasks with means of 25.8%, 15.2%, and 12.3%, respectively. This data
indicates that principals believe in the importance of shared instructional leadership, which is
defined as the “active collaboration of principals and teachers on curriculum, instruction, and
assessment” (Marks & Printy, 2003, p. 371). By sharing instructional leadership responsibilities
with key staff members, principals are showing their staff that their expertise is valued and
integral to the school’s continual development and improvement.
Principals were asked to respond to questions related to instructional leadership job
functions that were separated into the following ten main categories: (1) frame the school goals;
(2) communicate the school goals; (3) supervise and evaluate instruction; (4) coordinate the
curriculum; (5) monitor student progress; (6) protect the instructional time; (7) maintain high
visibility; (8) provide incentives for teachers; (9) promote professional development; and (10)
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provide incentives for learning (Hallinger, 1990). Within each category, principals were asked to
ask answer five questions. Principals believed they almost always framed the school goals,
promoted professional development, and supervised and evaluated instruction. Principals
believed that they only sometimes completed the following job functions: provide incentives for
learning; provide incentives for teachers; and maintain high visibility. The other instructional
leadership job functions were scored on the lower end of the frequently classification.
Overall, principals identified framing the school goals as the instructional leadership
function they almost always performed. The standard deviation for this particular job function
was 0.19, which indicates that principals scored very close to the mean of 4.58. Principals
reported that they almost always use student performance data when developing the school’s
academic goals and when developing a focused set of annual school-wide goals. Developing and
framing school goals is an important element of school improvement and set goals provides
faculty and students with a sense of purpose. Leithwood et al. (2006) identified setting goals as
the most important out of three important basic categories of leader practices. Data from this
study indicates that surveyed principals’ beliefs are aligned with existing literature in that
framing the school goals is a critical element of school success.
The instructional leadership job function of promoting professional development received
the second highest mean of 4.45. This category had a low standard deviation of 0.53, which
indicates that principals scored themselves very close to the mean. Principals also scored
themselves highly in the instructional leadership job function of supervising and evaluating
instruction. This category also had a low standard deviation of 0.31, which indicates that
principals scored very close to the mean of 4.33. Principals reported they regularly conducted
informal, unscheduled classroom observations. Principals also reported to giving teachers post-
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observation feedback and pointing out specific strengths and weakness in instructional practices.
However, the surveyed principals did not believe they dedicated very much time to reviewing
student work products when evaluating classroom instruction. By supervising and evaluating
instruction, principals are using their role as the instructional leader to “facilitate and promote
active learning experiences for all students” (Quinn, 2002, p. 452). This action impacts teachers’
instructional practice, which in turn, impacts student learning.
In sum, the self-perceived instructional leadership behaviors that surveyed high school
principals report they most commonly perform is framing the school goals as well as supervising
and evaluating instruction. Surveyed principals place less of a priority on providing incentives
for learning, providing incentives for teachers, and maintaining high visibility.
Research Question Two: What Instructional Leadership Strategies Do Principals Employ
that Influence Positive Outcomes of Academic Achievement?
Phase II of the study provided necessary insight to answer Research Questions Two.
Transcriptions of the interviews and field notes were critically analyzed. Five common themes
of instructional leadership arose from the hour-long interviews with three principals: (1) shared
instructional leadership functions; (2) teacher empowerment; (3) professional learning
communities (PLCs) and other forms of professional development; (4) creating opportunities for
all students to be successful and college-eligible; and (5) evolving the school culture.
Each of the three interviewed principals believed in the importance of delegating and
sharing instructional leadership functions with key leaders on staff at their school site. Most of
the responsibilities were shared with the assistant principals and department chairs. Additionally,
some instructional leadership responsibilities were delegated to various other teacher leaders as
well. This contributes to the recurring stance that principals must work to empower the teachers
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on their staff. Each of the three interviewed principals created other positions and roles within
their school site to give other teachers a chance to lead. The action of empowering teachers sent
teachers the message that their abilities, expertise, and wealth of knowledge was not only valued
but necessary for the professional growth of other teachers and academic achievement of
students.
Teachers at each of the three school sites engaged in PLCs separated by departments.
Reinforcing the idea of empowering teachers, principals give department leaders autonomy in
determining how PLC meeting times are structured and executed. Time for PLCs were
embedded in the school schedules but some PLC groups also agreed to meet outside of the set
times. The interviewed principals also encouraged teachers to engage in other forms of
professional development to improve and deepen instructional practices. This included both on-
going and one-time opportunities. Principals also engaged with their staff in conducting
informal observations to gain ideas and learn from one another. Principals referred to this act of
observing and learning from peers as “Action Walks” and “Instructional Rounds.”
Ultimately, the reason for conducting the various forms of professional development is to
improve instruction so that student learning and academic achievement can also improve. The
main mission at each school site is to get all students into college. The interviewed principals
and members of their faculty are striving to create opportunities for all students to be successful
and eligible for admission in the CSU or UC system. Each of the interviewed principals stressed
the importance of ensuring that all students at their school site are given ample opportunities to
learn and grow. This reflects the belief that the interviewed principals belief that all students can
learn and are capable of success.
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Interviewed principals employed a variety of instructional leadership strategies to
influence positive outcomes of academic achievement. Based on what was shared during each of
the interviews, it is clear that the principals value the expertise – both skills and knowledge – of
the faculty. This expertise is used as a powerful tool to develop and improve all aspects of the
learning experience for students. It is clear that the three principals are working hard to evolve
their school culture to foster a sense of community within their school sites. Building
community and relationships allows for students to feel safe, cared for, and supported on the path
to academic success.
Research Question 3: What is the Relationship Between the Instructional Leadership
Behaviors of Principals and Student Achievement in Mathematics?
To answer this question, data from both phases of the data were comparatively analyzed
with student performance information from the mathematics portions of the CAHSEE and STAR
for the school sites of the interviewed principals. The STAR Program includes the California
Standards Tests, the California Modified Assessment, the California Alternate Performance
Assessment, and the Standards-based Tests in Spanish. All three high schools showed steady
and marked improvement on both the CAHSEE and STAR since the incumbent began his or her
tenure as principal.
Survey responses for each of the interviewed principals were compiled and
comparatively analyzed with interview data. On average, the three interviewed principals served
of 17.3 years as a classroom teacher. The three interviewed principals served an average of 4.3
years as principal of their current school site and a mean of 12 overall years as an administrator.
Each of the three principals indicated they shared the instructional leadership responsibilities
with key leaders at their school site while reserving a mean of 40% for themselves. Assistant
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principals, department chairs, and teacher leaders were delegated instructional leadership
responsibilities. Interviewed principals identified the following four instructional leadership job
functions as behaviors they often engaged in: supervising and evaluating instruction; framing the
school goals; promoting professional development; and coordinating the curriculum. Data
collected from each of the three interviews supported principals’ survey responses.
With respect to mathematics, three common themes of instructional leadership arose from
the Phase II data: (1) data-driven decision-making; (2) professional learning communities (PLCs)
and other forms of professional development; and (3) creating opportunities for all students to be
successful and college-eligible. Each of the three principals spoke to great deal about using data
to drive the decision making process, particularly when students are being impacted. Principals
guided their staff in analyzing student performance data on statewide, district-level, and school
assessments. Each of the three principals also spoke highly about the pivotal role that PLCs have
played in strengthening mathematics instruction for students which has led to marked
improvements in student achievement. Ensuring that all students are given opportunities to be
successful and competitive applicants for CSU and UC schools was of upmost importance for
each for the three principals. This notion was engrained in the mission for each interviewed
principal’s school sites.
Data from both Phase I and Phase II of this study indicate that each of the three principals
have used their role as the primary instructional leader to help their staff learn and grow as
educators. Student achievement data shows a steady increase in scores since each of the three
principals began their tenure at their specific school site. This data is discussed in greater detail
in the preceding chapter. Based on the steadily improving scores, it is clear that the interviewed
principals’ instructional leadership behaviors have had an impact on the school’s performance on
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the mathematics portion of the CAHSEE and STAR exams. School performance data coupled
with data from the first two phases of this study indicates that a correlation exists between the
interviewed principals’ instructional leadership abilities and student achievement in mathematics.
The three interviewed principals were able to use their roles as the instructional leaders to effect
positive change at their school site.
Implications
Improving student outcomes in secondary mathematics is an urgent problem that must be
addressed immediately. Success in secondary math courses is essential as it is considered the
primary indicator for a student’s ability to be successful in higher education. In addition to
create better outcomes for students in the long run, principals are under tremendous pressure to
improve the overall performance of their schools due to the current era of educational
accountability. Students’ academic success is essential to meet the demands set by
accountability mandates as well as to ensure that all students are provided the opportunity to be
successful beyond high school. To create better learning outcomes for students, instruction must
be improved. Principals must use their position as the instructional leader of the school to help
teachers learn, develop, and grow their practice as educators. The results and conclusions of this
study emphasize the impact a principal can have on student achievement in mathematics.
Principals in the field can use the results and conclusions from this study to inform their
practice as the instructional leader of their school site. This study indicates there is a correlation
between a principal’s abilities as an instructional leader and how students perform in secondary
mathematics. Principals should identify how they rank on the ten instructional leadership
behaviors found on the Principal Instructional Management Rating Scale instrument. A teacher
version and supervisor version of the PIMRS instrument has been developed and tested by the
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creator. School principals should obtain permission for this valuable tool so teachers and
supervisors at their school site can complete the survey as well. This will allow principals to get
a sense of how the staff perceives the principal as the instructional leader. Principals can use
survey results as the basis for their own professional development and work towards improving
their instructional leadership practice.
Those designing and leading principal leadership programs can use the results and
conclusions of this study to inform what is taught by their program. This study reveals the
correlation between the principal as the instructional leader and student achievement in
secondary mathematics. Principal training and preparation programs should equip those earning
an administrative credential with the knowledge and ability to execute each of the ten
instructional leadership job functions defined by the PIMRS.
Recommendations for Further Research
The mixed methods study analyzed the instructional leadership behaviors of principals
that led to improved student achievement in secondary mathematics. Although the researcher set
out to conduct an all-inclusive study, results and conclusions led to further questions pertaining
to the impact of instructional leadership on secondary mathematics. Opportunities for further
research are plentiful. In particular, the following questions arose:
(1) How do Professional Learning Communities impact the learning, development, and
growth of teachers’ instructional practices? Of teachers’ instructional practices for
secondary mathematics?
(2) How can Professional Learning Communities be improved to better serve teachers
and in turn, better serve students in secondary mathematics?
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(3) How does teacher empowerment affect a teachers’ instructional practice? In turn,
how does this impact student learning in secondary mathematics?
(4) How might district leaders, school administrators, and teacher’s collaborate more
effectively to better serve the needs of all students in secondary mathematics?
(5) How does the school culture impact student achievement in secondary mathematics?
Student success in secondary mathematics is critical. As evidenced by the findings of
this study, principals must effectively use their role as the instructional leader to effect
improvement in student achievement and outcomes in secondary mathematics.

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APPENDIX A
IRB APPROVAL

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APPENDIX B
RECRUITMENT LETTERS
Email Letter (Phase 1 – Initial)
Dear [Name],

My name is Michelle Pyo and I am a doctoral candidate in the Rossier School of Education at
University of Southern California. I am writing to ask your help and participation in my
doctorial dissertation study of successful high school principals and their leadership practices.
Your input is invaluable and will be used to gain a better understanding of what principals do to
create positive learning outcomes for all students.

Your identity as a participant will remain confidential at all times during and after the study. No
school demographic information or individual answers will be linked to you or your school. For
the first phase of this study, your input is requested via a survey that will take approximately 30
minutes to complete. The second phase of the study is an interview, which is anticipated to take
approximately 45 minutes of your time. Participation is voluntary at both phases of the study. If
you prefer, you may simply complete the survey and opt out of the interview pool. If you would
like to opt out of this study altogether, please let me know simply replying to this email with the
phrase “opt-out”.

Below is the link for the survey which will take you to my survey which is housed on the
Qualtrics website. Please follow the directions carefully and answer all questions truthfully.

If you have questions, comments or concerns, please do not hesitate to contact me at (310)400-
0796 or pyo@usc.edu. Copies of the study will be made available upon request once the study is
complete.

Thank you for your time and participation!

Sincerely,

Michelle Pyo
Doctoral Candidate
University of Southern California

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132
Email Letter (Phase 1 – Reminder)
Dear [Name],

Happy New Year! I hope you had an enjoyable and rejuvenating holiday season.

I am writing because I really need your help! Several weeks ago, you should have received an
email requesting your participation in the first phase of my dissertation research project. Your
response on the Principal Survey is vital to my study because you are part of a small, select
group of principals chosen to participate. It is only with the sharing of views and beliefs of
principals, such as you, that a greater understanding can be gained on principal leadership among
effective schools.

If you are receiving this message in error and have already completed the online survey, please
accept my sincere gratitude. If not, please complete this survey today. Below is the link for the
survey.

If you have questions, comments or concerns, please do not hesitate to contact me at (310)400-
0796 or pyo@usc.edu. Copies of the study will be made available upon request once the study is
complete.

Thank you for your time and participation!

Sincerely,

Michelle Pyo
Doctoral Candidate
University of Southern California

THE PATH TO MATH: LEADERSHIP MATTERS

133
Email Letter (Phase 2 – Yes)
Dear [Name],

Thank you very much for taking the time to complete the Principal Leadership Survey! Your
responses have been received and recorded. Without the participation of leaders like you, I
would not be able to complete my study. I have no doubt your input will be invaluable as I
continue to learn more about principals and their leadership practices.

Additionally, thank you very much for volunteering to continue on to the next phase of this study.
I will be conducting interviews beginning this Thursday (January 24
th
) until next Friday
(February 1
st
). Please let me know of a few dates/times that you are available for an interview.
I would like to schedule our time together after 4:00pm, if possible. However, I am happy to
come meet you at any other time that is convenient for you.

If you have questions, comments or concerns, please do not hesitate to contact me at (310)400-
0796 or pyo@usc.edu.

Again, thank you for your time and participation!

Sincerely,

Michelle Pyo
Doctoral Candidate
University of Southern California

THE PATH TO MATH: LEADERSHIP MATTERS

134
Email Letter (Phase 2 – No)
Dear [Name],

Thank you very much for taking the time to complete the Principal Leadership Survey! Your
responses have been received and recorded. Without the participation of leaders like you, I
would not be able to complete my study. I have no doubt your input will be invaluable as I
continue to learn more about principals and their leadership practices.

You have opted out of the next phase of this study. However, if you have questions, comments
or concerns, please do not hesitate to contact me at (310)400-0796 or pyo@usc.edu. Copies of
the study will be made available upon request once the study is complete.

Again, thank you very much for your time and participation!

Sincerely,

Michelle Pyo
Doctoral Candidate
University of Southern California

THE PATH TO MATH: LEADERSHIP MATTERS

135
APPENDIX C
LETTERS OF PERMISSION FROM PHILIP HALLINGER

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136

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137
APPENDIX D
PRINCIPAL INSTRUCTIONAL MANAGEMENT RATING SCALE

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138

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139

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140

THE PATH TO MATH: LEADERSHIP MATTERS

141

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142

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143

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144
APPENDIX E
PIMRS SURVEY

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145

THE PATH TO MATH: LEADERSHIP MATTERS

146

THE PATH TO MATH: LEADERSHIP MATTERS

147

THE PATH TO MATH: LEADERSHIP MATTERS

148

THE PATH TO MATH: LEADERSHIP MATTERS

149

THE PATH TO MATH: LEADERSHIP MATTERS

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Abstract (if available)

Abstract The quality of school leadership is linked to student academic achievement (Leithwood et al., 2004

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Asset Metadata

Creator Pyo, Michelle Hyo Jung (author)

Core Title The path to math: leadership matters: effective practices of principals that improve student achievement in secondary mathematics

School Rossier School of Education

Degree Doctor of Education

Degree Program Education

Publication Date 08/06/2013

Defense Date 03/25/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag instructional leadership,leadership,OAI-PMH Harvest,principals,secondary mathematics,student achievement

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Castruita, Rudy Max (committee chair), García, Pedro Enrique (committee member), Hasan, Laila (committee member)

Creator Email michellepyo@gmail.com,pyo@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-317348

Unique identifier UC11293809

Identifier etd-PyoMichell-1967.pdf (filename),usctheses-c3-317348 (legacy record id)

Legacy Identifier etd-PyoMichell-1967.pdf

Dmrecord 317348

Document Type Dissertation

Format application/pdf (imt)

Rights Pyo, Michelle Hyo Jung

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA