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Improved math achievement in an urban high school: a case study of a high school in the Vista Unified School District

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Improved math achievement in an urban high school: a case study of a high school in the Vista Unified School District

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IMPROVED MATH ACHIEVEMENT IN AN URBAN HIGH SCHOOL: A CASE
STUDY OF A HIGH SCHOOL IN THE VISTA UNIFIED SCHOOL DISTRICT

by

Margaret Anne Abrahamson

___________________________________

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

August 2007

Copyright 2007 Margaret Anne Abrahamson

ii

DEDICATION

“There is no happiness except in the realization that we have accomplished
something.”
- Henry Ford

This dissertation represents an unparalleled journey and a dream realized. But
for the support of my family, friends and the unconditional love and much needed
kisses from Sofi (the family dog) it would have not come to pass. It is for this I
dedicate not the completion of this paper but the journey.
To my parents, Charles and Joan Abrahamson I am grateful for their belief
and unwavering support in me as a person. I am appreciative of the values and
principles they have conveyed to me throughout my life which have brought me
where I am today. The fact that I was able to engage in and complete this journey is a
reflection of what they have instilled in me: a sense that really I can do anything that
I put my mind to, with a little help, that giving up is not an option to be considered
and to ask “why” is a wonderful thing. As an adult I have embraced and tried to
reflect characteristics of a quality person through my choices and have sought to
have these as adjectives and not verbs that merely describe what I hold as important
but rather are evident through my actions. My parents sought to convey the
importance of knowledge, integrity, perspective, empathy, humility and humor as
principles essential in life and for this I am thankful and hope that I am able to
demonstrate these in my daily life. This journey and the finished product is merely a

iii
reflection of my spirit of determination and my appreciation and value for
knowledge.
To my nieces KR, JQ and Josie and my nephew Cam I dedicate this to you as
a message and vision of what you can do and to convey your Auntie’s desire for each
of you to reach high and far with your dreams. Each of you brings a special gift to
this world and whether this manifest through higher education (beyond a Bachelors
Degree) or another path I wish for you great and wonderful things. This has been a
long journey that you have witnessed and felt as I have said “no, I have to write” so
many times over the last three years. While this is an accomplishment that you may
not fully realize or appreciate yet I know that one day you too will celebrate many
accomplishments and understand the importance of reaching high. I have faith in
each of you and know that you too through the conversations and the passion of your
family are developing an appreciation for learning, and asking “why?” even though
today you may not see it. I will always be here to encourage you, to offer a
perspective and most importantly my unconditional love and support as you move
forward on your own path.
To Dr. Kathleen Mooney I dedicate this journey and the meaning beyond the
accomplishment that is contained within the journey itself. Over the many years I
have shared my frustrations, my celebrations, my tears, my opinions, my joy, my
fears, my feelings, my hurt, thoughts and laughter. Today I share my sense of pride
and accomplishment. On this larger journey called life I like many have had
challenges; some self inflicted some a reality of life in either case you have been a

iv
source of guidance and support. Were it not for the time I have had to just be and
share those many emotions I might not arrived at this particular place in my life so
again I thank you. During this journey you have once again been a fount of
encouragement and perspective during those moments of unbelievable fatigue,
frustration and doubt. While a unique dynamic and relationship is ours, it is one that
I look to as a significant source of empowerment, strength and perspective; forever I
will appreciate it, today and for years to come.

“Being deeply loved by someone gives you strength, while loving someone deeply
gives you courage.”
Lao Tzu

Last but certainly not least I dedicate this journey to my partner in life and
source of strength, Dr. Jennifer Smith. This journey began in actuality the day I met
you. A dream I had but had not realized and but for you being by my side may not
have. The above quote so eloquently captures the impact of our love; you give me
personal strength that I never felt before and my deep love for you gives me courage
to move beyond myself and my own inner insecurities.
Your spirit, strength, passion, intellect, determination and spirit are an
inspiration for anyone. Your ability to rise above and not give up on your dreams
when life has presented challenges that would cause many to retreat is enough to
make me in awe of you. I so admire you: certainly raise the bar for the rest of us. It is

v
who you are that allows me to be who I am and has been instrumental in facilitating
journey on this path to where I am today, in a really good place!
I cannot imagine having persevered through this process if I did not have you
sitting by my side, across the dining room table from me or continually cajoling and
pushing me, thank you. This has been a wonderful journey that has only strengthened
our relationship. The past three years have certainly provided opportunity for
discussion and debate on concepts and ideas that challenged us to look at things
using different lenses all while sitting looking over a lap top, sipping a glass of wine,
laughing until it hurts or taking a break in the hot tub! I would not trade this even
with the fatigue and “I am so sick of this” moments, for anything.
While we are done with this “chapter” I know my journey of discovery and
learning with you has only begun. This is what I so appreciate about you, about us;
we will always be learning and challenging ourselves to do more and to somehow
make a difference. We really are only just beginning on the true journey and to know
I have you by my side for many years is to know that there is so much more yet to
come. I love you madly Dr. Smith and I dedicate this accomplishment to you.
To all of you I am grateful, for each of you in a different way have
contributed to my life, this journey whether knowingly or not. I am fortunate to have
the presence of such quality people surrounding my daily experience and only hope
that in small way I am able to give back to you.

vi

ACKNOWLEDGMENTS

I would like to acknowledge my family, friends and colleagues who have in
many ways taken this journey and invested in this endeavor with me. I have
appreciated the supportive words, encouragement and the patience required at
different points during the past three years. I know to differing degrees over the past
three years I have been, otherwise occupied and as such not as present. Even when I
was not studying or writing, I knew that I should be so one becomes sort of frozen,
not getting anything accomplished! Just to let you know, those days are over!
I would like to thank my personal cheerleader Dr. Kathy Onoye (USC 2004)
who is a colleague and more importantly a friend. Each step of the way she has
encouraged me to keep pushing and to visualize the “big day’. She has been a source
of support and perspective that I enjoy each day both in terms of this journey at USC
and in life. Thank you for your gifts of delivered lattes and laughter!
To my friends Tara, Janis, Serena, Bryan, and Jeff in particular, who I have
not seen or spent enough fun time with but rather was forced to set aside I thank you
for your patience during this time. Thank you for realizing the work and time
involved with this effort. I look forward to having the time to on the spur of the
moment join each of you in fun, frivolity and debate!
To my Wilson crew I thank you especially Ninfa (the best assistant ever),
Ernie, and Diane, for your understanding and support when my head was elsewhere;

vii
you kept it all moving forward and I appreciate it! Also, for your friendship and
support during times of stress (related to this or otherwise) we made a good team; we
laughed, worked hard and always did what we could support each other. To
Caroline, Theresa and Ninfa (again) for stepping up when I needed support in
transcribing, sorting and coding trust me it made my life that much easier during the
increasingly tense time towards the end of this project. To the larger Wilson
community I thank you for your support and encouragement; you are a great group
of people that I am proud to have served!
I would be remiss if I did not acknowledge the support of my district
colleagues. My bosses Kathleen Duba, Dr. Jacqueline Cochran and Dr. Debra
Debose for their encouragement and patience when my head was somewhere else,
particularly in these last couple of months as the deadlines seem to come much
quicker and with greater intensity. I know I have sang but one song, “I have to write”
and you have listened and just allowed me to vent. To my support team, Joan, Gina,
and Carla thank you for also listening to this one song and dealing with my fogginess
when I came in with minimal hours sleep. I have appreciated all of you.
And last but not least my wonderful editor Dr. Shantanu Duttaahmed who
while correcting and trying to understand just what I was trying to say kept me
laughing and reminding me of the priorities in life! Thank you for your patience and
expertise you were a perfect match!

viii

TABLE OF CONTENTS

DEDICATION ................................................................................................ ii

ACKNOWLEDGMENTS ................................................................................ vi

LIST OF TABLES ............................................................................................ ix

LIST OF FIGURES ........................................................................................... x

ABSTRACT ..................................................................................................... xi

CHAPTER ONE: INTRODUCTION ................................................................ 1

CHAPTER TWO: REVIEW OF THE LITERATURE ..................................... 24

CHAPTER THREE: RESEARCH METHODOLOGY...................................... 80

CHAPTER FOUR: FINDINGS, ANALYSIS AND DISCUSSION ................. 116

CHAPTER FIVE: SUMMARY, CONCLUSIONS AND IMLICATIONS ...... 191

REFERENCES ................................................................................................... 215

APPENDICES .................................................................................................... 229

ix

LIST OF TABLES
Table 1 Academic Performance Index (API) for three years .......................... 87

Table 2 Relationship or Data Collection Instruments to Research
Questions .............................................................................................. 91

Table 3 Change Process Framework Bolman and Deal’s Four Frames
of Leadership ......................................................................................... 97

Table 4 Instructional Leadership Framework .................................................... 102

Table 5 Strategies to Overcome a Lack of Subject Competency ....................... 107

Table 6 California Standards Test (CST) Percent of Algebra Students
Scoring at of Above Proficient .............................................................. 119

Table 7 California High School Exit Exam (CAHSEE) Results for
Three Years ............................................................................................ 120

x

LIST OF FIGURES

Figure 1 Framework for Effective School Design ............................................ 94

Figure 2 Framework for Effective Math Programs ........................................... 95

Figure 3 Assessment of Principal’s Expertise in Math ...................................... 106

xi
ABSTRACT

The research consistently finds that our greatest challenge in California
public schools resides in our urban schools as defined by high poverty, high minority
and low performance. The math performance of our students is significantly lower in
public urban secondary school across the country and specifically in California. This
has been evidenced by student performance on state assessments and the high
percentage of students not passing the math portion of the California High School
Exit Exam (CAHSEE) which is a state required graduation requirement. These facts
of increased the focus on K-12 math performance from both state and federal
agencies.
The purpose of the study is to examine factors that positively influenced the
math performance of students in one urban high school. The study explores the
elements of the school design, the strategies and best practices used within the
classroom and the role of the school leader in shaping and directing the school
improvement efforts. The study will incorporate an understanding of how
instructional leaders lacking strong pedagogical content knowledge in mathematics
education, are able to impact significant mathematics achievement at the school site.
Currently our schools are utilizing a variety of standards based curriculum
and researched based strategies as their instructional program. There is limited
information on what instructional combination works best and what is contributing to

xii
the success of schools. Our educational institutions are striving to improve the
academic performance of all students, however the achievement gap persists.
Five conceptual frameworks that are grounded in educational research and
four data collection instruments are used to provide structure for the analysis
collected in alignment with the five research questions that were developed with the
purpose of gaining insight to factors that can be attributed to the improved math
performance of certain urban high school’s in Southern California.

1
CHAPTER ONE
INTRODUCTION

Background and the Problem

Many urban educators at both the district and school level are facing an
impatient public looking for immediate results to resolve the continuing crisis in
American education, and are reluctant to provide additional resources until material
results are evident, and a viable transformation within the educational system occurs.
Often the public is not interested in complicated and expensive solutions that take an
extended period of time, but are seeking more simplistic and less costly solutions
that might provide the “quick fix”. As a result of this debate between the immediate
and long range strategies to solve the problems endemic to education, and despite the
many reform efforts taking place, the public school system remains under attack
(Kaufman Foundation 2002). Given the heightened public scrutiny the momentum
and sense of urgency, specifically for high school reform, has increased. Given these
social and political dynamics in play, this is a crucial time in American public
education for innovation and change which presents the opportunity for real
academic progress. This is a daunting challenge that will require vision and
commitment in terms of leadership, policy and practice.
For many years improving the academic performance of students in the
American public schools, and specifically our secondary schools, has been a concern
founded and justified by the bleak performance on state and national assessments.

2
This is further highlighted when our students’ performance is compared to students
around the world. The poor performance is reflected across many groups of students,
with the achievement gaps remaining consistent and present, creates a perilous
situation for the future of our nation.
More than thirty years ago a landmark report, A Nation at Risk; The
Imperative for Educational Reform was issue by the National Commission on
Excellence in Education. The objective of this study was to regain the “competitive
edge on international business and national defense” once held by America (Nelson,
Palonsky & Carlson, 2000). The report found that our scores on achievement tests
on average had dropped considerably from prior decades; the number of students
requiring remedial math in college had increased by 75percent, SAT scores were on
a pattern of decline, half of those teaching in the sciences and math were poorly
qualified in the content area and when compared with other industrialized nations on
academic achievement tests the students in the US did not score in the top two at any
point and in fact the scores reflected the bottom tier seven times (Nelson, Palonsky &
Carlson, 2000).
Student academic achievement in math presents a significant area of concern
as evidenced by standardized tests. Math is a gateway subject and the poor
performance of our urban youth in mathematics further exacerbates the lack of
opportunities they already face, as well as their future access to higher education.
These test results consistently show that urban schools with a high minority
concentration and high poverty are unable to demonstrate proficiency on

3
standardized assessments across all subject areas (Blezard, 2003; Marzano, 2003).
This information presents an increased disadvantage and challenge for these “at-risk”
groups in terms of future economic, social and political standing. The U.S.
Department of Labor indicates a stronger correlation between math skills and
subsequent earning power; fewer math skills align with lower average wages (Stiff,
2006).
The effort to reform and improve math achievement at the high school level
has been a focus at both the state and national levels. This effort has focused on
solidifying the state content standards for instruction, improving upon the
instructional program, including the continuity of curriculum and ensuring that the
teachers are “highly qualified”—the criterion for which was defined in the 2001
federal legislation No Child Left Behind (NCLB), signed into law by President
George W. Bush in 2002. NCLB redefined what it was to be a highly qualified
teacher, articulating that experience was not enough and teachers could no longer use
the education code as a means of meeting criteria for teaching a subject they were
not credentialed in. Teachers were now required to become “highly qualified” and
were required to meet guidelines put forth by the NCLB in order to remain in the
classroom. The teachers who taught in the content areas of; math, science, English,
humanities, Art and foreign languages had to have the appropriate credentials,
demonstrate hours of professional development in the specific areas they taught
and/or passed exams as a means of demonstrating competency and thus being
identified as “highly qualified” teachers. The initial legislation gave teachers until

4
the end of 2006 to meet these guidelines; this was extended to 2007. Following this
deadline school district can only hire highly qualified teachers, while great progress
has been made in ensuring teachers have met credentialing requirements this will
continue to present challenges for the school districts in the areas of math and
science. All of these changes are occurring in tandem with the various reform efforts
that school - districts across the United States were implementing as a means of
improving the academic performance of all students and closing the achievement
gap.
The conversation regarding the importance and need for developing “content
standards’ for our schools has been occurring for many years; with the concept and
call for “new world-class standards” as the expected outcome of an education
summit of governors and business leaders in 1996 (Klein, 2005). These content
standards indicate a set of expectations for what students should know and be able to
master in particular subjects and grade levels. They define not only what is expected
of students, but also what schools should teach at a specific grade level (California
Department of Education, 1998). Subsequently many states developed standards for
the core areas and within this effort came the articulation of math standards. With the
authorization of NCLB in 2001 no longer were states being encouraged to develop
content standards but rather it has become a condition as part of NCLB that if school
districts are to receive any federal resources they must have developed content
standards for all core subjects. The goal is proficiency for all students as defined by
standardized state assessment, states and/or school districts and individual schools

5
could face sanctions if the students are not making adequate yearly progress towards
proficiency.
This has presented public schools receiving federal funds with a challenge,
particularly in urban school districts which experience the greatest difficulty
attracting “the best” in education. The research continues to support the importance
of “teacher quality” as a pivotal factor in closing the achievement gap and for the
improvement of student achievement in our urban schools; this is a significant and
confounding variable in that the quality of the teacher is a better predicator of student
achievement than is a students race/ethnicity or poverty level (Reeves, 2000). The
research by Betts, Ruben and Danenberg (2000) further establishes the achievement
of urban schools being impacted by not only the qualifications of the teacher but by
retention and on-going professional development. Urban school districts that are
demonstrating academic improvements as evidenced by standardized state
assessments are those which are not so narrowly focused on the high stakes
assessments but are putting resources towards ensuring teachers are being held to
highly rigorous standards (Darling-Hammond, 2000). Accordingly, Kati Haycock of
Ed. Trust argues that putting resources towards supporting our teachers toward being
“highly qualified” is the most important investment education can make and would
drastically reduce the achievement gap (Ed. Trust, 2004).
As part of this concerted effort to reform and improve secondary schools,
particularly urban school districts where the greatest achievement challenges
continue to exist, new curriculum frameworks were implemented. This has occurred

6
across the country and within the NCLB guidelines districts and states are
encouraged to implement a comprehensive school reform effort that includes one of
the many research-based designs (McCombs, Quait 2002). The implementation of
such reforms must meet an established criterion, which is intended to improve the
learning and achievement of students (U.S Department of Education, 1998). The
criteria utilized to identify an appropriate reform model includes a comprehensive
design with aligned components; effective researched-based methods and strategies;
professional development; measurable goals and benchmarks; support within the
school; parental and community involvement; external technical support and
assistance; evaluation strategies and the coordination of resources (DuFour, 2003)
The effort and commitment to improving student achievement and reducing
pervasive achievement gap in our secondary schools has brought forth new and
innovative design models which are intended to create the most optimum learning
environment and instructional program for diverse learners in our urban schools.
Three such efforts are the implementation of the Small Learning Community (SLC),
the Community for Learning program (CFL) (Wang, 1998) and the Professional
Learning Community (PLC) (DuFour, 2003).
The SLC is a structural phenomenon with the intent of personalizing the
instructional program by reorganizing larger high schools into smaller communities
of learners. This effort has been met with mixed results. The reform model of CFL is
a model that is focused on setting high standards for student achievement in the
context of building and maintaining positive self-perceptions. The instruction is

7
developed in tandem with the characteristics of the individual student and his/her
learning needs within the context of the school and the larger community. The
concept of a PLC as a reform model is predicated on developing a community of
adult learners that collaborate to create an environment and culture that supports the
stakeholders which then has direct impact on the students and their academic
achievement and development as individuals.
The school designs, initiatives and school policies being implemented to
address poor student achievement must be able to work collectively with the
community; thus increasing capacity for improvement. There are many factors that
play an important and influential role in the academic achievement of students. One
predictor of student success is the culture of the organization. Research has
demonstrated that a positive and healthy inclusive cultural climate in a school is the
link to student success and the opposite is true as well, negative learning
environments have a detrimental impact on students (van der Westhuizen, Mosoge,
Swanepoel, Coetsee, 2005).
The contribution of a collaborative school culture on student learning must be
cultivated by the leadership of the school. The leaders’ leadership skills are an
essential component of success, and s/he must build the capacity of all stakeholders
in terms of their knowledge and understanding of policy and the initiatives that are
guiding the school reform—research has shown that this knowledge is crucial. To
embark on this aspect of on school reform requires that support is offered to meet the
individual needs of the stakeholders. It is equally important to incorporate models

8
that increase the awareness of what “best practices” the school is embracing through
its reform efforts; in other words, everyone must be aware of the school’s vision for
improving student achievement (Leithwood, Louis, Anderson, Kyle 2004). This
effort to include all stakeholders, and the capacity building that ensues, will
necessarily look different at the large urban school than it would at a small
elementary school. As such, the leaders and stakeholders must work together keeping
these differences in mind, realizing that impact of effective leadership is much
greater at schools with challenges inherent in the urban setting (Leithwood, Louis,
Anderson, Kyle 2004).
The involvement of stakeholders not only helps to create school policy, but
the thorough understanding of policies that such involvement enables, helps the
facilitation of a common vision and understanding the overall direction of school
improvement efforts. This collective understanding further creates a sense of
purpose; how and why decisions are made that have the ultimate goal of improving
student achievement (Kanter, 2003).
In researching improved student achievement in our urban school districts,
the evidence shows that the role of the instructional leader is critically important in
the implementation of a successful school reform effort and must be able to
“mobilize people to tackle tough problems” (Barth, 2001, Murphy & Datnow, 2003,
Heifetz 1994). In 1996 Hallinger & Heck found that the role and impact of the
leader is only second when analyzing and comparing multiple factors which

9
influence student learning, the number one factor being the positive impact on
student learning that a quality instructional program provides.
The leader must have the capacity, skills and passion as a person to bring the
school community and larger community together to engage in constructive
dialogue, to garner the respect, trust and confidence of the community in an effort to
inspire individuals and group members to take initiative towards transformational
school reform (Kanter, 2003).
Fullan (2001) has identified characteristics that institutional leaders need to
have and has further defined them into five core competencies;
• Broader moral purpose- Leaders must have the capacity to inspire
and motivate people to accomplish the challenges inherent in urban
school reform. They must have the skills to work with a broad group
of constituencies in a consistent, fair and equitable manner when
implementing the reform.
• Keeping up with and understanding the change process- The leader
must be familiar with and comprehend the change process and
dynamics of change; approaching challenges with creativity and
innovation. Through the change process the leader must have the
capacity to reculture the community in a safe environment in an effort
to keep moving forward with change.
• Cultivating relationships- The leaders must have the capacity to
establish and support good relationships across all of the unique and

10
diverse groups within the school environment; fostering a community
spirit.
• Sharing of knowledge- This must be a core value of the leader;
sharing of knowledge and information creates a more inclusive effort
where people are informed, engaged and become active participants.
The leader must establish protocols and procedures to facilitate this.
• Creating coherence- A common challenge for the urban school leader
which offers so much diversity is bringing everyone together as a
collaborative group that can work as a group with a coherent vision
and action plan.
The research demonstrates that school reform efforts take many years of
consistent effort to create sustainable changes and improvement in student
achievement and learning (Murphy & Datnow, 2003; Borman et. al., 2002). School
leaders need time and the opportunity to foster and establish a culture that supports
this effort and to create structures that support a vision for school reform.

Statement of the Problem
The academic performance in the area of mathematics is significantly lower
at numerous urban secondary schools in the state of California. This is evidenced by
both the scores on the state assessments and the percentage of students who are not
passing the math portion of the California High School Exit Exam (CAHSEE).
These facts have increased the attention and focus that math performance of our

11
students in math at our secondary schools receives from both state and federal
agencies. The efforts to improve math performance, has been facilitated through
different policy initiatives and the publication of school accountability reports which
include the Annual Yearly Progress (AYP), the Annual Performance Index (API)
and the required passing of the high school exit exam. All of these have increased the
level of accountability and pressure on the school districts and the individual schools
to ensure that the instructional programs at every school are based on the California
Content Standards as a vehicle for improved math performance.
To facilitate duplication of success from one school to another it is critical to
understand and analyze how schools, particularly urban schools that face greater
challenges and obstacles, that demonstrate a consistent pattern of success in math are
achieving these improvements. In the case of successful schools, it is important to
identify what are the best practices being implemented and utilized, what is the role
of the leader in facilitating these improvements and what are the overall school
design models and how these work in tandem to improve the math performance of
the students in urban secondary schools.
Currently schools are utilizing a myriad of California content standards based
curriculum for their instructional programs in tandem with researched based
instructional strategies. But little is known about specifically which of these
approaches are contributing to the success of schools and specifically what strategies
used at the school and in the district are having a positive impact on student
achievement in math. The reality is that there is no single program that has been

12
designed which can meet the needs of all students, as evidenced by the poor math
scores across the state and specifically in our urban high schools. To increase the
number of schools and students that are achieving academic success in math it is
important to understand what tools and best practices are being used with success.
In the overall effort of urban secondary school reform the role of the
instructional leader is critical, and one that needs to be conceptualized in an effort to
identify what skills, knowledge and approach is most effective for the school leader.
The Principal as a leader assumes many roles and is responsible for creating the
environment in which student learning is optimized and continuous over time.
Understanding the role the Principal as an instructional leader is essential in
sustaining school improvement. There are many factors and elements to be
considered: the climate created by the leader, the communication of the vision to and
the engagement of the community, the style of monitoring and supervising the
instructional program, the use of data and his/her understanding of the content areas,
are all elements of successful leadership. How these factors work independently or
collaboratively is important in understanding how they translate into effective
instructional leadership.
There is limited information on the specific ways in which the Principal
supports improved teaching and learning; taking a school from “below basic” level
performance on the California Standards Test (CST) to proficient or above as
mandated by NCLB. Having such an understanding would be a critical element for
sustained and effective school reform that supports the inherent differences between

13
these students and the challenges of the urban school. The role of the Principal as a
leader and the use of effective instructional strategies are crucial elements in school
reform. This represents an essential and critical aspect of the Principal as the
instructional leader, which is embedded in the composite role of the Principal as the
institutional leader. As the institutional leader the Principal must establish the overall
tone, values and priorities of the school. This is different than the role the Principal
must play as the instructional leader.
An over-arching construct that binds the reform efforts together is the school
design model. How is the instructional day organized to support student learning and
are there interventions and support in place that are designed to meet the individual
learning needs of students at the school? The role of the school design can also serve
as reflection of the school priorities.
These represent just a few of the critical components that are essential to
understanding the school design model as an element of school improvement.
Purpose of the Study
The purpose of the study is to examine the factors that positively influenced
the math performance of students in one urban high school. The study explores the
elements of the school design, the strategies and best practices used within the
classroom and the role of the school leader in shaping and directing the school
improvement efforts. The study also sought to incorporate an understanding of how
instructional leaders, who lack strong pedagogical content knowledge in

14
mathematics education, were able to impact significant mathematics achievement at
the school site.
Research Questions
The following research questions paramatized and guided this study:
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives including curriculum, instruction and related
conditions seem to be related to improved math achievement at the school
3. What change process did the school use to enhance the math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in improving
A) the math programs/strategies and B) math achievement among students?
5. How did instructional leaders respond to academic areas in which they are
not experts?
Importance of the Study
The academic challenges that are facing our public urban schools have been
plaguing the system for years. The methods, policies, practices and the
corresponding academic achievement [or lack there of], among our students, have
raised critical concerns among the various stakeholders about the state of American
education. The extant literature in the field would suggest that the public education
system has been facing its’ demise since the launching of Sputnik by the Russians in
the 1950’s. This event launched the national conversation about the ability of our

15
public schools to prepare our students to compete against other countries on a global
level in the information age. Based on the findings from the Nation at Risk report, to
the Trends International Math and Science Study (TIMMS) report to the National
Assessment of Educational Progress (NAEP) findings, we as a country have reasons
to be concerned about the readiness of our students to become active leaders and
participants in the world.
While there has been increased accountability placed on school districts and
school sites by such federal mandates as NCLB, to improve student achievement,
there has been less emphasis placed on identifying the individual factors that
contribute to the improved academic performance of some schools and some
students. Hitherto, our accountability systems have been concerned not with the how
it is done, but rather that reform efforts have just been initiated. Poor academic
performance is most evident in our urban schools, specifically at the secondary level
and in the area of mathematics; we are being out performed by students in other
countries, as evidenced by the most recent TIMSS. Despite the important efforts that
have been made by districts and schools in improving academic performance, there
is little definitive data on exactly what has worked and why. While districts and
schools are striving to improve the academic performance of students, the
improvement gaps are not being bridged on a consistent basis; rather there appears to
be a “hit and miss” quality to such reform efforts. This study will seek to understand
and provide information on key elements that positively impact the academic

16
performance of the students, specifically at our urban secondary schools in the area
of mathematics.
Three aspects of such reform efforts will be examined at selected urban
secondary schools that have demonstrated consistent growth on the standardized
assessments in the area of math, who have met their API targets and AYP over the
past three years. The study will provide information on the impact the school design
has had on student performance, the instructional “best practices” that are most
effective and the role of the instructional leader in the improved math performance of
the students. Thus is attempting to identify what is working in our schools, by
identifying those efforts that can be replicated, this study should provide valuable
information that educational researchers, administrators and teachers will be able to
utilize to inform their practices aimed at improving student performance.
Limitations
The following is a list of limitations of the study and findings:
1. The study was limited by the number of high schools in California’s
Los Angeles, Ventura or Orange counties.
2. The study is not a longitudinal; data is collected within a short time
frame.
3. The participants’ possible biases and willingness to participate in the
study.
4. The researcher’s biases and interpretation of the data collect through
the interview and literature review.

17
Delimitations
The following parameters served as delimitations of the study;
1. Only schools in Southern California’s Los Angeles, Orange, or
Ventura counties were utilized for this study.
2. School sites were chosen based on their steady improvement in
student mathematic achievement as demonstrated by API, AYP and
Algebraic achievement.
3. One school was utilized for the study, which limits the sample size.
4. The study was based on the data and study of one secondary urban
school which impacts the generalizability of the findings.
5. The school was selected based on specific criteria of improved math
achievement.
6. The study was a qualitative case study, which impacts the ability to
draw definitive cause and effect relationships among the findings.

Assumptions
The following assumptions were considered to be understood in the study;
1 The instrumentations used were designed and utilized to be effective
in eliciting and providing the information sought.
2 The respondents were honest with their answers on the questionnaires

18
3 California Standards Test (CST) and the California High School Exit
Exam are valid predictors of student’s skills and thus the schools math
program.
Definition of Terms
For the purpose of this study, the following terms were operationally defined
below:
The Academic Performance Index (API): The API is the cornerstone of the
Public Schools Accountability Act (PSAA). The API ranks school performance, sets
growth targets, and provides similar-school comparisons. The API is a single
number on a scale of 200 to 1,000, indicating how well a school has performed
academically the previous school year (California Department of Education, 2001).
Adequate Yearly Progress (AYP): AYP is an individual state's measure of
yearly progress toward achieving state academic standards. "Adequate Yearly
Progress" is the minimum level of improvement that states, school districts and
schools must achieve each year.
Achievement gap: denotes differences in the academic achievement in of a
particular group of students. (Bridging the Great Divide (2002): Broadening
Perspectives on Closing the Achievement North Central Regional Educational
Laboratory (NCREL).
Assessment: The processes used to collect information about student progress
toward educational goals. The form varies with what is being assessed and the
purposes for which the results will be used. Secondary Periodic Assessments

19
measure student proficiency toward California Content Standards for the explicit
purpose of improving teaching and learning (LAUSD, 2005).
Benchmark: Formative uniform measure of student progress relative to
standards. Standards-aligned assessments and assignments provide information
about progress toward the end target (California Department of Education, 2001).
Best Practices: A best practice is a technique or methodology that, through
experience and research, has proven to reliably lead to a desired result. Target Teach,
SearchVB.com Needham, MA.
California High School Exit Examination (CAHSEE): A graduation
requirement, authorized by state law in 1999, which requires California public
students, beginning with the graduating class of 2004, to pass the CAHSEE in order
to receive a high school diploma. The CAHSEE covers the curricular areas of
reading, writing, and mathematics and is aligned with the state content standards
adopted by the State Board of Education (California Department of Education,
2001).
California Standards Test (CST): Pupil achievement by grade level, as
measured by the Standards Testing and Reporting (STAR). (California Department
of Education).
Content Standards: Stated expectations of what students should know and be
able to do in particular subjects and grade levels. They define not only what is
expected of students, but also what schools should teach (LAUSD, 2005).

20
Cultural Capital: Forms of knowledge, skill, education, any advantages a
person has which give them a higher status in society, including high expectations.
Parents provide children with cultural capital, the attitudes and knowledge that
creates an educational system that is a comfortable and familiar place in which they
can succeed easily (Bourdieu, 1986).
Cultural Deficit Theory - Assumes that some student cannot achieve at high
levels because of deficits inherent in their race, ethnicity, language, or culture.
(Villegas, A. M. 1991; Culturally responsive pedagogy for the 1990s and beyond
(Trends and Issues Paper No. 6). Washington, DC: ERIC Clearinghouse on Teacher
Education. (ED 339 698).
Data-driven decision making: The process of utilizing multiple indicators to
make decisions about student placements, curriculum and instruction based on the
analysis of classroom data and standardized test data (Massell, 2000).
Highly Qualified Teacher: A Highly Qualified Teacher (HQT) as defined by
No Child Left Behind (NCLB) is a teacher who has an appropriate credential to teach
in the area(s) assigned and who has demonstrated subject matter competency through
various acceptable most often through passing rigorous state exams or through a
highly objective uniform state standard of evaluation (HOUSSE) (NCLB, Title IX,
section 9101).
Instructional Leadership: An influence that guided the activities designed to
impart knowledge or skills to students (Olsen, 2005).

21
Leadership: Leadership is a process of influence leading to the achievement
of desired purposes. Successful leaders develop a vision for their school based on
their personal and professional values [and goals]. They articulate this vision through
their actions and words; they seek to ensure that their staff and other stakeholders
share the vision. The philosophy, structures and activities of the school are geared
towards the achievement of this shared vision (School Leadership Concepts and
Evidence, spring 2003).
Master Schedule: This is a construct that reflects the format of the school
day. The following elements are included in and are specified by the master
schedule: the length of each instructional period, when and how frequently courses
are offered, which teachers are assigned to teach specific courses and grouping of
students.
National Assessment of Educational Progress (NAEP): The NAEP is an
ongoing, national assessment of what America’s students in grades four, eight, and
twelve know and can do in various academic subject areas. NAEP is administered
by the National Center for Education Statistics of the U.S. Department of Education.
One NAEP component provides states with a measure of their students’ academic
performance over time and a comparison to the results of other states and students
nationwide (California Department of Education, 2001).
Pedagogical Content Knowledge: identifies the distinctive bodies of
knowledge for teaching. It represents the blending of content and pedagogy into an
understanding of how particular topics, problems or issues are organized,

22
represented, and adapted to the diverse interests and abilities of learners, and
presented for instruction (Shulman, 1987, p. 4). Reference-Shulman, L. (1987).
Knowledge and teaching: Foundations of the new reform. Harvard Educational
Review, 57(1), 1-22.
Performance Bands: Bands that identify levels of student achievement based
on a demonstrated degree of mastery of specified content standards. California has
identified five performance levels for its statewide standards based assessments:
Advanced, Proficient, Basic, Below Basic, and Far Below Basic (California
Department of Education, 2001).
Sanctions: The consequences imposed for not meeting expected performance
outcomes in accountability systems (Olsen, 2005).
Social Capital: The central premise of social capital is that social
networks have value. Social capital refers to the collective value of all "social
networks" [who people know] and the inclinations that arise from these
networks to do things for each other ["norms of reciprocity"].
Organization of the Study
This dissertation is organized by five chapters. Chapter One is organized as the
introduction of the study and includes; the statement of the problem, the purpose of
the study, the significance of the study, the research questions, limitations of the
study, the delimitations, the assumptions and the operational definitions of terms to
be used in the study. Chapter Two is the review of relevant literature addressing the

23
current status of secondary urban school performance in math, best practices used by
teachers, the role of the Principal as an agent of change and secondary school reform
efforts. The focus of Chapter Three is to outline the methodology used for the study
and the instrumentations that are used to gather information including the sampling
criteria and selection process of participants. The overall findings of the study are
presented in Chapter Four with a discussion and analytical perspective. The final
Chapter Five provides a summary of the study and offers recommendations and
potential implications based on the findings. The references and appendices are
included at the end of the five chapters.

24

CHAPTER TWO

REVIEW OF THE LITERATURE

“Our Nation is at risk. Our once unchallenged preeminence in
commerce, industry, science, and technological innovation is being overtaken by
competitors throughout the world… the American people can take justifiable
pride in what our schools and colleges have historically accomplished and
contributed to the United States and the well-being of its people, the educational
foundations of our society are presently being eroded by a rising tide of
mediocrity that threatens our very future as a Nation and a people. What was
unimaginable a generation ago has begun to occur—others are matching and
surpassing our educational attainments”
(Excerpt from National Commission of Excellence, p.1)

The academic performance of our students in the traditional comprehensive
American high school has been a source of concern, and presented a challenge for
many decades. Research indicates that our public schools have been under scrutiny
by experts in education since the 1950’s. Our educational system has been identified
as a significant contributor to the successes and challenges our country has faced in
competing globally. However, criticism has been aimed at our educational system at
all levels, from the state to the district to the individual schools. As such the
educational community has had to defend instructional practices, the quality of
instruction, and the teachers who prepare our students academically.
The beginning of a major and continuing focus on our public schools can be said to
have started with the launching of Sputnik by the Russians. This event fueled the
concept and idea of students being able to demonstrate “minimum competency” on
specifically developed exams. This led also to the seminal report on the state of our

25
public schools, “A Nation at Risk” followed by the TIMMS and then the NAEP.
The results of these reports and studies reveal a pattern of declining performance of
our students, additionally, annual standardized assessments have further exacerbated
our concerns about our students’ ability to participate and compete globally.
Some the most focused discussions about our schools can be traced to the
launching of Sputnik by the Soviet Union in 1957 when as our primary economic
and political rivals at the time, the Soviet Union, made it to space with the first
manned spacecraft before the United States attained this goal; this was unacceptable
to our society.
Our nation was not accustomed to the feeling that we might not be the best;
as a nation we believed that we surpassed all others as a country and that we would
lead all other nations; this belief in our invincibility extended to our school systems.
However, the launch of Sputnik provided evidence that as a society we were not able
to match the skills and talents of those overseas and as such it was our American
educational system that was identified as the problem; it was dropping behind other
countries, particularly in the areas of mathematics and science. Our public school
system was not adequately preparing our students and if this continued we would not
be able to compete in the world (NAR, 1993). The school system was immediately
considered sub-par and in need of immediate interventions and policy changes that
would ensure our educational system would be the leader and provide the standard
that other countries would aspire. The focus of this criticism was directed at the
teachers and at the school site level (Wagner, 2004). The increasing concerns

26
regarding the American education system created a call for educational reform
efforts to be a priority to meet the demands on our educational system (Elmore,
1997).
Sputnik would lead to the development of educational goals and objectives,
studies and plans to be generated from the United States Department of Education.
Our policy makers called for the implementation of educational policies that would
foster our focus on our public schools (Bybee, 1998). The launching of Sputnik
challenged the foundation of Americans and brought much needed attention and
resources to our public education system.
While the launching of Sputnik provided the impetus for our politicians and
policy makers to examine the K-12 public education system in America the concern
for low academic achievement was predicated on assessment data that was
collected by the school districts; county offices of education; the state and the federal
departments of education. This extended to include and further highlight the
disparity of academic achievement that is consistently present when American
students are compared to their counter parts in other countries.
The achievement gap has been a point of discussion, debate, and study for
decades; as far back as the 1960’s. Prior to President Johnson’s declaration of a “war
on poverty” in an public address in 1964 the collective interest of society was not as
focused on the quality of education but rather ensuring that minority and poor
students had equal access to public education.

27
It was this declaration by President Johnson that brought forth the Civil
Rights Act which stipulated that the educational opportunities in our public schools
be studied and a survey conducted. The subsequent study commissioned by the
Department of Education was titled, “Equality of Educational Opportunity” but more
commonly referred to as The Coleman Report after the American Educational
Sociologist James Coleman who was instrumental in conducting the research. The
study was the first to use data from over 600,000 educators and students all across
the country that included using test scores as an indicator of whether students were
receiving an equitable education (Kiviat, 2000). He found that the background of a
child had strong implications on their academic performance and success in school
and that student success were more closely related to there sense of control of their
environment and their individual future (Coleman et al. 1966; Kiviat, 200; Marzano
2003).
Many of the studies and programs which have been conducted and
implemented since Sputnik have further shown our discrepancies, particularly in
math and science as compared other nations.
Almost forty years following Sputnik the concerns for our schools to
adequately prepare all our students to compete in a global economy and information
age remains. Our students have made improvements in their academic performance
but remain behind their peers around the world. This is of greater import as it relates
to countries such as China and India who are quickly gaining in their status as
influential countries in the world economy and who are out performing our students;

28
particularly in the areas of mathematics (TIMSS and US Dept of Labor 2004). This
has potential ramifications on our abilities to remain as influential leaders in the
world as the advancement in technologies have created a world in which education is
essential and math is a gatekeeper to many of the new jobs that are available today
and for our future (Stiff, 2003)
Although there has been some improvement in mathematics performance of
our students in the past few decades, such improvement has been incremental and
insufficient, particularly for minority students. The achievement gap is of significant
import not just as a an issue of social injustice, but poses a crisis for the future of our
country by placing students at a disadvantage in their abilities to compete and
participate in our society as well as globally (Douglas, 2006). Statistics provided by
the United States Department of Labor (2005) indicate correlation between an
individual’s math ability and their average hourly wages, namely those individuals
who demonstrate a minimal level of math competency also earn less. The
achievement gap would then further impede the minority students’ future economic
power and ability to compete. Additional reports from the Department of Labor
(2005) find that the ten fastest growing occupations in the United States are all in
fields that require and depend on math, science and technological skills. This extends
to include occupations that are “vocational” in nature and as such traditionally have
been fields that individuals with limited post secondary education could participate.
The 21
st
century has brought rapid changes in the labor force and with the
advances made in technology is changing the required skills and knowledge base

29
once required for various careers to include both professional and vocational fields.
An example of this comes from the Department of Labor which reports that to
become a tool and dye maker requires a multi-year apprenticeship and/or
postsecondary education as well as skills and knowledge of algebra, geometry,
trigonometry, and statistics; these kinds of skills would extend to the occupation of
sheet metal worker or auto mechanic. These are subjects that are rigorous and not
traditionally or historically associated with trade vocations. In the 21
st
century the
important and significant ramifications of the persisting low achievement of many of
our students and additionally the achievement gap between our minority and
majority students presents a potential crisis for the future of the United States as a
leader in the world.
A Nation at Risk
In 1981 the Secretary of Education T. H. Bell established the National
Commission on Excellence in Education and charged this group with the task of
studying the quality of our public education system in the United States. This was
conducted as a means of providing evidence that as a country our public schools
were delivering an education that was structured and in a manner that ensured we
would regain our place as a leader in the global economy and defense (Amerin &
Berlinear, 2002).
The findings in the report presented a compelling picture of our schools
performance as compared to other countries: in short, students in the United States
were performing poorly. The Nation at Risk (NAR) report issued in 1983 provided

30
results that caused a further decline in confidence in our school system. The reported
stated that, “the educational foundations of our society are presently being eroded by
rising tide of mediocrity that threatens our very future as a nation and a people”
(National Commission on Excellence in Education, 1983, pg.5). In response to the
report the Department of Education moved to ameliorate the deficiencies of our
public schools by recommending changes in the system; all stakeholders in the
educational system sought reform.
The report facilitated a discussion and focuses on our schools and initiated
large scale school reform by legislators who were invited to be more engaged in
improving our schools across the country. The Nation at Risk report was responsible
for identifying critical statistics that highlighted many concerns about the academic
achievement and skills in America. This included the poor achievement on
standardized assessments, the startling fact that over 20 million American adults
were identified as functionally illiterate and that thirteen percent of seventeen year
olds throughout the country could also qualify as functionally illiterate, this
percentage was more than doubled for our minority students (NCEE, 1983). Prior to
the issuing of this report this kind of data and information was not part of the public
dialogue around education; but these findings pushed this conversation to the
forefront and pushed for subsequent research to be conducted in an effort to provide
additional data on student achievement.
The K-12 public schools throughout the country were directed to increase
the instructional content standards to include greater breadth and rigor; establish

31
mechanisms for increased accountability; to improve the curriculum and provide
rigorous assessments that would increase the level of accountability at the local level.
(A Nation at Risk, 1983, Elmore, 1997).
Trends International Math and Science Study
Over the past 40 years students throughout the United States have been
involved in eight different international achievement studies in the content areas of
math and science, beginning with the Coleman Report in the 1960's.
The Trends International Math and Science Study (TIMSS) was developed
and conducted for the first time in 1995 by a consortium of research leaders from the
International Association for the Evaluation of Educational Achievement (IEA). The
TIMMS sought to compare the academic performance in the curricular areas of math
and science of the United States students in the 4th, 8
th
and 12
th
grades as compared
to students in the corresponding grade levels from other nations. Subsequent TIMSS
studies were conducted using the same groups of students from essentially the same
industrialized nations in 1999 and again in 2003. This study was one of the most
thorough and often sited international studies that sought to complete an in-depth
analysis of both math and science. TIMSS studied the instructional practices, and
conducted a survey of student mastery of curricular content and the students’
attitudes (Robitaille et al.1993).
The findings from the first TIMSS (1995) indicated that the students in the
United States performed poorly in comparison to students at the same grade levels in
other countries (NCES, 2004). The fourth grade students performed significantly

32
better than both the 8
th
and 12
th
grade students in both science and math; ranking 3
rd

in science and 11
th
in math out of 25 nations. The 8
th
grade students scored close to
the international average in both science and math; scoring 17
th
in science and 28
th
in
math out of 41 participating countries. The results for the 12
th
grade students was the
most dismal scoring 18th in science and 16
th
in math out of 21 participating
countries.
In 1999 TIMSS demonstrated that while students in the United States
continued to perform academically behind students from other participating nations
in the area of math, 8
th
grade students demonstrated improvement; increasing the
average score by 10 points from 492 to 502, only three others countries made greater
gains in their average scores. The 4
th
grade students remained at the same score of
518 for both the 1995 and 1999 TIMSS (Gonzales, 2004).
The third TIMSS comparison study was conducted in 2003 with a total of 46
nations participating; only 11 of these countries including the United States
participated in all three studies in both science and math; 1995,1999 and finally in
2003. From the 1995 study to the 2003 the 4
th
grade United States students remained
consistent in their performance; no measurable gains were made. Whereas the United
States 8th grade students demonstrated growth in both science and math from 1995
to 2003. The greatest growth was attained from 1995 to 1999 in mathematics and
between 1999 and 2003 in science. Additional data suggested that 8
th
grade students
in the United States had an improved performance relative to participants from other
countries that participated in the TIMSS study; this was in both math and science

33
from 1995 to 2003. The fourth grade students during this same time frame were
performing lower in both math and science when compared to fourth grade students
in the other 14 participating countries (TIMSS, 2003).
All three of the TIMS studies disaggregated the student data looking at
different sub-groups: family income levels, students participating in the free and
reduced lunch programs, and the differences that obtained between different ethnic
groups. One common denominator present in each of the three TIMSS studies was
the achievement gap between these different sub-groups of students.
The findings of the 2003 TIMSS did identify a reduction in the achievement
gap between white students compared to Latino and African-Americans, but despite
the reduction, the gap remained significant. The discrepancies between the white
and Latino students had decreased from the initial study, but the math score of Latino
students still remained at 60 points less than their white counterparts. The
achievement gap between whites and African-Americans had also been reduced
since the first 1995 TIMSS study which had found a 97 point gap between African-
Americans and white students and in the 2003 study it had decreased by 20 points to
77. This reflects a slight closing of the achievement gap between the African-
American and Latinos students, with an increased average score of 448 for African-
Americans and a higher score of 465 for the Latino students. Out of the three
different groups the African-American students demonstrated the largest growth
increasing their average score from 1995-2003 by 29 points; the Latinos increased by

34
21 and the white students had the lowest level of growth, raising their average score
by only 9 points over this same time frame (TIMSS, 2003).
These findings presented a clear “crisis” in our public schools as identified by
the academic performance of our students. Discrepancies in academic achievement
were and are present within the United States; these differences are consistently
present: state by state, school by school and within minority to majority students.
This reflects a microcosm of the larger national concern in our country. The
“achievement gap”, is described as a correlation that is identified by race, high
poverty, and academic achievement.
National Assessment of Educational Progress (NAEP)
The “Nation’s Report Card” has become a trusted resource and reflection of
the academic growth of students across the country and the trends that are present in
mathematics, science and reading (Coley, 2003). The NAEP was first administered
in the 1960’s; this has provided significant longitudinal data on student achievement
across the country. The results from the NAEP have served as a tool for our national
leaders to assess the academic patterns and to identify states and districts that are
models and those that have significant areas of deficiencies in their academic
performance. The use of this as a resource has increased in recent years under the
NCLB (2001) as it became a required assessment as a means of monitoring student
achievement growth on the whole and providing disaggregated data by sub-groups.
The NAEP has also evolved through NCLB as a tool for monitoring state adherence
to the mandatory accountability system as defined in NCLB.

35
In recent years the findings from the NAEP results indicate that as a country
we are making academic progress; specifically our math scores continue to show
some level of improvement (NAEP, 2005). In 1997 the United States Department of
Education released a report stating that our public schools are improving student
learning as indicated by multiple measures; increased enrollment in rigorous course
work, college admission test scores have improved simultaneously while the
diversity of test takers has also increased and there have been sustained improvement
on the National Assessment of Educational Progress (NAEP).
As student achievement is measured the patterns must be focused on; which
students are improving and is the achievement gap closing or remaining stagnant
with everyone demonstrating some improvement each year? This incremental growth
from all groups of students will not close the gap; schools need to exponentially
improve the academic performance of our African-American and Latino students if
the achievement gap is to be decreased. The disparity between various sub-groups,
specifically minority students from high- poverty school districts, continues to reflect
that these students and thus our schools, are not making sufficient academic progress
and as such the achievement gap between our middle class majority students and low
income minority students persists.
The results from NAEP have found that for the past thirty years we have had
inconsistent results, with the 1970’s finding a trend of decreasing scores in math,
reading and science, which was counter to the 1980’a which saw an increase in the
students achievement which continued into the early 1990’s. The end results were

36
little net gain from the 1970’s to the 1990’s. One pattern that has remained
disturbingly consistent is the minimal change in the performance gap between white
students and the Latino and African-American students. While disaggregated data
indicates that Latino and African-American students between 1971 and 1999 have
decreased and risen, with a slight net gain, white students continue to achieve higher
scores, even though overall their net gain during this time frame was significantly
less (NCES, 2000).
When you compare these findings with the results from the 1990 to 2005
NAEP, the results are not any more encouraging. In 1990, 15 percent of 4
th
grade
white students were scoring at proficient or above in math as compared to only
1percent of African American students and 4 percent of Latino students scoring in
this same range. The most recent scores in Math for 4
th
grade white students found a
32 percent gain in students scoring at or above proficient level. During this same
time period African Americans improved by 12 percent and Latinos by 6percent. The
achievement gap between the 4
th
grade white students and their African American
peers has increased by 34 percent and the Latino gap by 29 percent, thus;
unfortunately, the results reveal that the gap is not closing for our elementary
students. The results for the 8
th
grade students reflect the same negative pattern. The
achievement gap between white students and their African American and Latino
peers was 13percent and 11percent; by 2005 this had grown exponentially with the
gap between white 8
th
grade students and African American students increasing to a

37
29percent gap and the gap between Latinos and whites increasing to 20percent
(NAEP, 2005, U.S. Department of Education, NCES 2005).
The NAEP findings for California reflect an achievement gap between white
students and their African American and Latino peers in both the 4
th
and the 8
th
grade. The gap is not as large as it is on a national level but is present and has
remained consistent from 1992 and 2005. In 1992 on a national level 22 percent of
white 4
th
graders were proficient or above while California white students were
scoring at 18 percent at or above proficient. The 4
th
grade African American and
Latino students in California were closer to the national average in 1992 but this gap
had grown extensively by 2005. On a national level African American and Latino 4
th

grade students scored at 12 percent and 19percent compared to California African
American and Latino 4
th
graders who were achieving proficient and above in single
digit percentages. The gap between California 4
th
grade white students and African
American and Latino students had increased to 33percent. This pattern continued
into the 8
th
grade.
In 1990 white 8
th
grade students in California were scoring at the national
average for proficient and above at 18 percent while 8
th
grade African American and
Latino students were scoring in single digits both in California and on a national
level. By 2005 the gap between white students and African American and Latino 8
th

grade students had increased to 30 percent and 24 percent, at this point white 8
th

grade students had exceeded the national average by 3 percent, California students
scored 37 percent at proficient and above while the national average for white 8
th

38
grade students was 34 percent (NCES, 2005) These results further highlight the
achievement gap on a national level presenting a performance gap that is chronic and
presenting a crisis for our nation. As student achievement is an increasingly
important measure in terms of our assessment concerns, these patterns deserve our
attention. We need to remain vigilant about which student are improving their
achievement and is the achievement gap closing or remaining stagnant with everyone
demonstrating some improvement each year? This incremental growth from all
groups of students will not close the gap; schools need to exponentially improve the
academic performance of our African-American and Latino students if the
achievement gap is to be diminished. The disparity between various sub-groups,
specifically minority students from high- poverty school districts, continues to reflect
that these students and thus our schools, are not making sufficient academic progress
and as such the achievement gap between our middle class majority students and low
income minority students persists.
Importance of Mathematics in Schooling
The importance of a strong mathematics education is not only a significant
indicator of success in college but is also important for the future of our country and
its ability to compete in the global information age. With many other countries out
performing our students in math achievement the issue presents an immediate
problem that needs to be addressed systematically in our country and by our schools.
Our public K-12 schools play a critical role in facilitating our ability as a country to

39
make progress in our mathematics achievement in high schools and our role in
shaping the future.
Developing a foundation in mathematical computation skills beginning with
the elementary years is critical to the student’s ability to have future success in
higher level math coursework which is necessary for the student’s future economic
competitiveness and success (Loveless and Coughlan, 2004). The state of California
has prioritized math by increasing expectations for students graduating from the
public schools; the grade level math standard for 8
th
grade is Algebra. California
High School graduation requirements have been raised to ensure that all students
pass Algebra I as a graduation requirement (CDE).
This realization and understanding of the important role of education and
math is highlighted in the increased focus being given to the math curriculum,
particularly courses that at one time were considered higher level, algebra and
geometry. The changes in graduation requirements reflect the responsibility that our
schools bear for preparing our young adults to become active member of our society
and as participants in our economy. The ability of our students to succeed in these
classes is a predictor of college completion and subsequent earnings (Rose & Betts,
2001). The average income of those with college education versus those with only a
high school diploma indicates a difference of almost $15,000. The average person
with a college degree makes approximately $43,000 as opposed to the individual
with a high school diploma earning only $27,000 a year (U.S. Department of
Commerce, Census Bureau, 2005). For a student to have the increased opportunity to

40
enroll and successfully complete college they must have the skill sets to complete
higher level math courses while in high school.
On a global level, we are immersed in the most rapidly changing and
technologically advanced times in our history. The technological advances that occur
daily have increased the level of accountability and demand on our schools, to
adequately prepare our students for the future. Even twenty years ago the necessary
math skills for individuals to be competitive and marketable for both the entrance
into the university and work force was much less demanding; to be admitted into a
four university the successful completion of geometry was sufficient (University of
California, 1983) or if one was to become a mechanic they did not have to have
algebra, geometry or calculus knowledge. Today for our students to meet the
minimum requirements for college they must have complete at least three years of
higher level math for entrance into the university (University of California, 2006).
The need for higher level math skills and a conceptual and operational understanding
extends to the vocational fields as well (NCES, 1997). This is a relatively new
requirement and a direct result of our increased level of sophistication and
technological advancements. Consequently, higher demands have been placed on our
public high schools; it is the role of our schools to prepare young people to be
successful in their pursuit of a college education or in the work force.
Based on research from the Center of Education Reform (1998) over 20
million of our high school graduates are lacking the skills to complete even basic
math; this presents a discouraging picture for the ability for our young people to

41
succeed. An understanding of math is critical for individuals to compete and
participate in our democratic society (Reyes & Stanic, 1998, p 26). The importance
of mathematics knowledge cannot be underestimated. “The critical lack of
technically trained people in the United States can be traced directly to poor K-12
mathematics and science instruction. Few factors are more important than this if the
United States is to compete successfully in the 21
st
century” (National Academies,
2005).
Role of Mathematics in College Success
One of the most valid and important predictors of success in college is the
preparation the students receive while in high school; this is most significant for
math, specifically the completion of higher level math while in high school
(Adelman, 1999). Students who take rigorous math and science courses are more
likely to go to college than those who do not; Algebra is the “gatekeeper” course
that high school students must take to enroll in advanced mathematics in high
school (Gram, 2000). Examples of high-quality coursework include mathematic
classes beyond Algebra II. Of the students who completed a calculus class while in
high school, 83percent of these students received their bachelor’s degree (NCES,
2003).
The significance of enrollment in high level math coursework while in high
school for a student’s future college success is most evident in our students, who
regardless of their ethnicity, come from low social economic status and who are the
first generation to go to college. Out of these students who enrolled in universities

42
64percent had completed advanced math course in high school and went on to
receive their four year college degree (Tierney, Colyar, & Corwin, 2003). Despite
the importance of taking high level math classes as a predictor for college
enrollment (Riley, 1997) these students are less likely to be enrolled in rigorous
math courses. A student’s future college success is correlated more highly with the
levels of math courses that students enroll than is the school they attend.
Role of Mathematics in the Economic Future
“Knowledge of mathematics is essential for all members of society. In order
to participate fully in democratic processes and to be unrestricted in career
choice and advancement, individuals must be able to understand and apply
mathematical ideas” (Stanic & Hart, 1995)

According to Secada (1997) those who are able to demonstrate a higher level
of “mathematical competencies” have an increased opportunity to overcome societal
barriers, which can increase the chances for economic independence. This highlights
the challenges of our secondary schools to ensure that that all students are improving
their skills in math (NSF, 2006). In a study conducted by Secretary of Education
Riley in 1997 his findings reinforced the importance of our students demonstrating a
level of mastery in math. The implications for this directly relate to our future adults
having the capacity to compete and participate in the job market. This again
highlights the importance of improving math achievement of all our students. If we
do not continue to improve the math skills or our students in our public K-12 schools
we are jeopardizing our ability as a country to remain as leaders who are competitive
in the global economy and within our own country and our economic stability.

43
Findings consistently reiterate that our students in K-12 are not mastery the
math skills required for higher level math which in turn foster critical and complex
thinking skills. In 1998 the Center for Education Reform conducted a study in which
they found that over 20 million 12
th
grade students had ended their high school
career not having mastered basic math skills.
Research confirms the financial advantages for those who complete college
and earn a degree. Those who hold a bachelor’s degree will earn almost twice as
much every year in comparison to those who only have high school diploma (Carey,
2005)
Studies conducted by the Bureau of Labor identified the role of math in the
workforce. They found that those who demonstrate strong skills in math have an
increased rate of employment. These math skills translate into hire earnings,
earning more than those who do not have strong math background and skills.
The talent of our future workers is critical in our ability to maintain our
standing in the “global economy”. As we continue to make technological progress
in a global world the level of conceptual knowledge and skills in math with
continue to grow in terms of relevance and importance; this will impact the earning
potential of our workforce (Bureau of Labor Statistics).
Role of Mathematics in the Workforce
“Mathematics is important not just in the education of scientists, engineers
and economists but also in the education of every working citizen in the
United States. It is hard to see how anybody can pull down anything better
that a minimum wage job in the years ahead without quantitative skills”
(Press, 1990).

44

According to a study conducted by American College Testing (ACT) found
that high school students whose future plans include entering the workforce upon
graduation from high school requires academic skills that are “similar to those
needed by students planning to enter college”. This study concluded that the math
skills and conceptual understandings necessary for entering a training program for
entering the work force are similar to those skills a first year college student would
require.
This study by ACT examined various types of jobs that provide sufficient
income to support a family; these were occupations that are traditionally considered
“vocational”. They looked at fields that most often required some training either on
the job or structured training or a two years associates’ degree; the fields they
included were plumbers, electricians and construction workers etc. The report
restated the importance of having the same level of expectations for students whether
they are planning to enter college or a vocational training program; the skills and
knowledge base for the entry level are similar.
The manufacturing industry is an example that many might think of as not
requiring higher level thinking, reading and math skills. The fact is into today’s
society with the advancement of technology and the level of sophistication for
manufacturing products a person must have been successful in higher level course
work in high school. What were once thought of as strictly vocational fields that
might not require math and reading skills now do. For a person beginning in the

45
sheet metal industry requires algebra, geometry, trigonometry and technical reading
skills and the auto mechanic and aviation mechanic must have college reading levels
(EdTrust, 2004). This further emphasizes the critical need to improve our overall
public education instruction but also highlights the detrimental impact on our
students who are not anticipating going to college and may not understand the
implications of their high school education on their future career paths in the work
force. Historically the areas of education that are most associated with economic
“success” are math and sciences. Those that have demonstrated adeptness for math
are in a advantageous position to minimize the barriers that stand between economic
dependence and independence (Secada, 1995, 1997). While mathematics has been
considered the subject that has significance in one getting into college (Reyes &
Stanic, 1988) it is no longer just the key to college but rather is a critical knowledge
set for many positions that at one time were not thought to require math skills. The
gradual changing of our society over many years allowed us to make changes and
adapt in moderation. With the exponential changes brought forth with the
advancement technology we no longer have the luxury as a society to ignore the
demands our advancement place on the individual and the larger workforce.
Reform Efforts to Improve Math Achievement
The call for the reform of our public school system has been occurring in the
public sector for decades. Based on results from both national and international
studies the content areas of math and science have been the subject areas in which
students have demonstrated the poorest performance. An effort to improve the

46
achievement of math in the high schools has been a priority at both the state and the
national levels. The accountability of public schools systems has been increased by
the implementation of the accountability system of NCLB which has called for
standardized state assessments to be administered annually, disaggregating the
student data, establishing benchmarks for student academic growth as measured by
these assessments and requiring that teachers are “highly qualified” as defined by
NCLB.
The NCLB accountability reform is a mandate and has facilitated focus
nationwide on providing a standards-based instructional program that is predicated
on state content standards in specific grade levels and content areas. In response to
the increased accountability schools have sought out research based approaches and
ideas that have demonstrated positive impact on student academic performance. This
encompasses the standards based instructional programs as the foundation for
improving student achievement. It also extends to ensuring that every class has a
quality teacher, implementing different school design models, effective professional
development for teachers and administrators, and understanding the role and
influence of the school instructional leader.
State Content Standards
The report, A Nation at Risk generated much fervor throughout the country
about our students’ skills, which resulted in the realization for the need for “systemic
reform” in our public schools. Part of this reform was the realization that we needed
to have standards for each curricular area; which is something that was already in

47
place in other countries around the world (Anderson, B., Brown, C., and Lopez-
Ferrao, J., 2003). The first goals established for math were published in 1989 by the
National Council of Teachers of Mathematics (NCTM) (Schoenfeld, 2004). The
objective of these standards-based goals was to identify common standards for math
instruction and content of instruction.
The standards-based reform effort grew from President Clinton’s program
called Goals 2000 which had as its objective that all students would be held
accountable to a set of grade and content level standards. The individual states were
expected to create their own standards and these would become the road map for the
specific state’s instructional program. By 2001 all but one state had developed their
state content standards in at least one content area and 44 states had accomplished
this in the four core subjects of Mathematics, Science, English and Social Studies
(Hirsch et al, 2001). The development of these standards for the instructional
programs across the country would provide a consistent instructional program for all
students in the individual states and were intended be one aspect that would improve
the instructional program and thus student achievement.
The development of academic standards created a “road map” for what
teachers were required to teach and correspondingly what the students were expected
to learn; ostensibly, standards would ensure a consistent education for every child.
Establishing standards increased accountability for instruction and content and
helped to focus the larger educational community to keep teaching and learning as
the primary factor (Elmore & Fuhrman, 2001). Student learning was measured

48
objectively and not based on possible bias or student to student comparisons
(Jamentz, 2001). It was agreed by many researchers that this would help improve the
achievement of all students in that the teacher’s expectations of the students is
removed from the equation. This according to Codding & Tucker (1998) would have
tremendous impact on student achievement because the low expectation that is held
for all students is a predictor of student achievement. The development of standards
as an implementation of a larger accountability system helped to create a system that
is more supportive of student learning (Darling-Hammond, 1999). The standards
while a critical piece of the instructional program is only one piece of a larger
picture. This effort to increase accountability and student achievement also included
assessments, professional development, interventions to support students, and
appropriate allocations of resources in an effort to support the student and the
schools (American Association of Educational Research, 2000).

Teacher Quality
The legislation of NCLB (2001) has had broad and sweeping impact on the
public education system. One area in which this legislation has had dramatic
influence has been in the definition of “Highly Qualified Teachers” and the
requirements that all teachers in designated curricular areas be deemed as highly
qualified based on a criteria set forth in NCLB. This requirement has had
implications for virtually all curricular areas with the essentially the only exception
being in the area of physical education. Physical education teachers at the secondary

49
level are not required to meet criteria for NCLB. All teachers must be deemed as
“Highly Qualified” by January of 2007. This legislation has expanded the role and
influence of the federal government in the educational system and has contributed
immensely to the accountability of our public schools ensuring that all students are
being taught by teachers who have met a stringent set of protocols.
Unfortunately school districts and schools have consistently been challenged
to “find” enough math teachers and certainly NCLB requirements have further
impacted this effort (2001). In previous years the number of teachers appropriately
certified or credentialed who taught math had decreased. Over the past decade and
into the most recent years the certification rates have decreased; from 90 percent in
the 1990’s to 80percent by 2002, furthermore only 71 percent of our secondary math
teachers had either majored or minored in math for the undergraduate degrees (NSF,
2006). With NCLB legislation teachers while not required to have majored or
minored in math, or any subject that falls under the NCLB umbrella, do have to
complete designated coursework and/or pass rigorous subject examinations.
These requirements and the heighten accountability for teaching
qualifications set forth in NCLB legislation support the most influential factor on
student learning; teacher preparedness and qualifications (Marzano, 2003).
Researchers support that one of the most critical aspects for increasing student
achievement is the quality of the teacher and instruction Teachers having to
demonstrate competency in their content area either through certification or
examinations will directly impact the student learning and performance on

50
standardized assessments which serve to convey and communicate the progress in
our public schools (Darling-Hammond, 2000).
Improving Instruction
Another area in which work is being done to improve instruction has been to
utilize Lauren Resnick’s (2000) Principles of Learning model which sought to
provide a “blended” instructional model. Not only does this model seek to enhance
the quality of the classroom instructional program it also addresses the need for
higher expectations by the teachers for all students which in turn supports students
performing better. The “Principles of Learning” supports and facilitates the
instructional program through six elements that are the foundation of this
constructivist model of instruction:
Organize for Effort
In which hard work replaces aptitude as a measure of success. Everything is
organized for the student to work as hard as they need to achieve high standards.
Clear Expectations
Student, parents, school, and community know and understand benchmarks that
mark each stage of learning. Students participate in setting goals and evaluating
progress.
Recognition of Accomplishment
Recognition of accomplishments that takes the form of celebrations of work that
meet standards or expectations. Families, community members or peers take part in
these celebrations.

51
Fair and Credible Evaluations
Assessments are not based on the normal curve, but students are evaluated on their
progress towards absolute standards. Assessments are connected to and imbedded in
instruction and are not in isolation of other student work.
Academic Rigor in a Thinking Curriculum
“Knowledge-Based Constructivism” means that students are engaged in thinking a
solid base of knowledge-process and content are linked.
Accountable Talk
Student-to-student questioning, probing, and questioning appropriate to the
discipline uses evidence and appropriate knowledge to develop ideas.
Socializing Intelligence
By calling on students to use intelligent thinking—problem-solving, reasoning, and
using their ability to make sense of the world—educators can teach intelligence.
Learning as Apprenticeship
Students engaged in “authentic learning”. Apprenticeship learning can be done
through the use of extended projects and presentations of finished work to an
interested and critical audience. Learning strategies are overtly modeling and
discussed (Resnick, 2000 p. 92).
The critical important of teacher quality and the relevance and rigor of the
instructional program has become central to the success of students. As educational
reform efforts continue these factors are increasingly embedded in what changes are
being implemented throughout our public education system.

52
School Design
School Schedules
The traditional school day consisting of six one hour long classes has
morphed over the years as secondary schools search for a schedule that provides
sufficient time and frequency for students in core subject areas. The changes that
have been implemented to modify the instructional organization of the day have
resulted in encouraging results. The block schedule in which students have fewer
classes in a day, possibly alternating classes every other day but have more
instructional time in a class has resulted in positive impact on student achievement
(Walberg, 1987). Not only does alternative block schedule provide for additional
instructional time but also reduces the transitions between classes in a given day
which also diminishes the opportunity for disruptions and behavioral problems. The
impact of block scheduling, specifically providing increased time for critical subjects
of math and English Language Arts has both increased graduation rates and has help
to decrease the percentage of students dropping out of school (Queen, 2000).
However increased instructional time in and of itself is not sufficient as research
finds that the level of engagement of students is a critical predictor of student
learning as well (Sandowski, 1998). It is also important that teachers are provided
the training and sufficient planning time before the transition from a traditional
schedule to a block schedule in an effort to ensure teachers learn strategies that
support teaching in the extended block of time (Canady & Rettig, 1995)

53
Small Learning Communities

Over the past ten to fifteen years, research in the field has increasingly
focused on the value of reorganizing our secondary schools into smaller more
personal units in an effort to positively impact student achievement. These “small
school” models have morphed into what are not commonly referred to as Small
Learning Communities (SLC) which not only reference the size of a program but
also the design. Many SLC’s are parts of a larger whole, meaning they are schools-
within-a-school on a larger school campus. They may be categorized as academies in
which there is a specific focus, usually on a given career area. There is as well the
“house” model in which students are organized into “houses” with a school having
many different “houses”, these may or may not be organized around a common
theme beyond grade levels (NCSL, 2006). This concept of smaller schools and
school-within-a-school provides students with a more personalized educational
experience. The school, house or academy becomes an entity in which the student
and teachers are identified as belonging to (U.S. Department of Education, 2001).
These different kinds of SLC’s create a setting in which relationships between the
students and their teachers and even teacher to teacher is fostered as a result of the
smaller units and greater interaction with one another (Cotton, 1996). The SLC’s
model has also been found to have a positive impact on the performance of all
students; reducing the achievement gap between different ethnic groups as well as
students from different socio-economic levels (Klonsky, 1998). Reorganizing the
large high school has been found to have measurable impact on many factors of a

54
school including having a positive impact on improved student achievement,
attendance and a reduction in drop-out rates (Cotton, 1996; Pluker, Zapf and Spradin,
2004). Beyond this it has also been found that SLC’s provide a important element in
the improvement of over all school conditions while also improving student
outcomes (Wood, 1992).
Professional Learning Communities
The structure of the day and the organization of the school have implications
for the teachers as well as the students. To encourage the learning and growth of the
teachers as professionals a school design that is supported by much research is what
educators have called, Professional Learning Communities. Organizing schools into
learning communities supports both students and adults in developing a respect for
learning, and honors teaching as a profession. These beliefs have been supported by
research from the Darling-Hammond (1996) commission that serves in an advisory
capacity on educational issues, specifically teacher education and quality. The
compellation and purpose of a PLC is defined by the priority or it can be a
department within a school, a grade level team or even a district level grade level
team of educators with a common purpose; the key indicator of a PLC is a common
goal and like focus. Additional research finds that, “developing a professional
community among educators is a key ingredient in improving schools” (Fullan 1999;
Langer 2000; Little and McLaughlin 1993 et., al.) The structure of the PLC provides
an opportunity for educators within the school and the larger school district to learn
collectively how they can improve their instruction programs to improve student

55
learning and achievement. Dufour and Eaker (1998) have identified six essential
characteristics that define a PLC and that must be established for the success of a
PLC.
1- A shared mission, vision and agreed upon values
2- A commitment to “collective inquiry” as a means of discovery as a group
in which they question, strategize and evaluate.

3- Collaborative teams that are committed to the process

4- A action orientation and commitment to experimentation as a means of
seeing what works and sharing this to attain the PLC common objective.

5- Dedicated to continuous improvement

6- Taking a result oriented approach to the process.

The very nature of a PLC is action; to attain an identified goal or objective
thus improving student outcomes. The role of the school leader is critical to the
development and implementation of a successful PLC and they must be part of this
process as active learners. It is essential that the leadership empowers the teachers
through their active participation within the PLC, to be an integral part of the
decision making processes that positively impacts the school (Hord, 1997). As
Dufour (2003) determined from his research PLC’s are “action oriented with the end
in mind” and this philosophy as it relates to PLC’s is critical to the formulation of
immediate learning objectives that enables schools to improve the learning and
achievement for all students and adult educators alike.

56
Professional Development
The demands for continuous student improvement and the complexities of
student’s needs which our teachers are being asked to understand all reinforce the
importance of professional development that will allow the teacher to increase their
knowledge and remain informed about trends and advances being made in education
(Elmore, 2002). Accordingly professional development that is targeted to support
the teacher’s development as an instructional expert has been a priority at both the
state and federal levels. Professional development has evolved to ensure that the
teachers are having learning opportunities that enhance their skills in utilizing
different instructional strategies, and are able to appropriately analyze student work
within a standards based instructional context, all of which have an impact on
improving student achievement (Smylie, et al 2001).
While professional development is important as a means of improving
instructional practices in all areas of study it has been found to have a specific impact
as a strategy for improving math instruction and math achievement (Taylor-
Anderson, Brown, & Lopez-Ferrao, 2003). Professional development for teachers or
all educators must be deliberate in its development so as to meet the needs and thus
enhance the likelihood that this knowledge will transfer to the classroom and student
learning. Some researchers further advocate the importance of professional
development being conducted within the organization and not always facilitated and
created by those outside of the organization. In his book “Results NOW” (2006)
Mike Schmoker speaks to the importance of utilizing the experts in our schools and

57
districts to drive professional development. His beliefs being, that the teachers have
the most insight and understanding regarding their needs. He states in his book that,
The right kind of continuous, structured teacher collaboration improves
the quality of teaching and pays big, often immediate, dividends in student
learning and professional morale in virtually any setting. Our experience
with schools across the nation bears this out unequivocally. (p. 177).

Teachers need to be afforded opportunities that empower themselves to develop their
own skills as teachers. Through these opportunities they should also actively engage
the teachers and provide time for reflection because like students the teachers learn
most by doing (Resnick, 1999).This provides opportunity for collaboration with
colleagues which can provide a forum in which there are common experiences and
understanding of the needs and as such can partake in meaningful conversations
which can have immediate influence and impact on student learning. The
expectations and guidelines set forth in the reform efforts of NCLB assist in framing
the importance of teachers and the realization that they as professionals are
accountable for student learning.
A critical element that assists in increasing accountability is having a culture
established at the school that identifies the teachers as the first person who must be
responsible for student learning. If this is to be embraced and facilitated it is critical
that teachers have access to assessment data for each of their students and that this is
utilized as a tool for informing their instructional program and strategies.
The use of student assessment data must be analyzed on a consistent basis
(Schmoker, 1999). The schools and teachers that use data and a standardized

58
protocol for analyzing assessment data and student work will result in teachers
having valuable data that can guide and influence instructional practice in the
classroom immediately. This allows for students to be placed in the most
appropriate instructional programs based on the students needs.
A survey conducted by EdSource (2000) found that the kinds of professional
development a school engages in at a systemic level can be correlated with a schools
performance. They found that the use of assessment data was present at both low
and high performing schools. Additionally they found that high performing schools
engaged in professional development that was focused on providing quality
instruction and that which addressed the multi-cultural issues such as analyzing the
cultural biases in the curriculum and the cultural awareness of teachers. Conversely,
they found that schools that had professional development which focused on school
visions and instructional strategies for English Learners were correlated with low
performing schools. The role of professional development that is research based and
is focused on improving instruction to meet the needs of our increasingly culturally
diverse student population is critical. The leader of the school then must provide or
create the opportunity for teachers to take part in professional development that is
research based and is focused on the instructional program and instructional practices
that improves their practice as teachers (Grossman, Thompson, & Valencia, 2002;
Marsh, 2002)

59
Math Programs
The importance of an effective math program and its ability to impact student
learning and achievement cannot be ignored; it is critical and must be coupled with
sound instruction. A mathematics program that is effective has been identified as
having nine elements all of which contribute to the students having demonstrated
mastery, knowledge and understanding; assessment, instruction, instructional time,
instructional resources, instructional grouping, classroom management, professional
development, administrative practices, community, and involvement (Beaton et al.
1996). Additionally there are three other elements that have been identified as
essential for an instructional math program to be effective: students must be able to
demonstrate a basic computational and procedural skill levels; to have a conceptual
understanding and be able to problem solve (Geary, 1994; Sophian, 1997).
There are many math programs being utilized in our schools but a limited
number are recommended by the U.S. Department of Education and are identified as
“exemplary” or “promising” in there ability to improve math achievement. These
math programs are all research based, are aligned with the relevant content standards
and they have a professional development component to support teachers and their
ability to effectively utilize and instruct with the program. Five of the top programs
that were identified and recommended by the U.S. Department of Education were;
Core Plus Mathematics Project (CPMP), Interactive Mathematics Program (IMP),
Cognitive Tutor Algebra, College Preparatory Mathematics (CPM) Connected Math

60
Program (CMP). Three of these five programs are discussed in this paper; Core Plus
Mathematics Project, CPM and Cognitive Tutor Algebra.
Core-Plus Mathematics Project ((CPMP)
Developed by an international advisory board, mathematics instructional
specialists, and classroom teachers CPMP is a four-year curriculum that is designed
to be used in lieu of the conventional Algebra-Geometry-Advanced
Algebra/Trigonometry-Pre-Calculus sequence. It is a program designed to identify
big mathematical ideas that are connected and make meaning of these complex ideas
for students. The curriculum is organized into four courses. The first three cover a
wide range of “useful” mathematical concepts that are designed to support and
prepare students for college, careers and daily life experiences that require math
knowledge. The final fourth course is a more structured course that is focused on
essential mathematical ideas and concepts that integrates all four strands of math;
Algebra-Geometry-Advanced Algebra/Trigonometry-Pre-Calculus
(http://www.nychold.com/cpmp.html).
CPMP is a curriculum design that has several elements which make it unique
from other math programs. One such distinction is the program’s focus on active
learning in which the instruction is developed around collaborative small group work
where students engage in problem-solving and investigative learning. This is
balanced with direct instruction and whole class activities that lead to analysis and
application of mathematical ideas. The program has a focus that is referred to as
“mathematical modeling” which includes the collection, processing of data and the

61
interpretation of this data which is utilized to make predictions. The organization of
the curriculum is intended to provide opportunity for students, whose skill levels are
at either end of the continuum, making higher level math accessible to a greater
number of students. The curriculum is differentiated so as to be challenging for all
students and can accommodate students’ levels based on the “depth and level of
abstraction” that topics which are explored require. An additional element is the use
of technology which allows for the instruction to focus on reasoning, utilizing
multiple representations; verbal, graphical, symbolic or numerical which helps
facilitate thinking and problem solving skills. Students are assessed utilizing multiple
indicators that determine student understanding of mathematical concepts and
processes (www.wmich.edu/cpmp/overview.html).
Like most programs CPMP has both its advocates and its critics, this said,
most of the research that has been conducted has been favorable in its assessment of
the CPMP model. Research conducted by Schoen and Hirsh (2003) found that
students who had taken CPMP courses as opposed to a traditional math course did
much better on the Iowa Tests of Educational Development. The findings indicated
that after having completed two courses of CPMP students performed much better on
contextual algebra and coordinated geometry subtests whereas on the procedural
algebra subtests there were less significant differences in outcomes. The most
significant difference was on the subtest that measured skills in making inferences,
reasoning and applying quantitative procedures.

62
Carnegie Cognitive Math Tutor
This curriculum was both funded and developed by Carnegie Learning and is
based on years of scientific research conducted by the Carnegie Mellon University.
The curriculum begins with a Bridges to Algebra and moves up to integrated math
and a math prep course. The curriculum utilizes a blended approach of technology
based software, textbook support and coaching. The Algebra Bridge and Algebra
courses identifies connections between different mathematical representations; to
include fractions, percents, decimals and using visuals as a means of increasing
understanding of these different representations. Both of these courses cover content
strands identified by the National Council of Teachers of Mathematics Standards;
these (NCTM) standards and are also aligned with the state standards. While focused
on developing problem solving skills each of the strands are also addressed. These
include; number sense, geometry, measurement, probability and statistics and
algebra (www.carnegielearning.com).
The Carnegie Melon University has conducted extensive research across the
country over the past 20 years on the program. The findings indicate that their
Carnegie Tutor program has consistently supported and improved student
achievement in math. One of their studies found that schools and students who had
used their program had performed significantly better on the TIMSS scoring
30percent higher than peers who had not been instructed using Carnegie Math.
Scores on the SAT and the Iowa Algebra Aptitude Test (IAAT) were also better for
students trained in this program (Carnegie Learning). Further studies determined that

63
students who had completed the Bridge to Algebra and the Algebra course had a 70
percent greater chance of completing geometry and Algebra II.
An independent study on the effectiveness of the Cognitive Tutor Algebra I
when compared to a traditional curriculum was conducted during the 2002-2003
school year in the Kent, Washington Public Schools. The study examined both pre
and post test increases for 779 ninth-grade students throughout the district. Students
were placed in either a conventional math course or the Cognitive Tutor course based
on their grades they received in math during their eighth-grade year. Students who
had received an “A or “B” were scheduled into a conventional math course while
those students receiving a “C’ or lower were enrolled in Cognitive Tutor course.
The findings supported the Cognitive Math Tutor, since students who were
enrolled in these courses for that year had demonstrated “significantly greater
knowledge gains”. Additionally, the study found that the results were “pronounced”
for the English Language Learners (ELL) and for students identified as coming from
a low-income family. The Kent Washington schools determined from this study that
Cognitive Math Tutor would be an option for all students and that the ELL students
and students from low-income families would be “placed directly” into this math
program (Cognitive Learning, Inc 2004).
College Preparatory Math (CPM)
CPM program is a math program that is designed for both the middle school
grades and the secondary high school level. The program was designed by 70 high

64
school math teachers over a six year period in tandem with professors from the
University of California at Davis and California State University Sacramento. The
motivation for this undertaking was precipitated by the professor’s frustration and
experience with high school students consistently entering the university with a
limited and “shallow” understanding of the math they were studying. In 1999 CPM
was designated as one of five “exemplary math programs” in the country by the U.S.
Department of Education.
Research has been conducted in California on the impact of CPM on student
achievement, using the California Standards Test (CST) results from 2004-2006 for
comparison. The research compared student CST results from approximately 50
middle schools that use CPM as their primary math curriculum with the state average
and found that 6
th
grade students at schools utilizing CPM had an average of
6percent more scoring proficient or above and 7
th
grade students results found that
27percent more of the students scored at proficient or above on the CST
(www.cpm.org)..
A similar study was conducted in the state of Washington in 2005 with middle
and high school students. The research analyzed student performance on the states
standardized assessment, Washington Assessment of Student Learning (WASL).
The WASL math assessment is administered to all 7
th
and 10
th
grade public school
students. This study looked at the performance of 12 middle schools and 17 high
schools that use CPM for math instruction. The reports show that those middle
schools and the high schools that use CPM were scoring better on the Washington

65
state assessment. The state average for proficiency in the 7
th
grade for the 2005
school year was 48.1 percent while 7
th
grade students enrolled in CPM scored 63.5
percent at proficient. The 10
th
grade students in CPM were performing better as
well, 53.8 percent were proficient compared to the state average of 40.6 percent
(www.cpm.org).
These two studies are mirrored in over 20 studies that the CPM organization
has conducted over the past years using different assessment, enrollment and
achievement gap data. Consistently the findings across the country demonstrate a
positive impact for students when their school’s math curriculum is CPM.
While each of these three math programs have been found to have had a
positive impact on student achievement; no program will garner these positive results
without the combination of effective teachers, the use of sound instructional methods
and a positive learning environment for kids. Each of these programs was identified
by the U.S Department of Education as “exemplary”. Additionally, all of these
programs are research based and predicated on utilizing a student centered approach
to teaching and learning that provides students with the ability to draw from prior
knowledge and to develop problem solving skills within a well organized and
sequenced instructional program.
Role of Leadership
“The great leaders are like the best conductors- they reach beyond the notes
to reach the magic and the players” (Lee, 2000). This quote provides a perspective
and understanding on what we want our leaders to do; to bring out the best in people

66
so as to reach the goals and objectives whether it is in the arena of music, business,
or education. Interestingly enough the concept of “leadership” was not widely
applied to schools or found in educational resources until the 1970’s (Donaldson,
2001). Until that point “we” were comfortable with the “administration” running our
schools. It was at during the 70’s that schools began actively addressing the inherent
challenges of educating a diverse population of students whose educational needs
had all but been ignored in our schools (Donaldson, 2001-pg.4).
Today the instructional leader of our schools is expected to be the person who
is able to serve as the guide in moving the organization forward through a vision,
passion, clear objectives, the understanding of and ability to motivate people towards
a common goal; student learning (Fink & Resnick, 2003), This is a belief that is held
by many in education, more often than not the Principal is perceived more as the
instructional leader and not just the manager of their school. But this can present a
challenge for the school leader as they are usually person in charge of “keeping the
vision” and ensuring that the path is set for the realization of this vision (Fullan,
2001). According to Manasse (1986) “… we can distinguish management from
leadership conceptually, but in reality we often find the two roles coexisting in the
same position and the same person. This is often a significant challenge that faces
the instructional leader on a day to day basis as the functions of the school Principal
can become mired in the more mundane activities such as addressing concerns with
the parents and the community, handling the many crisis’s that are part of a regular

67
school day, all of which takes them away from the classroom (Fink & Resnick, pg
1). While these actions are perceived as outside of what the leader of an organization
is responsible for, there are responsibilities that must be tended to if the school is to
run in a manner that supports the learning of students, this reflects the operational
side of leadership.
According to Marzano (2005) there is a relationship between how a school
operates and academic success of its students; if a school operates effectively the
student’s chance for academic success is increased. In effective schools Marzano
found that students had a 44 percent increase in the expected rate of passing a test
(table 1.1—Marzano pg 4). The findings are the mirror opposite for those students
who are enrolled in schools where the instructional leader has not successfully
established the culture of the school and as such is not perceived as an effective
school. This is evident by a passing rate of 28 percent versus a 72 percent failure
rate.
The reality is that the role of the instructional leader extends to creating an
environment that is not only rich in academic pursuits but one in which the school
leader has the capacity to “keep many balls in the air” creating a learning
environment with agreed upon standards for student behavior and as such providing
a learning environment that is safe, orderly and effective in terms of student learning
(Supovitz 2001?). In this situation the instructional leader is able to foster and
cultivate a positive environment through authentic personal concern and interest in

68
supporting the total student not just the academic aspects of the student (Cotton,
2003 pg 8). It is the leader who demonstrates a willingness to extend themselves
beyond the boundaries of expectations that are quite often the effective leaders; these
are “the non-compliers” (Meier, 1995).
To achieve the learning objectives of moving the achievement of all students
forward the leader must challenge the status quo of our educational institutions and
have convictions that are such that they are willing to challenge the day to day
behaviors and belief structures of our teachers, students and community (Wagner &
Kegan, 2005). The instructional leader must be secure and certain of their
convictions and belief in what their vision is for the school and how this will
transform a school (Fullan, 2001).
Research on the role of and what an effective instructional leader is and does
to impact student achievement and learning in schools is extensive and varied
creating a long list of personal attributes. Over the years instructional leadership has
risen as one of the more debated and discussed aspects of effective schools. This is in
part a result of ideological disagreements about how and what should be the done to
move schools and because of the varying definitions of what instructional leadership
means. However, it is commonly agreed that effective leaders must possess a vision
as it relates to their position, a dedication and passion to this vision and their role and
personal strength (Marzano, 2003, Bolman & Deal, 2003(339), Collins, 2001 ). In
addition to these aspects of the effective leader, leadership looks different in different

69
settings and as such leadership can be characterized as situational. Being a school
leader requires that he/she have the capacity to adapt to the varying situations and
roles of a school leader.
A framework often utilized as a means of understanding the various aspects
or lenses of leadership is from the “Reframing Organizations” book by Bolman &
Deal (2003). This framework challenges the leaders of school to “step back” and
look at their leadership style and approach using what they call the “four frames”.
Bolman and Deal define these frames as; structural, political, human resource and
symbolic. The use of these frames allows for the leader to gain perspective and
insight using different lenses as a tool for assessing situations and realizing that the
value of approaching leadership utilizing these different paradigms are as an
essential part of the change process of a school and in effectively impacting the
larger school community and their belief system. The four frames offer an
opportunity for the leader to engage a different perspective and approach in their
leadership style. The leader is able to have a greater understanding of both
themselves and the people they lead by utilizing the four frames as a tool for
understanding.
The instructional leader who is empowered with the knowledge of and
understanding of the various perspectives and approaches that Bolman and Deal
outline is better prepared to utilize additional strategies and approaches in their
leadership approach. The circumstances of each situation and the understanding of

70
the frames allow for the leader to determine which “lens” is appropriate, the effective
leader is one who will be able to utilize and pull from each of the four frames as a
tool in their leadership.
Leadership: Vision for positive change
For positive change to occur in an educational system or business setting
there must be leadership. A valuable aspect of being the leader is having the skills
and knowledge to provide the purpose and to help shape meaning for the
organization (SEDL, Char. of Leaders of change). They possess a personal vision
which they are able to utilize as an instrument of change. The leader is able to create
the roadmap that answers the how and the why’s for the stakeholders. This includes
demonstrating the capacity to take difficult and perhaps negative situations and turn
them into learning opportunities (Bennis &Thomas, 2002; reader for 618). This is a
real life, often day to day, experience for leaders who work in urban school districts
and preside over schools in which this diversity is reflected. In the book, “Standards
for What Principals Should Know and Be Able to Do” published by the National
Association of Elementary School Principals (2004—pg. 9) the enormous feat that
the schools, particularly urban schools face and are asked to address is articulated:
“The growing diversity in our communities and schools adds richness to the daily
experience, but also stretches our capacity to address the needs of all children. The
achievement gap of poor and minority populations continues to lag despairingly
behind that of their more affluent counterparts.”
The challenges are present both in terms of the academic achievement gap
and in how differing cultures, values and mores impact the school day. According to

71
Fullan (2001-Culture of Change) the leader must have the ability to work with and
move staff forward in situations of “uncertainty and conflict” and use this as an
opportunity to engage and motivate the school community. This requires a leader to
possess the leadership skills to build and cultivate a community that is able work
toward a common goal of student learning, predicated on the articulated and shared
vision of the leader and school community (Cotton, 2001).
The value and relevance of the leaders having a clear vision of where they
want to take the school is one that is regularly found by researchers as a key element
for those in the role of leadership. The value of and the commitment the leader has to
the vision is critical to its success and realization. The leader must have the capacity
to inspire others to believe and engage themselves in the process and in the work
required to attain and move towards the vision, this is accomplished when the leader
has the capacity as the advocate (Fink & Resnick, 2003). This must be reflected in
actions; the leader must model the changes and behaviors that are necessary for
progress. This communicates the leader as “authentic” which in turns fosters
motivation of the school community. To accomplish this she must seek to engage
and communicate the vision and present a compelling path towards the realization of
the vision (Evans, 1996 p 201-203).
To ensure progress in reducing the achievement gap between the reality and
the “global “school vision “of improving achievement for all children”, the leader
must establish a community in which all stakeholders take ownership of the vision
and the necessary steps to attain this goal. The leader of the school has to permit,

72
foster and encourage the seeking of new knowledge and practices (Donaldson, 2001
p.3) that support realization of the vision.
Subsequently the school community must transition from the traditional
model of teaching in isolation which can only facilitate “islands of excellence” to a
more collaborative model which is exemplified by “community of learners” that is
grounded in conversations, practices and activities that focus on student learning
with engagement of groups of teachers increasing the accountability of individuals to
the group (Wagner & Kegan, pg.16) The work of everyone, including the leaders
becomes increasingly “transparent”. The leader must model working collaboratively,
taking risks through sharing and being open to feedback (Wagner & Kegan, pg. 17).
Through active engagement and the willingness to take risks the instructional
leader is helping to create a “culture of learning” (Fink & Resnick, pg 5) which is
reflected in the conversations and focus of the stakeholders; teachers and
administration. They are focused on improving the teachers’ capacity to improve
student learning. Rather than the conversations being limited to a 1:1 conversation
about teaching the conversation transforms to a consulting approach in which each
participant is sharing their skills and knowledge. This approach is one in which the
expertise of each of the community is engaged, everyone learns from each other and
draws from individual particular skills and strengths of the larger community
(Georgetown, National Center for Cultural Competence). This kind of engagement
represents a paradigm shift for many educators. The learning environment of the
school must be supportive of continuous teacher learning as a vehicle for improved

73
student achievement; as not all of the focus can be on student learning but the adults
must also be engaged in continuous learning of their own and of their colleagues
(NAESP, 2004-pg10) If the on-going learning and reflection of the adults ceases so
to does the learning of students.
Supervision and Monitoring of Instruction
The demands on our schools are great and are occurring from different
directions simultaneously; it is expected that meaningful, relevant school reform is
happening and that these transformation will ensures places of “excellence” for all
our students. This responsibility and call for school reform can be a daunting
challenge that must include many people and as such must be distributed between the
administrators, the teachers, the parents and our students. While this effort must be
one that involves all these stakeholders there is a heightened level of responsibility
and expectation placed on the teachers. This presents a massive challenge for our
educators and our school leaders in that this must include the education of our
teachers. (Clair, Adger, Short, & Millen, 1998).
In recent years and certainly with the authorization and implementation of
NCLB the teachers have been held more accountable for what they teach. While
content standards are not a completely new concept in California the level of
expectations that teachers are providing all students with a grade level standards
based instructional program is far greater.
This has forced not only our teachers but our educational system to approach
instruction differently. It “involves building new conceptions about instruction (e.g.,

74
teaching for understanding and using new forms of assessment) and new forms of
professionalism for teachers” (Fullan, 1996, pg. 7). This has shifted the paradigm of
instruction and required teachers and schools to engage in new learning and
instructional practices.
In 2003 Gilman and Gilman identified nine different areas that can be
obstacles to teachers effectively implementing a standards-based instructional
program for their students;
1) Limitations of curricular focus as only a few subject areas and few ways of
learning.
2) Interventions for students who do not meet the benchmark targets on
assessments are ineffective.
3) The ability for parents who have lost confidence in public education to
choose alternative educational settings.
4) The assessment results may reflect more of the students’ test-taking skills
than their knowledge level.
5) Facilitates “tracking’ of students into prescriptive programs as a result of
perceived ability.
6) Increased expectations can negatively impact the staff morale and fosters the
“us against them” relationship between teachers’ and administrators.
7) Assessment data that results from standardized testing increases negative
perceptions of schools.
8) Limited resources are allocated to facilitate testing

75
9) Expectations that vary and are conflicting between the stakeholders at each
level; schools, districts, states and national mandates
These present a challenge for the leader; she must acknowledge these as valid
concerns to be considered. However, it is crucial that the leader have the
relationships, the knowledge and the skill set to continue to move the school forward
and not let these issues be utilized as justifications for not keeping the focus on
student learning. These concerns are unique to each school and require that focused
attention and conversations are given to ensuring that teachers are developing
strategies that allow them to refocus and view these accountability issues as a means
to facilitating increased student learning for all students.
Data reflection and analysis as a tool
The goal of education is to educate our children; to increase their learning.
This should be the goal for all conversations, actions and practices in our education
system. As we look to our teachers and their instructional programs as the vehicle by
which this occurs it is important that we use information from student performance
as a tool for assessing our successes and our “deltas”.
Assessment data helps us to this; data allows us to understand where we are,
determine our goals and measures our progress (Johnson, 2004) towards improved
student learning. Unfortunately in our “high stakes testing” environment “we” want
to run from the data as it is used in a punitive nature as opposed to a tool for
progress.

76
Teachers often express that they are the victims in a system that holds them
accountable for student learning and achievement. This presents a reactive mode
which causes them to look for other people, students or adults to blame for lack of
progress. This is because they do not know what should do to improve the results
(Johnson, 2004).
According to Fink (2003) in Developing Principals as Instructional Leaders
the Principal is the leader and as such must make continuous learning a part of the
culture by ensuring that the teachers are exposed to and engaged in “specialized
professional development”. The instructional leader must demonstrate through action
an understanding of the pressures that our age of increased accountability and
standard-based instruction has had in the classroom; as such they must be committed
to creating and providing an environment that supports teachers in this effort. The
expectations of our teachers and our public education system to ensure that all our
students demonstrate adequate progress in their academic learning is quite high. This
“phenomenon” is relatively new as is the expectation that the instructional program
in each class room prepares students;
If all students are to achieve to high standards, teachers must be prepared to
work in new ways, from developing shared expectations for student
performance to expanding their repertoire of strategies and skills (Jamentz,
2002).

One of the most essential pieces to ensuring effective grade level standards-
based instruction in every classroom is to provide focused meaningful professional
development. Research finds that the focus and goal of professional development

77
with teachers is to improve the teaching and learning in the classroom (Brennan,
2001). Professional Development is critical as a tool for empowering schools to meet
and exceed the challenges that face them and the demands of school reform where
are schools are expected to places of excellence that supports the learning of all
students. This is especially true in our urban schools where teachers’ work with
students who often come with greater needs.
To maintain and facilitate the school as a community of learners the
instructional leader must provide opportunity for all adults must be exposed to,
engaged in and reflective about their own learning. To foster continuous learning all
stakeholders must be involved in the sharing and imparting of their knowledge and
perspective. The instructional leader is responsible for facilitating this structure.
Professional development should align with what are identified as appropriate
and effective instructional strategies: “Principles that describe effective teaching for
students in classrooms should not differ for adults in general and teachers in
particular” (Rueda, 1998). It is important that professional develop is targeted,
focused on the vision and goals, supporting critical reflection and purposeful
collaboration; providing opportunity for active engagement of the teachers and
leaders together (Clair & Adger, 2003). It must be aligned with what “good”
teaching looks like in the classroom. To facilitate professional development that
supports the learning of all students’ calls for certain conditions to be in place:
1) District and school policies must support coherent and integrated
professional development.

78
2) District and school leadership must make student, teacher, and
organizational learning a priority.
3) There must be sufficient time and resources for promising professional
development to take hold (Clair & Adger, 1999).
These indicators articulate the foundation upon which effective professional
development can be designed. If we want our teachers to provide an instructional
program that positively impacts student learning, having meaningful professional
development is essential. Effective teachers are “created” through participation in
professional development that is meaningful and relevant to their craft. This supports
them in improving their skills and thus student learning (Marzano, Pickering &
Pollock, 2001). The greatest impact on student learning and achievement is the
quality of the teacher and the instructional program (Ferguson, 1999). This fact
further solidifies the need for professional development that purposeful and relevant
the classroom.
Instructional Leader as a content expert
It has been a long held belief that leadership is a critical component for any
organization (Marzano, 2005), nowhere is this more evident than in the public high
school where the Principal of the school is viewed as key to the success of a school
and thus student achievement.
The instructional leader is looked at as the site “expert”. This requires that
that instructional leader be familiar with the district adopted curriculum that is used

79
in each content area, this is critical for the leader to effectively and with credibility
guide the instructional program (Fink & Resnick, 2003) The Principal must have
sufficient knowledge and familiarity with the curriculum that allows them to
recognize the alignment of the lesson with the standards (Jamentz, 2002). Jamentz
extends this to include the importance of the leader possessing a level of
understanding that allows them to serve as a coach for the teachers; providing
examples and explanations.
Equally important is the leaders’ willingness to demonstrate their openness to new
ideas, learning and the use of data as a tool to inform.

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CHAPTER THREE

RESEARCH METHODOLOGY

This chapter provides an overview of the research methodology utilized for
the study, as well as the rationale for the particular sample, the process of data
collection, and the method of data analysis and the instruments used for the study.
The purpose of this study is to examine the factors that positively influence the math
performance of students in urban school districts and at the secondary level.
Predicated on the objective of this study to construct an understanding of
how a school design, best practices and school leadership impact the math
achievement of a urban secondary school, a qualitative method and a systematic case
study was selected as the most appropriate and effective approach which “provides
depth, detail, and individual meaning” (Patton, 2002, p.16). The use of a qualitative
case study creates a conceptual framework that supports the researcher in building a
comprehensive picture, and allows the views and beliefs of the interviewees to be
shared in a natural environment which fosters more authentic responses (Creswell,
1998). As such the patterns, perspectives and themes that evolve from case studies
and the rich material for analysis is the essence of qualitative inquiry (Patton, 2002).)
These kinds of case studies are appropriate because they explore, “in depth a
program, an event, an activity, a process, or one or more individuals” (Stakes, 1995).
Furthermore, the nature of case studies is that they are, “bounded by time and

81
activity and researchers collect detailed information over a period of time” (Stakes,
1995).
To support the case study a mixed methods approach was utilized to collect
the data to support the study. This included the gathering of quantitative data to
support the descriptions found through the qualitative data collection in the study.
The qualitative approach provided data and information from interviews; and the
analysis of documents and artifacts of the school are cross referenced as a means of
gathering findings.
For the purposes of this case study one public high school based on an
established criteria was selected, information about the school and participants is
factual. But to maintain confidentiality and protect the anonymity of the participants
and the school, pseudonyms were used throughout the study. The instruments that
were developed for the study were created using current educational research with
the purpose of eliciting relevant responses that related to the research questions. To
support the analytical style which was utilized in the study, conceptual frameworks
were used so as to provide a context for the reader. The data was validated through
triangulation, which meant that analyses of all documents were cross referenced with
the interview and questionnaire results whenever possible.
To provide a conceptual framework and guide the research the following
research questions were used:
1. What was the pattern of math achievement for various students at the
school?

82
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement at the
school?
3. What change process did the school use to enhance the math program
and strategies to assist students in math?
4 To what extent was strong instructional leadership important in
improving A) the math programs/strategies and B) math
achievement among students?
4 How did instructional leaders respond to academic areas in which
they are not experts?
Sampling Criteria and Process
A purposeful sampling process was used in order to provide an opportunity to
conduct a thorough investigation and to explore more deeply the processes related to
the research questions of this study. The school selected for the study was chosen
for consistent with the following criteria:
1. Improvement in math achievement as evidenced by results on the California
Standards Test (CST) in Algebra I.
2. Student diversity as defined by a student population of at least 50percent
from traditionally ethnic minority groups.
3. Public high school in the Southern California region of at least 1200 students.
4. An Academic Performance Index Score of at Least 600
5. A State Wide Rank of 5 or higher

83
6. Leadership stability as defined by a Principal being at the school for at least
three years during the time the improvement was made.
The eleven members in the cohort group led by Dr. Marsh at the Rossier
School of Education at the University of Southern California, worked together to
develop the sampling criteria, and then to identify schools in southern California that
met those criteria. Qualifying high schools were identified using the following
process:
1. A data file was downloaded from the California Department of Education’s
web site using the DataQuest service.
2. The datafile was exported into Microsoft Excel to create a spreadsheet that
was used to analyze and filter the available data in an effort to identify
schools fitting the profile.
3. Knowing that the group would need to research improvement in CST in
Algebra in a later step and that many schools would not have demonstrated
improvement, the group set a goal of a sample size of no less than 100
schools in the southern California region.
4. Preliminary efforts to use more stringent requirements did not yield a
sufficient sample so adjustments had to be made. For example, when the
student enrollment parameter was set to 1500, the percentage of minority
students was set at 65 percent; the statewide rank set at 6 or higher, the
sample was limited to only 28 schools in southern California.

84
5. The second iteration included adjusting the parameters to an enrollment of no
less than 1200; a minority population of 50 percent or more and a statewide
rank of 5 or higher. The sample population then rose to a satisfactory level of
110 schools in the southern California region.
6. Students in the group were then assigned to research 10 schools each by
looking up and recording CST scores in Algebra I for the years 2003, 2004
and 2005 onto a common spreadsheet which one person in the group
compiled.
7. The group then assigned an absolute value to the improvements made in two
areas. First, decreasing the number of students scoring in the bottom two
performance bands; and second, increasing the number of students scoring in
the top two performance ands. These totals were added to indicate an overall
level of improvement. For example, if a school decreased the numbers of
students scoring in the bottom two performance bands by 3 percent and
increased the number of students scoring in the top two performance bands
by 5 percent, the school would have an overall improvement score of 8
percent.
8. The group then reviewed the scores of all schools in the sample and
eliminated any school that:
a. Evidenced a decrease in the number of students scoring in the top two
performance bands from 2003 - 2005.

85
b. Evidenced an increase in the number of students who scored in the
bottom two performance bands.
c. Failed to evidence an overall improvement score as calculated in the
example detailed in number 7 above.
9. Using this process resulted in 44 schools qualifying for the study.
10. A geographic map was then developed of the qualifying schools to help
cohort members select a school for their study based on proximity and other
relevant factors.
Selected School Profile
The high school that was selected for this study is Vista High School in the
Vista Unified School District. Vista High School is located in the San Gabriel Valley
in Los Angeles County in Southern California. The district is approximately 15 miles
southeast of the Los Angeles basin, 30 miles from the local mountains and
approximately 25 miles north of the beach. The community is a well established
community with many generations remaining; there is stability. The district is
comprised of mainly “working class” families with an average family income of
$40,850 and the average age of its residents is between 35 and 40 years old. Many
people chose to live here, due to the easy commute to work in Los Angeles, the city
also became known as an upwardly mobile community for Latinos who wanted to
leave the urban environment of Los Angeles.
The city and school district are relatively young, the city was established in
1948 and the school district in 1949 making it only 58 years old. Prior to this,

86
students living in Vista attended schools in a nearby district. To create the district
three connecting cities came together. As such the district draws from three cities but
the school is located in the largest city represented by the district. The population of
the city of Vista is approximately 65,000
The district demographics are correspondingly reflected in the school
enrollment demographics. The school reflects the diversity of the city with the
Hispanic enrollment representing 95.7 percent of the school population, 2.2 percent
Caucasian, .7 percent African American and 1.4 percent “other” respectively. More
than 26 percent of the students are English Learners (EL), with Spanish being the
dominant second language. Approximately 54 percent of the students at Vista High
School are eligible for the federal free or reduced lunch program. The school has
decreased its drop out rate each year for the past five years and currently the drop out
rate is 2.4 percent, one of the lowest in the San Gabriel Valley.
It is a district that supports students’ pre-k through the twelfth grade. The
district vision is, “We are committed to providing an enriched curriculum with high
expectations for all students which emphasizes the skills, concepts and processes
necessary for the technological and cultural challenges of the 21st century”. The
district is rich in history and works in a collaborative manner with the community to
support the students and the entire school district. The mission statement of the
district reflects this partnership as being important and valued, “The mission of the
Vista Unified School District, in partnership with the community, is to provide an
innovative and challenging learning environment that promotes excellence. We will

87
prepare students as life-long learners to succeed academically, intellectually,
socially, emotionally and culturally”. This mission is communicated throughout the
district and is held as a valuable message by everyone.
The Vista Unified School District is comprised of 12 elementary schools,
three middle schools, one traditional high school, one continuation school, one adult
education school and one children center. The total district enrollment is 6,287
Vista High School has an enrollment of 3,412 students and is the largest school in
the district, receiving all the students from the three middle schools.
Student Achievement
The motto for Vista High School is, “Quality Education Today for a Better
Tomorrow”. This is commitment to ensuring a quality education and is reflected in
there consistent growth on their API scores (Table 1), the school has increased there
API scores 189 points over the last six years with a baseline score of 484 and an API
score of 673 in 2005. In addition to this the school has met its AMO targets each
year since the start of the program, including all their sub groups.

Table 1: API Scores for Three Years

2003 2004 2005
621 640 673

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Participants
The administrative team at Vista High School is comprised of a Principal, three
Assistant Principals and three grade level Deans of Discipline. For this study, the
Principal and the Assistant Principal for Curriculum and Instruction participated in
the interviews. In addition to the administration the core subject instructional
managers (similar to department chairs), math teachers and other core subject area
teachers were interviewed or completed a questionnaire.
As a means of collecting data, structured interviews were facilitated by the
researcher. The researcher conducted interviews in three rounds of meetings with
each identified interviewee in an effort to gain in-depth information and
understanding. The interviews were conducted at the school site and were based
upon the Interview Guide (Appendices A and B) which has its foundation in
educational research. The study was conducted in a manner that provided for
triangulation of data from multiple sources. This is important when conducting
qualitative case studies as a means of addressing individual or cultural biases which
can influence the validity and reliability of the study. In addition to interviews and
questionnaires document analysis provide valuable information about the school and
the priorities of the school site. An example of a document analyzed was the master
schedule, this provided information on a number of sections, who taught what
classes and the average class size. This allowed for patterns to emerge within the
data, and also provided validations for perceptions that were presented in the
interviews and questionnaires.

89
The following individuals participated in the study and provide valuable
information as it related to the research questions being examined for this study.
Site Administrators. The school Principal, who participated in an interview,
has been the Principal of Vista High School for the past eleven (11) years. Prior to
this she was the Assistant Principal for Curriculum and Instruction for six (6) years
and the Assistant Principal of Business and Activities for four (4) at Vista High. The
Principal was very clear in communicating the vital role that the Assistant Principals
play in the facilitation of the school vision and the improved student achievement.
As such the Assistant Principal for Curriculum and Instruction was also interviewed
to gain additional information and to assess the degree of continuity between the
different administrators. The other Assistant Principals work in facilities, operational
and activity capacities and as such were not part of the Principal’s identified
instructional leadership team
Teacher Leaders. This group of participants consisted of teachers who
represented the four core areas of English, History, Math and Science as the
instructional managers for their respective department and leaders in the school.
This group also included the school site math coach and other teachers that are part
of the site leadership team. They were selected to participate in the study based on
their roles at the school providing instructional support for the math department and
leadership for the other core content areas. All of the department chairs are fully
credentialed in their content area (English, History, Math and Science) and have
been at Vista High for a minimum of four years. The math chair, Instructional

90
Manager has been teaching at Vista High School for five years and has been teaching
for a total of nine years; this is his first year as the Instructional Manager.
Math Teachers. All 24 math teachers participated; all of them completed the
survey and 20 of them were interviewed. The collective teaching experience of the
math department ranges from very new, with only one year of experience, to veteran
status for two teachers who have been at the school for the past 25 years. The
majority of the teachers have been with the school for five to seven years. The ethnic
make-up of the math department while diverse does not correspond with the
dominant Latino student representation. The department is comprised of three
African-American teachers, two Asian, seven Caucasian and three Latino. The math
department is split 60 percent female and 40 percent male teaching staff. Out of the
twenty-four teachers 16 of the teachers are fully credentialed in math and eight are in
programs working towards this objective and towards becoming Highly Qualified as
defined by NCLB.
Teachers. All core teachers, ninety-four (94) in total were given a
questionnaire to complete; this questionnaire was different from the one given to the
other participant groups. Ninety-one (91) of surveys were completed and returned to
the researcher of these seventy (70) were from non-math and twenty-four (24) from
the math teachers. The purpose of involving all teachers across the school was to
gain a broader perspective of the school and strategies, programs and policies that
have implemented over the past three years that the teachers perceive as having
positively influenced the math achievement of the students at Vista High School.

91

Instrumentation
The instrumentation was developed by an eleven member doctorial research
study team. All members of the team were doctorial students at the University of
Southern California, who participated in a seminar led by Dr. David Marsh,
Associate Dean of Academic Programs from the winter of 2005 through the summer
of 2006. The research team worked during the summer of 2006 to refine the
instruments prior to beginning the data collection process. A matrix was created to
delineate the relationship between research questions and the data collection
instruments. This tool ensured that each research questions was properly addressed.
Table 2 indicates the relationship between the various data collection instruments
used in the study and the research questions examined.
Table 2: Relationship of Data Collection Instruments to Research Questions
Research Question
Instrument 1 2 3 4 5
School Profile X X
Key Leader
Interview
X X X X
Math Teacher
Interview
X X X X
Math Teacher
Questionnaire
X X X X
Teacher
Questionnaire
X X X X

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Validity and Reliability
This study used multiple sources of data in an effort to minimize threats to
internal validity. This process of triangulation of data included interviews with key
informants, document analysis, teacher questionnaires as well as direct observation.
This process allowed for the researcher to follow-up on unanswered questions, vague
points, and validation of claims and questioning of multiple parties involved in the
educational effort at the school. In addition, participants reviewed their interview
notes to validate their contents. External validity is beyond the scope of the study
which used a single, case study methodology. While the findings in this study are
reasonable given the data collected, via a careful analysis, they are not generalizable
to other settings beyond the comfort level of the reader.
After the members of the cohort developed the chart depicted in Table 2 they
worked in small groups to develop the instruments. Through this process the
conceptual frameworks, which identified the themes associated with each of the
individual research questions, were developed. As a result of this effort four
frameworks were developed and were utilized to facilitate the processing of the
developing data collection instruments which included questions that were associated
with each of the instruments.
Framework for Research Question 1: School Profile of Student Achievement Data
Research question one was intended to identify patterns of math achievement
at the school and asked, “What was the pattern of math achievement for various

93
students at the school?” The school profile was developed as a framework for
research question one. It provided a template that allowed for the identification of
student math achievement and the organizational factors that may have contributed
to the improved math achievement. The master schedule, bell schedule and teacher
assignments were examples of indicators that were analyzed as a means of
identifying patterns and influential factors.
Framework for Research Question two: Effective Math Programs and School Design
Research question two asked “What policy initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math achievement
at the school? This question was designed to foster an understanding of what factors
contributed to the consistent increased math achievement at the school. For this
question two different frameworks were developed to assist with the analysis of the
research question responses. The first framework described effective school designs
utilizing Marsh and Codding’s model of school design and which basic elements are
reflected in Figure 1 (following page):

94
Figure 1 – Framework for Effective School Design

School
Design
Curriculum Learning
Activities
Challenge
Students to
Think
Students
Solve
Problems
School
Culture
Based on
Enhanced
Learning
Meaningful
Staff-Student
Interactions
Ongoing
Professional
Development
Collaborative
School -to-Career
Applications
Constructivist
Knowledg e
Based on
Student
Outcomes
Student Performance
Assessments
Capture
Conce ptual
Understanding
Capture
Problem
Solving
Cap ture
Communication
Skills

First the framework has a focus and emphasizes curriculum foundations
which are created around a student-centered approach and outcomes. Secondly
school cultures which directly relate to the effectiveness of the school design and are
those that have meaningful relationships between the students and the adults on
campus, improved and extended learning opportunities through professional
development that is on going and targeted. A “school within a school”, small design
is another element of Marsh’s and Codding’s design model, however for the
purposes of this study, this aspect of the design model was considered as a possible
factor contributing to a positive school culture and as such is included in this
framework as relating to “meaningful interactions” between students and staff.

95
Activities which contribute to the overall learning for the students, which for this
framework would be characterized as Learning Activities are those that challenge the
students to engage in and use higher order thinking skills, collaborate with others as
a means of problem solving, are also important aspects of this framework. Finally the
framework includes student performance assessments.
The second framework for math instruction addresses the elements of
effective math programs and is reflected in Figure 2.
Figure 2 – Effective Math Programs
Effective
Math
Programs
Classroom Practices

o Effective and
coherent lesson
design
o Promotes high
levels of student
engagement
o Makes use of
prior knowledge
o Cultural
relevance
Curriculum Design
• Student-centered
curriculum
• Driven by learner outcomes
• Emphasizes Conceptual
• Focuses on problem-
solving
• Incorporates current
learning theory
• Scope & Sequence is
supported by learning
theory
Standards Based Instruction
o Assessments
aligned to
standards
o Student
achievement data
drives instruction
and decision
o Common
performance
rubrics through
collaboration

96

The essential aspects included in this framework are: curriculum design,
standards based instruction and classroom practices; each of which relate to creating
a student centered curriculum that is guided by learner outcomes and ensuring that
students are gaining a conceptual understanding of content that facilitates the in-
depth mastery of computations and manipulations of mathematical symbols and
procedures as tools to support the learning of problem solving processes. Within the
standards-based instructional practices are the delineation assessments that are
aligned with grade level/subject content standards and result in data driven decision
making occurring at the site level to support student learning. Finally, classroom
pedagogy has influence on student learning. The importance of well developed
lessons that make connections and require students to draw from prior knowledge,
which is culturally relevant and as such, is prompting a higher level of student
engagement.
Framework for Research Question 3: Change Process
Research question 3 asked, “What change process did the school use to
enhance the math program and strategies to assist students in math”. The purpose of
this question was to develop an understanding of what processes were established
and implemented as a means of changing the school math performance. In 2004
Blasé and Blasé emphasized the fact that a significant characteristic of an effective
instructional leader is the ability to understand and embrace the inherent challenges
of change. The leader must have a well developed understanding of the different

97
aspects of the change process and how it differs from the individual and the
organizational points of view. The leader must have this knowledge and level of
understanding if they are to manage the change process.
In the book by Bolman and Deal, Reframing Organizations (2003) they
provide a very useful framework for understanding the different approaches or
“lenses” that leaders utilize, indicating that each leader has frames that are more
dominant within their individual leadership styles, but it is important for an effective
leader to have the capacity to move back and forth between the frames based on the
dynamics and needs of the situation. These frames provide a “guide” for
understanding the complexity of organizations that need to be utilized to modify
leadership style so as to effectively manage a continually evolving change process.
The individual aspects and characteristics of each frame are detailed in Table 3.

Table 3- Bolman and Deal’s Four Frames
Structural Human Resources Political Symbolic
Top Down
Hierarchies
Employees as
Partners & Family
Power Vision
Rules, Policies,
Procedures
People of the
Organization
Bargaining Belief and Faith
Specialized Tasks Productivity
through Group
Effort
Compete for
Limited Resources
Stories
Goals &
Objectives
Self-actualization Negotiations Culture

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Bolman and Deal thoroughly detail four different frames that allow the
change process of the organization to be viewed: (a) Structural, (b) Human
Resources, (c) Political and (d) Symbolic. These four frames were utilized as a
means to better understand the site’s efforts and ability to foster and develop
improved student achievement in math. These efforts were described as it relates to
the four different frames and practices.
The structural frame defined by Bolman and Deal is one that is focused on
providing order and structure in the approach to situations, as well as the potential
for change. It is a frame that places the emphasis on the roles of individuals, the rules
that guide the process and the policies, and the ultimate objectives of a situation or
organization. The individual leader who works within this frame is able to
effectively align the different aspects that contribute to meeting the goals and
objectives in the change process.
The inability of the leader to appropriately implement structures and position
people will have negative impact on the ability to facilitate change. This can
potentially impede the change process as individuals within the system become
embroiled in defining structures and positions and thus the efficiency by which goals
are met is diminished. To mitigate these potential obstacles the leader must use
effective and timely communication as a means of ensuring that there is a common
understanding of processes, roles and objectives as they relate to the change process.
The human resource frame might be considered the “people person” frame in
that this relates to the providing the positive connection between the people in

99
facilitating change. For change to occur the leader must have the capacity to move
people and works as the conduit that connects the individuals with the organization
and the goals and objectives for change. The ability of the leader in the organization
to merge these factors together creates a synergy that empowers the entire
organization thus enhancing the capacity to move forward. The overall climate of the
working environment is positive and as a result the organization gains momentum
over other organizations where this aspect is not working effectively.
In organizations where this aspect--the people and relationships--is not a
priority, the organizational climate can be come inefficient, caustic and apathetic to
the larger goals. Such a working dynamic can impede the change process and
progress as individuals and social beings are not having needs met and thus may not
develop the sense of ownership and commitment to the process and the larger
organization. A leader who has strong skills and understanding within this frame will
work to ensure that organizational systems continue to support and provide
opportunities for learning and engagement.
Organizations are comprised of people with different aspirations, visions,
goals and purpose and as such are by nature political entities. This is supported in the
work done by Bolman and Deal in that they state that organizations are by nature an
arena which has interplay of competing needs which are vying for the same, perhaps
limited, resources; these needs may be manifest in terms of time, money, materials or
power. As such they describe the political frame as one in which competition is

100
inherent within the organization; people are motivated by different needs which
foster the political aspects of the organization.
Our public schools reflect an environment in which the political aspect of the
education enterprise can be vast and all encompassing. The school leader must have
the capacity to work with the various constituencies all of which in one way or
another want to take from the limited resources to support their specific group’s
priority. These different groups might include the different bargaining units, parents
and community members who may not be directly connected to the district yet have
opinions on how resources should be utilized and distributed.
The leader’s capacity to navigate the different demands and opinions while
fostering alliances with the groups is necessary in keeping the change process
moving forward. If the leader is not able to “build bridges” between the various
groups--those who feel empowered and those who feel slighted in the struggle for
resources--the momentum for change can be derailed. The leader must be able to
recognize the signals and work to foster, “new arenas where issues can be
renegotiated and new coalitions formed” (Bolman and Deal, 2003).
The final frame defined by Bolman and Deal is the symbolic frame which
relates to the celebrations, rituals and the traditions in an organization or community.
The leader with an understanding of this, uses these to build and create connections
and meaning within the organization. The school leader is able to use traditions,
recognitions and honoring of the community members as a means of fostering the
community spirit and provide the “buy-in” for the direction and purpose of the

101
organization. The effective leader however must not over use such events, language
or celebrations as this can diminish the sense of authenticity and thus take positives
and turn them into objects for cynics to use as a means of undermining the change
process. The effective leader must know and have relationships with the community
and the stakeholders and use this as a means of creating meaning and purpose
through rituals and traditions.
Framework for Research Question 4: Instructional Leader
Research Question 4 asked, “To what extent was strong instructional
leadership important in improving A) the math programs/strategies and B) math
achievement among students? The purpose of this question was to understand what
the role of the instructional leader is in the improvement of math achievement and
what were the strategies utilized. Table 4 reflects the intellectual framework that
was utilized in the study as it supports and delineates concepts associated with
instructional leadership.
The role of the instructional school leader is demanding and diverse in terms
of the demands and expectations of what the leader is responsible for engaging in,
facilitating and the leadership they must provide in moving a school forward and
improving student learning. The Educational Testing Services (ETS) published, “A
Framework for School Leaders: Linking the ISLLC Standards to Practice” which
identified standards for what the instructional leader must demonstrate an
understanding for and knowledge of. (See Table on following page):

102
Table 4- Instructional Leadership
Instructional Leadership Framework
What an effective leader must have knowledge of…
Vision for
Learning
Supervision and
monitoring of
instruction
Community and
Political
Culture of
Teaching and
Learning
Data Driven
Decision Making
Analysis
1.0--Facilitates the
development,
articulation,
implementation,
and stewardship of
a vision of
learning that is
shared and
supported by the
school
community.

A. Developing
vision

B.
Communicating
the vision

C. Implement the
vision

D. Monitor and
evaluate the vision

E. Addresses
obstacles to vision
implementation
and realization

Observes and
monitors
instructional
program.
Provides
constructive
feedback in a
timely manner to
all teachers.
A. Classroom
observations on a
daily/weekly
basis.

B. Allocates
resources ensure
successful
teaching and
learning.
*time
*peer support
*materials
*professional
development

C. Supervision of
personnel

D. Hiring of
personnel that
supports the
learning goals and
vision of the
school
4.0--
Collaborates
with families
and community
members,
responds to
diverse
community
interests and
needs, and
mobilizes
community
resources.

A. Understands
the value of
diversity

B. Understands
communities
needs

C. Involves
community in
the school

D. Provides
opportunity for
community
involvement
2.0 Advocates,
nurtures, and
sustains a
school culture
and
instructional
program
A. Valuing of
students and
staff

B. Developing
and sustaining
the culture

C. Culture that
is inclusive of
and respectful
of diversity

D. Implements
practices for
culturally
relevant
teaching and
learning

E. Celebrates
students,
teachers and
staff
Uses data as a
tool for informing
instruction and
supporting
student learning

A. Utilizes
assessment data
to place students
appropriately

B. Formative
benchmark school
site assessments

C. Summative
standardized
assessment

D. Disaggregate
data by students,
classes and
cohorts

E. Use data to
guide and
improve teachers
instructional
program

F. Use data to
create master
schedule

G. Using data to
inform and
improve pacing
instructional
plans

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The instructional leader must be the “keeper of the vision” and must facilitate
the implementation the vision of the school and the larger district for student learning
through the daily activities of the school. As well the leader’s decisions and actions
taken at the school must reflect this understanding and appreciation of how they both
directly and indirectly impact student learning. To ensure the successful
implementation of the vision the leader must communicate with and engage all the
stakeholders who are on the site and to those who are part of the larger school
community. In doing so the leader must have the skills to navigate obstacles whether
it is individuals or systems that impede the schools capacity to move the vision
forward. This relates back to the frames as defined by Bolman and Deal in which the
leader must have an understanding of how best to engage the community in an effort
to implement the vision for all students.
The school leader is ultimately responsible for the instructional programs at
the school site and as such is responsible for monitoring and supervising the
instruction in the classroom. The instructional leader must develop relationships at
the site that provide for professional conversations regarding daily and weekly
observations in which the leader participates. As result of such observations the
leader must provide the resources, time and professional development opportunities
for the teachers.
To facilitate this learning environment the instructional leader must make the
creating a working environment that is inclusive, safe, nurturing and supportive of
staff and students a priority. The culture of the school is set by the leader of the

104
school and accomplishments should be acknowledged and celebrated by the
leadership and shared with the larger school community. This aspect of leadership
relates to the symbolic frame describe by Bolman and Deal which speaks to the
importance of celebrations, rituals and traditions in an effort to support and foster a
collaborative and collegial school culture.
In creating a learning community that engages all stakeholders the leader
must reach out to families and community members acknowledging their role in
supporting the vision and purpose of our public schools. In doing this the leader,
particularly in the urban setting, must embrace and respect the diversity of the
community and engage the strengths and perspective that different backgrounds,
experiences and cultures can bring to the school. The leader cannot work in isolation
of the larger community and must realize the political aspects of the leadership role
in our schools. To facilitate this, leaders must provide opportunities for the
community to be involved in the school and viewed as a resource to support the
school.
Finally, the instructional leader must understand the value of using data as a
tool for guiding and influencing the instructional program. The analysis of
assessment data and informational must be used to inform the instruction that is
developed and used to ensure that all students are learning. As the instructional
leader both formative and summative data should be utilized as tools to monitor
instruction, sustain improvement and to create such aspect of the school as the

105
master schedule which can be developed using data to determine appropriate
placement of students.
The role of the school leader is complicated and involves many different
aspects. In today’s educational setting the leader cannot be simply a manager but
rather must have the capacity to lead with passion and commitment for all students
and their learning. This framework defines essentials aspects of instructional
leadership: vision for learning; supervision and monitoring of instruction;
community and politics; culture of teaching and learning; and data driven decision
making are the focal themes in effective instructional leadership. The instructional
leaders whose primary focus is to guide the learning of students in their schools will
not only understand, but practice the behaviors which are associated with these five
themes.
Framework for Research Question 5: Assessment of Individual Leader’s expertise in
math and Leadership Strategies to Improve Student Achievement.
Research question five asked, “How did instructional leaders respond in
academic areas in which they were not experts?”
The goal of this question was to understand the impact that the Instructional
Leaders expertise or lack of, had in their ability to support the teachers and the
instructional math program. This framework was developed to address this question
of expertise and was divided into two distinct components predicated on the two
different parts of the research question. First, an assessment tool, flow chart, was
created to allow the investigator to ascertain the level of expertise the instructional

106
leader, in this case, the Principal, had in math. The criteria for the tool was developed
based on the definition of a “highly qualified teacher” (HQT) under the NCLB
legislation guidelines. This was used specifically because these guidelines are
intended to determine the instructor’s level of subject matter competencies in the
content area in which they teach. The assessment utilized is detailed in Figure 3. The
response to the prompts led to the instructional leader being assigned a high, medium
or low level of expertise.
Figure 3: Assessment of Principal’s Expertise in Math

Step 1
Is the Principal
HQT
Compliant?
Yes No
High
Expertise
Does the Principal
have a credential or
major in math?
Yes No
Medium
Expertise

tise
Has Principal minored in
or taught math?
No
Step 3
Step 2
Yes
Medium Expertise
Low
Expertise

107
Secondly, a range chart of strategies that are based on school literature and
research on school improvement was developed to assist the investigator in
identifying categories around efforts that were implemented to improve student math
achievement. The second part of this framework is detailed in Table 5.
Table 5 – Strategies to Overcome a Lack of Subject Matter Competency

Item Strategy Approach/Source
1
Delegate Leadership to Assistant
with greater expertise
Delegation Approach
(Northouse, 2001 p. 58)
2 Empower Department Chair Teacher Leadership (Gabriel, 2005)
3 Bring in Outside Expertise
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
4
Emphasize inquiry and problem
solving
Action Research
(Stringer 1999)
5 Emphasize quality instruction
Instructional Strategies
(Marzano, 2003 pp. 78-87)
6
Emphasize strategies to engage
students in the learning process
Student Engagement
(Marzano, 2003 pp. 149-150)
7
Emphasize articulation with
feeder schools
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
8 Emphasize raised expectations
Challenging Goals and Effective
Feedback (Marzano, 2003 pp. 35-46)
9
Emphasize Strategic Teacher
Assignments
HR Frame
(Bolman & Deal, 2003)
10
Emphasize Revised Course Scope
and Sequence and/ or Curriculum
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
11
Emphasize Interventions for lower
performing students
Supplemental Services
(NCLB, 2001)
12
Emphasize Professional
Development
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)

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Data Collection Instruments
For this study data was collected utilizing five data collection instruments:
School Profile, Key Leader Interview Guide, Teacher Interview Guide, Math
Teacher Questionnaire, and General Teacher Questionnaire. The questionnaire was
utilized with teachers and the interview guides were utilized with Key Leaders and
the Math teachers. Each of the instruments was created collaboratively between the
doctorial student team during the summer of 2006. They were developed to ensure
alignment with the individual frameworks.
Instrument 1- School Profile
This instrument was developed to provide a “picture” of the different aspects
and informational characteristics that make up the schools that were studied. The
secondary reform cohort under the leadership of Dr. David March worked
collaboratively to determine and identify elements about the school that would
provide a comprehensive picture of the individual schools. The data collected was
then organized into three primary areas; demographics, student academic
performance and general school information; the majority of this data was collected
from the California Department of Education’s website.
The demographic data collected for the school profile reflected both the
student and teacher information. The information gathered regarding the students
included ethnicity, free and reduced lunch status, English Learner (EL) status, and
student enrollment patterns. This data provided the investigator with insight on
potential challenges the school may have, kinds of programs necessary to meet the

109
needs of the students and student learning. The demographic information gathered on
the teachers included: the total number of teachers, credentials, NCLB Highly
qualified status, and years in teaching. This information provided information about
potential strengths and challenges for the school and the impact on the instructional
program. Like the information gathered about the student population this information
about the teacher provided perspective and possible insight into the school.
The student performance data was an important piece of the school profile as
it provided insight on patterns of student achievement at the school site; this data
relates directly to one of the research questions being examined. Among the items
collected were the Academic Performance Index (API) scores at the site for the most
recent three years; the passing rates for the CAHSEE; standardized test score data;
and additional assessment data to include benchmark, formative and summative. The
examination of this data provides perspective and insight on the areas of strength and
challenges areas that might warrant further study.
Instrument 2: Key Leader Interview Guide
This instrument was developed to facilitate the collection of data that is
relevant to research questions numbers 2 through 5. The key leaders were
interviewed as a means of ascertaining their perceptions and the factors they believe
were responsible for the improvement in the math performance of their students.
This instrument was developed collectively by the cohort group which ensured the
alignment between research questions and the conceptual frameworks. The interview
guide assumed an interview not to exceed 40 minutes and included two to four

110
questions per resource question for a total of 16 open-ended questions in an effort to
allow the interviewer the latitude to explore emergent themes and issue that may
have been present during the interview. This semi-structured interview process was
based on the protocol of Creswell’s (1998). This Key Leader Interview guide was
incorporated into this study as Appendix A.
Instrument 3: Teacher Interview Guide
This instrument was developed to facilitate the collection of data that is
relevant to research questions numbers 2 through 5. Consistent with the process and
protocol with key leaders, the teachers were interviewed with the objective of
identifying what their perceptions were regarding factors that influenced and
impacted the improvement of math achievement. This instrument was developed
collectively by the cohort group which ensured the alignment between research
questions and the conceptual frameworks. The interview guide assumed an interview
not to exceed 30 minutes and included two to three questions pertaining to each
resource question with a total of 16 open-ended questions in an effort to allow the
interviewer the latitude to explore emergent themes and issues that may have been
present during the interview. This semi-structured interview process was based on
the protocol of Creswell’s (1998). This Key Leader Interview guide was
incorporated into this study as Appendix B.
Instrument 4: Math Teacher Questionnaire
This instrument was developed to facilitate the collection of data that is
relevant to research questions numbers 2 through 5. As with the interviews, the

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teachers were asked questions as a means of ascertaining their perceptions and the
factors they believe were responsible for the improvement in the math performance
of their students. This instrument was developed collectively by the cohort group
which ensured the alignment between research questions and the conceptual
frameworks. The teacher questionnaire utilized a five point Likert scale that had a
range from Strongly Agree to Strongly Disagree. The questionnaire was developed
with the objective that it would not take in excess of 30 minutes to complete, there
were 50 items on this questionnaire. It was understood that the investigator would be
required to return more than once to collect the questionnaires as completed and
submitted. The Math Teacher questionnaire guide was incorporated into this study as
Appendix C.
Instrument 5: General Teacher Questionnaire
This General Teacher Questionnaire was created to include 30 items that provided
the teachers who taught in subjects other than math to participate in the study and to
share their ideas and perceptions as to factors contributing to the improved math
achievement. This instrument is attached as Appendix D.
Data Collection
This study collected data over a four month period from September 2006
through December 2006. The data was collected in three distinct rounds to allow for
a more thorough comparison of data sets and documents. All participants were
afforded the opportunity to review notes compiled form their respective interviews to
ensure the notes accurately reflected their words and the spirit of their intended

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message. In addition, this multiple round strategy allowed for the follow up
investigation in later rounds for pursuing emergent themes and issues that arose in
earlier rounds. The reliability of the triangulated data using these methods was
thereby increased.
A key step in the process of data collection was obtaining the approval of the
Institutional Review Board (IRB) prior to the collection of any data. The IRB
process is intended to protect the protection of the participants through a close
examination of the methods involved in the study. This examination required the
submission of several documents to the IRB by the researcher. The main document
submitted was the Request of Claim of Exemption for Non-Medical Research, in
which, the researcher described the purpose of the study, the population to be
studied, and the methodology used in the study. For this particular study, Dr. David
Marsh submitted one IRB proposal for the series of related studies being done by
members of the cohort described earlier. This process limited flexibility in some
respects, yet increased consistency amongst the researcher by requiring the same
data collection instruments and methodologies.
Once the IRB gave final approval for the study to begin, the cohort group
returned to their list of qualified schools and approached the schools selected for
study. Site principals were contacted and informed about the details of the study and
once the site gave approval, data collection started soon thereafter. Participants were
informed of the need to give voluntary consent and informed that they could end

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their participation at any time. The questionnaire was voluntary as well and the
researcher made more than one effort to collect those that were submitted.
During the first round of data collection the objective was to foster a broad
overview of the school. As such, the first interview conducted was with the site
principal and key school leaders. These interviews were designed to provide an
opportunity to learn more about key leaders on campus, instructional programs in
general, the math program specifically, and school-wide cultural factors affecting the
school’s academic progress. The researcher spent time on campus to get a feel for
life at the school. Key documents such as the school’s master schedule and school
site plan were also gathered during this first round visit. The Teacher Questionnaire
was also distributed during this round with the expectation that to maximize the
number of questionnaires returned it would require a sustained effort over time and
allow for multiple efforts. This was not my experience, all 94 surveys distributed to
the four core department teachers were returned the following week when I return for
my second round of interviews.
The second round of data collection served as an opportunity to follow up on
aspects of the school’s culture and instructional program learned after analyzing the
data collected during the first round. During this second round math teachers and a
few remaining key leaders were interviewed. In addition, completed teacher
questionnaires were collected and the data from these questionnaires was compiled
into a database of information.

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The third and final round of interviews was conducted with the remaining
math teachers and a second discussion was conducted with the Principal and
Assistant Principal of Curriculum and Instruction to follow-up on items gleaned from
the rounds of data collection to that point and to conduct brief interviews consisting
of follow up questions based on questions arising from data collected in earlier
efforts. This process of “filling in the gaps” allowed the researcher to effectively
eliminate guesswork and tie up all the loose ends. Subsequent communication
occurred through phone conversation and the use of email exchanges.

Data Analysis
The purpose of the study was to examine the factors that positively
influenced the math performance of students in urban school districts at the
secondary level. The study explored the elements of the school design, the strategies
and best practices used within the classroom and the role of the school leader in
shaping and directing the school improvement effort. Five research questions were
developed by a cohort to assist in framing and completing the study. Additionally
data collection instruments that were aligned with the research questions were
developed with the goal of ensuring efficiency and reliability of the findings.
Interview notes were taken and transcribed and were provided to the
participants for review. Following this verification, an effort was made by the
researcher to identify relevant points made during the interview and to make
connections with the appropriate conceptual framework. Copies of the interview note

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transcripts were made as necessitated by the cross filing onto the thematic files
indexed by the relevant points of the framework. This process assisted in the
retrieval of data and the identification of themes that emerged from different
participants.
A spreadsheet was compiled in which similar thematic concepts would be
sorted and grouped by research question and data collection instrument in order to
help in the identification of patterns in the data and in establishing the relative
frequency of a given response.

Conclusion
The purpose of this chapter was to describe the methodologies used in this
study. This included a detailed description of the sampling criteria, the data
collection instruments, data collection process and data analysis methods. The
procedures used for this study were collectively developed by the students in the
cohort led by Dr. David Marsh and were approved by the IRB of the University of
Southern California. The concepts and methodologies were reviewed by and
received the approval of the school principal at Vista High School. Data collection
was primarily comprised of teacher and key leader interviews and a teacher
questionnaire. Document analysis was performed and direct observations were made
to triangulate data whenever possible. The findings presented in the next chapter are
based on a thorough analysis of the data collected and will be expressed in terms of
the research questions that have guided this study.

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CHAPTER FOUR

FINDINGS, ANALYSIS AND DISCUSSION

Introduction

The research in the field consistently finds that our greatest challenges in
California public schools resides in our urban schools which are often defined by
high poverty, high numbers of minority students and low performance as measured
by our state standardized assessments (Betts, Rueben, & Danenberg, 2000). Given
these findings, coupled with the increased state and federal accountability measures
and public interest in our schools, this study examines how one urban high school,
Vista High School, has met these challenges in the area of mathematics by
consistently improving their performance in the content area of mathematics.
Specifically, the study examines the relationships between school design, the math
program and instructional leadership. This was completed through the review and
analysis of policy initiatives, school based programs and the role of leadership;
specifically the impact when the instructional leadership lacks content knowledge
and/or mathematical pedagogy, expertise, and how the influence and interplay of
these three critical components supported and facilitated the improved math
achievement”.
Using these indicators this chapter discusses how they provided answers to
the five research questions. As a means of framing the conversation the research
questions were supported by four conceptual frameworks for research questions two

117
through five and the following four data collection instruments: Key Leader
Interview Guide, Teacher Interview Guide, Math Teacher Questionnaire and Non-
Math Teacher Questionnaire (Appendices A-D). Utilizing the frameworks and
instruments as tools to understanding the means by which the school has attained
consistent academic growth in math the research questions will be utilized to frame
and establish an understanding. To triangulate the findings the interviews,
questionnaires and school source data were used as validating and answering the
questions.
The first part of this chapter will describe and frame the academic
achievement patterns of the students at Vista High School in response to the first
research question: What was the pattern of math achievement for various students at
the school? The second part of this chapter discusses the findings regarding
procedures and policies that have been established and implemented to effectively
improve student achievement in math, responding to research question number two:
What policy initiatives including curriculum, instruction and related conditions seem
to be related to improved math achievement at the school? The third section in this
chapter will discuss the efforts that were implemented so as to have positive impact
on student achievement in math, answering the third research question: What change
process did the school use to enhance the math program and strategies to assist
students in math? The next section will discuss and analyze the impact of strong
instructional leadership, the perception on and how it is defined by the site teachers
providing a answer to the fourth research question: To what extent was strong

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instructional leadership important in improving A) the math programs/strategies and
B) math achievement among students? The fifth section will be respond to the
findings as they relate to answering the fifth research question: How did instructional
leaders respond to academic areas in which they are not experts? The discussion will
focus on whether the academic background and knowledge in math played out at the
school site and the subsequent impact. Finally the chapter will close with an analysis
and discussion of the findings and what they mean and how they are connected with
the research on the role of school design, the math program and the role of the
instructional leader.

Research Question #1: What was the pattern of math achievement for various
students at the school?
To respond to this question it was necessary to conduct a review and analysis
on the academic performance of Vista High School over the past three years utilizing
both qualitative and quantitative data. The California Standards Test (CST) was used
as the primary indicator of academic performance. To support and provide a broader
picture of the pattern of student academic achievement other indicators were
analyzed these included: the passing rate of the California High School Exit Exam
(CAHSEE); the percentage of students taking and passing College Board Advanced
Placement (AP)

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California Standards Test (CST):
Vista High School has demonstrated consistent growth since 1999 on the
state assessment, California Standards Test (CST) and prior to this becoming the
state assessment, Scholastic Achievement Test (SAT9). The teachers and leadership
attribute the greatest growth during the years 2002 and 2005 to the change in the
master schedule and the implementation of the Project ALPHA math professional
growth model that was developed by the math coach. While Vista High has had
improved their math performance, specifically Algebra as indicated by an increase in
students scoring proficient or above on the CST, the school remains below the state
average (Table 6).
Table 6- California Standards Test (CST) - Percentage of Students at Proficient of
Above
2002 2003 2004 2005
Ca State Average 35 21 18 19
Vista High Average 11 11 9 13

The growth on the CST demonstrates a positive trend, even if the progress
has been incremental. The scores of the largest group of students, Latino, who
comprises over 95 percent of the student population at Vista High School mirrors the
schools scores for students performing at or above the proficient level, 13 percent.
The next largest ethnic subgroup which only constitutes slightly over 2 percent of the
school population is white students who also scored at the 13 percent proficient or
above. This is consistent with the only other “significant” sub-group of students,

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socio-economically disadvantaged which represent 54 percent of the students on the
campus, 13 percent of this group is scoring at proficient or above in math as well.
California High School Exit Exam (CAHSEE)
According to the administration at Vista High School the performance on the
California High School Exit Exam has either met or exceeded the state average since
it was first administered in 2001 which would indicate they had a passing rate higher
than 89.3 percent. They reported that only four students did not pass the CAHSEE in
the 2006 graduating class at Vista High. The researcher accessed the DataQuest
website as a means of triangulating the information and this data reflects a different
passing rate of students Vista High (Table 7). This information garnered from
DataQuest which is a website affiliated with the California Department of Education
reflects a passing rate that would indicate that there is a substantial number of
students not passing the Math CAHSEE by the end of their 12
th
grade year.
Table 7- California High School Exit Exam (CAHSEE) Percentage Passing
Math
2003 35
2004 57
2005 43
2006 61

While the overall school passing rate appears much lower than the state average 73
percent of 10
th
grade students who took the CAHSEE for the first time during the
2005-2006 school year passed all sections, this is consistent with the state average of

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73 percent. This increase number of 10
th
grade students passing the CAHSEE gives
the administration encouragement that the overall performance will improve.
The state average on overall passing rate also illustrates an ever present
achievement gap between different ethnic groups of students. The same patterns of
passing are reflected in the performance data for the CASHEE as found in other state
assessments. The white students are outperforming all other groups of students with
a 96.5 percent passing rate. Asian students had a passing rate of 94.6 percent, Latino
82.5 percent and our African American students with the lowest passing rate of 81.1
percent. This poor performance is also represented by the economically
disadvantaged students which is above both Latino and African American students
by an insignificant margin, 82.7 percent (California Schools Boards Association,
2006). While these findings on a state level are discouraging and further highlight
the discrepancy of academic performance and a consistent achievement gap, Vista
High Schools majority group, Latinos did outperform both the state level for Latino
students and all students with a passing rate of 9 percent for the 2005-2006 school
year.
Advanced Placement (AP) Courses
The Advanced Placement (AP) program is based in both the United States
and Canada. It provides opportunities for high school students to enroll in courses,
most often in the 11
th
and 12
th
grade, that are quite rigorous. The courses each have
an exam administered by the College Board in May that allows the opportunity for
students to earn college credit while in high school. The AP exam is scored on a 1-5

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scale. College and Universities recognize these exams as an indication of a student’s
academic commitment and as such most will give some level of credit for a score of
three(3) or higher on these exams (College Board website). The College Board
which is a non-profit organization has organized and led this effort since 1955. The
College Board works to support teachers, who teach AP courses, assist in the
monitoring of the rigor, content and over all instructional program design. They
work with the colleges and the universities in developing their policies as they relate
to AP grades and credit. They are also responsible for the administering of the exams
and provide workshops and opportunities for students.
The enrollment patterns for Advance Placement (AP) courses have increased
at Vista High School, however the overall number of course offerings is quite low. In
math there are currently two course sections, one each in Calculus and one in
Statistics. The Calculus course has been offered for a number of years while the
Statistics course was first offered beginning in the 2004-2005 school year. For the
2006 school year 71 percent of the students in the Calculus course that took the AP
exam passed with a score of three (3) or higher on a scale of one to five. Colleges
and Universities have different cutoff scores for students receiving college credit,
some schools will give credit for a score of three (3) while others will only give
credit for scores of four (4) or five (5).
In 2006 Vista High had 297 students take one or more AP exams with a total
of 492 AP exams taken. The number of tests taken indicates an increase of almost
50pecent since 2002 when 238 AP exams were taken at Vista High. While there has

123
been a significant increase in the number of AP exams taken at Vista High the 297
individual students in 2006 who took an AP exam only represents 19 pecent of the
students in the 11
th
and 12
th
grade at Vista High. This is lower than the state average
of students taking one or more AP exams. During the 2005-06 school year 355,309
11
th
and 12
th
grade students across California took one or more AP exams, this
represents 46pecent of the 11
th
and 12
th
grade students state wide.
Other content areas at Vista High have improved in the percentage of
students earning a passing score of three (3) or higher on the subject specific AP
tests. The European History AP exam was the most popular with students, with 74
students taking the exam in 2006. However, this exam had only 24pecent of the
students scoring a three (3) or higher. Although fewer numbers of students took the
English AP exam—49—the passing rate was very close to that of the European
History exam at 24 percent. The Biology AP exam in 2005-2006 was taken by 64
students but again only 21pecent of those students passed with a three (3) or higher
score. The lowest performance on an exam, in terms of the number of students
passing it during the 2005-2006 school year was in Statistics with only 19 pecent of
the 37 students passing.
The pattern at Vista High School of consistently improved math achievement
in Algebra has been a result of deliberate decisions to support student learning for all
the students. The school leadership and the math department leaders have responded
to the critical need for students to increase their levels of achievement in an effort to
ensure that the students at Vista High are sufficiently prepared to meet the demands

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of passing the California High School Exit Exam (CAHSEE) for graduation and to
ensure that all students meet at the minimum graduation requirement of passing
Algebra. This has been a sustained effort for the Vista High math department for the
past five to six years when the school first began making both systemic and
instructional changes to meet increasing academic expectations.

Research Question #2: What policy initiatives as well curriculum, instruction and
related conditions seem to be related to improved math achievement at the school
site?
To answer this research question multiple resources were accessed and
analyzed as a means of triangulating the findings which provided a broad
understanding of the progress and that which it was predicated upon. Two different
conceptual frameworks were utilized for this question, Marsh and Coddings’
Effective School Design (1998) and a Effective Math Programs conceptual
framework which was developed based on findings from research conducted by a
variety of researchers (Stigler, 1999; Ball 1998; Franke and Fennema, 2001) and
research to include data from TIMSS. In addition the following instruments were
used to facilitate the data collection: Leadership Interview Guide, Teacher Interview
Guide, Math Teacher Questionnaire, Non-Math Teacher Questionnaire and the
review of school provided documents. These tools were utilized as a means of
responding to the various aspects of research question two.

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Policies
No Child Left Behind
The leadership and teachers at Vista High School indicated different
perspectives on the influence of NCLB (2001) as a policy impacting the school
practices and the improved achievement in math. The leadership at Vista High
School indicated that the legislation of NCLB has provided an increased sense of
accountability and assisted in moving forward the conversation and subsequent
school level instructional decisions. One aspect that was specifically indicated by the
leadership responses was the greater use of data as a tool for understanding the
strength and challenges of the students understanding and an impetus for improving
the instruction in the classroom. To convey this point one leader stated, “ …the use
of data has helped to level the learning community in terms of the willingness to
change paradigms…moving those teachers who are more “stuck” in how they have
always done things to using the data, so NCLB has assisted with this effort on a
school wide level”. This sentiment was reiterated by other leaders indicating that
NCLB has “increased pressure” and that there is a greater sense of accountability to
the federal level of education and not just California. As it related specifically to
instruction one leadership team member stated that NCLB has increased
accountability and has “driven the curriculum to better places; toward more effective
instruction.” Another leader who is part of the leadership team but not an
administrator had the strongest feelings in terms of how NCLB has served as a
“lever”. Leader D stated, “NCLB has helped with implementing the professional

126
development activities…we can design professional development that is focused on
improving math achievement…and since people are very focused on meeting the
Average Yearly Progress (AYP) targets identified as part of NCLB it helps”.
These sentiments were not has strong when teachers responded to questions
relating to the role or impact of NCLB as a policy on the school. The responses to
the questions were an average score of 3.04 for the math teachers and a 2.96 score
for non-math teachers (on a 1.0 -5.0 likert scale) both of which are “neutral” or
slightly lower The math questionnaire had three questions; 1, 10 and 12 which
sought a response relating to NCLB and the non-math teacher questionnaire only had
question number one. During the interviews with the math teachers they did not on
their own offer NCLB as a policy that was impacting the instructional program and
decisions being made at the site level. When prompted specifically about NCLB their
thoughts on how NCLB has or has not had influence at the site level no teacher
identified a direct correlation or relation between guidelines as they understand them
in NCLB that had affected school instruction. The connection made with NCLB by
the teachers was as it related to them in terms of “meeting all the requirement for
credentialing”. One teacher who had been teaching at the site for the past seven
years said that they thought there was a greater focus on standardized test results and
that this may be the impetus for using student assessment data to influence the
department discussions and instructional decisions.
The school has also made efforts to increase the number of Highly Qualified
Teachers (HQT) as defined in the NCLB legislation. Utilizing the support of federal

127
funding, Title II which in part are intended to support teachers in becoming HQT
they have been successful in reducing the number of teachers who are not HQT.
Currently out of 24 math teachers only eight (8) are not HQT and only 75 of the
overall teaching staff that are required to be HQT are not, this represents 80 percent
of the total teaching staff. This has improved each year through the schools effort to
hire HQT teachers and by providing opportunities and support for teachers in their
effort towards HQT. However, while the number of non-HQ teachers has decreased,
Vista High and the larger school district are facing rapidly approaching deadlines
that require that all teachers be HQT by the end of the year. This is particularly
challenging for Vista High in that they have had a consistent pattern of teacher
turnover through either teacher choice or teachers who are released from their
position. During this school year, 2006-2007 three math teachers have received
notification that they are not being asked back for the 2007-2008 school year and in
total 10 teachers have been released; this does not include teachers who may leave
for personal reasons. This presents challenges for the school, specifically in math as
many districts are in need for highly qualified math teachers and as such the teachers
are provided more options.
Graduation Requirements
The policies regarding graduation, both local and state have had significant
influence on the focus and vision of the math program at Vista High School. The
graduation requirements have become more stringent over the past few years. The
California standard for 8
th
grade math is Algebra which places greater responsibility

128
on the schools to ensure that students are prepared in Algebra and can successfully
pass Algebra. While Algebra is the 8
th
grade standard many students have not yet
passed this course by the end of 8
th
grade are enrolling in this course for the 9
th

grade. This coupled with the CAHSEE requirement for high school graduation has
resulted in school districts making Algebra and passing the CAHSEE a primary
focus. Like many districts in California Vista Unified requires that all students must
pass three years of high school math, one of which must be Algebra and pass the
CAHSEE as part of fulfilling graduation requirements. These two policies were
identified on the questionnaires as the most significant factor for non-math teachers
in decisions made regarding improving student achievement overall.
Question number two (2) on both the math and non-math teachers’
questionnaires spoke specifically to the policy requirement of the CAHSEE as
having significant influence on the focus for improved student achievement. On the
non-math questionnaire the response was 4.2, which was the highest response to any
question on this survey. This score on the 1-5 scale indicated a “strongly agree”. For
the math teachers, while they responded in the affirmative regarding the impact of
the CAHSEE policy on the focus for improved student achievement, their response
was slightly less at 3.8 which would indicate “agree somewhat.” This focus is
reflected in the site level decisions that have been made relative to providing
instructional support to students in preparation for passing the CAHSEE and
successful completion of Algebra.

129
Vista High has two very specific instructional structures in place that are
designed to provide additional support for students who have not been successful in
passing the CAHSEE. Within the “regular” school day 11
th
and 12
th
grade students
that have not passed the CAHSEE are enrolled in an additional support class, in
either math or English; they must take “CAHSEE Math” in lieu of an elective. This
provides additional time on task and is a relatively small class that allows for the
teacher to work more closely with the students. As one leader put it, “…we teach to
the weaknesses of the students in the class. The teachers analyze the data of the
students and teach directly to what the greatest need are that are in that class”.
Another leader spoke to the CAHSEE classes as providing “target assistance”. The
administration has created this in the master schedule as a means of providing
additional assistance within the school day. In addition to this, for students in the
12
th
grade who do not pass the CAHSEE by the end of the first semester are
“required” to enroll in an after-school 40 hour tutorial program. This provides the
students with a very small student to teacher ratio which allows the students to
receive even greater attention and support in their greatest areas of need. The manner
by which they can “require” this is that students who have only the CAHSEE to pass
in order to meet all the graduation requirements can walk in the graduation ceremony
if they complete the 40 hours of tutoring. Students who still do not pass the
CAHSEE following this have the summer to continue receiving support and take the
test again. Students who do participate in the graduation ceremony but have not
passed the CAHSEE do not receive any certificate or diploma. However, the

130
opportunity to participate with their peers is motivation to participate in the 40 hours.
In speaking with the leadership about this, it has proven a great incentive to focus the
students.
The impact of the requirement of Algebra for graduation has influenced the
math program and the organization of courses. The biggest increase in math course
offerings and enrollment has been in Algebra, which makes it the most frequently
offered math course at Vista High. There has been a decrease in the number of Math
A (pre-algebra) courses offered. During the 2
nd
trimester out of the 71 sections of
math offered 42 of the courses were one of the three different sections, A, B or C of
first year Algebra. Not only has the number of sections increased, the Algebra course
is also organized into three trimesters; the students take this course over the course of
the entire year. This is not consistent with the organization of other classes that are
offered over the more traditional timeframe of two semesters. This has increased the
success rate of students, given that they have more time with the material. In addition
to this, students in 10
th
grade and higher who do not pass successfully in one
trimester will repeat this trimester immediately, which is possible due to the
flexibility of the master schedule and one reason why teachers often have different
courses and students from one trimester to the next. Each of these systems or
structures have been specifically created and designed in response to graduation
policies and Vista High’s effort to ensure that students have multiple opportunities to
meet the graduation requirements.

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School Design
Master Schedule Design
The organization and structure of the school day was identified by the school
leadership as a critical component and factor that needed to be reorganized to support
and improve student learning and achievement. Following a three year study
conducted by the school in which they looked at different models utilized by high
schools across the country they made decisions to change the way the school flowed.
At the completion of the three year study 85pecent of the teachers indicated they
were supportive of making the changes in their day and year from the traditional
model which had been in place since the opening of the school.
As a means of implementing this the student day and the year were
reorganized, moving away from the traditional 55 minute 1-6 period school day into
a 88 minute four period day with students having math and English everyday and the
teacher planning period was extended to 88 minutes as well which provided
additional time for collaborative work with colleagues. The school year was
redesigned to move away from the traditional model of two semesters, 90 days each
to a trimester model of 60 days each, both systems totaling 180 instructional days.
Based on this the administration and the math teachers postulated that the
frequency of instruction coupled with increased time for instruction would have
positive impact on student learning as well as the overall school campus discipline.
They identified the advantages for both students and teachers to include: reducing
the daily student teacher ratios and students would interact with four teachers and

132
peer groups in a given day; opportunity for teachers to provided increased
opportunities for student learning through the use of different instructional strategies
in a given period thus improving the potential for strengthening the curriculum; more
in-depth learning and less percentage of instructional time in a given class dedicated
to “administrivia”.
The change in the structure of the school year from the traditional two
semesters to the trimester which was organized into three 60 day units was
influenced how students are placed in specific math courses and has impacted the
instructional assignments of the teachers perhaps more than anything else. Students
are moved to subsequent math class based on their performance. This is most strictly
enforced for the 9
th
grade students in Algebra I (Math Course I). A student in the 9
th

grade must earn a “C” or higher before they can move forward in the sequence, they
do not wait until summer to retake this course which is the more common schedule
for high school predicated on master schedule limitations. The class assignment is
decided based on the student’s grades and the benchmark assessments taken at the
end of the trimester.
Vista High School’s “fluid” master schedule was organized based on the
academic needs of the students not the teachers or the master schedule; the master
schedule and what teachers taught changes from one trimester to the next. This is
unique and has been a shift for the teachers in that they do not know what they will
teach from trimester to trimester. Most of the teachers interviewed had completely
different teaching assignments from trimester one to the second trimester and do not

133
know what they are teaching until one or two days prior. The teachers did convey to
the researcher that having such short notice and more often than not having different
students and courses was a challenge but that ultimately it was better because, “
students are really placed in appropriate level courses and not programmed based on
the needs of the master schedule and adults” . While interviewing the teachers it was
very clear by the responses that they are “math teachers” not an “algebra” or
“geometry” teacher, not one teacher identified themselves as a specific type of math
teacher. This is a result of the changes each trimester, no teacher teaches specifically
one subject; it is determined by the number of sections needed of a specific math
level in a given trimester.
The negative implications of the trimester are that students may not have
math every trimester; a student could conceivably have math the first and second
trimester and then not have math the third trimester. This results in students not
being exposed to math for up to a five month period. One teacher stated the
frustration that teachers have with this, “over all the schedule is good, but it would be
more beneficial if all the math classes could be designed like the Math 1 (algebra)
classes. Because the kids do not retain over a summer break, then extend that and it
is worse. We have to spend too much time catching the students up”. As this teacher
pointed out the two trimester design is not applicable for all the students, as the Math
1A-C, which it the CPM Algebra course is a three trimester course so students do not
have break in their instruction. In addition to this, the 11
th
and 12
th
grades students
who struggle the most as evidenced by their inability to pass the CAHSEE are

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required to take a Math CAHSEE prep course so in essence the total number of
students who do not have math each trimester is limited to those on grade level,
having the greatest impact on 10
th
grade students taking Geometry which is taken
over two trimesters.
The leadership team administered surveys with a likert scale response
measure to a representative sample of stakeholders from the school community:
teachers, students and parents/guardians about their attitudes and beliefs about the
value of the block schedule as it pertained to both instruction and their attitudes
regarding their instruction in the classes. They received completed surveys from 263
students from all four grades, 9-12 from varying levels of courses. The survey asked
students questions such as, “ I think I am learning more in Block Scheduling than I
did in a traditional six period day”, “My teachers use the whole period for
instruction” and “My teachers use a variety of different activities”. All of the
responses were in the affirmative; indicating they thought the block schedule had
made a positive impact on their learning, they gave it a grade of “B” in terms of how
they felt about the alternate schedule.
Out of the 94 teachers on the campus 60 of the teachers completed the same
kind of survey, with a likert scale measurement of 1-5 with a ranking of 1 registering
a “disagree strongly” and a ranking of 5 reflecting a response of “strongly agree”.
This survey contained questions that asked teachers about how they saw the block
scheduling impacting their instruction in terms of quality, innovation, and use of
different instructional strategies. A sample of a couple of the prompts are; “ Block

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Schedule helps me do more in-depth teaching” and “I think my students are learning
more on a Block Schedule than they did in the traditional six period day”. The
teachers were asked to provide a “grade” for the schedule; it received an “A” from
33 of the teachers while another 10 gave a grade of “B”.
The parents who responded to the surveys also indicated that they believed it
was a positive change for the school. The school received 166 surveys from
parents/guardians across the four grades. Examples of the kind of survey items the
parent/guardians were asked to respond to are; “My child’s grades have improved”,
“It is better for my child to concentrate on only four classes instead of six” and “My
child get more individual attention with Block Schedule”. The majority of the
responses on all of the prompts were “strongly agree” with slightly less indicating
“agree”. These findings and site reporting supports the research done by Carroll
(1994) that the implementation of an alternative schedule has an overall positive
impact in the course completion rate, that students demonstrate a greater level of
mastery prior to moving on to the next course.
Curriculum Organization
The changes in the organization of the instructional day provided for a
shortened day one day a week, with an early student release. This time is utilized by
the math teachers to engage in activities that are designed and focused on curriculum
and instruction. Over the course of a month the Mondays are identified for different
priorities. One Monday each month is reserved for individual teachers to determine
and define for themselves, which can include working alone or with other teachers.

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Two times a month the department meets for information sharing and operational
items and the final Monday is utilized for what the school calls Curriculum Sharing.
The math department utilizes this time for activities that are organized to maximize
teacher learning and collegial interaction. They identified four primary areas that are
the focus on department meetings and curriculum sharing:
ß Curriculum Sharing-
o This is a practice which is used by all the four core areas once a
month on the shortened instructional day. The teachers share
lessons on specific skills or concepts that are currently being
addressed in the pacing guide for the specific subject. On one
Monday each month the teachers will bring sample lesson and/or
model instruction are with like content teachers. As a extension of
this practice the Math Department also meets once a week during
prep time in “like” subject groupings to share practices.
ß Scoring Assessments
o The department works with the district math coach to improve
skills on scoring written responses that are part of the school
benchmark assessments which are given at the end of each
trimester.
ß Technology
o The department is dedicated to utilizing technology as a tool to
improve their instructional program and has provided them

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increased knowledge on how to access to standards based lessons
on-line. They have increased the use of technology and work as a
department to better utilize technology based graphing programs
as one tool to better reach and engage students.
ß Algebra Readiness
o The Math coach for the district and the site provides extensive
professional development that is specifically designed to support
the math teachers to ensure that students are Algebra ready and
thus meeting high school graduation requirements.
This time was described as very valuable and was viewed by all of the
teachers interviewed as a large factor in the improvement the students and school
have had in math over the past few years. One teachers stated, “The curriculum
sharing time we spend together is really a valuable time for the teachers, and it is not
seen as a waste of time…I think it is one of the best things we do in our math
department The two areas that the teachers and leadership team consistently
identified as essential and unique to their school was the curriculum sharing time and
the math coach. It is these two indicators that stood out as being valuable and critical
to the progress of the school. The item on the math questionnaire that spoke to the
use of math coaches to improve student achievement had the highest positive
response from the teachers with an average score of 4.63, this represents 83 percent
of the teachers indicating a score of five, “strongly agree”. During each of the
interviews the researcher was told that the math coach was the best part of the

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department and that his leadership and support was critical to the math department’s
ability to work as a team, sharing ideas, strategies and struggles together.
The response on the math teacher questionnaires to questions that specifically
related to the collaboration of teachers around curriculum and instruction received
very positive responses. The average responses all fell within the range of “agree
somewhat” to “strongly agree”.
The curriculum sharing on Mondays not only encourages collaboration but it
was noted that it is very useful for the fact that teachers are able learn from one
another, and if a teacher has not taught a specific Math Course since the prior year
they are able to “brush up” on best practices from their colleagues. There is an
additional allocation of time which provided time for the teachers to work in discrete
subject groupings so as to ensure that the time is focused and directive in its support
of the teacher’s current instructional assignment.
Each of the these collaboration opportunities provide the teachers the time to
ensure that each teacher in the department is more accountable to their colleagues
and as teacher K stated “…I came from another district where we did not meet as a
department to collaborate the way we do here and I think this structure is much
better. I am able to work with other math teachers and we are better at making sure
we are “all on the same page”. I think our [math] department is really responsible to
each other”.

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Student Performance Assessment
Vista High School uses the assessment data, from both standardized state
assessments and local standards based quarterly benchmark assessments, as tools for
improving student achievement and making appropriate instructional decisions based
on this information that supports student learning. Vista High School developed
benchmark/quarterly assessments at the site level which was a reflection of a site
level decision. The fact that Vista High is the only traditional high school in the
district often such instructional issues are not “district” but rather emanate from the
high school leadership. The school uses the assessment data, from both standardized
state assessments and local standards based benchmark assessments, as tools for
improving student achievement and making appropriate instructional decisions based
on this information that supports student learning. This effort was a result of the
schools’ leadership’s effort to engage teachers in conversations around student
performance as it relates to ensuring that students are improving performance and
moving towards proficiency as measured by standardized assessments specifically
the CST.
The value of the benchmark assessments is reflected in the response of the
teachers on the questionnaires and through the interviews. Specifically the math
teachers indicated a higher rating in response to the question that asked about the use
of benchmark assessments as a support for increasing student achievement. The math
teachers had an average score of 4.29, which is strongly agree and the non-math
teachers indicated a score of 3.96 which is still in support of the value of the

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benchmarks. Through the interviews with the math teachers it was evident to the
interviewer that the benchmarks provided information regarding instruction that was
utilized through the various structures in which they come together as a department
or in content specific groupings. During the curriculum sharing and subject specific
meetings specifically they utilize the benchmark assessments to discuss where the
teachers are having instructional success or difficulty conveying the concepts as
predicated on the ability of the students. One teacher shared both the value of the
discussion around the student results on the benchmarks and the frustration as it
relates to not engaging in these discussions not often or quickly enough following the
assessments. The teacher spoke to the value of these conversations as a means of
informing the instructional program. The subject specific weekly meeting she said
were “really helpful” because of the smaller group and that the teachers were able to
“relate” to each other and increase their comfort level in saying what worked, what
didn’t and what they “needed” from their colleagues in a “safe” environment. The
curriculum sharing once a month was valuable but because it only occurs once a
month the benchmark data that is shared and discussed is not always in “real time”.
So there is not the immediate impact of what is happening in the instructional
program. But the overall value the teachers placed on the curriculum sharing is
apparent despite this shared frustration.
School Culture
The School Culture reflects the effectiveness of the school design and its
impact on meaningful relationships between the students and adults on the campus.

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As well it includes improved and extended learning opportunities through
professional development that is targeted and sustained over time. These are aspects
that influence the school culture in terms of the quality of experience of both
students and staff and the improved quality of the instructional math program. This is
evidenced by the outcomes as measured by state and local assessments, passing rate
of the CAHSEE and standardized assessment student performance.
The re-design of the school day from the traditional 1-6 period school day to
the four 88 minute blocks trimester has enhanced the learning of the students and
improved the level of interaction between the teachers and the students. On a school
survey which 60 of the teachers completed 80pecent responded “agree” or “strongly
agree” with the statement that the block-schedule has allowed them to get to know
their students better, and that the students get more individual attention with the
block schedule and has ultimately enhanced the overall learning at the school.
One teacher who has been at Vista High School for over 10 years when
talking about the overall school said, “…I think the school and the kids behavior has
improved over the past five or six years, I think this has something to do with our
schedule, there is not as much activity because the kids only have four classes and so
the campus is quieter and the culture of the school is better”. The findings in the
school source data provided from the school do reflect an improvement in student
behavior as reflected in suspension data. The quantitative data on discipline as
reflected by the number of suspensions indicate that there was a decrease in the
incidents of student behavior that was cause for suspension. The first year of

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implementation of the block schedule there was drop of behavior referrals from 1457
to 963, a 66 percent decrease. It was communicated also by teachers that they
believed that the overall campus climate had “slowed” down as a result of less
student movement, not having six passing periods in which the student activity was
high.
Professional Development
To facilitate interactions between students and staff that is meaningful and
thus positively effects the students learning at Vista High School the adults
participate in learning opportunities that are designed to help improve their teaching.
This is clearly and deliberately defined within the Math Department.
Over the past four years the math department at Vista High School has
embarked on a purposeful and focused professional development effort under the
umbrella of the Project ALPHA math initiative and led by the math coach this effort
is reflected in their curriculum sharing. During this time they share lessons with each
other, analyzing benchmark assessments and while not directly related to the Project
ALPHA the training, they discuss the use of technology as an instructional tool.
These professional development activities have evolved from a school culture that
was resistant to “sharing” with colleagues to one that fosters a collegial environment
in which the teachers as professionals engage with one another.
The math leadership has developed the master schedule so that groups of like
teachers have the same conference period allowing them to meet together. For
example a group of eight Algebra teachers would have the same prep period. During

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their prep period the teachers meet to discuss their lessons, share observations and
essential work as a support team for one another
As part of this structure the teachers share with each other feedback on their
observations of classrooms they have observed. The school has deemed this activity
as Evidence of Quality Teaching (EQT). This involves teachers of like subjects and
the math coach doing informal observations of each others classes and subsequent
sharing. At one time these meetings were “mandated” by school policy and were
much more formalized with documentation, it has evolved into a practice that is
expected but is essentially voluntary and has become part of the math department’s
instructional culture. While there remains some documentation it is much less than in
prior years.
Another key factor that the school leadership and math teachers felt had
contributed to the commitment made by the teachers to actively engage in
professional development is that all of the professional development has come from
within, it is not something that the teachers perceive as one of “those” programs that
comes and goes. Rather the teachers are active participants in the evolving and
important professional development. One teacher who has been part of the school for
a number of years stated, “…the time we spend as a [math] department on our own
professional development has gotten better and more important each year, maybe
that is because more teachers are buying in, by having the Math coach that every
[math] teacher thinks it is really great, it helped create the ownership of students
performance, at least for me”. This sentiment was echoed by many of the teachers,

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the collaborative time they spend together is viewed as critical to the progress and
commitment by the teachers.
In addition to these professional development activities that have become part
of the school, and math department culture for the past three years, the math coach in
partnership with California State University at Fullerton (CSUF) host a “Summer
Institute” which further focuses and extends the conversation around improving math
instruction and student learning. The partnership with CSUF was established prior to
the Math and Science grant and according to math leaders has been a “real lever for
teacher involvement”. The partnership has involved two math professors from CSUF
who have worked with the teachers on test item analysis. They have collaborated
with the teachers to unwrap the questions on the CST and the CAHSEE in an effort
to understand the mathematical concepts that are embedded within each of the
questions and the skills the students must have in order to be successful. The
Summer Institute, while separate from the partnership with CSUF, has many of the
same components and tasks as those that have been the focus in working with CSUF.
The institute is designed specifically to support the teachers in the use of CPM as the
Summer Institute is investigative and constructivist in its organization which is
aligned with the structure and approach of CPM and is a time to create resources for
the teachers. With the trimester schedule, the teachers sometimes teaching
completely different classes from one trimester to the next, and not knowing what
they will be teaching until one to two days prior having a “bank” of lessons and
information is viewed by the teachers and the administration as very beneficial.

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During this past summer, the 2006 Summer Institute theme was responding to
the “why” questions that students often ask. The following is an excerpt that
describes the objectives of the 2006 Institute,

The purpose of the investigations is to increase our own understanding of
mathematics by discovering why algorithms work and exploring alternative
methods of solving problems…. The following is a sample of questions (most
of them whys) that your students may ask, in some form or another, at some
point during your math teaching career.

ß How does the multiplication algorithm work?
ß Why do you line up the decimals when you add but not when you
multiply?
ß Why don’t we need common denominators when multiplying
fractions?
ß Why do you need common denominators to add or subtract fractions?
ß Do we really need common denominators to compare fractions?
ß How does the long division algorithm work? Where did it come
from?
ß Why do we multiply (denominator by whole) and add (numerator) to
convert a mixed number back to an improper fraction?

We must also understand math in such a way that we could effectively teach
our students to make sense of it for themselves. Therefore, for each question
you will not necessarily fin an answer that you could quickly retort to that
curious student. What you will find is the math background you will need to
know and understand, as a teacher, to effectively teach the concepts at hand.
This way, the questions may never arise—but if it does, it could be answered
accurately. (www.vistaschool.com)

The Summer Institute continues to evolve with active participation by the
teachers. Some teachers indicated that they had participated more than one time
because they view it as a valuable to what they do in the classroom everyday. All of
the new teachers are encouraged to participate either during the summer prior to the
start of the school year or the following summer, depending on hire date. However it

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is not only limited to new teachers but do due the percentage of new math teachers
every year it is often more “new” teachers that are the participants in the summer
institute.
While teacher professional development speaks to the interaction of the
teachers, the exposure of teachers and school leaders to research based information
and professional knowledge, this aspect of the conceptual framework really is about
how this is manifested in the classroom with the students. These are the activities
which contribute to the overall learning of the students, which in the context of this
framework is characterized as Learning Activities that challenge the adults as
learners which translates to the students by providing them with an opportunity to
engage in and use higher order thinking skills and collaborate with others as a means
of problem solving.
Math Program Design
Curriculum design, Classroom Practices and Standards Based Instruction
The curriculum, at Vista High School is aligned with the California Content
Standards, with their larger goal being defined by NCLB (2001) that all students will
be proficient by 2014 as measured by the CST. To facilitate students improving their
learning and achievement Vista High School uses California Preparatory Mathematic
(CPM), which is the instructional program used by Vista High School to assist the
school in realizing its goal of improved student achievement for all students. The
high school CPM courses are provided in the same sequencing as “traditional”
program: Algebra 1, Geometry, Algebra 2 and Mathematical Analysis. All of the

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courses within the CPM model have integrated within the instruction a conceptual
understanding of the basic skills with an emphasis on students utilizing problem
solving skills. To facilitate students gaining problem solving skills and developing a
conceptual understanding of the science of math, a variety of instructional strategies
are used. The teachers balance the instruction between using a traditional lecture and
class discussion model while also ensuring time for students to work in small
structured groups using math manipulatives to allow for learning through a guided
investigative activity. The teacher lectures and summarizes based on observations of
the student groups and identified learning needs of the students. Students practice
basic skills over an extended period of time and such skills and procedures are
integrated into application problems the students are assigned.
A distinguishing aspect of the CPM model is the extensive focus on investigation
through small group work. The teachers and school leaders both communicated that
this was very effective for their students but that it was an approach and philosophy
that required teachers to move from their “comfort zones” of teaching in more
traditional models, which did not necessarily encourage student engagement with
each other. This approach to instruction is supported by Vygotsky’s concept of
“Zone of Proximal Development” (ZPD) which speaks to the value of students
developing problem solving skills through a collaboration of heterogeneously
grouped students. So the students may be grouped by their current or “actual
development level” with other students as a means of developing the students
problem solving skills towards their “potential level of development”. The teachers

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role in this is as more of a facilitator, but S/he is critical in that the teacher must
provide the guidance for the students that “scaffolds” their learning (Guerrero &
Villamil, 2000). This is reflected by the student collaboration in which students
develop the skills of working collaboratively in small groups and the instruction is
balanced between a guided instruction model and this group work where students
learn strategies that fosters higher level thinking, those are: questioning, clarifying,
summarizing and predicting (Brown & Palinscar p.413).
The teachers reported that CPM was effective with the students at Vista High
School because students were able to work together and to gain knowledge and
understanding of greater complexity through the discovery learning process. To
develop the skills to work in small groups took some time. The learning was not a
product of the teacher telling them the rules, steps and procedures but rather the
students learn through doing, which deepens the retention of knowledge and also
reduces the anxiety often associated with learning mathematical concepts. The
investigative group work aspect of CPM is designed around real life experiments that
allow students are to make authentic connections. The design of CPM is such that it
fosters connections for students; it takes the math from an abstract irrelevant
discipline to something that is related to their lives and future opportunities.
The leadership and staff at Vista High School acknowledged to varying degrees
the impact of federal, state and local policies. The teachers lesser connection to
these policies may have been more of a reflection of their lack of knowledge for the
terminology than an indication that they did not identify the impact of such policies

149
as NCLB, CAHSEE and graduation requirements. Because within the context of the
interviews, there was a greater acknowledgment by the teachers that such policies
had influenced the instructional decisions and subsequent student performance. The
leadership was more cognizant of the direct implications of state and federal policies
on the decisions made in respond to the guidelines and policies regarding improving
student achievement.
Overall the math teachers are a cohesive department that is united around
common structures, practices and expectations for both the students and the adults.
They clearly identified the design of the master schedule, the practices of curriculum
sharing, EQT, department meetings, the use of CPM and especially the math coach
as all critical components of their increase in achievement.

Research Question #3: What change process did the school use to enhance the math
program and strategies to assist students in math?
The purpose of this section is to focus on the change process using the four
leadership frames presented by Bolman and Deal (1997) as the conceptual
framework. It is important for the school leader(s) to understand their role in the
change process around improving student learning and to address the challenges that
are inherent in any change that requires a “paradigm shift” of thought (Blasé and
Blasé, 2004). This question was designed to facilitate an understanding of how the
approach, philosophy, style, strengths and challenges of the leader impacts the
change process that has specifically improved the math program, and the utilized

150
strategies that assisted the students in their improved math achievement. These four
frames of leadership are not in isolation of one another and it is not the intent to
identify one frame utilized in the change process of Vista High School but rather the
findings support an interaction between the four frames. The structural frame is in
essence the frame which looks to create change using order, roles, and rules. A key
aspect of the structural frame is the view that the organization’s very purpose is to
provide the structures that support the goals of the organization, which are attained
through a clear objective and understanding of individual responsibilities and roles.
The human resource frame uses the relationships and collaboration of people to
create the momentum for change. A distinguishing aspect of the human resource
frame is the emphasis on the needs of the human needs as opposed to the
organizational needs; they are not in isolation of one another but rather when the
needs of the people are met then the organization increases its ability to engage in the
change process and improve the organization. The political frame leverages
resources through prioritizing, negotiating and asking “who gets what?” from the
scarce resources. This frame makes conflict central to the process as individual
stakeholders compete for allocation of resources as a means of attaining the goals
and objectives of the organization. The symbolic frame seeks to celebrate the
individuals and the larger “community as a way of finding meaning and using this as
a tool for creating change through the culture of the community as a cohesive group
around a set of shared values and beliefs. This frame creates rituals and ceremonies
to help individuals find purpose in their work as it pertains to the larger goals. This

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question seeks to understand the interconnectedness of these frames in the change
process at the school and the ultimate outcome of improved student learning and
achievement (Bolman and Deal, 2003).
The Structural Frame

The progress of Vista High School both in terms of the academics and the
more collegial culture of the school are connected to the different elements that
reflect the assumptions of the Structural Frame. The conceptual indicators of the
structural frame are present on the campus as indicated by the teachers. During an
interview with a teacher it was articulated that the school over the past few years had
developed and increased structures and/or opportunities that facilitated the teachers
(specifically math) to engage in collegial conversations that were very focused on
instruction in the classroom, in the present and not just looking at what students had
done, which the teachers do, but really discussing the practices in their classes that
day and the prior day which translates into real time impact on the instructional
program. The response from the math teachers to question #23 which asked a
question in relation to Research Question #3 was very positive with 80pecent of the
respondents “agreeing somewhat” or “strongly agreeing” that collaboration was
important. The question stated, “Teacher collaboration has played a key role in
increasing student achievement in math”. One means by which this is evident is the
classroom assignments. Two years ago the leader “turned the campus upside down”
by moving teachers out of their classrooms and assigning rooms based on
department. The goal was to have content specific areas so the math department is

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grouped in three different locations on the campus as are the sciences and the
English department. The Social Science department is not as clustered. The math
teachers indicated that the school leader has made efforts to provide and create
structures that support teachers engaging with one another. On the math teacher
questionnaire one question asks if the leader “encourages” faculty (math) to discuss
effective math strategies. The response to this question was an average of 4.29 which
is “strongly agrees’. This was elaborated on in the interviews by two of the teachers
who spoke directly to the fact that the campus was organized by departments which
was a positive in terms of teachers talking with one another and sharing more
frequently. The leadership appreciated that making these structural changes would
be met with resistance as teachers become attached to “their” room and location and
do not appreciate it when leadership moves them. However, ultimately this has
proved to be a positive change in fostering a collaborative group. It reaffirmed the
importance the leadership places on having a clear and consistent structure in place
that supports teacher interactions.
The master schedule is perhaps the most obvious structure that is pointed to
as supporting and helping to facilitate the goals and vision of the school. The
schedule is created around ensuring that students are appropriately placed, groups or
teachers who teach like subjects have the same prep period, and time is created by a
shortened instructional day to allow for teachers to have expended time within their
work day to meet as instructional teams; this is embraced and utilized by the math
department. A reflection on how school policies are reflected through the master

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schedule are the 11
th
and 12
th
grade CAHSEE mandatory “elective” course that
students who have not passed the CAHSEE by this time must be enrolled in.
When the school received the California Math and Science Project (CaMSP)
grant this provided for a new structure which provided for a math coach that would
work with the feeder schools on a math articulation and professional development.
This has evolved into a relied upon and valued part of the math department culture.
Following the end of the grant the school leadership was able to gain the district
office support in maintaining this position sharing the cost with the school site. This
insight and action by the school leadership in essence reflects a significant role that
the Principal holds for the campus; creating and maintaining systems and structures
that support the instructional program and creating change in the structures as a
means of facilitating increased student math performance.
The Human Resources Frame

This is a frame which conjures for most the notion of the leader as the
nurturing care taker, while this characteristic is most aligned with this frame a leader
who identifies with the Human Resource frame is more than this. The leader who is
operating from a Human Resource frame is viewed as respecting the role and value
of the professional relationships of teachers and staff. The relationship between the
adults and the adults with students is a critical component in creating a learning
environment that supports students learning. The responses from the questionnaires
and the interviews would indicate that the leader of the school operates in this frame
in terms of the ability to empower people to take leadership roles. The leader is

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effective in realizing the value for the organization when the individuals and the
organizations work together, this relates directly to the 4
th
assumption of the Human
Resource Frame. The “feelings” of the campus and discussions left the interviewer
with a sense that the leader of the school while not engaged with staff in a “social” or
personal level is as a source of support through actions and decisions that are made
by the leader to support the staff and the students. This was summed up by teacher C
during our interview, “… the administration does a good job because it is not a feel-
good administration, and it’s a tough administration. You feel that the administration
keeps its distance. So if I want to be stroked, they are not going to stroke me. I am
going to feel good about scores…and my relationship with my students. I do not
think it is a bad idea…it keeps teachers on their toes”. This response captures much
of the sentiments articulated in the interviews and can be inferred from the
questionnaire responses.
One of the core elements of the human resource frame is the leader’s ability
to ensure that the “right people” are part of the team, and that there is a “fit” between
the individual and the organization. As part of the leaderships focused effort to
improve math performance of the students it has been critical to ensure that the math
teachers are able to provide a sound instructional program and that they are able to
work with the structures and CPM instructional program that is non-traditional. As
such there has been consistent turnover in the math department each year while
creating a department that continues to go through change is creating a more solid
math team of teachers. The administrative leaders work closely with the leadership

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team within the math department to hire and then support the teachers in the “Vista
High way”. The teachers shared that they did feel that there was strong support for
all of the teachers to be part of the larger math department and that they are not
teachers in isolation of others. The response to the question about “regular support”
from school leaders was 83 percent indicating they “agreed somewhat” or “strongly
agreed” that they are supported.
The leader did utilize elements of the Human Resource frame in her efforts to
move the school and change practices in the department’s quest for raising the math
performance of all the students at Vista High. The researcher did not however find
those aspects of the Human Resource frame that one first thinks of with this frame
such as strong interpersonal relationships with teachers and staff. The leader as
articulated by interviewees is not considered “social” with the staff but is responsive
and supportive in a very professional manner. The leader is a facilitator of the
community; there are specific structures that have been implemented by the
leadership team with the support and the guidance of the leader, which take a more
behind the scenes approach in creating the leadership team as the implementers of
the change process.
The Political Frame

This frame is defined by Bolman and Deal (2003) as one that speaks to
leadership skills and ability to utilize resources, not just in terms of financial but also
the skills and strengths of individuals. While not identifying the actions of the
leaders as “political” the teachers both in response to the questionnaire and the

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interviews identified “behaviors” or action of the leadership that clearly fall within
the context of the Political Frame. This is evidenced by the leader’s capacity and
skills at utilizing the resources of the school district and the community to support
the needs of the school. One way in which this was reflected was the leader’s ability
to engage the school district in supporting the math coaching structure that was in
place and had been implemented to support the math program and the instructional
articulation from the elementary school to the high school. The leader leveraged the
schools ability to provide the instructional resources to the district in as much as the
district was able to provide the financial resources beyond the life of the CaMSP
grant. This was a significant funding commitment on the part of the district and
required the leader’s commitment to establishing structures and practices that would
garner support.
The teachers described the leadership of the school as being facilitators of the
larger school goal; putting in place systems and structures that support the teachers
and the instructional program. They indicated that the leadership, specifically the
principal would listen to the administrative leadership, the instructional manager and
the math coach about their professional opinion and suggestions that support the
math department and through these discussions resources both financial and of time
would be determined. During the interviews with the math teachers it was articulated
by one teacher that,” the Principal and administrators are very supportive of what we
do, they encourage us…they will go to the district to ensure we have resources or
support for teachers…” This was shared as the means by which the teachers

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interacted with the leadership, not so much one to one interactions but through the
math department leadership.
The school leader has a history with the district which has provided insight
and perspective on how to use the organizational dynamics of the district to support
the student learning goals of not just Vista High but for all the students K-12 in the
Vista Unified School District. This knowledge has served the leadership in the effort
to sustain systemic changes that have evolved over the past three to four years and
have help create the foundation from which the school continues to move student
performance forward.
The Symbolic Frame
The Symbolic Frame is a perspective that looks to utilize symbolism either
through actions or communications that gives meaning and that celebrates and
recognizes events and/or people. This frame is described by Bolman and Deal
(2003) as one that helps the organization, the school community in this scenario,
to find meaning and provide an anchor for the community.
The leadership of the school speaks of “Blue Pride” as not only an adjective
that describes who they are but also embraces this as a verb; an active belief that
supports the goals and vision of the school. When visiting the campus there is a
sense of a strong connection among the individuals who come together as a cohesive
community. They have an identity and there is a sense of pride and a culture that is
unique to whom they are. They celebration of staff and students is evident in the
halls with displays of student accomplishments and recognition by the students for
teachers and staff that supported their efforts as young adults to be successful in their
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During the leadership interview a tradition of “Teacher of the Year” has been
in place for at lease the past ten years. This has become part of the school and
community celebration. This was started by a community member who wanted to
honor teachers for their strong instructional program. A process was put in place that
involved teachers and the community member to make the final the selection from
the list of teacher nominees. There are two awards and one of the teachers must be a
teacher for a core academic area. The first year the individual gave a $10,000 award,
since then it has decreased to $600.00 to be used for anything the teacher wants. This
has become a symbolic event and celebration of the teachers that serves to validate
the effort and progress in the classroom, recognizing peers for their excellence in
supporting the students and their learning.
Additionally Vista High has many events that celebrate the students, the staff
and the school as a larger community. They have a “Project Fair” that over 40
teachers and their students participate in. This is an evening where incoming 9
th

grade students visit the school in the spring and the staff and students show off
creative projects all around the campus. The school also works to ensure recognition
of student progress. One example is that students who improved their standardized
test scores from one year to the next were given a week of free lunches, not from the
cafeteria but from outside providers. Additionally for the students during the testing
window the school has a raffle; each day the students attend and take the test they get
a ticket, if they are really putting in effort they get additional ticket. They conduct
drawings through out the week and students receive I-Pods, MP3 players, items that

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the students are enthusiastic about. This creates a fun and energizing climate for the
campus and the students are engaged. This past summer the school held an event for
the incoming 9
th
grade class called, “Ninth Grade 2010”. This was in response to the
prior 9
th
grade class that had been identified by teachers and administration as “a
difficult class”. The leadership team and teachers saw the importance of creating an
immediate identity for the students, to create a sense of team and belonging. The
students came prior to the opening of school and were introduced to the school,
participated in structured fun activities and met teachers. This event was shared by
one teacher who said, “… this was a great event, the class before was very
challenging and so the leadership and others got together to find a way to get the kids
right from the beginning connected to the school. Some teachers did not buy in, but it
turned out to make a difference, the class is much better”. This opportunity for the
students and adults that participated was symbolic in that it brought the students
together and allowed them to see adults in a different light and to make connections
to the school from the start of the school; they experienced “Blue-Pride”.
The staff comes together for social events to celebrate individuals or the
season. Over the years staff meetings and development days have provided time for
staff to have fun through fun games and interactions. All of these according to
response from leadership help to bring the community together, to foster interactions
outside of the academic realm that provides meaning and appreciation of each other.
Having these different celebrations, events and opportunities help to create a sense of
belonging to a larger community. No person indicated that any of these alone

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impacted the schools effort to change and improve student math performance but it
was stated that, “…people, kids and students, have a sense of belonging to a
community”. This is clearly reflected in the “Blue-Pride” mantra of the school.
The change process of the school towards improved math performance was
connected to all four of the frames. Overall the structural frame is specified through
interviews, review of documents and researcher observation as the most dominate
frame having the most significant impact, each of the other frames fall within this
Structural Frame. Question #19 on the Math Teacher Questionnaire specifically asks
the perspective of the math teachers on the role the Principal plays as a “change
agent, 25pecent of the responses were “somewhat agree” and “strongly agree” with
16pecent responded that they “disagree somewhat” and “disagree strongly” with the
statement, “The Principal has served as a” change agent” for improved student
achievement in math”, the majority of the responses were neutral. The response from
the teachers during the interview consistently reinforced the Principal as the
facilitator who put systems in place to move the school but that the real change in the
math program was coming from the leadership of the math coach in terms of
instruction and the math Instructional Manager as it pertained to the operational side.
Through the questionnaire responses, both from the math teachers and the “non-
math” teachers, and the interviews there was evidence of leadership utilizing skills,
actions, and decisions that connect with differing aspects of the four frames.

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Research Question #4: To what extent was strong instructional leadership important
in improving A) the math programs/strategies and B) math achievement among
students?
The purpose of this section is to understand the role of the instructional leader
in developing, implementing, monitoring and sustaining the math program and the
achievement of the students in math. It is important that the leader play a role in the
leading and/or facilitation of moving the math program forward as evidenced by
improved math achievement. This question was designed to understand what role
the leader played. The framework for Instructional Leadership indicates five areas in
which the effective leader must have knowledge: Vision for Learning, Supervision
and Monitoring of Instruction, Community and Political, Culture of Teaching and
Learning, and Data Driven Decision Making Analysis. To respond to this question
analysis from both the non-math and math teacher questionnaires was utilized as
well as responses to the interview questions from the math teachers and the
leadership. In addition to this the researcher accessed source data from the school
site.
Vision for Learning

Within this framework the leader is viewed as the person who leads the effort
to develop and communicate the vision for learning that is supported by the school
community. Vista High School is committed to providing all students with a solid
educational program that will ensure their successful completion of high school
graduation requirements and their contributions as life long learners to the global

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community. This vision and mission of Vista High is part of a belief system for the
leadership and the teachers. The administrative leadership team is viewed as those
who facilitate the operationalizing of the vision for student learning through their
empowerment of teacher/department leaders. This further supports the idea that the
administration is responsible for creating and maintaining the systems and structures
that provide for implementation and realization of the school community’s vision for
student learning. The top leadership monitors this through interactions with the
teacher leaders and is not viewed as being in the forefront of the implementation of
vision for learning but assumes a supportive role in this process.
Supervision and Monitoring of Instruction

This element of the framework for Instructional Leadership concerns the
observing and monitoring of the instructional program and the feedback to teachers.
The leadership at Vista High School places significant importance on ensuring
fidelity to the instructional program and the import of supporting the teachers in their
ability to be effective. This is evidenced by the systems and structures that have been
implemented over the past four years and the empowerment of the math coach and
the instructional manager.
While there is little evidence to support that the administration is actively
involved with the direct supervision and monitoring of the instructional program
there is strong evidence the administrative leaders provide support, the feedback and
resources to the math teacher leaders. The math teachers recognized the support of
their classroom instructional program by the math coach and instructional manager.

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On the math teacher questionnaire there are two items, #30 and #31 that were
designed to provide insight on research question four. Item #30 asked if of math
coaches had helped teachers become more reflective about their instruction. The
average score was 4.6 which is a high “strongly agree” and item # 31 asked if math
coaches have been a resource in improving their math instruction, this too had a high
score of 4.08. Conversely on the non-math teachers survey question #19 which
specifically asked if the Principal “works hard to monitor and supervise instruction
in the classroom” the response was “neutral” as indicated by an average score of
2.98. On the questionnaire for non-math teachers item #22 asked the same kind of
question, namely if the school leader utilizes department leaders for their expertise
when making curricular decisions, this did not have as positive of response, with an
average score of 3.52 which is “agreed somewhat”.
While all of the departments have instructional managers not all have a
content specific coach as math does and this appears to be the significant factor
influencing the effectiveness and collaboration of the math department. During the
interviews with the math teachers it was shared that their department is more
collaborative than others, and this is largely attributed to the leadership of the math
coach and the instructional manager who was referred to as, “someone who loves
math, lives and breaths it”. The administrative leadership has worked with the math
teacher leaders to establish systems and structures that encourage observation,
monitoring of instruction and collaboration among teachers about their practices. The
administrative leaders ensure that resources including time, professional

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development and materials are available for the instructional program. This effort
was reflected by the math teachers on the questionnaire with a response score of 4.04
which indicates that over 80pecent of the math teachers strongly agreed or somewhat
agreed that “the school leader provides opportunities for faculty members to discuss
effective math instructional strategies”.
The hiring of math teachers that support the instructional program and
learning goals of the math department is done with input from both the
administrative leadership and the math teacher leaders. The administration values the
perspective and expertise of the math leaders and sees this as a responsibility: that
while ultimately the administration’s is most effective if completed with together.
They also communicate and collaborate not just in the hiring of personnel but also
discuss teachers throughout the year who are struggling. Between the math
leadership and the administrative leaders there is effort to support all personnel to be
successful.
Community and Political

This aspect of the Instructional Leadership Framework looks at how the
instructional leader engages and collaborates with the families, the larger community
and how she mobilizes the community as a resource and support for the diverse
interests of the school community. The researcher realized, in analyzing school
source data and the responses to the non-math teacher questionnaire, that this area
while important in terms of communication and information exchange, it is not an
area in which there is a clearly defined plan for engaging the larger community.

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The internal school community (administration, teachers and support staff) is
certainly committed to ensuring that there is communication going out to the
community as reflected by different mediums in which activities and announcements
are made. The school has a wonderful website that is very informative and is current
with up to date information about events, deadlines, general information about the
school and a message from the Principals that shares her dedication, vision and seeks
to highlight the pride of the school as a cohesive community, “Blue Pride”. There is
also a school marquee that is utilized to communicate opportunities for students to
receive academic support, upcoming activities and gain general information.
On the non-math teacher questionnaire there are two items that speak to the
leadership’s effort to garner community support for the academic efforts of the
school and to establish and create a learning environment that works to maintain
respect for cultural diversity. In terms of engaging the community, the response to
this item was neutral and the question about respecting diversity had a slightly higher
response of 3.6 which is in the lower range of “agree somewhat”. Neither of the
response ratings should imply an “unfriendly or inviting” school campus. The school
does have a strong feeling of community when one visits the campus; it feels like a
“close knit” school community which is rather self-contained and confident in whom
they are.
The fact that the findings do not indicate a “high level” score related to
outreach and diversity, is not a negative reflection on the leadership but rather a
reflection of the school setting and community: The school is not very diverse with

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the Latino ethnic group representing over 95 percent of the student population. There
is a strong sense that the focus of the leadership is on teaching, learning and
celebrating all who are part of the school community on a day to day basis.
Culture of Teaching and Learning

This element of the framework seeks to provide a comprehensive
understanding of the role the leader plays in using different aspects of leadership to
improve the math instruction in the school. As such this element tries to understand
how the leader works to create a learning environment that advocates and nurtures a
positive school culture. This component of the Instructional Leadership Framework
is similar to the prior one, Political and Community as it describes inclusiveness of
diverse backgrounds and ideas from community as important aspects of leadership.
As noted in the prior component of this framework there is a sense of
community at Vista High School, a sense that the school is self-contained, comprised
of adults and students who convey the concept of “Blue Pride”.
The non-math teacher questionnaire had one item that spoke specifically to
two different elements, “valuing student and staff” and “celebrates students, teachers
and staff”. The overall response to this item was not very high, 3.37 which falls
within the “agree somewhat” band. This appears inconsistent with the perception as
conveyed by both math teachers and leadership in terms of events and activities that
are available on the campus, specifically within the math department. Additionally
however, the teachers and leadership did identify means by which staff is celebrated;
teacher of the year, teacher recognition by students display case and “teacher of the

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trimester” which is a more a light hearted teasing of teachers but nonetheless an
opportunity to acknowledge staff.
As part of the school’s mission statement as stated in the School
Accountability Report Card (SARC) they articulate their commitment as a school to
ensuring that, “…students will acquire the abilities and skills to fulfill their role in a
global society and be lifelong learners. This commitment will be achieved through a
student-centered, teacher-guided curriculum that recognizes diversity and
incorporates positive parental involvement”. In the schools effort to provide an
instructional program that meets the diverse learning needs of the student population
at Vista High the math department sought a curriculum that engages students by
implementing multiple learning modalities through the instructional program. Their
math program is developed utilizing different approaches and strategies to include
teacher guided instruction and small group, hands-on work for the students. The
selection of CPM as their math program was done in part as an effort to acknowledge
the diverse learning styles of their students. While the teachers and administrators
identify that there is value in the use of CPM as the math program because of the
hands-on and small group approach, this is not a reflection of culturally relevant
instruction. On the math teacher questionnaire, item #35 was designed to provide
information for research question four, it asked, “The school instructional leader
encourages faculty members to discuss effective math instructional strategies”. This
question received a high rating of 4.29 which is “strongly agree”. However, this in
and of itself is not an indication of culturally relevant instruction but rather confirms

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the practice of teacher collaboration. During the interviews with the teachers the
concept of culturally relevant instruction was not highlighted by the teachers. Their
was one teacher who spoke of making connections for students to a word problem
for which the students had little or no frame of reference, which made it difficult for
the students to understand the question, but this is more a reflection of utilizing good
teaching strategies than it is of making the instruction culturally relevant for the
students.
Because a high majority of students at Vista High are identified by one ethnic
group it appears to the researcher that a need for culturally relevant instruction is not
a primary focus on the campus. The fact that the teaching staff does not reflect the
dominant culture of the school presents a need for teachers and staff to have
opportunities to increase their understanding of cultural mores and experiences of the
majority of students on the Vista High School campus. The school identity or
culture is reflected in the communities embracing of “Blue Pride”, which appears to
be the rallying point of the school community and in essence reflects the culture of
the school.
Data Driven Decision Making Analysis
This final component of this conceptual framework is intended to identify the
extent to which the school utilizes data as a tool that informs the instructional
program and ultimately supports student learning. In an effort to move students
forward in their academic performance the school and specifically the math
department is committed to utilizing data to guide and improve the instruction in

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their classrooms. Specifically, item #8 on the math teacher questionnaire asked about
the use of student benchmark assessment data as a means of “driving instruction”.
This item had a positive response of 4.29 which indicates that the teachers “strongly
agree” that this kind of data is utilized by the teachers to inform the instructional
program.
The importance of data as an instructional tool is further highlighted in the
teacher interviews. As stated by teacher J, “… it is really helpful the way we look at
the data during our curriculum sharing and subject specific weekly meetings… it
helps me to learn from the other teachers, what they are doing that I am not”. This
kind of sentiment was prevalent in the conversations with the math teachers. One
teacher summarized it best by conveying her thoughts about how the data from the
mid-terms is used to facilitate teacher conversations about students. “…what we do
is take the results from the test and ask, “Why did 67percent of the students pick the
wrong answer?”…is it because of the wording of the question? ...did one of us have
more students that did better? Why? ...the questions just go on from each question
we ask…it is really helpful for the teachers to have an understanding of why students
did how they did”.
The school utilizes a variety of student performance indicators to measure
student progress. They have developed both formative and summative assessment
tools as reflected by the teacher developed formative chapter quizzes and tests and
the end of trimester summative exams. In addition to this they utilize the results of
the standardized state assessments to monitor school progress. The school has in

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place and utilizes the tools of their assessment management system Edusoft. This
system allows the administration, teacher leaders and teachers to access student
assessment information and provides the staff and teachers with user friendly reports
that allow the data to be disaggregated by a variety of parameters. This system is
embraced by the leadership and the teachers as a tool that provides valuable
information about student learning that is utilized as a means of guiding the
instructional program.
The student information that is gathered from this management system allows
the leadership to make appropriate student placements into subsequent math classes
from trimester to trimester. This student assessment data is utilized to develop the
master schedule each trimester and truly drives the master schedule and what the
teachers will teach each trimester. The master schedule, specifically the math classes
are not simply rolled over each trimester based on a schedule that was developed
earlier in the year, it changes to meet the needs of the students based on the analysis
of the student data available from the chapter tests, benchmark assessments and
grades students earn. The importance of the student data that is gleaned from these
various means and the support of the management system were identified as crucial
to the progress of the math program at Vista High.
The role of leadership at Vista High School has been the impetus for many
structures and practices that have been implemented to support student learning.
However, the role of the Principal in this effort has been from a more facilitative
leadership role. The Principal does not assume the role of the instructional leader but

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rather has delegated this to those in supportive leadership roles. The math coach is
most frequently identified by the teachers as the instructional leader in their
department and the instructional manager for the math department to a lesser degree.
The administration are viewed as the leaders on a larger scale, as the ones
responsible for the school in it’s entirety and as a resource for support specifically as
it pertains to providing necessary resources. One math teachers summed it up by
saying, “…the administration pretty much lets the math department leadership run
our department, I mean they support us but they trust the coach and instructional
manager to make decisions that influence our classroom instruction”. So the role of
the leader both at the administrative level and the department level have been
essential to the progress and improved achievement in math.

Research Question #5: How did instructional leaders respond to academic areas in
which they are not experts?
The instructional leader of Vista High School has made deliberate choices
and has been active in her decision making to empower and draw from the strength
of her leadership team to improve student achievement in the area of math. Using the
assessment of Principals Expertise in Math Model the Principal had a “low level of
expertise” because she had not majored in math, did not have experience teaching
math and as such was not considered a Highly Qualified math teacher under NCLB
guidelines. While the Principal does not have an instructional background in
mathematics she had the leadership skills and foresight to listen and be willing to

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engage others who did have greater expertise and helped them develop as
instructional leaders in their own right and in their content area.
Twelve of the most validated research-based strategies and/or approaches for
leaders to mitigate their lack of content [mathematics] expertise were utilized as a
means of understanding how a school leader can improve the school and overcome
the dilemma presented from lack of content knowledge.
In sharing and discussing the strategies with the leadership they identified
eight of the twelve strategies that they believed had been utilized as a means of
compensating for the lack of math leadership by the Principal. Based on the
interviews and the questionnaire responses from teachers the researcher was
surprised that the leadership did not identify the strategies of “emphasize inquiry and
problem solving” (Stringer, 1999) and “Emphasize articulation with feeder schools”
(Marzano, 2003).
The interviews and the questionnaire responses all spoke to the ability of the
leadership to delegate. This was specifically evident in the Principal’s willingness to
acknowledge the limitation of the leadership in math content and as such they have
engaged school leaders and delegated the math leadership to those with greater
expertise (Northouse, 2001). This is reflected by the empowerment of the math
coach and the instructional math manager to lead, organize and guide the Math
Department. This was reiterated by a number of the teachers: that the administrators,
specifically the Principal, works in the capacity of facilitator who has created and

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provided a structure that utilizes the talents of the teaching staff to lead the efforts in
all changes related to math instruction and department organization.
This conceptual framework for research question five utilized twelve
strategies that support leaders as leaders and as instructional leaders that have limited
expertise in specific areas; how do they mitigate and utilize resources and strategies
to compensate.
Strategy Item 1: Delegate Leadership to Assistant with Greater Expertise
This is almost a hallmark of the school structure, as the Principal has had the
confidence and foresight to utilize the strengths and expertise of others. In doing so
she has sought to empower the Assistant Principal for Curriculum and Instruction,
the instructional manager and the math coach to take the instructional lead in moving
the math department forward. The leader was able to identify her skills of delegating
to those with greater expertise as a strength and strategy that supports the teachers
and ultimately the students. While the Principal clearly is in charge, she is viewed as
taking more of a “facilitator” role. The Principal assumes the responsibility of
supporting the math leadership through her commitment to support and collaborate
with the math leadership to move forward with the goals of their program. To
accomplish this she has empowered the math department leadership; she supports by
providing resources and working in a collaborative partnership. In this respect her
skills as a leader have compensated for her lack of expertise in math.
Additionally the Principal has sought the expertise of her administrative team
with the greatest math expertise and background to conduct the evaluations of the

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math teachers. On the non-teacher survey question #23 asked about the Principals
delegation of “curriculum authority” to an administrator with greater expertise, this
too had a response of “strongly agreed”. This further highlights the leader’s insight
and strengths as a leader by her willingness to utilize the skills and expertise of her
administrative team in an effort to support the math program.
Strategy 2: Empower Department Chair
Vista High School has redefined the role of the department chair into what
they call the instructional manager. The teacher’s spoke of and delineated between
the role of the instructional manager and the math coach. The person who is
currently the instructional manager only took over this responsibility this year. His
passion and love of math were noted by teachers during the interviews. The
instructional manager assumes the responsibility of operational items; ensuring
teachers have necessary support materials, working with the administration to
develop the master schedule, lead the development of course maps, assessments,
planning and organizing the professional development. Whereas the math coach is
just that, providing instructional support in and out of the classroom; modeling
lessons and working on lesson development. Each of these roles has supported the
leadership dilemma of limited expertise in math. She has a collaborative working
relationship with these two individuals and uses their experiences and relationships
with the math teachers to establish a coherent math program.

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Strategy 3: Bring in Outside Expertise
The teachers and the leadership communicated a belief that their professional
development and growth as a department has come from within, which has fostered a
greater commitment from the teachers. The overall response on the math teacher
questionnaire on the item which asked about utilizing “outside experts” to promote
math instruction was neutral which was somewhat surprising based on the clear
articulation of the math teacher’s belief’s that progress and improved instruction has
come from within the resources of the school site. With the exception of the
partnership with California State University Fullerton which has been a partner with
the school prior to the school receiving the Math and Science Grant which ended last
year, all of the math professional growth activities have been designed and created
by the math department leadership in collaboration with the larger math department.
The school has created their own actions and objectives with regards to moving and
improving the instructional math program and student achievement. The leadership
has sought to utilize the skills and expertise of those in the building, looking to build
capacity within the school. The response on the non-math teachers’ questionnaire to
the same question, with the language slightly modified to be more applicable to all
departments, had a higher response indicating they do believe that outside experts
have been both utilized more and have helped the departments build capacity in their
instructional program. This may be a reflection that while each of the core
departments do have instructional managers that are the leaders of the departments,

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they do not have a dedicated content specific coach to support the teachers and the
instructional program, as such they engage outside experts to provide this support.
Strategy 4: Emphasize inquiry and problem solving
The leadership and the teachers believe, as reflected by their responses to
questionnaire items and interviews, that embedded within the math curriculum was
the teaching of inquiry and problem solving skills. This is at the core of the CPM
curriculum, as investigative teaching methods are utilized and emphasized in the
instruction. One teacher stated her feelings regarding the approach taken by the CPM
program that was shared by many of the math teachers. She stated, “…the kids get
to investigate and discover the math for themselves…which is really different than
the traditional math…the kids understand not only how to do the math but the why as
well…” This reflects the approach that is unique to this instructional [math] model.
However it was not a strategy identified by the leadership that was utilized to
compensate for the Principals lack of content expertise. While the Principal did not
identify this as a strategy she uses or has utilized, it did seem to the researcher that
the Principal through the process of collaboration does engage members of the
leadership team in problem solving activities that assist them in the facilitation of
adult and student learning. Each time the researcher was present on campus the
Principal was actively participating with department and administrative leaders in
conversations that focused on ensuring that an effective standards based instructional
program guided by researched base strategies was in place and informing the
instruction in the classroom. The process of inquiry and problem solving may not be

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conducted in a formalized or articulated manner, but it does appear based on
observations and teacher responses that the leadership does uses these strategies to
support the teaching and learning.
Strategy 5: Emphasize quality instruction
The Instructional Leader has established structures and systems as a means of
ensuring quality instruction and collegial support in an effort to ensure that all
teachers are providing effective instructional strategies. This is reflected in the
structure of Evidence of Quality Teaching (EQT) in which the teachers observe one
another and share observations. This was a system that was initially met with
resistance, possible in part because the formal documentation, a formality that has
since been lessened. This process has assisted in making teachers feel less isolated,
as one teacher stated, “it has taken us from islands of isolation from one another
when one teacher has no idea what the teacher next door to them is teaching”. Now
the teachers partner with the teachers they select and support each other through
informal observations; providing feedback on what appeared to work and what were
the specific challenges of the lesson. This focus has provided the teachers with a
greater sense of accountability to each other and has positioned the leadership as
facilitators of change in how teachers interact and support their colleagues to
improve math instruction. The protocol of EQT was a process that the teachers and
the coach indicated as really having a positive impact on the teacher’s ability to
support each other and to provide opportunity for, “collegial conversations”.

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Strategy 6: Emphasize strategies to engage students in the learning process
The math curriculum of CPM is organized in a manner that creates active
student engagement and is an essential component of the design of the program. This
has been viewed by the leadership and the teachers as a positive factor in improving
the math achievement and learning of the students at Vista High School. Rather than
the students being passive receptors of information they are engaged with solving
problems and with their own learning. The teachers report that having the students
engage in solving word problems has increased their level of understanding, and they
have an increased level of knowing why a math problem is solved in a certain way.
Based on the aforementioned indicators it was a surprise to the researcher that the
administrative leadership did not identify this as a strategy utilized.
Strategy 7: Emphasize articulation with feeder schools
The relationship with the feeder schools was at the core of the ALPHA Math
Project as shared by the math coach who shared that articulation with the different
level math teachers and feeder schools has been a result of the grant. The design
included identifying math coaches, who were then trained to work specifically with
the different schools and the school feeder patterns. The intent was to strengthen and
in some cases create a vertical articulation of the district math program. The
leadership of the school identified this as a critical component as students were
arriving at the high school without having had a consistent math experience,
exposure and expectations. When the math coach wrote the grant he included vertical
instructional articulation between elementary, middle and high school as an essential

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aspect of a cohesive and consistent math program for all students. However the
administration did not identify this as a strategy for compensating for the lack of
expertise. Rather they identified this not as a strategy but a decision that was based
on the fact that they did identify the vertical articulation structure as sound
instructional concept that would ultimately lead to better prepared students based on
the familiarity and common understanding of math teachers across grade levels.
Accordingly the coaches have worked together to create curriculum maps,
which describe what concepts should be taught using the California Content
Standards and the CST Test Released Items. The math coach at Vista High School
has been the impetus of this effort and has worked with the instructional leader along
the way, receiving comments and suggestion but the true leadership of the
instructional and design aspects must be given to the math coach. This
acknowledgment by the leadership to empower the math coach’s leadership goes
back to her ability as a leader to turn “power” over to those who have the expertise
and skills.
Strategy 8: Emphasize raised expectations
This strategy of emphasizing raised expectations is one the leadership and
teachers identified as being evident and expressed by the practices and structures the
leadership has facilitated, in an effort to ensure that the teachers are improving their
craft as evidenced by the improved student performance. When interviewing the
math coach he stated that the improved achievement was related to expectations that,
“…there is a sense that this school is about students achieving and that it is not ok for

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groups of students to not be successful”. Given this as a belief at the school and
specifically within the math department the expectations for the teachers and the
delivery of a quality math program is clear.
There is evidence that there is a structure in place that Vista High School
calls, Evidence of Quality Teaching (EQT) that is utilized as a process and a tool for
teachers to share and learn from each other. The leadership’s commitment to EQT
and the willingness to modify the structure from a more formalized process to an
informal observational process reflects the leadership’s commitment to providing
opportunities and expectations for the teachers to be active in the process of
improving what they do in their classrooms to teach students, while also responding
to the needs of the teachers. As one teacher stated,” the administration has high
expectations for what we do in the classroom and I think they realized that if they
didn’t change the EQT structure it would get lost and resisted by the teachers, which
they didn’t want because it is a good process. EQT let’s us share what is working and
helps me in my classroom”. The structures and processes within the math
department are developed around the objective of improving instruction so as to have
positive impact on the student’s performance. While the teachers clearly look to the
math coach and the instructional managers as the instructional leaders of their
department they at the same time acknowledge that the Principal and the Assistant
Principal of Curriculum are providing the support, guidance and expectations for the
instructional program and the math leaders do meet on a regular basis to discuss the
progress toward the goals of improving instruction by setting high standards. As the

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math coach put it, “…they have been good at the higher level leadership…this has
been in the background of what is happening in the math department”.
Strategy 9: Emphasize strategic teacher assignments
The selection of which teachers will teach what courses is done with
deliberate effort. The leadership identified this as critical to creating the master
schedule; the teaching assignments are made based on the need of the students and
the need of the master schedule. There is no one teacher that “gets to” teach select
courses. An example of this is the instructional manager for math the department; he
teaches Calculus but also has had the lower level of CPM Algebra. This type of
course distribution has been the priority of the department, and has become part of
the culture; everyone does their part to support each other and the students. As
indicated by the math coach, “It [math teaching assignments] has been real important
in terms of keeping the veteran teachers in contact with all the students, not just
leaving the more challenging classes, in terms of student behavior to the new
teachers”. He went on to say, “…there has been a kind of commitment to doing our
best to provide a quality experience for kids at all levels of the math program”.
Strategy 10: Emphasize revised course scope and sequence and/or curriculum
As a means of providing a consistent math instructional program the
leadership has ensured the development of course curriculum resource guide maps
that articulate the standards and concepts to be taught and when this is to occur in the
trimester and it further delineates the specific materials and teacher resources for
each math course. This serves as a valuable tool for the teachers and provides the

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leadership with a clearly articulated calendar and structure that allows them to
effectively monitor the instructional program and to ensure that (the appropriate)
material is being taught. As one of the newer teachers shared, “the maps we have for
each of the classes we teach are really helpful. As a newer teacher it allows me to
focus more time on preparing instead of trying to figure out what I am supposed to
teach everyday”. In addition to this the math leadership has also developed the
“Power Standard’s Pacing Guide” which is predicated on the standards identified in
the test blueprint for the standardized assessment, California Standards Test (CST) as
those that are essential and that the students must know for the CST that is
administered in the spring. The guides identify Power Standards and articulate the
time that teachers must allocate to teaching for student understanding.
Strategy 11: Emphasize interventions for lower performing students
This is a strategy that is part of the Math Department’s philosophy of
supporting all the students and ensuring they are able to successfully meet and/or
exceed the math graduation requirements which includes passing Algebra as one of
the three year requirements and passing the CAHSEE. The leadership realizes the
need and the importance of providing opportunities for the students who struggle
with math to receive additional time and support. This is evidenced by the classes
and support that the administration has sought to create within the school day and
after hours.
Within the regular school day the Principal and Assistant Principal for
Curriculum and Instruction have focused conversations with the math leadership to

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create additional learning opportunities for the students. One course that has been
created are the CAHSEE support classes that 11
th
and 12
th
grade student must enroll
in if they have not passed the CAHSEE, this is true for both English and math. The
Assistant Principal has sought the input and expertise of the math leaders and
teachers in creating these courses to meet the learning needs of the students. A math
leader spoke to this saying, “… the administration is really good at talking with
people to get input like when the CAHSEE math course was being created…the
leadership asked about the best materials and the structure of the classes”. This same
kind of effort was made by the administration when the tutoring club was created for
the students after school. The leadership seeks to utilize the expertise of the math
leaders and the teachers by describing their instructional objectives of supporting the
student and then taking the input to create the courses and supports based on the
input from those who are actively engaged in the instruction of math.
Strategy 12: Emphasize professional development
As a means of ensuring quality instruction, developing the teachers as
professionals and as experts in their respective content areas, the leadership has
provided professional development as a critical component of the math instructional
program. This is evidenced by the ALPHA Math Project which has as its guiding
principle the value and importance of professional development. The administration
has utilized the expertise of the math leadership to help organize and facilitate this
which has been instrumental in creating a cohesive well articulated math program.
Outside of the this, as a means of ensuring that the teachers are talking with one

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another the administration has also established in collaboration with the math
leadership the Curriculum Sharing process, created a master schedule that allows for
teachers teaching the same math course to have a common preparation period, time
is created for department meetings and the system of EQT further fosters
collaboration and has “pulled” teachers from their comfort zones providing veteran
and new teachers opportunities to learn from each other.
The administrative leadership, while they are not the math experts on the
Vista High Campus, is able to utilize their leadership expertise to access strategies
that have created an instructional program across the school that is designed with the
student and adult needs in mind. This ability and willingness to reach out and engage
others is not only a reflection of leadership but also an indication of confidence. The
teachers identify the administration as participating in a facilitator capacity,
recognizing that were it not for the willingness and insight of the administration to
acknowledge the expertise of others much of what is happening to support the math
instructional program would not be in place.

Analysis and Discussion

The acceptances of new policies and of new programs in an organization are
impacted by the culture and political climate (Marsh, 2002). This is reflected in our
public school system as it is in the private sector; change is often met with resistance.
The leadership and community of Vista High School recognized the need to re-
evaluate how they were instructing students in math. Accordingly, they made

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changes in the instructional program in math, the school design and the leadership
made decisions that would engage the leadership of the math department resulting in
a greater capacity coming from within the department to lead the efforts in math.
Vista High School recognized the need for change in math, over the years their
English Language Arts scores were doing “ok” the school had implemented a
Language Arts program that was addressing the needs of students who were having
academic challenges, but the math scores were consistently low, and/or remaining
stagnant. The Principal worked with the department leadership to begin making
changes that related to the school design, curriculum and how teachers were being
supported.
The findings of this study were reflected in this chapter. The process of
ascertaining the findings was done through analysis of information provided by the
school and outside objective indicators. This information was then organized in
response to the five research questions. Although there were many factors that
contributed to increased math achievement at Vista High, there were three themes
that emerged as the foundations that have ultimately created the conditions for
improved math achievement at Vista High School.
Theme One: (Instructional) Leadership
The math achievement as reflected by the standardized state assessment
results show that the student math achievement at Vista High has increased
consistently the past six years, with some years reflecting substantial growth and
others more modest improvement. This was not the case prior to the Principal

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making and supporting decisions that would reorganize the instructional program,
support and provide the means by which teachers were enabled to become part of the
process.
According to Fink and Resnick (2001) instructional leadership ensures a
sufficient knowledge of the instructional program that is utilized by the school and
more specifically the departments. This knowledge allows for the Instructional
Leader to facilitate the implementation of the program. Vista High’s leadership,
while not math content experts themselves, demonstrated that through action and
decisions that reflected an understanding of the math program, they were able to
implement the systems and structures necessary to fully implement and improve
student achievement.
Accordingly, the leadership at Vista High School fostered and created a
shared vision for student achievement within the math department. They, specifically
the Principal, were able to accomplish this by developing a school culture that was
focused on teaching and learning as reflected in the collaboration of the teachers
using data as a means of making instructional decisions and fostering the underlying
tenet of this effort; a learning community that is student focused but respectful of the
need to support and provide opportunity for teachers to develop as professionals.
The Principal had the skills and the confidence as a leader to engage key
personnel within the math department that did have content expertise with regard to
the implementation of policies, designing the instructional program and changes that
would ultimately influence the math achievement. Her leadership style has served as

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a source of empowerment and insight for the math leaders in the math department.
This was most evident in the selection of the math coach and through the process by
which the math department determines who will be the instructional manager
(department chair) for their department, this was essentially a decision made by the
teachers from within the department.
The Principal stepped back from the overall day to day instructional
leadership, instructional decisions and implementation of the math instructional
program giving much authority to the math coach. This provided the opportunity for
the math coach and instructional manager to assume more active and essential roles
in the success of the students and improved math achievement.
The ability and insight of the Principal to delegate instructional authority to
the math coach and the instructional Manager afforded her the ability to support
other needs of the school community. As noted through the responses to the
questionnaire and more so in the interviews, the respondents indicated that the
administrative leadership offer support to the math department by their ability to
navigate challenges and problem solve so as to take more of the operational side of
the school out of the focus or concern for the department. As was shared in the
interviews the administration is very supportive and is involved but more as a
resource to the math leadership and as shared within the interviews, “pretty much let
the math coach and manager run the department”
The math coach, while very modest, demonstrated a leadership style and the
skills to create the enthusiasm and dedication necessary to actively engage a high

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school math department as a professional learning community (PLC). The math
department utilized the strengths of each other and student performance assessment
data to make instructional decisions. This has influenced how the math department
responds to the changes made and the increased accountability for teachers to
improve student achievement; the department has coalesced as their own PLC and is
accountable as a whole for the performance of their students.
The Principal has been the catalyst for the many changes that were made to
improve the overall math program and department at Vista High School. She
certainly has served as the leader of the school sharing the instructional leadership
with those who have the expertise and she taking a more Facilitative Leadership
position as a means of engaging the school in a change process. She utilized her
years as a professional educator to access resources to support the math department.
She communicated clear directions, high expectations and her knowledge of the
importance of relationships as a means of attaining instructional goals. As a means of
meeting goals she sought to ensure that she was engaging the right people in and out
of the classroom.
Theme Two: Teacher Collaboration
The role that teacher collaboration played has been a critical and essential
design element of the Vista High Schools improved math performance. Due to the
leadership from both the administration and the math department structures and
systems were created that support teachers and the instructional program. As well,
administration and the math department leadership increased accountability of the

189
teachers while acknowledging teachers and the importance of them engaging in
reflective thinking and collaborative conversations as professionals with the
knowledge and skills to improve student achievement.
The implementation of the curriculum sharing, common preparation periods
for same course teachers, shortened instructional day one day a week, department
meetings and the process of EQT all fostered a math department PLC that created
dialogue and an increased focus on how to improve student learning. This
collaboration facilitated a change of practice. The teachers with the support and
leadership of the math coach were unwrapping standards, discussing concepts and
engaging in analytical conversations about instructional practices that the prior to the
collaboration was not occurring. The ability to create a more “open door” policy that
forced teachers from the comfort of isolation and independence in their own
classroom appears to have been a critical aspect that changed the culture and
dynamic of the math department.
According to Marsh and Codding (1999) it is important that high schools
organize in such a way that they support professional development as a strategy to
improve math achievement for all students. This is in essence what the math
department at Vista High School did over the past six years. They regrouped the way
they interacted as a department and utilized these different structures as a tool for
their own professional development which is rooted in the concept of teacher
collaboration.

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Theme Three: School Design
The structure of the school and the flow of the school day has been a critical
aspect to the positive change in the school, both in terms of the student performance
and the culture of the department and larger school. The school made the decision to
explore different ways of organizing the instructional day; to analyze the findings on
which master schedule designs were positively impacting schools on the whole as
well as academics and student behavior. The leadership led the school community
through this effort and found that the trimester model of four periods a day, three for
teachers with one extended preparation period, would provide the structure needed to
support the Vista High School student and adult learning. It would provide additional
time in class for the students, fewer classes everyday and the teachers would have
more time for collaboration and few students in a given day. This model has proved
very instrumental in the consistent progress the school has made in student math
performance. The transition time had its challenges, certainly some teachers left the
school because this was not a schedule that worked for them, but overall the teachers
provided favorable feedback to the changes in the master schedule. This was echoed
by the response the school received in surveys provided to the students and the
parents; the changes in the master schedule structure was having a positive impact
and reception.

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CHAPTER FIVE

SUMMARY, CONCLUSIONS, AND IMPLICATIONS

Summary of Background

The public education system across America has been a source of debate for
at least the past fifty plus years. The conversations about what needs to be done to
improve the academic performance of our students has taken place at all levels of
society from the White House to the halls of congress, our school districts and even
our living rooms; from each conversation comes a different solution or idea as to
what will solve the dilemmas our public schools face. The poor performance of our
students in math has certainly been at the center of these conversations; other
countries are out performing our students as measured by international studies such
as the TIMSS. Additionally, the achievement gap remains consistent; especially
between our African America and Latino students when compared to their white
peers, and many of our schools are not providing rigorous and effective instruction to
prepare our kids--these issues reflect some of the areas for focus and concern.
The math performance of our students is cause for concern as they continue
to perform poorly on standardized assessment, which is further exacerbated as
students move from elementary to high school and perhaps most troubling is the lack
of progress in closing the achievement gap between not only the different ethnic
groups but between our students who come from socio-economically disadvantaged

192
homes as compared with those who do not. Nowhere are these concerns reflected
more clearly and more consistently than in our urban high schools.
There has been a plethora of policies, innovative instructional strategies and
curriculums all designed to support and improve student achievement, specifically in
the area of math. In isolation none of these are the answer however research does
identify some factors that have had more impact on student learning than others.
These include the teacher’s effectiveness and use of standards based instruction
(SBI), the role of the school leader and focused consistent professional development.
None of these provide “the” answer nor has there been a system that brings all of
these together translating into improved student achievement. This is evidenced in
our most challenged schools. These schools are charged with addressing unique
needs that are more prevalent in a diverse community and that is often complicated
by lower levels of social capital. Children who come from socio-economically
disadvantaged families are more likely to face challenges outside the doors of their
classrooms that may diminish the value of education or cloud their focus on the
import of education to their future.
In our efforts to improve math achievement at our public schools and
specifically at our high schools, educators have taken steps to redesign the school
day and the delivery of instruction. This reflects an effort to meet the different
learning styles of our children and to move away from a model of instruction and
school design that is not meeting the learning needs of our students. The new designs
models are intended to create the most optimum learning environment and

193
instructional program for our diverse learners in our urban high schools. These new
designs include reorganizing schools into small learning communities (SLC), the
community for learners program (CFL) and the creation of professional learning
communities (PLC). Each of these seek to personalized and improve the academic
performance of our students in the urban high school. All of these school designs,
school policies and initiatives have been implemented to address poor student
achievement and must work in a cohesive way towards improving student
achievement.
In this context for student learning the role of the leader has become
increasingly more critical. Research confirms that the role of the school leader in our
urban schools is an essential component towards the successful implementation of
school reform efforts. The leader must be able to “mobilize people to tackle tough
problems” (Barth, 2001, Murphy & Datnow, 2003, Heifetz 1994). To this end the
leader must have the capacity, the skills and the passion to engage the school
community in a constructive dialogue that results in actions that transform the school
and the approaches utilized to improve the learning and achievement of all children.

Purpose of the Study
The purpose of the study was to examine the factors that positively
influenced the math performance of students in one urban high school. The study
explored the elements of the school design, the strategies and best practices used
within the classroom and the role of the school leader in shaping and directing the

194
school improvement efforts. The study also sought to incorporate an understanding
of how instructional leaders, who lack strong pedagogical content knowledge in
mathematics education, were able to impact significant mathematics achievement at
the school site.
The research questions that guided this study were:
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement at the
school?
3. What change process did the school use to enhance the math program
and strategies to assist students in math?
5 To what extent was strong instructional leadership important in
improving A) the math programs/strategies and B) math achievement
among students?
6 How did instructional leaders respond to academic areas in which
they are not experts?

Methodology
This case study utilized a mixed method approach: both qualitative and
quantitative that included document analysis, interviews, and questionnaires to find
conclusions about the conditions present in one urban school that supported

195
improved math achievement and the role of the instructional leader in this effort.
The qualitative findings were able to provide insight and were identified through the
interview process with administrative and teacher leaders and the math teachers.
Through this process and in conjunction with the five frameworks the researchers
was able to identify and organize themes, patterns and factors believed to have
attributed to improved math achievement and the role of the instructional leader.
The quantitative data was collected using the two item response
questionnaires administered to the math teachers and the non-math teachers. This
data was subsequently calculated and coded to identify areas of strengths and
weaknesses as it related to the research questions and frameworks. Additionally
source data from both the school and the California Department of Education was
collected as a means of providing additional quantitative data. Using both the
qualitative and quantitative data sources and the review and analysis of documents
the findings were triangulated as a means of improving the validity of the findings.

Conceptual Frameworks

Five conceptual frameworks were used as a means of framing the collection
of data for this study. Each of these frameworks was developed in alignment with
research questions two through five. The first research question did not have a
conceptual framework. Two conceptual frameworks, Conceptual Framework 1
(CF1) and Conceptual Framework 2 (CF2) were designed to provide structure in
answering the second research question. CF1 delineated effective research-based

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school designs utilizing the elements of the Marsh & Codding (2002) school design
model. CF2 addresses the research-based elements of effective math programs.
Conceptual Framework 3 (CF3) is designed around the Four Frames of
Leadership described by Bolman and Deal (2003) which are labeled; structural,
human resources, political, and symbolic. These were utilized as a means of
understanding the way by which the instructional leader of the schools was able to
facilitate and move the change process forward. CF3 was organized to collect data
on the third research question. The fourth Conceptual Framework (CF4) was created
using the intellectual background theory of the Interstate School Leaders Licensure
Consortium (ISLLC) which identify the elements and/or standards of effective
instructional leadership (Hessel & Holloway, 2002; Johnson, 2002). CF4 was
developed to respond to the fourth research question. The fifth conceptual
framework (CF5) was designed using two components to answer the fifth research
question. The first component of CF5 was the flow chart which was adapted from
the No Child Left Behind (NCLB) act that is utilized to determine whether a teacher
is a highly qualified teacher (HQT). This instrument was used to determine the
instructional leader’s level of math expertise as low, middle or high. The second
component included a list of 12 of the most common strategies used by school
leaders to support them in content areas in which they are not experts.
Sampling
A purposeful sampling process was used to provide an opportunity to conduct
a thorough investigation and to explore more deeply the processes related to the

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research questions of this study. The 11 member research team, under the guidance
of Dr. David Marsh from the Rossier School of Education at the University of
Southern California, defined a criterion by which school selection was determined.
The first criteria was that it was a Southern California urban high school as defined
by a student population with at least 50 percent minority students, a total population
in excess of 1200 students and that the school had demonstrated an improvement in
student math performance as measured by the California Standards Test (CST) in
Algebra I. In addition to these factors the criterion included an Academic
Performance Index score of 600 or greater and a state wide ranking of five (5) or
higher. Additionally the stability of the school leadership was a consideration and as
such the Principal had to be in their current capacity for at least three years during
the time of improvement in math.
Instrumentation, Data collection and Analysis
The instrumentation for this case study was developed collaboratively by a
cohort of eleven doctorial candidates at the University of Southern California’s
School of Education. All members of the team participated in a seminar led by Dr.
David Marsh, Associate Dean of Academic Programs from the winter of 2005
through the summer of 2006. The research team worked during the summer of 2006
to refine the instruments prior to beginning the data collection process. Through this
process the team identified the themes that were associated with each of the
individual research questions and the four conceptual frameworks were developed as
a means of organizing and framing the research. The four conceptual frameworks

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(described in detail in the subsequent section with the corresponding research
question) were utilized to facilitate the process of the data collection instruments. All
of these are reflected in Appendices A-D as a means of organizing the collected data.
The data was collected utilizing five data collection instruments: School
Profile, Key Leader Interview Guide, Teacher Interview Guide, Math Teacher
Questionnaire, and General Teacher Questionnaire. The questionnaire was utilized
with teachers and the interview guides were utilized with Key Leaders and the Math
teachers. Each of the instruments was created and developed to ensure alignment
with the individual frameworks.
1. The School Profile instrument was to create a “picture” of the school the
characteristics of the school that was selected for the study. The cohort
worked together to select data points that would provide a comprehensive
picture of each school. After the elements were identified and collected it
was organized into three different domains; demographics, student
academic performance and general school information. The primary
sources for this data were collected by accessing the California
Department of Education’s website and source data provided by the
school leadership.
2. Two Interview Guides were developed to facilitate the collection of data
from the school leadership and the math teachers that was relevant to
research questions two through five. Both groups were interviewed as a
means of ascertaining their perceptions regarding the factors they

199
believed were critical to the improved student performance in math. The
questionnaires were developed by the cohort to ensure their alignment
with the conceptual frameworks. The interview guide was designed with
consideration for the time needed and as such neither interview would
exceed 40 minutes. Each of the instruments had 16 open ended questions
and were designed based on the semi-structured interview process based
on the protocol of Creswell (1998).
3. Two Teacher Questionnaires were administered: one that was designed
specifically for the math teachers and one for non-math teachers. Both of
these instruments were developed to facilitate the collection of data that
was relevant to research questions two through five. Consistent with the
design of the interview guides the questionnaire items were asked as a
means of gaining understanding for all of the teachers perceptions and
attributions for improved student math performance at the school. The
design of the questionnaires utilized a five point likert scale that had a
range of five; from strongly agree to strongly disagree. Both
questionnaires were designed to be completed in a time frame not to
exceed 30 minutes. The math teacher questionnaire had a total of 50 items
and the non-math teacher’s questionnaire had only 30 items.

200
Summary of Findings
The findings and the conclusions for each of the five research questions were
answered through an analysis of data retrieved from source documents, interviews,
and questionnaires collected in the process of this study. Selected findings for each
research question are reviewed.
Research Question One
The first research question asked “What was the pattern of math achievement
for various students at the school?” To answer this question data collection and
analysis was done utilizing documents that the cohort had identified from both the
school site on student performance and information from independent sources to
include the California Department of Education (CEE) website, the DataQuest
website and the School Accountability Report Card (SARC). The findings supported
the initial school selection criteria for improved student performance; the school had
demonstrated consistent improved student math achievement over the past five years.
The pattern of student achievement in math for Vista High has been positive
for the school as a whole. The Latino students represent 95.7 percent of the student
body at Vista High School as such the pattern of achievement for the “various groups
of students” is positive in that the school does not have true various ethnic subgroups
of students. The only other sub-group that is higher than one percent are the white
students who comprise just 2.2 percent of the student body and the remaining
percentage of students are African American, Indian American, Asian, and “other”
students combined. Thus we can see, that the achievement gap that persistent in the

201
state of California, and in the country at large, is also reflected in the academic
performance of Vista High School students. The pattern of growth for all students
has reflected a positive trajectory but the gap between different student groups is not
closing.
Research Question Two
As a means of understanding what the decisions were to create the conditions
for progress research question two asks, “What policy initiatives as well as
curriculum, instruction and related conditions seem to be related to improved math
achievement at the school?” In response to the larger educational accountability
system of No Child Left Behind (NCLB) and of those coming from the California
Department of Education (CDE) the school leadership made decisions regarding the
kind of instructional support and structures necessary to improve student
achievement.
The requirement that all students pass the California High School Exit Exam
(CAHSEE) beginning with the graduating class of 2006 and pass Algebra I to
graduate from high school has placed increased pressure and accountability on the
school to ensure that all students are sufficiently prepared to pass the CAHSEE exam
and that each student has the math knowledge and skills to successfully complete
Algebra I. In response to these increased requirements the leadership at Vista High
identified the need for additional instructional support and worked in a collaborative
manner with the leadership of the math department to create a course that had a low
student to teacher ratio and was focused on the individual instructional needs of the

202
students who had not passed the Math CAHSEE. As well, the number of Algebra
courses offered was increased by close to 20 percent in past four years.
The students in the 11
th
and 12
th
grade who had not passed the CAHSEE were
required to enroll in a CAHSEE focused math (or English) course in lieu of an
elective course. Additionally, not only had the number of Algebra I courses been
increased the leadership realized the need to organize these courses differently,
specifically in the context of a trimester where most courses were over two trimesters
as opposed to all three. The Algebra I courses were organized to be delivered over all
three trimester which not only mitigated the possible loss of retention of knowledge
but also gave additional time within the course. The one year course was spread out
what is equal to a year and half of instructional time.
On a broader level and in response to the national accountability guidelines
identified within the NCLB policy Vista High dedicated time and effort to the use of
student performance assessment data to address the instructional and learning needs
of the students. While the teachers on the whole had not identified as strongly as the
leadership the influence of NCLB on the policy decisions at the school, it was
apparent to the researcher that the school and math department leadership did make
decisions that were based on what is good for kids and the instructional program and
that the underlying impetus for these decisions were influenced by NCLB.
As a means of gathering performance data to measure the progress of
students Vista High created benchmark summative assessments for all core classes,
furthermore the teachers use formative assessments within their classrooms that are

203
created not as a department but by individual teachers. The benchmark assessments
were the foundation of teacher conversations either during the curriculum sharing,
the department meetings or during the subject specific group meetings. One teacher
articulated the general impact of the benchmark assessments when she said, “…the
benchmark assessment results have been helpful because it has improved the overall
instructional program, because teachers have a better understanding of what is
working and what is not”.
A decision that influenced the improved student achievement is the design of
the master schedule. Vista High switched from the more traditional one through six
period day six years ago when they implemented the trimester schedule they
presently follow; this has its pros and cons. Overall the master schedule provides
more flexibility for the students and the teachers in that the teachers have more time
for preparation and collaborative conversations with their colleagues and have fewer
courses each day. The students benefited from the increased time in each class and
the fact that they have fewer subjects to focus on each trimester.
Perhaps the most effective element of this school design model is not so
much specific to the trimester four-period day as it is to the leadership’s vision and
teachers’ buy in to the flexibility of the schedule from one trimester to the next. The
fact that the master schedule is organized based on the instructional needs of the
students as identified through the analysis of the data generated from the benchmark
assessments has been critical to ensuring students are appropriately placed into

204
classes and that they are not moved on only because the master schedule limits what
students can take.
Another positive aspect of the school design is reflected by the master
schedule’s organization which provides the teachers within their work day to
collaborate. The master schedule is organized to allow for teachers teaching the same
math course in a given trimester to have a common preparation planning period. This
made it possible for the teachers to use this time to collaborate and share
information.
All of these specific measures: shortened day, curriculum sharing, data
analysis, department meetings, common preparation periods and the use of
technology reflect the larger vision of the leadership to provide effective professional
development. The professional development which certainly includes these pieces
but is not limited to them has been a critical to the improved math performance. Two
other ways in which the commitment to professional development is evident is the
ALPHA Math Project which provides further time during the summer for the
teachers to participate in the “Summer Institute” with teachers from elementary to
high school and the commitment to having a Math Coach to lead and give shape to
this effort. The overall professional development for the Vista High Math
Department has been an essential element to the improved student achievement.
Research Question Three
The third research question focused on the change process, “What change
process did the school use to enhance the math program and strategies to assist

205
students in math?” The findings from both the interviews and the questionnaires of
the math teachers and the non-math teachers all indicated that the role of the leaders
was more as the facilitators of the change process and the department leadership--
specifically the math coach and to a lesser extent the instructional manager for the
Math Department--were the instructional leaders in the change process. This
question utilized the lens provided by Bolman and Deal’s Four Frames of
Leadership; Structural, Human Resource, Political and Symbolic to understand the
change process at the school.
The findings identified that the Structural and the Human Resource Frame are
the most influential and dominant in the implementation of any change towards
improved student achievement in math, and to a lesser degree the political and
symbolic frames. The administrative leadership clearly approaches leadership and
change from both of these two frames. The structures and systems that are in place to
support teaching and learning at Vista involved the administrative team as those
responsible for creating a structure that supports this effort and ensuring that the
“right” people are part of the implementation and leadership of the Math
Department. There are clearly articulated roles and responsibilities that are in place
to assist in the realization of the goals of the Math Department and larger school. The
administration as facilitators utilizes the strength of those they have selected for math
leadership positions by both the administration and the teachers.
The Political and Symbolic Frames are evident to a lesser degree as part of
the change process. The administrators are very business like and deliberate in their

206
policy decisions and allocation of resources, however there is no sense on the
campus that competition among staff, nor that resources are used as a means of
leveraging change. While Vista High does have in place opportunities for
recognition and celebration of students and adults it is not something that is the rally
point of the school community and as such the symbolic frame is not central to the
change process.
The change process of the school has come as a result of the administrations
confidence in their roles as facilitators and their ability to delegate and empower
others. They are definitely viewed by the teachers as the person(s) responsible for
allowing the leadership of the Math Department to make decisions regarding
instruction, professional development and to a slightly lesser extent the hiring and
releasing of staff. The administration, the Principal and the Assistant Principal for
Instruction and Curriculum are the leaders of the change process through a facilitator
role.
Research Question Four
This research question sought to understand, “To what extent was strong
instructional leadership important in improving A) the math programs/strategies and
B) math achievement among students? The purpose of this question was to
understand the role of the instructional leader in the improvement of the math
program and student math achievement. The framework for this question,
Instructional Leadership, identifies five areas in which the leader should have strong
knowledge: Vision for Learning, Supervision and Monitoring of Instruction,

207
Community and Political, Culture of Teaching and Learning, and Data Driven
Decision Making Analysis. The findings from the interviews and the questionnaire
indicate a level of understanding by the administration of each of the five areas but
two of the five areas were found to be more dominant, the Supervision and
Monitoring of Instruction and the use of Data Driven Decision Making.
Supervision and Monitoring of Instruction is an area that the administrative
leadership clearly identifies as important for improving student achievement. They
have sought to ensure that there are systems and structures in place that foster an
environment which provides the teachers with focused and dedicated time around
instruction for collaboration with colleagues. The evidence did not find that the
administration was the leader of the monitoring and supervision of the instructional
program. The department leaders for both the math and the non-math teachers were
viewed as those who led the effort and assumed the responsibility for monitoring the
instructional program.
As it related to specific teacher evaluations the Principal has been deliberate
in assigning what administrators are responsible for which departments, based on the
individual administrator’s level of content expertise. The leadership of the school
views the monitoring, supervision and the overall implementation of the instructional
program as best done in collaboration with those with the content expertise.
The element of this framework regarding Data Driven Decision Making and
Analysis relates to the extent to which the leadership utilizes data as a tool to inform
the instructional program, and to positively impact student learning and influence the

208
master schedule. This is an area that the leadership has given consistent focus to.
The teachers identified this as an area that is emphasized by the school leadership
and that data is an essential tool used by the teachers to improve their instructional
program. The school leaders have sought to infuse the use of data into conversations
between teachers and with administration as a means of making instructional
decisions and student placements.
The findings confirm the value the school leadership places on data as a tool
and is evidenced in the use of data by the administration to make teaching
assignments, designing the master schedule each trimester and the appropriate
placement of students into math classes.
Research Question Five
The fifth research question was designed to provide information on how the
school leaders compensated for areas in which they do not have background). The
question asked, “How did instructional leaders respond to academic areas in which
they are not experts?” This question utilizes the expertise flow chart which maps the
leader’s level of expertise and whether they have a low or high level of content
expertise and 12 research based strategies a leader can use as a means of
compensating for their low level of expertise. The list of strategies identified
includes: delegate leadership to an assistant with greater leadership; empower
department chairs; bring in outside expertise; emphasize quality instruction;
strategies to engage students in the learning process; articulation with feeder schools;
raised expectations; strategic teacher assignments; revised course scope and

209
sequence and/or curriculum; interventions for lower performing students and
professional development.
The findings highlight the Principal’s strengths as a leader, perhaps not in the
sense one thinks of the Instructional Leader but more in the capacity of Facilitative
Leader. She has a low level of math expertise based on the expertise chart but has the
confidence as a leader to acknowledge this and is secure enough as a leader to
delegate and empower others as department leaders. In addition to her ability and
vision for delegating leadership to others the administration has utilized other
strategies, structures and systems to compensate for lack of content expertise while
providing the math teachers with the resources to improve the achievement of the
students in math.
Of the twelve different research strategies the five that have been utilized
most consistently both because they are sound practice and to compensate for the
low level of expertise of the leader are: delegating leadership to assistant with greater
expertise, empowering the department chair, emphasizing quality instruction,
interventions for lower performing students and professional development. These
were identified within the interviews and revealed by the responses to items on the
questionnaires completed by the teachers.
The administration has utilized and empowered the math coach and the
instructional manager to assume much of the leadership of the math department.
Both the math coach and the instructional manager have developed the structures and
systems to support the collaboration and sharing between the teachers. This is

210
reflected in the curriculum sharing, the department meetings, and the subject specific
meetings. The teachers utilized these opportunities to establish a consistent and
valuable instructional program for the students and as a means of supporting one
another’s professional growth and skills.
The focus the school leader is on ensuring there is quality instruction in each
classroom as a means of improving student learning. The departments adopted and
implemented a process they call Evidence of Quality Instruction (EQT) a process by
which the teachers through informal observation of peers inform and improve their
instruction. This has been a structure that has assisted in the teachers having a greater
comfort level in sharing what is working in their classroom and what is not with the
larger group. This not only serves to provide insight for the teachers, it also provides
a level of accountability the teachers have to each other as professionals.
Each of these aforementioned strategies supports the next strategy of
emphasizing the importance of offering students additional instructional support
through intervention courses. Vista High has used the data, the teacher expertise and
the teacher collaboration to develop courses that are created based on the
instructional needs of the students. This is reflected in the 11
th
and 12
th
grade
CAHSEE courses for students who have not passed the CAHSEE prior to this point.
The administrative leadership emphasizes professional development as a
means of improving instruction and as a tool for developing the teachers as
professionals and experts in their respective content areas. Each of the structures and
systems used on a daily, weekly and/or monthly basis are functions of professional

211
development that the administrative leadership has organized with the department
leadership serving in the capacity of facilitator.
The schools overarching ALPHA math project which instituted the role of the
math coach has been the catalyst by which the professional development for the math
department has evolved. The expertise of the math department has been accessed as
a means of ensuring that the teachers are engaged in collaboration with each other.
The professional development of the department is not only reflected in the student
free days identified as “professional development days” but rather the concept of
professional development is realized not only as a department but also in smaller
dyads or triads of teachers who are growing as professionals through the structures in
place.

Conclusion

The findings in this case study of one urban high school in Southern
California, Vista High School provides confirmation for the importance of a focused
and deliberate approach to school reform. Vista High School has demonstrated
consistent, if incremental at some points, academic growth in the area of math. This
is a daunting challenge for our urban high school and Vista High under their current
leadership has taken the challenge to establish systems and structures that support the
improved math performance of their students. Certainly the policies at both the
federal and state level regarding monitoring the progress of all students have been

212
influential in the school reform efforts but it has been accomplished with the needs
of the students in mind.
The role of the leadership has been critical to the progress of the school. This
is reflected in the ability of the Principal and the Assistant Principal of Curriculum
and Instruction to empower others and utilize the strengths of teachers as valuable
resources without positional power interfering in decisions that support students. The
math coach and to a lesser extent the instructional manager of the math department
are definitely positioned as leaders of the department; this could only happen as a
result of choices made by the Principal.
The school design of Vista High has been organized to support both the
students and the adults as learners. The master schedules flexibility from one
trimester to the next is an essential and unique design; it is not common for teachers
to have different courses two or three times a year. This highlights the priority of
supporting the learning of the students and not the needs of the adults. The
organization of the master schedule into four blocks of extended instruction, only
three courses per day for the teachers, like subject preparation time, a shortened day
each week and the open door climate all support the concept of adult learning as key
to improved student achievement.
The selection of College Preparatory Math (CPM) as the primary math
program appears to be meeting the developmental and learning styles of the students.
By selecting a program that moves away from a traditional direct instructional
program at the exclusion of collaboration and utilizing, and program that integrates

213
both as a means of supporting the students and fostering their problem solving skills
and critical thinking, supports the finding that we “learn by doing”. The use of this
program also speaks to the focus on supporting the many English Learners (EL)
students they have as CPM is in essence the implementation of a hand on approach
used to support EL students.
Overall Vista High has confirmed that school design, instructional practices
and leadership all influence the achievement of a school. These three elements are at
the foundation of Vista High School’s effort to reform their instructional program to
support student learning. As they continue in their efforts the researcher hopes that
Vista High will continue to “raise the bar” for student achievement and expectations
and that this will be evidenced by an increase in the number of students taking
Advanced Placement (AP) courses, the number of students meeting the A-G college
entrance requirements and an increase in the number of students entering a four year
college from Vista High School.

Implications for Further Research

Based on the findings of this study, the following reflect recommendations
for additional research in this area:

1. To conduct similar research with other urban high schools with the
instruments improved and refined to better capture the information.

214
2. Further research on urban schools outside of the southern California region
would provide a broader perspective and insight on what is working in
schools across the country that have similar demographics and challenges.
3. A longitudinal study on the same topic of math achievement in our urban
high schools could provide and identify sustainable practices that have been
utilized by like schools.
4. Research that seeks to identify a connection between different content area
instructional programs and student achievement in math.
5. Research that assesses the role of the school design model as a single data
point on student achievement.
6. Research that identifies consistent elements that are present in math programs
utilized by urban high schools that have demonstrated positive growth.
7. Additional research that uses Bolman and Deals Four Frames of Leadership
as a means of understanding how the Instructional Leader pulls from these to
influence all aspects of school reform.

215
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Appendix A

Key Leader Interview Guide

Research Question Two: What Policy initiatives as well as curriculum, instruction
and related conditions seem to be related to improved math achievement in the
school?

Directions to Interviewer:
Describe the purpose of the interview, expected timeline, and introduce each topic as
the RQ changes. For this section:

“The first part of our interview, I will be asking you to describe your perceptions
about how policy issues have affected your efforts to improve student achievement
in math. Specifically, we will cover policy issues related to:”

POLICIES
ß NCLB- AYP/HQT
ß District
ß State Policies/API
ß CAHSEE

1. How do you perceive NCLB as having influenced your efforts to increase student
achievement?
AYP?
HQT?

2. What board policies and/or practices (if any) are in place that support increased
student achievement in math?
ß Benchmarks assessments
ß Financial resources
ß Additional Staffing / CSR

3. How has Standardized testing and the requirements to meet your API growth
target influenced your efforts to increase student achievement in math?

4. How do you feel the CAHSEE requirement has influenced your efforts to increase
student achievement in math?

230
CHANGE PROCESS

Research Question 3: What change process did the school use to enhance its math
program and strategies to assist students in math?

“Let’s turn our attention to how you handled the change process related to your
efforts to improve student achievement in math. Specifically, I will be asking you
about different aspects of the change process as described in Bolman and Deal’s
Four frames. In case you are not familiar with either of these models, here is a copy
of the frameworks for your reference and clarification. (Provide frameworks for the
interviewee). OK, so I will be asking you about”:

ß Structural changes (school design, leadership, use of facilities, etc. )
ß HR – Key Personal Changes
o Teacher assignments and master schedule
ß Political issues related to the changes made at your schools
o How did you negotiate the political aspects associated with you
change process
ß Symbolic Methods used to add meaning and importance to your initiatives
such as:
o Vision/mission
o Culture/climate
o Ceremonies/ awards/recognition

1. What structural changes have you made that you feel have contributed to
improved math achievement?
o School design
o Leadership
o Facilities
o CSR

2. What personnel changes have been implemented that has positively influenced the
math achievement?
o Teacher assignments
o Leadership roles

3. How did you negotiate the political aspects associated with the change process?
o Site level
o District level
o Community level

231
4. What did you do symbolically to support and engage in the change process that
has been implemented to improve math achievement?
o Vision/mission
o Culture climate
o Ceremonial/awards

Leadership Instrument RQ 4

Research Question 4: To what extent was strong instructional leadership important in
improving (a) the math programs/strategies and (b) math achievement among
students?

“I would now like to ask you about issues specifically related to the role of
instructional leadership in your efforts to improve student achievement in math.
Specifically, I will be asking about the roles leaders played and issued related to the
development of a professional learning community on your campus.”

1. Who were the leaders on your campus who helped bring about the improved
achievement in math?
a. What were their roles?

2. How was the professional growth of the math teachers supported?

3. To what degree was teacher collaboration and/or reflection fostered and
encouraged?

4. How has the school leadership worked to implement a professional
community on your campus?

a. Teacher empowerment
b. Teacher leadership
c. Peer collaboration
d. Reflection

5. In what ways have site leaders attempted to make the focus on student
learning and results

232
Leadership Questionnaire RQ5

Research Question 5: How did leaders in the school resolve dilemmas about
instructional leadership?

“Now let’s talk a little about how the site leadership went about overcoming any
obstacles you may have faced as you worked to improve student achievement in
math. You may find it useful to refer to the frameworks on change that I provided to
you earlier.”

1. What particular obstacles did you school face in the implementation of you
changes related to improved achievement in math?

2. How did the site leadership work to overcome these obstacles?

a. Structural Changes / Solutions
b. Human Resource Changes / Solutions
c. Political Changes / Solutions
d. Symbolic Changes / Solutions

233

Appendix B
Teacher Interview Guide

1. What is your current position?
2. Describe your educational background, credentials held, years of experience
and any specialized training you have had in math instruction.
3. What policy initiatives and/or curricular programs do you feel have
contributed to improved student achievement in math?
4. What teaching strategies, methods and/or instructional materials do you feel
have contributed to improved student achievement in math?
5. Over the past few years, what changes, if any do you feel have made a
significant impact on student achievement in math? How were they
implemented?
6. What role did school leaders (administrators, department chair, lead teachers,
math coaches) play in the development and implementation of the math
program?
7. What actions taken by school leaders most directly affected student
achievement in math?

234

Appendix C
Math Teacher Questionnaire

Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey in a sealed envelope to the
principal’s secretary by____________. Please be assured the questionnaires will
only be viewed by the researcher and not be viewed at all by site leaders. Once
again, your assistance is greatly appreciated.

Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

1. The No Child Left Behind Legislation has promoted increased student
achievement at
our school.
1 2 3 4 5

2. The requirement that students pass the CAHSEE to earn a high school diploma
has contributed to the school’s effort to improve student achievement.
1 2 3 4 5

3. Board Policies in our district have contributed to improved math achievement in
our school.
1 2 3 4 5

4. Our school has successfully implemented common assessments that support
increased
student achievement.
1 2 3 4 5

5. Teachers at our school teach standards-based lessons.
1 2 3 4 5

235
6. The master schedule at our school is built based on student need.
1 2 3 4 5

7. Teachers at our school use researched-based instructional strategies to increase
student achievement.
1 2 3 4 5

8. Periodic benchmark assessments provide useful data that our teachers use to drive
instruction.
1 2 3 4 5

9. Student need is a major consideration when making teacher assignments in math
at our school.
1 2 3 4 5

10. The NCLB Act has been one of the main external pressures for improved math
achievement at this school.
1 2 3 4 5

11. The requirement that students pass the CAHSEE in math in order to earn a high
school diploma has contributed to the school’s effort to improve math
achievement.
1 2 3 4 5

12. Our school’s effort to improve student achievement in math instruction had
nothing to do with external accountability such as NCLB regulations and the
CAHSEE requirement.
1 2 3 4 5

13. Support classes have been included in our master schedule to improve student
achievement in math.
1 2 3 4 5

14. The implementation of standards-based instruction has served as an important
foundation in improving student achievement in math.
1 2 3 4 5

15. Our school has added the use of math coaches or experts to assist in the effort to
improve student achievement in math.
1 2 3 4 5

236
16. Teachers collaborate to develop common assessments and rubrics.
1 2 3 4 5

17. Professional development offerings at our site are based on student achievement
data.
1 2 3 4 5

18. Teachers have helped develop strategies used at our school to improve
instructional practice in math.
1 2 3 4 5

19. The principal has served as a “change agent” for improved student achievement
in math.
1 2 3 4 5

20. Student achievement in math was made a priority as the school allocated its
financial resources.
1 2 3 4 5

21. Our school had a clear strategic plan to improve student achievement in math.
1 2 3 4 5

22. Professional Development has played a key role in increasing student
achievement in math.
1 2 3 4 5

23. Teacher collaboration has played a key role in increasing student achievement in
math.
1 2 3 4 5

24. Changes in the curriculum have played a key role in increasing student
achievement in math.
1 2 3 4 5

25. Our school has implemented effective intervention strategies for students having
difficulty in math
1 2 3 4 5

26. My district supports teachers with effective staff development in Mathematics
Instruction.
1 2 3 4 5

237
27. My principal actively supports opportunities for staff members to collaborate
and plan Mathematics lessons and units.
1 2 3 4 5

28. Teachers learn by watching each other teach and discussing best practices.
1 2 3 4 5

29. Our school has effective strategies to support students of various learning
modalities.
1 2 3 4 5

30. Our school uses math coaches to help teachers become more reflective with their
math instruction.
1 2 3 4 5

31. I have gained valuable resources from math coaches/instructional leaders that
have improved the quality of my math instruction.
1 2 3 4 5

32. My school's instructional leader provides professional development resources
that I use in my mathematics instruction.
1 2 3 4 5

33. The school leader is aware of the mathematics instruction and academic progress
of the students in my class.
1 2 3 4 5

34. The school leader provides opportunities for faculty members to discuss
mathematics instruction.
1 2 3 4 5

35. The school instructional leader encourages faculty members to discuss effective
math instructional strategies.
1 2 3 4 5

36. My school's math instructional practices are developed from evidence-based
strategies.
1 2 3 4 5

37. I have regular support from proven instructional leaders in math instruction.
1 2 3 4 5

238
38. The math achievement goals and measures for my school were clearly
articulated and easy to understand.
1 2 3 4 5

39. I received coaching and mentoring from instructional leaders or peer coaches.
1 2 3 4 5

41. The district personnel, school leaders and teachers all have a shared vision for
increased math achievement.
1 2 3 4 5

42. My district and school leaders seem knowledgeable about instructionally
effective math practices and assessment strategies.
1 2 3 4 5

43. The Math Department Chair has been entrusted with and is empowered to make
important curricular decisions.
1 2 3 4 5

44. Outside experts have been used to promote greater capacity in the area of math
instruction.
1 2 3 4 5

45. The school’s leaders emphasize the importance of quality instruction as a
primary mission of the school.
1 2 3 4 5

46. Professional Development in math has been a key tool used by site leaders in our
effort to improve instruction on our campus.
1 2 3 4 5

47. Site leaders emphasize having high expectations for student achievement in
math.
1 2 3 4 5

48. Quality interventions in math have been implemented on our site to help
students at risk of failing academically.
1 2 3 4 5

49. Our site leaders emphasize a culture of collaboration as a means of improving
instruction at our site.
1 2 3 4 5

239
50. Teacher assignments in the math department are made strategically and with
student need in mind.
1 2 3 4 5

240

Appendix D
Non-Math Teacher Questionnaire

Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey to the principal’s secretary
by October 15, 2006. Once again, your assistance is greatly appreciated.

Directions: Please rate each item on the following scale by circling the response of
your choice:

5= Strongly Agree
4 = Agree Somewhat
3= Neutral
2 = Disagree Somewhat
1= Disagree Strongly

Research Question Two: What Policy initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math
achievement in the school?

1. The No Child Left Behind Legislation has promoted increased student
achievement at
our school.
1 2 3 4 5

2. Our school has successfully implemented common assessments that support
increased
student achievement.
1 2 3 4 5

3. Teachers at our school teach standards-based lessons.
1 2 3 4 5

4. The master schedule at our school is built based on student need.
1 2 3 4 5

5. Student need is a major consideration when making teacher assignments in math
at our school.
1 2 3 4 5

241
6. The NCLB Act has been one of the main external pressures for improved math
achievement at this school.
1 2 3 4 5

7. The requirement that students pass the CAHSEE to earn a high school diploma
has contributed to the school’s effort to improve math achievement.
1 2 3 4 5

8. Our school’s effort to improve student achievement in math instruction had
nothing to do with external accountability such as NCLB regulations and the
CAHSEE requirement.
1 2 3 4 5

9. Board Policies in our district have contributed to improved math achievement in
our school.
1 2 3 4 5

10. Support classes have been included in our master schedule to improve student
achievement in math.
1 2 3 4 5

11. Our teachers exercise researched-based methods in instruction to increase
student achievement
1 2 3 4 5

12. Periodic benchmark assessments provide useful data that our teachers use to
drive instruction
1 2 3 4 5

Research Question 3: What change process did the school use to enhance its
math program and strategies to assist students in math?

13. The implementation of standards-based instruction has served as an important
foundation in improving student achievement in math.
1 2 3 4 5

14. Our school has added the use of math coaches or experts to assist in the effort to
improve student achievement in math.
1 2 3 4 5

15. Teacher collaborate to develop common assessments and rubrics.
1 2 3 4 5

242
16. Professional development offerings at our site are based on student achievement
data.
1 2 3 4 5

17. Teachers have helped develop strategies used at our school to improve
instructional practice in math.
1 2 3 4 5

18. The principal has served as a “change agent” for improved student achievement
in math.
1 2 3 4 5

19. Student achievement in math was made a priority as the school allocated its
financial resources.
1 2 3 4 5

20. Our school had a clear strategic plan to improve student achievement in math.
1 2 3 4 5

21. Professional Development has played a key role in increasing student
achievement in math
1 2 3 4 5

22. Teacher collaboration has played a key role in increasing student achievement in
math.
1 2 3 4 5

23. Changes in the curriculum have played a key role in increasing student
achievement in math.
1 2 3 4 5

24. Our school has implemented effective intervention strategies for students having
difficulty in math
1 2 3 4 5

25. My district supports teachers with effective staff development in Mathematics
Instruction.
1 2 3 4 5

26. My principal actively supports opportunities for staff members to collaborate
and plan Mathematics lessons and units.
1 2 3 4 5

243
27. Teachers learn by watching each other teach and discussing best practices.
1 2 3 4 5

28. Our school has effective strategies to support students of various learning
modalities.
1 2 3 4 5

Research Question 4: How was instructional leadership important in improving
a) the math programs/strategies and b) math achievement among students?

29. Our school uses math coaches to help teachers become more reflective with their
math instruction
1 2 3 4 5

30. I have gained valuable resources from math coaches/insturctional leaders that
have improved the quality of my math instruction.
1 2 3 4 5

31. My school's instructional leader provides professional development resources
that I use in my mathematics instruction.
1 2 3 4 5

32. The school leader is aware of the mathematics instruction and academic progress
of the students in my class.
1 2 3 4 5
33. The school leader provides opportunities for faculty members to discuss
mathematics instruction.
1 2 3 4 5

34. The school instructional leader encourages faculty members to discuss effective
math instructional strategies.
1 2 3 4 5

35. My school's math instructional practices are developed from evidence-based
strategies.
1 2 3 4 5

36. I have regular support from proven instructional leaders in math instruction.
1 2 3 4 5

37. The math achievement goals and measures for my school were clearly
articulated and easy to understand.
1 2 3 4 5

244

38. I received coaching and mentoring from instructional leaders or peer coaches.
1 2 3 4 5

39. The school leaders consistently monitored math achievement outcomes.
1 2 3 4 5

40. The district personnel, school leaders and teachers all have a shared vision for
increased math achievement.
1 2 3 4 5

41. My district and school leaders seem knowledgeable about instructionally
effective math practices and assessment strategies.
1 2 3 4 5

Research Question 5: How did instructional leaders respond in academic areas
in which they were not experts?

42. The school leaders used data-driven information to address problems/issues
related to math performance and achievement.
1 2 3 4 5

43. My students' math performance was systematically measured.
1 2 3 4 5

44. There is a regular and routine process for teachers to communicate math
instruction and performance problems to school leaders.
1 2 3 4 5

45. The school leaders solicit my input when attempting to resolve dilemmas or
make important instructional decisions.
1 2 3 4 5

46. The leadership behaviors of the school administrators greatly contributed to the
growth in math achievement.
1 2 3 4 5

47. The school leaders and teachers worked collaboratively to solve math
performance problems and dilemmas.
1 2 3 4 5

48. The school leaders have regular and quality interactions with math teachers.
1 2 3 4 5

Abstract (if available)

Abstract The research consistently finds that our greatest challenge in California public schools resides in our urban schools as defined by high poverty, high minority and low performance. The math performance of our students is significantly lower in public urban secondary school across the country and specifically in California. This has been evidenced by student performance on state assessments and the high percentage of students not passing the math portion of the California High School Exit Exam (CAHSEE), which is a state required graduation requirement. These facts of increased the focus on K-12 math performance from both state and federal agencies.

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Asset Metadata

Creator Abrahamson, Margaret Anne (author)

Core Title Improved math achievement in an urban high school: a case study of a high school in the Vista Unified School District

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 08/13/2007

Defense Date 05/08/2007

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

Tag instructional leadership,math program,OAI-PMH Harvest,secondary reform

Place Name California (states), San Diego (counties), school districts: Vista Unified School District (geographic subject), USA (countries)

Language English

Advisor Marsh, David D. (committee chair), Olsen, Carlye (committee member), Rousseau, Sylvia G. (committee member)

Creator Email mabrahamson@pusd.us

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m789

Unique identifier UC1126215

Identifier etd-Abrahamson-20070813 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-545201 (legacy record id),usctheses-m789 (legacy record id)

Legacy Identifier etd-Abrahamson-20070813.pdf

Dmrecord 545201

Document Type Dissertation

Rights Abrahamson, Margaret Anne

Type texts

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

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu