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High school math reform and the role of policy, practice and instructional leadership on math achievement: a case study of White Oak Tree High School

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High school math reform and the role of policy, practice and instructional leadership on math achievement: a case study of White Oak Tree High School

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Content HIGH SCHOOL MATH REFORM AND THE ROLE OF POLICY, PRACTICE
AND INSTRUCTIONAL LEADERSHIP ON MATH ACHIEVEMENT: A CASE
STUDY OF WHITE OAK TREE HIGH SCHOOL

by

Jennifer Denise Smith

___________________________________

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 Jennifer Denise Smith
ii

DEDICATION

This dissertation is dedicated to my father, James P. Nobles. Daddy, even
though you did not have the opportunity to share in this celebration, I know you are
doing that “grin” thing from on high. I know you would be exceptionally proud that
my educational journey ran full-circle back around to the University of Southern
California (USC), one mile from where we lived. I remember you wanted me to
attend USC and become a “Trojan” as an undergraduate so we could walk to the
Coliseum on Saturdays and do our college “football thing” together; I opted to start
as an Arizona State University Sun Devil instead.
This dissertation is also dedicated to my uncle and aunt, Hadie and Verna
Sanders of Phoenix, Arizona. My aunt has always been my biggest cheerleader and
loves to “brag” about her niece in California at her job, the Beauty Shop, and to
anyone that she chats with. She prays for me regularly, supports me unconditionally,
and loves me passionately. My aunt is so proud and positively acknowledges that I
have, “exceeded all expectations”.
I would also like to dedicate this dissertation to my surgeons, doctors and
nurses and USC Norris Comprehensive Cancer Hospital. Words cannot express the
thanks and appreciation for the stellar treatment and care that I received during my
illness with Breast Cancer. I would like to publicly express my gratitude to my
surgeon, Dr. Dennis Holmes and Oncology Nurse, Sally Golingay, who ensured that
my spirit as well as my body continued to thrive. I cannot thank you enough Sally for
iii
also taking care of Meg with the big easy chair and blankets as she steadfastly
remained by my side during two surgeries, almost 100 hours of chemotherapy, and
over 14 months while we pursued our doctorates.
And finally, but in no way last, this dissertation is dedicated to my partner,
Dr. Meg Abrahamson. We began this educational journey together and finished it
together, on time, and with our relationship the stronger for it. Words cannot express
the love and gratitude I feel for you for your untiring love, support, patience and
“editing skills” especially when “chemo-brain” had me writing in circles in Chapter
1. I know I could not have gotten through this process without you, even though you
know I believe I am “superwoman”. I look forward to our new life together, post-
doctorate, and our growth as professionals, colleagues and as life-partners who will
continue to support each other, challenge each other and share laughter for years to
come. I love you, Dr. Meg.
iv

ACKNOWLEDGMENTS

I would like to thank and acknowledge my family, friends, and colleagues
who have provided endless words of encouragement and support during this arduous
educational journey towards my Educational Doctorate (Ed.D.) at University of
Southern California. I would like to acknowledge my skilled and masterful editor,
Dr. Shantanu Duttaahmed who pushed and challenged, and occasionally sent me
running to my English teacher friend, Carolyn Fagan for review on literary devices.
To my only niece, Aurianne Duncan who I regularly encourage and try to
model that life has no limitations; it is all about how hard you want to work to attain
success. I am also grateful to my parents, Olon and Jennie Wafer, who always
encouraged me and forbade other family members to call me during the final stages
of the writing process. I am so appreciative that my entire family came out en
masse, from as far as Texas and Arizona for the graduation and festivities; your love
and support have established the foundation upon which I have grown both
personally and professionally.
I would like to thank my AVID colleagues at the Los Angeles County Office
of Education, especially Dr. Paolina Schiro (USC 2006) and, Dr. Laurie Wiebold,
Project Director, who recognized a year ago, the scope of the work ahead of me and
insisted on shifting many of my work responsibilities to the fall. Laurie, I appreciate
your cheerleading and support with all of the health appointments, the sharing of
v
resources that were helpful to you in your dissertation process, and the coaching
during the “Chapters”.
Dissertation committee members Dr. David Marsh, Dr. Sylvia Rousseau and
Dr. Carlye Olsen, thank you for your guidance and support during the process and
especially for the intellectual rigor and discourse. Dr. Olsen you were right, Dr.
Marsh is an expert in creating just the right amount of cognitive dissonance to keep
you focused on the writing goals. To professors Dr. Keith Howard and Dr. Richard
Brown, thank you so much for your support during the very difficult times both
academically and personally. I feel that I was able to successfully finish this program
because of your collective belief that I was capable of achieving at this level, and
that I had a legacy to build for our urban students.
I want to thank Dr. Caroline Bermudez and Dr. Kristen McGregor, part of the
original San Gabriel Cohort, and Dr. Kimberly Tresvant, Dr. Sergio Flores, and Dr.
Staci Erlandson Block, members of our cohort – we shared ideas, chapter drafts,
frustrations and finally success. Thank you for your contributions to this life-
changing process.
vi

TABLE OF CONTENTS

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

ACKNOWLEDGMENTS .......................................................................... iv

LIST OF TABLES ...................................................................................... vii

LIST OF FIGURES ..................................................................................... viii

ABSTRACT ................................................................................................ ix

CHAPTER ONE: Overview of the Study...................................................... 1

CHAPTER TWO: Review of the Literature ................................................. 25

CHAPTER THREE: Research Methodology ............................................... 75

CHAPTER FOUR: The Findings and Analysis ............................................ 117

CHAPTER FIVE: Summary, Conclusions and Implications ........................ 188

REFERENCES .............................................................................................. 213

APPENDICES ................................................................................................ 228
vii

LIST OF TABLES

Table 1: Academic Performance Index (API) for three years ....................... 83

Table 2: Relationship or Data Collection Instruments to Research
Questions ............................................................................................. 88

Table 3: Change Process Framework Bolman and Deal’s Four Frames
of Leadership ..................................................................................... 95

Table 4: Instructional Leadership Framework ................................................. 97

Table 5: Strategies to Overcome a Lack of Subject Competency ................... 101

Table 6: Sub-Groups Achieving at the Proficient or Advanced Level
in Math ................................................................................................ 122
Table 7: Comparison of the Percentage of Students Scoring Proficient
or Above ............................................................................................... 123

Table 8: Percent of Students Passing CAHSEE in Mathematics
by Ethnicity .......................................................................................... 125

Table 9: Percent of Graduating Students Meeting College
A-G Requirements ................................................................................ 128

Table 10: Report Card Analysis ........................................................................ 129
viii

LIST OF FIGURES

Figure 1: Framework for Effective School Design ........................................ 91

Figure 2: Framework for Effective Math Programs ...................................... 93

Figure 3: Assessment of Principal’s Expertise in math ................................. 100
ix

ABSTRACT
Poor student mathematics achievement in American public schools, as
determined by national and international rankings in math has resulted in tremendous
public and political pressure to reform our public educational systems. Current
federal and state accountability policies and systems have been focused on this issue
consistently for almost the last two decades. A plethora of school reforms have been
scattered across the public education landscape in response to the myriad needs of
our students and stakeholders. However, despite heroic efforts and financial
maneuvers, student achievement wanes and the gaps persist between white and
Asian students and students of color. The new paradigm of school management,
instructional leadership, has dominated the conversations and several configurations
of school designs, curriculum and instructional modifications have been pursued
with the goal of finding just the right recipe for student success.
The purpose of this study is to examine the conditions that fostered
mathematics achievement at one high school. Specifically the study examines school
design, school and classroom policies, conditions and best practices that enabled the
improvement in student achievement, and the role of the instructional leader in
shaping and directing the reform efforts in improving student achievement in
mathematics. The study also aimed to increase our understanding of how
instructional leadership impacted the creation of a culture for mathematics
x
achievement when the instructional leaders lacked strong, pedagogical knowledge in
mathematics as a subject area

1

CHAPTER ONE

Introduction

Background and the Problem

The historical debate over the rigor and efficacy of the American educational
system is not a new one. Public schools have not enjoyed the people’s trust and been
under public scrutiny that can be traced back to the 1800’s with the Industrial
Revolution and the centralization of the profession, which the public felt, would
eliminate professionalism and lead to the downfall of the education system (Murphy
& Beck, 1995). Then, through the first three decades of the twentieth century, public
schools struggled to take back local decision-making power and decentralize,
especially around such issues as curriculum and instruction (Murphy & Beck, 1995).
During the space race of the 1950’s, the collective public attention focused on the
global competitiveness of the United States and realized we were losing. The
American people wanted answers and looked to the public high schools for the
solutions. The focus on the mathematics achievement of high school students can be
cited to have started with the Sputnik launch in 1957. The launch of Sputnik by the
Russians indeed was a defining moment in America’s quest for mathematics and
science superiority. The Russians, America’s political and economic rivals, had won
the race to space, and the United States press reported this as a major humiliation
from a world perspective. This “loss” also highlighted the poor quality of

2
mathematics and science instruction in the public high schools. Prior to this period in
history, the federal government’s role in education policy had been virtually non-
existent, in response to the American public’s opposition and fear that federal
assistance would lead to federal control. Education analysts credit Sputnik with
spurring policymakers to mandate far-reaching educational reform (Bybee, 1998).
The need for reform, with respect to high school student performance in the United
States, clearly is not a new conversation between all stakeholders in the American
educational system. However, the dialogue has intensified over the last few decades
as issues such as American competitiveness on a global scale, the focus on all
students receiving a quality education, and the persistent achievement gap, have risen
to the forefront. These concerns have been justified in light of the performance of
American students on national and state assessments, and when compared with their
peers from other nations, clearly our students are not keeping up. Even though
American students are increasing slightly in mathematics and science achievement,
the United States’ “relative standing” to other nations has not improved (US
Department of Education, 1998). The pervasively poor performance of American
high school students has generated a series of educational reforms aimed at the
national, state, and local levels.
In the landmark report, “A Nation at Risk: The Imperative for Educational
Reform (1984), the National Commission on Excellence in Education (NCEE),
created by the Reagan-Bush administration, several indicators of deficiency were
highlighted, most notably declines in academic achievement since Sputnik, increases

3
in the number of remedial classes required at public 4-year colleges and universities
and the lack of mathematical problem-solving skills of 12
th
grade students. The
public outcry for a prioritization of public education above health care and military
spending reverberated throughout the states. A Nation at Risk “precipitated a shift in
the structure” of high school curriculum (NCEE, 1983), resulting in an increase in
the number of required years of English, Mathematics, Science, Social Studies and
Computer Science subjects at the secondary level. According to Olsen (2003) the
student enrollment in these courses nearly quadrupled in the decade after Nation at
Risk. The report described the binary goals of equity and high quality in the pursuit
of excellence in education, and specifically called for a commitment to minority and
low-socioeconomic student access to educational environments that foster success.
However, great disparities continue to exist in the achievement levels of these
students as compared to their white and Asian peers.
According to international, national and state assessments, overall student
achievement in high school mathematics continues to represent a failure of our
public high schools. The Highlights From TIMSS Report (2003) shows an increase in
the number of nations scoring at a much higher percentage than the United States in
mathematics at the 12
th
Grade level; additionally, these percentages increased
dramatically between the 4
th
to 8
th
grades (NCES 1999-081R). This data underscores
the challenges at the high school level to sustain patterns of student achievement
throughout a student’s educational tenure. According to Education Trust (2003),
African-American, Hispanic, and poor students were more than three years behind

4
their white and Asian peers by the end of twelfth grade. The challenge of high school
student mathematics achievement was further exacerbated in The Trends in
International Mathematics and Science Study (TIMSS, 1995). TIMSS is on record,
as the largest and most comprehensive comparison study done on science and
mathematics achievement of students from over 23 countries. American students
were reasonably competitive until the twelfth grade, a point at which their
performance had dropped precipitously and was among the lowest in mathematics
and science when compared to students in other countries (NCES, 1999).
The achievement gap in math presents a critical problem for our students,
particularly in our urban secondary schools. Mathematics achievement is especially
important for urban youth because those who demonstrate mathematical competency
are better positioned to reduce structural barriers that lead to economic dependence
(Secada, 1995, 1997). The poor performance of our urban youth in math presents
another obstacle to future success as math is considered a “gateway” subject to
higher education and as such students must have the skill set to achieve in higher
level math. The results from standardized assessment find that our students in urban
schools that have high poverty and large populations of minority students have the
greatest difficulty reaching the “proficient” level on standardized assessments
(Blezard, 2003; Marzano, 2003). The U.S Department of Labor has identified a high
correlation between individual future earning power and math skills. They find that
individuals with lower skills in math have a lower average income (Stiff, 2006). In
the job market, workers who have a strong mathematics background are more likely

5
to be employed and generally earn more than workers with lower achievement even
if they have not gone to college. In urban areas, it is critical to have a trained
workforce able to provide economic stability to those communities.
Mathematics education, particularly for urban youth presents an equity issue. In
the Curriculum and Evaluation Standards (NCTM, 1989), there is a call for
restructuring of mathematics education for all students, but specifically addresses the
issues of equity. In particular,
The social injustices of past schooling practices can no longer
be tolerated. Current statistics indicate that those who study
advanced mathematics are most often white males. Women
and most minorities study less mathematics and are seriously
underrepresented in careers using science and technology.
Creating a just society in which women and various ethnic
groups enjoy equal opportunities and equitable treatment is no
longer an issue. Mathematics has become a critical filter for
employment and full participation in our society. We cannot
afford to have the majority of our population mathematically
illiterate. Equity has become and economic necessity. (p.4)

There has been a concerted effort at both the state and national levels to
improve mathematics achievement in high schools by focusing on state standards,
improve curriculum and instruction, to better prepare teachers, and related reform
efforts. These efforts have resulted in increased rigor and accountability within
content standards and subsequent aligned assessments. The focus on subject matter
and grade level “content standards: is not new, it has been at the forefront of many
conversations over many years and was the focus of an education summit that
occurred in 1996” (Klein, 2005). The purpose of identifying and creating content

6
was to provide a “blueprint” for what students should have demonstrable proficiency
in, and articulated by the identified standards. It also provided a framework of what
the priorities are for teaching each subject and grade level (California Department of
Education, 1998). When congress authorized the No Child Left Behind (NCLB)
legislation (2001) states were mandated to create content standards for all grade
levels and subject areas as a condition of receiving federal funds.
The accountability system instituted by NCLB also had impact on staffing for
school districts as a key component of this legislation, re-defined the criteria of a
highly-qualified teacher (HQT). Previously a teacher with a pre-defined number of
years of experience was considered “highly qualified”. If they did not hold the
appropriate credential for a subject they were teaching, the district was able to utilize
special education codes as a means of “qualifying” them to the teach a subject.
Within the NCLB legislation, HQT requires that all teachers with the exception of
physical education and other miscellaneous courses such as home economics be
HQT by 2006, which has subsequently been extended to 2007. This meant that the
teachers had to have the appropriate credentials, had to have participated in a
required numbers of hours of professional development or instruction specific to
their course and/or passed exams in order to become HQT. School districts are
required to have all their teachers to have achieved HQT status; this has presented a
significant challenge for urban school districts and specifically in math and science
for all schools districts. Kati Haycock of Ed. Trust states that allocating sufficient
resources towards ensuring our teachers are becoming “highly qualified “ is a critical

7
investment in our public education system and that this will have significant positive
impact on our ability to reduce the achievement gap. (Ed. Trust, 2004).
These new guidelines have placed extensive burdens on our public schools
with the most significant challenges faced by our urban schools which historically
have had trouble recruiting teachers to come to a district in which there are perceived
inherent challenges that are not as prevalent in our suburban school districts. Along
with the strict guidelines stressing the importance of having HQT teachers, research
continues to confirm the importance of having high quality teachers as a means of
reducing the pervasive achievement gap and that this factor is a high predictor of
student performance, greater than is race/ethnicity or poverty levels (Ferguson,
1999). Also, within the NCLB guidelines both states and school districts are
encouraged to initiate comprehensive school reform efforts utilizing research- based
design models(McCombs, Quait 2002).These efforts would include utilizing
instructional strategies, professional development that have their foundation in
research that serve as a means of improving both the student achievement and the
quality of instruction.
None of these aforementioned changes are occurring in isolation, but rather
simultaneously with a variety of reform efforts occurring across the United States in
our public school systems in our effort to reduce the achievement gap while
improving student achievement for all students.
With the increasing demands and expectations on schools to increase student
achievement for all students, and in doing so, accelerate the lower performing

8
students in an effort to reduce the achievement gap, school district and site
leadership are more apt to explore different models for the organization of their
school. This call for reform has generated new and innovative school design or
organizational models. Urban schools in making these changes seek to create a
learning environment and organizational structure that is created with the diverse
learning needs of the students.
Three models that have become most common and have the greatest amount
of research and time behind them are: the Small Learning Community (SLC), the
Community for Learning program (CFL) (Wang, 1998) and the Professional
Learning Community (PLC) (DuFour, 2003.) The SLC structure is organized around
creating smaller communities that support and foster a more “personalized”
instructional learning environment. The design is established around the
reorganization of a larger high school into smaller learning communities that often
are organized around a theme, instructional focus or even grade level. The CFL
design model has the focus of establishing an environment in which positive self-
perceptions, created with the individual learning needs and characteristics in mind, in
the context of high standards for student achievement. The PLC is considered a
comprehensive reform model as well as a model for professional development. The
organization is organized with the adults as learners in a collective group that works
to support adult learning, which in the school site setting, translates into student
learning.

9
The school designs, initiatives and school policies that are being implemented
to address student achievement must work collectively with the community,
increasing capacity for improvement. There are many factors that contribute to the
academic performance of our students one predictor that is not strictly academic, is
the notion of the psycho-social development of the student and it is important for us
to assess if the organizational culture of the school supports that kind of growth. The
value of a collaborative, positive learning environment has been identified as a factor
in student academic success (Westhuizen et al, 2005) both academically and on a
social and personal level as well.
Through policy and action the school leader sets the tone and facilitates the
school climate and culture. Accordingly, the leader must act purposefully and
decisively to create an environment that is inclusive of both the internal site
stakeholders, to include adults and students alike and the larger external community,
comprised of the parents and community members that are impacted by the school.
By creating a positive culture and increasing the capacity of everyone to understand
the policies and the vision behind school reform efforts, creates the likelihood for
success in executing those efforts (Leithwood, Louis, Anderson, Kyle 2004).
Much of the existing research confirms that leadership is second only to
classroom instruction among all school-related factors that contribute to student
learning in the school context and that total effects of leadership on student learning
account for about a quarter of the total school effects (Hallinger & Heck, 1996;
Leithwood, Jantzi, 2000). Instructional leadership is distributed across the school

10
community, with the principals, superintendents, teachers, and policymakers having
complementary responsibilities in this context with each role leading to a different
kind of expertise that leaders must both respect and cultivate (King; Richard Elmore
2000; Spillane et al, 2000). In this era of standards-based accountability, the role of
the instructional leader is ever expanding. According to the National Association of
Elementary School Principals (NAESP), instructional leaders have six roles:
1. Making student and adult learning the priority
2. Setting high expectations for performance
3. Gearing content and instruction to standards
4. Creating lifelong learners
5. Using multiple sources of data to assess learning
6. Activating the community’s support for school success
Instructional leadership has become a “dominant paradigm” in public
education as a result of identified correlations between effective schools and the
leadership capacities of the principal. The six aforementioned roles provide a
framework for understanding the role of the school leader, and a target for personal
and professional development; these are strengths that must be developed for
effective instructional leadership. As the leader of the school they must model their
personal commitment and ability as an individual to engage all levels of
stakeholders, which must include teachers, parents and the larger community. This
must be facilitated through constructive conversations that build the trust and respect
for the leader. This is necessary as a means of improving schools and initiating

11
school reform for improved student outcomes (Kanter, 2003.) Additional research
finds that for any school reform to be effective and sustain improved changes there
must be a commitment of many years (Murphy & Datnow, 2003; Borman et. al.,
2002). The leader must be provided the time but more importantly possess the
capacity to create a learning environment that supports the hard work necessary for
school reform.
Successful educational instructional leaders develop their effective schools
that support and sustain the performance of administrators and teachers, as well as
the students by strengthening school cultures, modifying organizational structures
and building collaborative processes (Leithwood, Louis, Anderson and Wahlstrom,
2004). Instructional leadership provides the catalyst for change in professional
development, comprehensive school reform, and leading learning communities.
Statement of the Problem
For the past several decades, there has been a multitude of educational
reforms at the national, state and local levels, aimed at increasing student
achievement in urban high schools. More specifically, these reforms have targeted
academic performance in mathematics, particularly, Algebra I, which serves as the
gatekeeper for all advanced courses. The role of instructional leadership is central in
the current debate. However, the consistent underachievement in secondary schools,
particularly in mathematics provides a fertile ground for studying all factors that
contribute to successful student achievement.

12
So far, research in the field has provided mixed results for understanding
standards-based reform at the secondary level, thus it is important that we carefully
and critically examine those instances of success to better understand the “nexus” of
issues that affect standards-based instruction: curriculum and assessment,
mathematics programs and strategies and the effect of instructional leadership to
determine the optimal conditions for increasing student achievement.
Districts and school leaders are on a continuous search for the most optimum
recipe of curriculum, instructional materials, strategies and “best practices” to
improve student achievement. Identifying the curriculum and instructional policies
that are most effective provides insight to other educators looking to enact a change
in their instructional design. However, simply knowing what curriculum programs or
instructional strategies are being used does not translate into successful
implementation; consequently, more needs to be known about the related conditions
that foster improved mathematics achievement. Understanding these conditions will
help educators implement similar policy initiatives in an effective manner that yields
positive results. However, more specific information is needed on the actual change
process that schools experience when they identify the specific outcome or goal.
According to Fullan (1993),
There is a pattern underlying the eight lessons of dynamic change
and it concerns one's ability to work with polar opposites:
simultaneously pushing for change while allowing self-learning to
unfold; being prepared for a journey of uncertainty; seeing
problems as sources of creative resolution; having a vision, but not
being blinded by it; valuing the individual and the group;
incorporating centralizing and decentralizing forces; being

13
internally cohesive, but externally oriented; and valuing, personal
change agentry as the route to system change. (p. 40)

Research has provided considerable theoretical understanding of how the process of
change occurs in organizations. However, understanding how schools move from a
theoretical understanding of reform efforts to practical implementation is of value,
because how schools navigate the dynamics of change is of critical importance as
similar socio-political challenges await almost all educational leaders within the
urban setting. Educational practitioners need more concrete examples of successful
outcomes of reform efforts to emulate in similar school settings.
The daunting task of school reform in our urban secondary schools further
highlights the importance of the instructional leader, accordingly it is a role which
needs to be conceptualized as a means of understanding the essential knowledge,
skills, and approaches that are most conducive to implementing school reform. The
role of the Principal is multi-dimensional in that they must have the capacity to fill
many roles and responsibilities that provide for a learning environment that improves
incrementally overtime and is sustainable. Accordingly this is a role that must be
understood as it is a key factor in school reform (Fullan, 2001). The leader must be
cognizant of the many factors that contribute to successful leadership and successful
school reform. The leader must be able to communicate the vision and direction for
which they are striving, understand the import of using data as a means of
accountability and ensuring a skill set for monitoring and supervising the
instructional program are a fraction of what a school leader must have the ability to

14
do. The manner by which these pieces work in tandem to create effective leadership
is essential for successful school reform.
Examining the extent and effectiveness of instructional leadership has great
implications for systemic reform in similar organizational settings and also provides
invaluable data to inform the professional development for these vital members of
the school community. Even though many school leaders espouse the title and role of
instructional leader, Fiore (2004) maintains that many administrators consider the
assignment as a curricular leader to be both impractical and impossible due to their
lack of instructional expertise and curriculum training. Given this premise, more
needs to be known about how leaders in the school resolve the dilemmas regarding
instructional leadership, especially in content areas where they lack strong,
pedagogical background and knowledge.
Mathematics continues to be one of the most challenging subject areas in
meeting the requirements that have been prescribed by the No Child Left Behind
(2001) act. Specifically, requirements for mathematics proficiency remain a barrier
to increasing student success.
Additional research is needed in the following areas:
Understand student achievement patterns to inform instructional practice
Identify policy initiatives in curriculum and instruction and under what conditions
these relate to student achievement

Analyze the change process to understand how to progress from theoretical
knowledge to effective application

15
Examine the extent of instructional leadership on the effective implementations of
mathematics programs and associated classroom strategies and the impact on student
achievement

Understand how school leaders resolve the dilemmas of effectively monitoring the
curricular program in content areas where they lack pedagogical background
knowledge

Purpose of the Study
The purpose of the study is to examine the conditions that fostered
mathematics achievement at one high school that met the purposeful sampling
criteria. Specifically the study examines school design, school and classroom
policies, conditions and best practices that enabled the improvement in student
achievement, and the role of the instructional leader in shaping and directing the
reform efforts in improving student achievement in mathematics. The study also
aimed to increase our understanding of how instructional leadership impacted the
creation of a culture for mathematics achievement when the instructional leaders
lacked strong, pedagogical knowledge in mathematics as a subject area.

Research Questions
The following research questions paramatized and guided this study:
1. What was the pattern of mathematics achievement for various students at the
school?

16
2. What policy initiatives including curriculum, instruction and related conditions
seem to be related to improving mathematics achievement at the school?
3. What reform efforts and strategies did the school initiate and utilize to enhance
the mathematics program and improve student achievement in mathematics?
4. To what extent was strong instructional leadership important in improving the
following:
a. Mathematics programs and associated classroom strategies? and
b. Mathematics achievement among students?
5. How did leaders in the school resolve dilemmas regarding instructional
leadership, especially in content areas where they lack strong, pedagogical
background?
Importance of the Study
The very future of the United States rests with the ability to improve student
achievement, especially in our urban high schools. Indeed it becomes an issue of
civil rights when accountability systems fail to uphold the requirement for all school
systems to provide every child’s democratic right to a fair and appropriate, and
equitable education. It has been argued, that an adequate mathematics education that
includes at least Algebra I is the gatekeeper for a viable economic future.
This study benefits a wide population from policymakers to curriculum
designers, from district governance boards to classroom teachers, from teacher
educators to researchers. Policymakers can use educational experts as resources in
providing solutions to many of the educational “gaps”. Curriculum designers will

17
benefit by gaining a greater understanding of the proven research-based design
elements that must be incorporated into instructional materials and mathematics
programs. School District personnel can use this information to redefine support for
principals as they evolve into instructional leaders who are required to address issues
of equity, access and rigor for all students. Instructional leaders will benefit as they
can mirror the “best practices” at their school sites. Mathematics teachers will benefit
from a deeper understanding of how teaching concepts and problem-solving are
more effective for teaching and learning than merely “drill and kill” arithmetic
concepts.
This study, though limited by the bounds of one school site, can provide a
broader understanding of those factors that proved materially effective at the site
studied. Moreover, this study can aid educational researchers by providing rich case
study data about how our students are achieving within our systems.
Limitations
As the data for the study was collected from the staff and faculty at one
grades 9-12 comprehensive high school in Southern California, it limits the ability to
generalize specific results to other schools. The ten-week data collection period was
at least two full years after the schools’ reform efforts occurred, resulting in reliance
on participant perception for the data in some instances rather than having actual
results. Efforts were made to prevent bias, however, the researcher did not have
control over participant bias in the interview process. The study is a qualitative case

18
study and as such, the data analysis may be subject to the interpretation of the
researcher.
Delimitations
This is a qualitative case study of one high school. Purposeful sampling was
used in the selecting the school.
The school was selected based on 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 50% from
traditionally ethnic minority groups.
3. Public or Magnet, comprehensive high school (Grades 9 -12) of at least 1200
students in the Southern California region.
4. An Academic Performance Index Score of at Least 600
5. A State Wide Rank of 5 or higher
6. Leadership stability as defined by a Principal being at the school for at least
three years during the time the improvement was made.

Assumptions
The following methodological assumptions were considered to be implicit in the
study:
1. The data were accurately recorded and analyzed.

19
2. The instrumentations used were designed and utilized were effective in providing
the information sought.
3. The respondents were honest with their answers to the questionnaires.
4. Those interviewed for this study responded with honest and authentic
information.
5. California Standards Test (CST) was a valid indicator of student performance on
achievement tests.
6. The case study guide and research procedures, developed during a summer
research design seminar, were used by all members of the group.
7. The schools chosen were reflective of schools that met the sampling criteria.

Definition of Terms
For the purpose of this study, the following terms were operationally defined below:
The Academic Performance Index (API): California’s numerical indicator of
student achievement, used as a basis for a comparative ranking of schools statewide
(California Department of Education [CDE], 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

20
Perspectives on Closing the Achievement Gap). North Central Regional Educational
Laboratory (NCREL).
Assessment: A measurement of a student’s particular skill or knowledge that
may be written, oral, or performance in nature. Standardized assessments were
administered and scored in exactly the same way for all students to measure specific
skills and knowledge (Olsen, 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 that 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, 2001)

21
Conceptual framework: A consistent and comprehensive integration of
research literature, theories, and other pertinent information that was the basis for the
collection of data and analysis of findings within the study (Olsen, 2005).
Content Standards: As the foundation of a standards-based system, content
standards described what content knowledge and skills students were required to
master (American Federation of Teachers, 2001).
Cultural Capital: The term cultural capital represents the collection of non-
economic forces such as family background, social class, varying investments in and
commitments to education, different resources, etc. which influence academic
success.
Cultural Deficit Theory: Assumes that some student cannot achieve at high
levels because of deficits inherent in their race, ethnicity, language, or
culture. (Villegas, 1991)
Data-driven decision-making: The process of making decisions about
curriculum and instruction based on the analysis of classroom data and standardized
test data. Data-driven decision making used data on operational functions, the
quantity and quality of inputs, and how students learn to suggest educational
solutions (Massell, 2000).
Highly Qualified Teacher: A Highly Qualified Teacher (HQT) is one who
has an appropriate credential to teach in the area(s) assigned and who has
demonstrated subject matter competency through various acceptable most often

22
through passing rigorous state exams or through a highly objective uniform state
standard of evaluation (NCLB, 2001).
Instructional Leadership: An influence that guided the activities designed to
impart knowledge or skills to students (Olsen, 2005).
Leadership: "Leadership is a process of influence leading to the achievement
of desired purposes. Successful leaders develop a vision for their schools based on
their personal and professional values [and goals]. They articulate this vision at every
opportunity and influence their staff and other stakeholders to 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, p.8,
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 student’s in grade 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

23
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,
represented, and adapted to the diverse interests and abilities of learners, and
presented for instruction (Shulman, 1987, p. 4). 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.
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"].

24
Organization of the Study
This dissertation is organized around five chapters, each with a specific structure and
purpose. Chapter 1 presents the overall framework for the study. It includes an
introduction to the study, the statement of the problem to be studied, the purpose and
significance of the study, the research questions, limitations and delimitations,
assumptions made within the study and operational terms and definitions that are
used in the study. Chapter 2 contains the literature review of research that is relevant
to the study; best practices influencing improved math performance, and the role of
the leader as a facilitator of the change process and school reform design models.
The purpose of Chapter 3 is to outline the methodology used for the study and the
instrumentations utilized to gather information. The findings of the study are
presented and discussed in Chapter 4. Chapter Five is a summary of the study, and
provides conclusions and discusses implications for subsequent studies. The
references and appendices are included at the end of the five chapters.

25

CHAPTER TWO
Review of the Literature
Introduction
Concerns over student achievement in the United States continue to dominate
the national conversation among policymakers, the media, politicians, and all
stakeholders within the educational community. When the performance of American
students was compared to their international peers on the Third International
Mathematics and Science Study (TIMSS) and Programme for International Student
Assessment (PISA), and contrasted with their domestic counterparts using the
National Assessment of Educational Progress (NAEP), those conversations turned to
a call for action and demand for changes in our schools. The 1983 publication of A
Nation at Risk reinforced the gravity of the situation and made recommendations for
changes in the structure and operations of schools. In fact, A Nation at Risk is
considered the catalyst for events that culminated in a national call for content
standards (National Education Goals Panel, 1991). Subsequent national and state
educational reforms have emerged in efforts to improve “equity, opportunity, and
excellence” in American schools. However, there is much more to be learned about
how these reforms have transformed schools generally, and in math performance,
specifically.
The federal role in secondary education reform had been virtually non-
existent for most of the 20
th
century. Even with the passing of the National Defense

26
Education Act in 1959 the dialogue for approximately the next twenty years about
mathematics reform was held primarily between educational reformers, mathematics
teachers, mathematicians and parent groups. However, during this period in our
nation’s history, there was an increased awareness about the needs of poor and
minority children resulting from the passing of the Civil Rights Act (1964).
In the wake of broadening awareness of the problems of educating a more
equitable, skilled and proficient future workforce, an awareness that was exacerbated
by the American embarrassment with Russia’s launch of the Sputnik, and coupled
with the country’s new consciousness, the Elementary and Secondary Education Act
(ESEA) was passed in 1965. The passage of this act is considered by many to be the
first commitment by the Federal Government to address the issues of equity in the
public schools and the beginning of corresponding national reform efforts. The
ESEA provided supplementary resources to schools with students from low-
socioeconomic backgrounds, including provisions for staff development to address
the ever-widening achievement gaps in the public schools through its Title 1
program.
Legislators changed the Title I program in 1994 to complement Goals 2000.
Receipt of Title 1 funds was now contingent upon the development of standards,
assessment, and accountability systems in each state. Political distress and lack of
consistent implementation of Goals 2000 by the states undermined its potential to
reform the accountability systems. In essence this attempt at school reform failed
because there was a lack of focus and a lack of leadership including a misalignment

27
of political interests and organizational structures at the federal, local and school
levels (Corwin, 1975).
Over the last two decades, educational reforms focused on improving
mathematics achievement have emerged through standards-based education. Resnick
and Zuraway (2005) describe four tenets of standards-based education that emerged
in the 1990s from national-level discussions among educators, business leaders, and
legislators: (1) a public process to establish standards for what students should know
and be able to do at different grade levels, (2) standards-based assessment to inform
students about their learning and teachers about their instruction, (3) standards-based
instructional program and teacher professional development provided by schools and
districts, and (4) accountability systems to determine whether students are achieving
standards. As most states have adopted the standards-based movement, it is even
more critical to examine their influence on the teaching and learning environments.
This review of literature will discuss the academic performance of students
from a national and international perspective, closely discuss the importance of
mathematics education as a vital dimension of schooling, review key California state
and national efforts to improve mathematics achievement with respect to standards,
curriculum and instruction, delineate the role of the instructional leader, and reflect
upon those actions taken by instructional leaders who lack strong pedagogical skills
and content knowledge in math but nevertheless are able to create the conditions that
foster positive student performance in mathematics.

28

Status of Student Performance

Nation at Risk

The report A Nation at Risk forewarned, “our nation is at risk…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.” (NCEE, 1983, p. 5) A
Nation at Risk categorized its findings into the four areas of: content, expectations,
time, and teaching, and made explicit recommendations for each of those areas.
Based on the findings and indications of this report, it predicted a generation of
Americans who would not be as well educated as the average graduate 25 or 35 years
prior. The report highlighted that public schools were performing poorly in
comparison to other countries and that the United States was in jeopardy of losing its
standing as a world economic leader because the American public school system was
failing to produce strong students particularly in mathematics and science. Pundits
and analysts alike described the U.S. mathematics education as the product of an
“underachieving curriculum”. As a result, national school systems were directed to
increase the instructional standards to include greater breadth and rigor, establish
mechanisms for increased accountability, improve the curriculum, and provide
rigorous assessments to increase the level of accountability at the local level
(Elmore, 1997). However, reform efforts were slow-moving and student
achievement remained relatively flat. Trends in student performance fluctuated a
little in terms of the achievement gap in the 1970s and 1980s; however, the 1990s

29
were a period of intense transformation and the educational system began the
arduous journey towards greater accountability, equity and access for all children.
Trends in International Mathematics and Science
A product of the International Association for the Evaluation of Education
Achievement, the TIMSS study is considered to be the most comprehensive
international study of mathematics and science (NCES, 2001, 2002). This assessment
was developed by a consortium of research experts from different countries,
calibrated against a variety of methods to ensure validity and stability in the
submitted student samples. American student performance on TIMSS examinations,
administered in the early 1960s, early 1980s and 1988, were dismal; however, the
findings were discounted due to technical procedures and differences in sample
populations (National Center for Educational Statistics [NCES], 1992). However, in
1995, the Third International Mathematics and Science Study (TIMSS) was
administered to students from 41 countries in fourth, eighth and twelfth grades. This
time, the results were valid. Poor American student performance generated similar
national embarrassment experienced decades before with Sputnik.
The data from the TIMSS study revealed, that elementary students continued
to achieve greater results than secondary students nationally. It was not a surprise
that the fourth graders participating in this study performed well in science and
exceeded the international average in mathematics, because according to O’Connell
(2006), “overt policy decisions to invest in Elementary Education have resulted in
higher performance”. The eighth and twelfth grade performed lower than their

30
international counterparts; in fact, TIMSS results showed American seniors ranking
third from last in mathematics and fifth from last in science when compared to 21
other countries.
More disturbing, was the news from the Third International Mathematics and
Science Study Repeat (TIMSS-R, later renamed to Trends in International
Mathematics and Science Study, or TIMSS 1999) that the mathematics performance
of the U.S eighth-graders was lower than it was for these same students as fourth-
graders in 1995. Analysis of “trend” data by subgroup indicated minimal gains for
African-American students in mathematics only; there was virtually no change for
White or Hispanic students in mathematics or science. Once again the data revealed
that the performance of American students continued to lag behind their international
counterparts (NCES, 2001a, 2001b, 2003b).
The most recent results of the TIMMS (2003) appear to be more promising.
Fourth-grade students from 26 countries and eighth-grade students from 48 countries
were assessed. In TIMSS 2003, America’s fourth and eighth grade students
“significantly” outperformed many of their international peers, scoring well above
the national average in both mathematics and science. Eighth-grade students
improved their scores across most student groups, e.g., gender and minority
subgroups from the previous two assessments (1999, 1995). American eighth
graders, especially African American students, showed significant gains in both
science and math over the last eight years, while scores for US fourth graders
remained relatively flat in both subjects (National Science Teachers Association,

31
2004). The results of TIMSS (2003 are reflected in U.S. Secretary of Education Rod
Paige’s comments regarding the link between the TIMSS assessment and the
curricula of the participating countries. He notes, “… in that sense, they are a good
indicator of our schools’ performance as well. Therefore, we must remain committed
to staying the course of reform to ensure every student in every school has a real
opportunity to learn” (U. S. Department of Education, 2004).
Program for International Student Achievement
The Programme for International Student Assessment (PISA), developed in
1997, and implemented in 2000, is a triennial multi-nation test of 9
th
and 10
th
grade
student performance, developed by the Organisation for Economic Co-operation and
Development (OECD) in 1997. The ultimate goal of the PISA study is to improve
and standardize educational methods around the world. The first assessment in 2000
was conducted in reading literacy; the focus of the second examination was
mathematics literacy. Over 275,000 students from 41 countries participated in the
study, which tested real-life situations in which mathematics is useful, and problem
solving (OECD, 2003). Pisa’s 2003 focus was on mathematics literacy defined as:
“…an individual’s capacity to identify and understand the role that
mathematics plays in the world, to make well-founded judgments and
to use and engage with mathematics in ways that meet the needs of
that individual’s life as a constructive, concerned, and reflective
citizen. (OECD 2003, pg. 24)”

32
In the PISA Report (2003), the ranking of fifteen year olds in the United States
places them 24
th
among 29 participating countries in 2003, down from a ranking of
19
th
among 32 participating countries in 1999. In addition, the United States ranks
23
rd
out of 30 nations in the percent of students in the highest achievement levels in
mathematics. The PISA international report validates the educational community’s
efforts to provide the organizational structure, leadership and effective curriculum
and instruction in mathematics to ensure American students are prepared for the
global world.
It is important to note that the results from the PISA and TIMMS often
contradict each other because their respective sponsoring organizations employ
different philosophies or approaches in their definition of the math concepts and
skills students need to master for success in the global world. The PISA mathematics
literacy test includes educational matter such as “fuzzy maths”, also known as the
National Council of Teachers of Mathematics (NCTM) constructivist math, which
includes the general topics of quantity, space and shape, change and relationships,
and uncertainty (PISA, 2003). TIMSS, on the other hand, measures more traditional
classroom content such as an understanding of fractions and decimals and the
relationship between them (TIMMS, 2003). PISA argues that international
assessment should not be restricted to a set body of knowledge. Instead, it deals with
education that is applicable to real-life problems and life-long learning
(www.pisa.oecd.org).

33
However, both assessments are considered reliable and valid. Upon release of
the TIMMS finding, Grover Whitehurst, Director of the Institute for Educational
Sciences, commented, “[i]nternational assessments such as the TIMMS and the PISA
provide important information about education in the United States and in other
industrialized nations and an external perspective on U.S. performance”. The
TIMSS not only shows that U.S. Eighth-graders are making strides in mathematics
and science when measured against their prior performance, but they are also making
gains relative to their international peers, with fewer countries outperforming them
and more countries underperforming them” (U.S. Department of Education, 2004).
Goals 2000
The Goals 2000: Educate America Act (Goals 2000, 1994) was an attempt to
promote education reform on a national scale as a response to many of the well-
publicized challenges of the public education system. One of the six formally
adopted education goals was that, “[b]y the year 2000, United States students will be
the first in the world in mathematics and science achievement”. These goals were to
be reached by furthering the standards movement by providing grants for states to
develop their own standards and assessment systems linked to these standards. The
federal government believed that the major components of Goals 2000, systemic
reform, standards, assessments, flexibility, and accountability, could stimulate the
American Education system.

34
National Assessment of Educational Progress (NAEP)
Through the expanded role of the federal government in the educational
sector, the National Assessment of Educational Progress (NAEP) was created and
has been collecting student data since the 1960s providing longitudinal data on the
achievement of students across the United States (National Assessment Governing
Board [NAGB]). The NAEP report provides essential data on student performance
trends on assessments in reading, mathematics, and science, compared by states
(Coley, 2003). This data has been a resource of information on the progress,
deficiencies and challenges for our students and their academic abilities.
Under the No Child Left Behind Act of 2001, the NAEP became the required
assessment to ensure state compliance with mandatory accountability systems to
measure student performance. NAEP provides reliable measures of changes in
national achievement longitudinally, and by student subgroup. Over the last three
decades, the NAEP has reported trends in reading, mathematics, and science scores,
showing a decrease in the mathematics scores in1970s, an increase in the
mathematics scores in the 1980s, and a continued increase into the early 1990s,
resulting in similar scores between 1971 and 1999. This data has provided
information on the challenges of our students and the subsequent academic abilities
of our students across the country and the public school system.
It has served as an indicator of which students are improving their
performance and which students are falling behind or remaining stagnant not

35
demonstrating any growth. Disaggregating by subgroups reflects gradual increasing
scores of white students, always remaining higher than the scores of their African-
American and Hispanic peers. African-Americans and Hispanic student
demonstrated a “net increase” between 1971 and 1999; however the “achievement
gap” still persists, between their scores and the scores of the white students. The
achievement gap narrowed in the 1980s, then widened again in the early 1990s
(NCES, 2000c). These small growth patterns will not help to eradicate or even
reduce the achievement gap between our minority students and our white students so
improvement in the performance of our minority students must be accelerated.
In reviewing the results from 1990 to 2005 NAEP the findings are consistent
and reflect a need for concern. In 1990 only one percent of the 4
th
grade African
American students were scoring at proficient or above in math, and only four percent
of the 4
th
grade Latino students compared to their white peers who scored fifteen
percent proficient or above in math. The most current scores from the 2005 NAEP
reflected growth for each subgroup but did not reflect a decrease in the achievement
gap. The white 4
th
grade students found a 32 percent increase in the students scoring
at proficient or above while their African American peers had improved by only 12
percent and the Latino students had an increase of six percent of students scoring in
this same range. The results for 8
th
grade students in 2005 presents a similar
disturbing finding with the gap between the white students and their African
American peers extending to 29 percent and the performance gap between white

36
students and Latino students in the 8
th
grade had increased to 20 percent (NAEP,
2005, U.S Department of Education, NCES, 2005). The findings in California reflect
an achievement gap however it is not as significant as is reflected on a national level.
The small growth of our African American, Latino and white students further
highlight the importance of and pressure on our public schools meeting the diverse
academic needs of all our students.
Student Achievement Gap
The term achievement gap is used to denote differences in the
academic achievement of particular groups of students. Actually,
it is more accurate to say that there are achievement gaps rather
than merely one achievement gap. The issue is not as simple as
difference between blacks and whites or rich and poor. There are
many gaps, and the gaps themselves have changes over time
(NCREL, 2002, p. 6).

The achievement gap in schools is apt to have lifetime consequences, limiting
opportunities for minority students in higher education, employment and earnings
(Carnervale, 1999; Jencks, 1992; Murname & Levy, 1996; Ogbu, 1994). The
persistent achievement gap represents a grievous and detrimental social injustice
representing an increasing crisis for the future as students are at a disadvantage
because of their limited abilities to actively participate in our increasing more global
world (Douglas, 2006). The cause of this achievement gap is not a reflection of
“faulty genetic make-up” but rather can be attributed to the limited exposure to such
things as pre-school and/or being read to that many of the minority children have not
had in their early developmental years (Whitmire, 1997).

37
More African American (19%) and Hispanic (37%) students fail to obtain a
high school diploma or its equivalent by the age of 24 compared to white (10%) and
Asian (6%) students (Haycock, 2001; Maruyama, 2003). The material consequences
of this data are that it will have calamitous impact on the socio-economic foundation
of the United States, with additional implications of compromised natural security. If
we are unable to provide an educated work force to meet the escalating demands of
our increasingly complex, sophisticated and technologically advanced society we
will not be able to compete which will diminish our contribution and influence in the
global economy.
The continuing achievement gap means that a bleak future awaits many poor
and minority students in the United States. This achievement gap portends a life of
limited opportunities for African American and Hispanic students and other
members of the citizenry that lack a high school diploma or its equivalent, making it
less likely that these students will enroll in postsecondary education, and even less
likely that they will graduate from it (Anyon, 1997; Maruyama, 2003; Newman et
al., 2000; Singham, 2003). Demographic statistics indicate that minority students
comprise one-third of the nation’s students (Johnson & Viader, 2000); in some
states, minority states comprise well over half the student population (Anyon 1997;
Datnow, Borman, Stringfield, Overman, & Castellano, 2003). Within the next 15
years, they may comprise as much as two-thirds of the nation’s student population
(Anyon, 1997; Maruyama, 2003). There are grave implications for the United States

38
economic future with the possibility of almost two-thirds of its constituency living
below the poverty line.
Since A Nation at Risk was published in 1983 there has been a reduction in
the achievement gap between white students and African Americans and during this
time frame the African American and Latino students have made greater gains than
their white counter parts in the grade levels that were assessed (Forgione, 1998, p. 3).
While the achievement gap has remained a constant it is most significant at the upper
grades, the gap is at its lowest margin during early elementary years and increases
from elementary to middle and then markedly declines in high school.
The NAEP report, National Achievement Results by Race and Ethnicity
(2000) found that the percentage of students who performed at proficient or above
doubled for all groups from 1990 to 2000. During this time frame the performance of
white 4
th
grade students who met this target increase each year from 1990. The
percentage of African Americans and Latinos meeting this target decreased during
this same time frame. The gap is most evident and concerning for our African
American students who perform fifteen percentage points below Latino students and
only slightly above students with disabilities
Our public education system is engaged in an ongoing effort to reform our
schools in a climate of increasing accountability of high stakes assessments and
potential sanctions if sufficient progress is not made. That said it is imperative that
interventions and support systems be implemented as a means of supporting our
African American and Latino students if the achievement gap it to decrease. The

39
Advancement Via Individual Determination (AVID) program is one such reform
effort. The AVID program’s goal is to ensure that all students, especially
disadvantaged students, will succeed in a rigorous curriculum and enroll in four-year
institutions of higher learning (www.avidonline.org). AVID students are enrolled in
college preparatory courses concurrent with their AVID elective class. They receive
academic instruction in reading and writing skills, study skills, time management,
test-taking strategies and college board test (PSAT, SAT, ACT) preparation that
prepares them for college admissions. In addition, motivational activities are
integrated into the program to allow students the opportunity to explore college and
careers through guest speakers, college field trips, individual and class projects and
technology. Students participate in an AVID class every day in both middle school
and high school levels and receive elective credit. Students are strongly encouraged
to enroll in AVID for at least three years or until they complete high school. Two
periods a week they receive tutorial support which uses questioning rather than
answer-giving to help students solve their own problems. During these tutorial
sessions, students are aided by collaborating with their peers and through the
guidance of a college tutor assigned to their group. (Cunningham, Redmond, &
Meriosotis, 2003).

40
Role of Mathematics

Mathematics is an especially important dimension of schooling. The role of
mathematics achievement is critical to college success, the economic future of our
country, and job achievement in this information age. 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). This
further highlights the critical fact that students graduating from our public schools
must have a strong foundation in mathematics. According to Reyes and Stanic
(1988), “[k]nowledge 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” (p. 28). The fact that students from other countries are performing better in
math brings the conversation to the forefront in both our schools and the larger
society about the challenges our schools face if we are to remain competitive in a
global society.
This acknowledgement is evident in the increased requirements for higher
level math courses for high school graduation and the focus on standards-based
instructional math programs in our K-12 public school system. The increased
graduation requirements reflects the realization of our public schools that students

41
must have skills equal to those only found through the completion of higher level
math courses.

Role of mathematics in college success
Public high schools continue to wrestle with the challenge of preparing
students for postsecondary endeavors in this technological age. Greater emphasis has
been placed on math curriculum, especially advanced courses such as Algebra and
Geometry, as attainment of these courses is positively correlated with college
graduation and future earnings (Rose & Betts, 2001). The quality of the mathematics
curriculum is considered the most significant indicator of the student’s potential for
success irrespective of quality of school or student’s background. According to the
National Educational Longitudinal Study (NELS), eighty-three percent of students
who took Algebra I and Geometry went on to college within two years after their
high school graduation. While only thirty-six percent of students who did not take
these two courses went to college. The study also showed that students who
completed at least algebra I had “markedly” higher levels of education and earned
significantly more income than those who only took lower levels of mathematics
courses such as vocational math or pre-algebra.
College completion is most likely when students take academically intense
and high-quality coursework during high school (Adelman, 1999). Examples of
high-quality coursework include mathematics classes beyond algebra II. Algebra I is
and continues to be the gatekeeper to higher mathematics courses (Gram, 2000).

42
According to NCES (2003) 83 percent of students who while in high school
successfully completed calculus graduated from a four-year university/college and
received a bachelors’ degree. Of first-generation students enrolled in four-year
colleges, 64 percent completed advanced math, regardless of their ethnic
background, and completed a bachelor’s degree (Tierney, Colyar, & Corwin, 2003).
Low-income students who took algebra I and Geometry were almost three times as
likely to attend college as those who did not (Riley, 1997).
Role of Mathematics in the Economic Future
In the 21
st
century, both technological and scientific advances demand that
high school graduates be both competent in high-level skills and prepared to attain
postsecondary education. Consequently, greater demands have been placed on our
public high schools to prepare young people for both the workforce and higher
education. According to the Center for Education Reform (1998), more than 20
million students reached 12
th
grade unable to do basic mathematics. There is an
effect on the workforce as students graduate without the requisite skills required by
employers. Murane & Levy (1998) found that almost half of American students left
high school without these necessary skills.
The percentages are even more dismal with respect to race, sex, and
socioeconomics. In 2005, Black students had an average score that was lower than
that of White students by 35 points. Fifteen years ago, the average score difference
between these two groups was 38 points. For Hispanic students, the numbers were a
little more positive. In 2005, Hispanic students had an average score that was lower

43
than that of White students by 29 points. This actually represents a five-point
decrease since 1990 (NCES, 2005). There is also evidence of sex-related differences
in mathematics achievement at the secondary level with males achieving at higher
levels (Reyes & Stanic, 1988). Welch, Anderson, and Harris (1982) found
differences by SES of students, with the high-SES students scoring higher than the
low-SES students on number recognition tasks. This data is significant as it relates to
the economic foundations of these communities that are often riddled with poverty
and high crime, in the absence of an educated, trained workforce.
Historically, educational reforms are viewed in light of their supposed
economic effects. The areas of education given the most attention as relevant to
economic goals and key to economic growth have been science and mathematics.
Mathematics achievement has a privileged role as a critical filter or "gatekeeper"
controlling entry into both mathematics and engineering (Reyes & Stanic, 1988).
Those who demonstrate mathematical competency are better positioned to reduce
structural barriers that often lead to economic dependence (Secada, 1995, 1997).
The import of a college education in terms of an individual’s ability to be
economically independent is reflected in part by the income discrepancy between
those with only a high school diploma and those who have graduated from a four
year college. Individuals who have a college degree make 37 percent more than
those without. The average yearly income of a college graduate is $43,000 while the
high school graduate’s average income is $27,000 per year (U.S. Department of
Commerce, Census Bureau, 2005).

44
Additionally, students who do not pursue technological professions still
require solid foundations in math and science in order to be productive members of
our society. Tyler (2003) investigated the benefit of mathematics knowledge even for
dropouts using the General Equivalency Diploma (GED) mathematics test as the
indicator. The results indicate that dropouts who scored a standard deviation higher
on the mathematics portion of this high stakes test had average earnings over the
subsequent three years that were 6.5 percent higher than lower scoring dropouts.
The technology advancements and/or changes in our world are occurring at a
rapid speed which has further focused the need for our public schools to improve the
performance of our students in the area of math and science. While average
mathematics scores rose during the 1990s and early 2000s, there exist great
performance disparities, by students from disadvantaged populations. If the U.S. is to
remain competitive and maintain economic leadership in the global economy, our
schools must better prepare K-12 students to succeed in college and subsequently be
prepared to participate in the technological workforce. This emerging technological
workforce will need to begin developing their mathematical skills early in their
educational career. This is reinforced by the increased knowledge and skill set a
person must demonstrate to be employed in an occupation and/or fields of
employment that prior to the rapid advancements in technology did not require such
sophistication and knowledge. In the job market, workers who have strong
mathematics backgrounds are more likely to be employed and generally earn more
than workers with lower achievement, even if they have not gone to college (Bureau

45
of Labor Statistics, 1999). This type of background will be critical for well paying
jobs in the future and could possible affect the United States performance in the
global market. Students who are leaving our high schools with limited math skills
will continue to separate our society with those who demonstrated greater
mathematical success in high school were able to translate this into an increased
likelihood of success in college. This impacts their future earning power
(Schoenfeld, 2002). This type of background will be critical for well paying jobs in
the future and could possible affect the United States performance in the global
market.

Role of Mathematics on Vocational Careers
While there is increased emphasis on preparing students for entrance into
four-year colleges and universities, there exist questions about what careers and jobs
will even be available upon attainment of bachelor’s degrees. In this technological
and information age, even if students are not pursuing a bachelor’s degree, it is
imperative that students possess the requisite technical skills for entrance into the
traditional vocational careers. The differences in the years of schooling directly
relate to the income gap, i.e., the greater the years of schooling, the greater the
earning potential (Rose & Betts, 1997).
Mathematics is important not just in the education of scientists and
engineers, but also in the education of every working citizen in the United States.

46
According to Ed Trust (2004) a person who is seeking employment working in sheet
metal requires that the person have skills in technical reading and have at least an
“elementary” understanding of mathematical concepts in algebra, geometry, and
trigonometry. The field of mechanics must demonstrate reading skills equivalent to a
college level. This makes it critical for all students planning on going to college or
not to be challenged and informed of the impact their academic skills will have on
their subsequent career or occupation. This is of great concern for groups that have
been traditionally shut out of many technical jobs and careers, i.e., women and
minorities, because of inadequate mathematics and general education preparation.
Students need to be especially prepared in this fast paced, constantly
changing technological economy. Workforce success means equipping high school
graduates with higher-level academic skills to be gainfully employed with livable
wages. However, employers clearly articulate the kinds of skills, background and
knowledge they need and require to move their organizations forward, and to receive
a competitive salary. Research has identified that high school graduates who plan on
going immediately into the workforce after they graduate must possess academic
skills that are similar those needed to be enrolled in college (American College
Training, 2004). Employers typically put school achievement below other
qualifications yet still seek employees who can demonstrate problem solving skills
and a conceptual and practical understanding of math. A recent survey by the
National Association of Manufacturers (NAM) identified “inadequate math skills” as
the 5
th
most common reason for rejecting worker applications.

47

National and State Reform Efforts to Improve Mathematics Achievement
A significant body of circumstantial evidence points to a deep,
systemic incapacity of U.S. schools, and the practitioners who work
within them, to develop, incorporate, and extend new ideas about
teaching and learning in anything but a small fraction of schools and
classrooms. – Richard Elmore (1996, p. 1)

An overabundance of school reform efforts has littered the educational
landscape for more than three decades. These efforts represent a priority that has
been laid at the door steps of our schools. The increasing accountability brought
about through NCLB has required the annual standardized assessments of all
students and the disaggregating of student performance as measured against
benchmarks that define adequate student academic growth. Additionally the
accountability system of NCLB has added an increased accountability on school
districts to ensure that all students are receiving instruction from teachers defined as
“Highly Qualified” based on NCLB guidelines. This accountability system has
resulted in states, districts and schools across the country increasing the use research
based approaches to improving the performance of all our students.

Standards Movement
Inherent within standards-based reform (SBR) is the belief that all students
should have the same high set of expectation for performance in our educational
system. Effectively implementing SBR is an integrated effort consisting of content
standards, curriculum and instruction, assessment and accountability (EdSource,

48
2000). The force of national efforts towards education reform through the use of
standards, assessment and accountability propelled the majority of the states to
implement their own versions of SBR.
In fact, a federal law passed in 1996 made receipt of Title 1 funds contingent
upon states adopting academic standards (U.S. Department of Education, 1996).
Consequently, most states have implemented some level of SBR, including new and
revised standards and frameworks, assessments tied to the standards, accountability
systems, professional development and graduation requirements. In California, over
58% of the schools participate in Title 1, which funds programs for socio-
economically disadvantaged students, providing an even greater incentive for the
districts to incorporate academic standards into their curriculum (EdSource, 2000).
The California Standards-based education systematic reforms have been
implemented through the lens of standardized testing and assessment, accountability,
standards-aligned curriculum and instructional materials, professional development,
assistance for struggling schools and class-size reduction.
There is a long-standing debate as to the depth, and the contexts in which
American students learn mathematics as compared to their international peers.
According to Klein (2005), California standards receive a grade of “A”, one of only
three states in the Country to receive such high marks. The California Department of
Education initially implemented standards-based reform in mathematics with the
Mathematics Framework (1985) which called for “more intellectually ambitious
instruction, for more engaging mathematics work for students, for teachers to open

49
discourse about math in their classrooms and to pay more attention to students’
mathematical ideas, and for teachers to help students understand math instead of just
memorizing facts and operations” (Cohen & Hill, 1998). Subsequent versions of the
Mathematics Framework (1992, 2005) seemed less in alignment with NCTM’s
philosophy of “downplaying the necessity of verifiable mathematical competence at
deepening levels of sophistication as students pass through the curriculum” (Wayne
Bishop, 1995, p. 1). However, many practitioners in the field bemoan the fact that
the California state standards do not really recognize the NCTM standards, perceived
as lacking rigor. These practitioners feel that the state standards do not take into
account how students learn, and contain holes and flaws therein. The California
standards authors, primarily university professors, are unwilling to modify or align to
the NCTM standards (Murphy, E. as cited in an interview, 2006). In addition to the
accountability measurement of the API, the PSAA provided assistance to schools
through various assistance programs. Grant programs such as the immediate
Intervention/Underperforming Schools Program (II/USP), Comprehensive School
Reform Demonstration (CSRD) program, and the High Priority Schools Grant
Program (HPSGP) were all designed to provide various types of resource and
assistance to improve student academic performance. Over the past decade,
California has enacted reforms in response to public or federal government. This
sequence of reforms to improve mathematics achievement has primarily targeted
students, teachers, and resources.

50
Based on the recommendations of the National Council of Teachers of
Mathematics (NCTM) and the NRC, Anderson (1995a, 1995b, 1996) identified
several common themes among standards-based mathematics reform. The common
themes encouraged the students to think in more systematic and complex ways.
Students were encouraged to understand and identify multiple solutions to problems,
become active participants in their own learning, and make connections to
mathematics in other academic subject contexts. Standards-based mathematics
courses focused more on concepts and problem-solving, while the more traditional
courses focused on mastery of skills. Schoen, Fey, Hirsh, & Cox (1999) looked at
reform-oriented mathematics courses that focused more on geometry, measurement,
descriptive statistics, and the use of calculators and computers. Conversely,
traditional mathematics courses focused on arithmetic, algorithms for whole
numbers, common fractions, decimals, algebra in high school, and more pen and
pencil computations.
Standardized Testing and Assessment
The California Standards Test (CST) in mathematics, aligned to the
California Mathematics Standards test has been administered to students since 2003.
This assessment is designed to measure mastery level as it relates to grade level
content standard. CST data is a significant factor in the calculation of the Academic
Performance Index (API), which is the accountability measurement for school
performance. The API was created as a result of the Public Schools Accountability
Act (PSAA), 1999. The PSAA, an integral component of the standards-based reform

51
movement, was adopted in an effort to provide a system for measuring school
performance in meeting academic growth for its students. The API holds schools
accountable, provides incentives for growth and implementation of interventions for
students, assigns sanctions for not meeting targets, and encourages the participation
of all stakeholders in student achievement.
Improved Curriculum and Instruction.
According to Schoenfeld (2002), current reform curricula can make a definite
impact when strongly implemented. Aspects of strong implementation include
“coherent and systematic efforts in curriculum, assessment and professional
development are aligned”. This alignment can ultimately mitigate the differences
between whites, underrepresented and linguistic minorities. One basis of argument is
whether it is possible to teach conceptual understanding without sacrificing
procedural skills. The results are in however, and students perform as well or better
on standards-based curriculum as on traditional curriculum; the students actually
performed better on the problem-solving strand (Schoenfeld, 2002). According to
NCTM (1989) in “Everybody Counts” there is a general unhappiness with the
curriculum in terms of equity, the narrow content used for college preparation, and
its impact on the future of economic national security.
In his book What Works in Schools (2003) Robert Marzano delineates the
importance of classroom instruction, the curriculum and its design as critical to
improving student performance. In this book he identifies deliberate actions teachers
should take that support creating and implementing effective classroom instruction:

52
ß Identify the important declarative and procedural knowledge in the
topics that are to be the focus of instruction (p.116)
ß Present new content multiple times using a variety of input models
ß Make a distinction between those skills and processes students are to
master versus those they are not (p. 117)
ß Present content in groups or categories that demonstrative the critical
features of the content and finally (p.118).
ß Engage students in complex tasks that require addressing content in
unique ways (p. 119)
Teacher Preparation
Through bipartisan efforts, the No Child Left Behind Act (NCLB, 2001)
expanded the role of the federal government into the educational policy sector. One
of its primary requirements is to ensure that every classroom possesses a highly
qualified teacher (HQT). Highly qualified teachers have to meet specific criteria to
become “subject-matter experts”, specifically in mathematics, science, English,
humanities, Art and foreign languages. All teachers are required to have the
appropriate teaching credentials, garnered by the taking the designated coursework
and/or by examination. However, there are exceptions made to this requirement in
subject areas such as mathematics, where recruitment remains a challenge. In fact,
certification rates for public high school teachers have been on the decline over the
last decade from 90% in 1990 to 80% in 2002 and only 71% of secondary public

53
school teachers had a college major or minor in mathematics (NSF, Science and
Engineering Indicators, 2006).
The changing and expanding demands of teaching jobs have prompted
increased attention to the importance of professional development in providing
teachers with opportunities to acquire new knowledge and keep abreast of advances
in their field (Elmore, 2002). A task force appointed by the NCTM to study issues
surrounding mathematics learning and teaching in urban communities made the
following statement:
… instructional approaches that emphasize conceptual understanding
of mathematics ideas and procedures within a broader range of
content offer the promise for effective mathematics instruction in
schools of poverty. Effective teachers organize their instruction to
build on students’ prior knowledge as they promote and maintain
solid classroom interaction with their students. Classroom discourse
can then be a mechanism to promote mathematical analysis,
reflection, verification and justification (Campbell & Silver, 2000).

This level of instructional pedagogy requires highly qualified teachers
equipped with the knowledge, skills, and dispositions to encourage
exceptional learning in schools (Darling-Hammond & Sykes, 1999).
As the quality of teaching is the most significant predictor of student
achievement, a response to the issue of improving teacher preparation is essential.
Concurrent with the content standards reform of the 1980s, and subsequent to A
Nation at Risk, the concept of a national board certification for teachers was
presented in a report titled “A Nation Prepared: Teachers for the 21
st
Century”
published by the Carnegie Forum on Education and the Economy’s Task Force on

54
Teaching as a Profession. While California has always had a considerable amount of
state interest in teacher preparation and licensing, this interest has only increased
with the advent of standards-based reform movement in the mid-1990s.
Teacher Incentives
State reform efforts to increase the efficacy of teachers are primarily focused
on incentives. National Board for Professional Teaching Standards (NBPTS)
certified teachers receive significant incentives. It appears evident that the NBPTS
certification process is rigorous, and has raised the level of conversation about
teacher preparation and garnered support from the government sector. However,
questions still remain whether the result of this expensive, rigorous training really
has a positive impact of student achievement.

Benefits of Diverse Teaching Staffs
Reports by the NCEE (citation) and related studies expound the imminent
shortage of teachers due to an aging current teacher workforce and attrition of
teachers. This shortage of teachers is exacerbated in subject areas like mathematics
and science. As our nation’s classroom increase with culturally, ethnically and
linguistically diverse students, it has been recognized that there is an additional need
for and shortage of teachers of color. Teachers of color can serve as language and
cultural translators, bridge the gap between home and school, provide role models
for students in underserved, high-poverty, multiethnic communities, and help foster
democratic principles to prepare children to live and work in a multiethnic society

55
(NCTAF, 2003). Villegas (2003) identifies one of the key reasons why all students
need teachers of color:
Teachers tend to be one person and authority figure outside of the
home that have a lot of influence on children. When they see only
white people as teachers that can reinforce the negative stereotype
– in white students and students of color – that people of color are
not capable of holding positions of authority. To students of color,
it’s even more damaging because it sends a message they
shouldn’t even bother.

The premise that teachers of color are needed for all students has been key in
efforts to recruit and retain these teachers. There has been an array of programs
developed to address this issue. These existing programs fall under several categories
such as Early Outreach/Precollegiate, Scholarship/Grant, Advanced Degree,
Paraeducator-to-Teachers, Community College, and Alternative Routes to
Certification programs.
While these kinds of programs have enjoyed limited success, external,
independent evaluations are needed however, to determine their efficacy in order to
truly have an impact on educational policy. Furthermore, the issue of a diverse
teacher workforce has to be a systematic mission at both the state and national levels.

Professional Development
There has been commitment at both the state and national levels to make
teacher professional development a component of their reform efforts. Using the
research literature, professional development has evolved to focus attention on
specific teaching strategies by content area, active learning opportunities such as

56
reviewing student work, and coherence in instruction by linking to other learning
activities, all proven to have a significant effect on teachers’ instructional practices
(Smylie, et al 2001). The professional development focused on improving math
instruction and thus student learning has yielded positive results when part of a larger
systemic reform effort of the educational system (Taylor-Anderson, Brown, &
Lopez-Ferrao, 2003).
According to Elmore (2001) the focus of NCLB is too heavily focused on the
assessment of our students and not enough on building capacity of our instructional
leaders and teachers. This focus results in school systems focusing on “quick fixes”
to improve student performance in the short term. This shifts the priority to
professional development that is focused on teaching and learning which will yield
more long term and sustainable results. The number one impact on student learning
is the effective teacher, thus looking to any one math program to improve student
learning as an isolated factor will not impact student learning. Teachers must have
the opportunity and mandate to participate in professional development that is
focused and purposeful.

School Based Efforts that Improve Mathematics Achievement
Small Learning Communities

Recent reform efforts have illuminated the commitment to improving student
performance and reducing the achievement gap in our secondary schools. The

57
research community has focused on some key school design models and related
school features that have proven successful in improving student achievement.
In Schools That Work: America’s Most Innovative Public Education
Programs, the findings suggest that making schools smaller is the first step toward
enhancing school conditions and improving student outcomes (1992). For over a
decade, this and other studies demonstrate that smaller learning environments
positively affect grades, test scores, attendance rates, graduation rates, drug and
alcohol use, and school safety. There are many forms of Small Learning Community
(SLC) models, some of these include school-within-school, career academies,
houses, magnet programs and small schools (NCSL, 2006). However, some of the
most common examples of these SLC models are academies and schools-within-a-
school (U.S. Department of Education, 2001 as cited in CEEP Brief 2004).
Academies are made up of subgroups of students within the larger school focused
around a particular theme. For example, career academies model, coordinate
curriculum and activities around a variety of occupations (Maxwell & Rubin, 2002
as cited in CEEP Brief, 2004). Here, academic subjects are integrated with
laboratory courses and emphasize the relationship between academics and the
workplace (Maxwell & Rubin, 2002 as cited in CEEP Brief, 2004). High school
career academies have been shown to decrease dropout rates and improve work
attendance and job performance (Maxwell & Rubin, 2002 as cited in CEEP Brief,
2004). School-within-a-school is an autonomous program housed within a larger
school building that has its own culture, program, personnel, students, budget and

58
school space (U.S. Department of Education, 2001 as cited in CEEP Brief, 2004).
This model seeks to foster relationships between students, their peers and their
teachers. Grouping students together to take courses with the same set of teachers
increases the support that teachers receive from their peers and teachers (U.S.
Department of Education as cited in CEEP Brief, 2004). Additionally, according to
Cotton (1996), smaller schools positively effect student achievement and students
perform at the same level or better than they do in larger schools. Klonsky (1998)
has indicated that smaller schools promote equity and help close the achievement
gap between students who come from higher income, mostly white, and Asian-
American families and students from lower-income, mostly African American and
Hispanic-American families.
Professional Learning Communities
The Commission recommends that schools be restructured to become
genuine learning organizations for both students and teachers;
organizations that respect learning, honor teaching, and teach for
understanding. (Darling-Hammond, 1996, p. 198)

Professional learning communities (PLC) consist of teams of educators,
regularly collaborating toward continued improvement with a shared vision of
meeting the needs of learners. There are certain conditions that facilitate the work of
professional learning communities: (1) supportive leadership and structural
conditions; (2) collective challenging, questioning; and reflecting on team-designed
lessons and instructional practices/experiences, and (3) team decisions on essential
learning outcomes and intervention/enrichment activities based on results of

59
common formative student assessments (Langston, 2006). The six key characteristics
of professional learning communities are: (1) shared mission, vision, and values,
(2) collective inquiry, (3) collaborative teams, (4) action orientation and
experimentation, (5) continuous improvement, and (6) results orientation (Dufour
and Eaker, 1998).
Effective PLCs maintain a strong sense of purpose towards student learning
as the key outcome. Decisions are made with the end in mind based on essential
learning outcomes reinforced in a community, in which staff members are committed
to a joint set of principles and values that all team members adhere to. In essence,
staff members hold a shared mission, vision, values, and goals; a transparency exists
concerning what student must know and be able to do (Dufour, Dufour, Eaker, &
Many, 2006). There is team commitment to continuous improvement towards
reaching the organization’s ideal mission and vision within the context of “collective
synergy”. Within the collective synergy, team members constantly expand their
competence to produce desired outcomes (Senge, as cited in Bierema, 1999, p. 51).
A culture of collaboration must be evident among the team members. This culture
involves a “systematic, goal-directed learning process in which people work together
in grade level, vertical, special topic, or subject matter teams to analyze and impact
professional practices in order to improve individual and collective results for
students” (Peel, J., as cited in E& R Report No. 06.05). Through collective inquiry,
team members work together to question, search, analyze, develop, test, and evaluate
new skills, strategies, awareness, attitudes, and beliefs that promote student learning

60
(Dufour & Eaker, 1998). As well, through this process there exists reflective
dialogue on curriculum, common formative assessments, instruction, and needed
job-embedded professional developments (Peel, J. as cited in E&R Report No. 0605)
on lessons, study and effective instructional strategies (Langston, 2006 as cited in
E&R Report No. 06.06). Team members analyze current practices in relation to
student results, experiment with new practices, and assess the relationship between
practices and the effects of practice (Mitchell & Sackney, as cited in Huffman, Hipp,
Pankake, & Moller, 2001, p.1) in the process of collective inquiry. Supportive and
shared leadership is at the center of strong PLCs as they are the facilitators of the
learning by all staff members. Within this model, the school leader is also a learner,
attending professional staff development and is willingly involved in facilitating
shared leadership, power, and authority by giving staff members their input and
judgment (Hord, 1997). Trust, respect and openness to improvement exist (Kruse,
Louis, & Bryk, 1994) with this type of leadership. Leaders must consider the
circumstances and environment of the school context in order to support PLCs.
Executing a school-wide plan that provides extra time and support for teachers
(Langston, 2006) may require school design, structural and culture-climate changes.
Hord (1997) stipulates that required supportive conditions, especially time, include
(a) reduced staff isolation, (b) increased staff capacity, (c) provision of a caring,
productive environment, and (d) improved quality of student programs. Through the
development and implementation of systematic interventions, students are
guaranteed to receive additional time and support for learning (Dufour, Dufour,

61
Eaker, & Many, 2006). Effective professional learning communities “begin with the
end in mind” and are results oriented. Initiatives, strategies and practices are
subjected to various forms of assessment. The effectiveness of teaching is assessed
on the basis of student results (Dufour, 2003); results show whether students have or
have not learned the essential curriculum (Dufour, Dufour, Eaker, & Many, 2006)
Scheduling Changes
Scheduling changes are often part of major school restructuring reforms. The
traditional six- or seven-period day formats produce hectic, impersonal, inefficient
instructional environments (Carroll, 1994). The National Education Commission’s
“Time and Learning” Report (1994) states “schools will have a design flaw as long
as their organization is based on the assumption that all students can learn on the
same schedule”. Much instructional time is lost with so many transitions during the
day, not to mention the opportunity for discipline and behavior problems to arise.
Watts & Castle (1993) state, “Traditional, inflexible scheduling is based on
administrative and institutional needs”. Flexible scheduling patterns are a much
better match for pedagogical practices that meet the educational needs of students
and the professional needs of teachers (Irmsher, K., 1996). Block scheduling is the
most commonly implemented flexible scheduling option in contemporary school
reform. By definition, block scheduling is any schedule format with fewer but longer
classes than traditional schedules permit (Jones, 1995 as cited in nwrel.org). Cawelti
(1994) states, “[a]t least part of the daily schedule is organized into larger blocks of
time (more than sixty minutes) to allow flexibility for a diversity of instructional

62
activities.” There are several variations of the block schedule that include the
following as possibilities:
The intensive block: students attend two core classes at a time. These core classes can
be coupled with up to three other year-long elective classes. Students complete the
core classes in 60 days and then move on to another two. School years are organized
into trimesters (Jones, 1995; Canady & Rettig, 1995

The 4x4 block: This format enables students to attend four classes per day, each
lasting anywhere from 85-100 minutes. Students complete in one semester what
would have taken them a full year in traditional schedules (Jones, 1995; Rettig &
Canady, 1996; Canady & Rettig, 1995).

The alternating plan (also known as the A/B plan): Using this format, students attend
eight blocks of classes over two days (Jones, 1995; Rettig & Canady, 1996; Canady
& Rettig, 1995).

The modified block: This is sort of a "build your own block schedule" format. For
example, schools may have students attend school based on a 4x4 block on Monday
through Thursday, and a regular eight-period schedule on Friday. Or, they might
have two blocked classes in a day, combined with three regular periods (Rettig &
Canady, 1996).

The parallel block: The parallel block is used primarily in elementary schools,
whereas the previous four formats are used primarily in secondary schools. Parallel
block takes a class of students and divides them into two groups. One group of
children stay with their classroom teacher for instruction in an academically
demanding subject such as math or language arts, while the other group attends
physical education or music, or visits the computer lab; after a prescribed length of
time the two groups swap. This schedule provides all students with a more individual
learning experience (Canady, 1990).

Many of the benefits of this type of scheduling strategies include: more
effective use of school time, decreased class size, increased number of course
offerings, reduced numbers of students with whom teachers have daily contact, and
the ability of teachers to use more process-oriented strategies (Sturgis, 1995).
Carroll (1994) reported that in schools implementing block scheduling, there was

63
evidence of more course completions, equal or better mastery and retention of
material, and an impressive reduction in suspension and dropout rates. He attributes
these positive outcomes to improved relationships between students and their
teachers. Canady & Rettig (1995) think the positive outcomes multiply when four
year-long courses are taught in longer time blocks, each compressed into one
semester. These outcomes benefit both strong students and students who need extra
support, as this kind of schedule allows students to enroll in a greater number of
elective courses, and offers greater opportunities for acceleration, while affording
earlier opportunities for students to retake courses they may have failed. However, it
should be noted that the Northwest Regional Educational Laboratory (NWREL,
1990) warns that merely, “imposing a scheduling model on a school will not ensure
success”. NWREL recommends a minimum of two years of planning time before
implementation. Canady & Rettig (1995) recommend that adequate staff
development time is essential to train teachers on how to modify their instructional
strategies to teach successfully in larger blocks of time. Structure alone will not alter
conceptions of what constitutes knowledge, content of courses, or changes in
classroom teaching that must occur for any new schedule to affect student learning
(Conley, 1994; Cushman, 1995; Newmann, 1991 as cited in Freeman, 2001)
Reform Efforts
From the educational psychologist perspective, one of the most promising
reform efforts to influence the framework for the re-design of secondary education is
Learner-Centered Psychological Principles (LCPs) [American Psychological

64
Association (APA), 1993]. LCPs were born in response to what many critics
described as a “crisis in education” in the late 1980s and early 1990s. The, APA’s
Presidential Task Force for Psychology in Education analyzed the “the personal and
environmental conditions that best support high levels of learning and achievement”
(McCombs, 2003), and created these fourteen research-validated knowledge base
principles, organized into four domains that reflect the “holistic nature of factors
influencing learners and learning” (McCombs, 2003). The LCPs summarize what
research shows about how students learn and the motivation, development, and
individual differences that influence learning (McCombs, 2003). Educational
psychologists believe that integration of this knowledge of learning and how students
learn into the classroom and school practices would positively influence student
achievement.
Transforming classrooms into student-centered, collaborative communities
where students jointly construct knowledge is at the forefront of current reform
efforts of the National Council of Teachers of Mathematics (NCTM, 2001). The
vision is for classroom students to build a personal relationship with the subject,
make an investigation into their own and peer’s learning and engage in genuine
inquiry (NCTM, 1991, 2000). This reform effort calls for mathematics teachers to be
facilitators in the learning process, encourage and support student autonomy, provide
opportunities for students to choose the most appropriate strategy for accessing the
content, and use various contexts to help students make connections, and deepen the
student’s conceptual understanding of mathematics. In the NCTM’s, Principles and

65
Standards for School Mathematics (PSSM), the “Equity Principle” is premised on the
belief that all students can be successful and should be held to the same high
expectations (Manouchehri, 2004). It explicitly states that all children regardless of
socioeconomic and cultural background should have access to the same visions of
teaching and learning as students receive in the more affluent schools.
Model Math Programs

The overarching goal of mathematics education falls into two categories:
goals for teachers and goals for students. One of the most important goals of
mathematics is to teach students logical reasoning (Mathematics Framework for
California Public Schools, Kindergarten Through Grade Twelve, CDE, 2005).
Mathematics education has three components that need to be presented using a
sound, balanced instructional program: become proficient in basic computational and
procedural skills, develop conceptual understanding, and become adept at problem
solving. Recent studies suggest that all three components are interrelated (Geary
1994; Siegler and Stern 1998; Sophian 1997).
Effective, well-designed mathematics programs have emphasis on the quality
of instruction, considered the single most important component in the development
of student proficiency. Nine other factors play an important role in facilitating the
student outcomes of mastery, knowledge and understanding: assessment, instruction,
instructional time, instructional resources, instructional grouping, classroom
management, professional development, administrative practices, community, and
involvement.

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These key factors combine to reinforce elements of the curriculum. The
research supports each of the nine factors as a critical component towards an
efficacious mathematics program and can be assessed uniquely. International
comparisons show a high correlation between the quality of the mathematics
instruction and student achievement (Beaton et al. 1996). This reinforces the critical
element of quality of instruction necessary for an effective program. Stigler, Lee,
and Stevenson (1987) have reported the relationship between instructional time on
task and student achievement. Adequate time must be allocated to mathematics
everyday. These effective math programs contain high-quality, well-designed
resources and materials aligned with the standards. They also incorporate the latest
research-based strategies, e.g., grouping, to improve learning, and are supportive of
the individual classroom environment. Effective mathematics programs are engaging
and foster intrinsic motivation resulting in fewer opportunities for inappropriate
student behavior. Professional development must be a component of these programs.
Research from other countries suggests that student achievement can improve when
teachers are able to spend time together planning and evaluating instruction (Beaton
et al. 1996). Administrative support is key to implementing effective math programs
with the reminder to all of the school community and stakeholders that mathematics
achievement is a high priority. Finally, these programs foster engagement by all
stakeholders in the community.

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Mathematics curricula and instruction
Effective mathematics programs have at their foundation sound, research-
based curriculum design elements, incorporate standards-based instruction and
aligned assessments, and promote effective and coherent lesson design and promote
high levels of student engagement in a culturally relevant classroom. The answer to
the proverbial question of what is the influence of reform-based mathematics
curricula on student achievement continues to be studied, resulting in some key
implications for further research. Some of the studies reviewed indicate that student
achievement improved with more exposure to the standards-based curriculum while
others suggest that a correlation of the achievement and curriculum goals influenced
the student achievement outcomes. What has been identified as critical is the
alignment of the assessments with standards-based curriculum. Positive relationships
were demonstrated with instruction recommended by the NCTM and performance on
state assessments.
Core-Plus Mathematics Project
Core-Plus Mathematics Project ((CPMP) is an “NCTM-oriented” program.
Schoen and Hirsh (2003) compared student achievement scores in CPMP and
traditional mathematics courses. Using pretest data to match groups, students were
given a subtest of the Iowa Tests of Educational Development (ITED) and CPMP
performance assessments. Results showed that CPMP students performed
significantly better on the contextual algebra and coordinated geometry subtests, and
similarly on the procedural algebra subtest after two courses in CPM.

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Another study by Ridgway, Zawojewski, Hoover, & Lambdin (2003) showed
positive changes in student achievement using CPMP after being exposed to the
curriculum for three consecutive years. A control group of non-CMP students were
matched according to “ability, locale, and ethnicity”. Comparative scores on the
Iowa Test of Basic Skills (ITBS) and the Balanced Assessment (BA) showed CMP
students were significantly ahead of non-CMP students by the end of the third year
on both assessments.
A study by Hannifin (2002) reinforces the premise that enrolling high school
students in Algebra and more advanced mathematics courses as opposed to remedial
programs, such as PLATO, does not increase student achievement. Using state
assessment data to compare groups enrolled in PLATO and not-enrolled in PLATO,
the control group’s average was “significantly higher” than the average for the
PLATO students by the end of the study.

Instructional Leadership

The accountability systems generated by high school reform efforts have
produced a new breed of school leaders. Less emphasized are the administrative and
managerial tasks of the proverbial sports-focused plant managers; in its place is the
instructional leader whose primary areas of focus are: defining the school’s mission,
managing the instructional program, and promoting a positive school learning
climate (Brewster, C., 2005). Leadership is second only to classroom instruction
among all school-related factors that contribute to what students learn at school

69
(Leithwood, Louis, Anderson, and Wahlstrom, 2004). The central task of
instructional leadership is to create the conditions for improving teaching and
learning in schools (Halvorson, Grigg, Prichett & Thomas, 2005).
Defining School Mission, Purpose and Vision
In defining the school’s mission, instructional leaders co-create the learning
environments that espouse common instructional goals, language and conversation.
They articulate these common goals and purposes to all constituents of the greater
school community. There is significant literature that reinforces the significance of
the marriage of purpose with commitment (Darling-Hammond, 1997; Helsselbein &
Cohen, 1999; Rees, 1991; Senge, 1990). Through inquiry and reflection,
instructional leaders bring to bear those issues central to creating a common vision
and moral purpose with respect to educating all children. The vision helps others
understand the core beliefs of the school community. Buell (1992) notes, “For
schools to be effective, they need effective leaders who express their values. These
individual values must become shared goals so that the entire school community
shares a vision” (p. 88).
Effectively setting school-wide academic goals is critical factor is promoting
student achievement and success. Mike Schmoker (1999) states, “setting academic
goals for the school as a whole has a powerful, coalescing effect on teachers and
administrators “(p. 24). Schmoker’s ideas beg the philosophical question: how do I
know if I have arrived, if I don’t know where I am going? Setting goals and effective
feedback is ranked second in the list of the five school-level factors (Marzano, 2003).

70
Concurrent with goal setting must be a system of monitoring progress towards
reaching those goals. Instructional leaders connect student outcomes and
achievement as well as professional development to school learning goals. Caution is
to be considered when setting goals; Fullan and Hargreaves (2001) note, “many of
the schools tackle one or two achievement goals annually to prevent the over-load
that is so clearly the enemy of improvement.” Use of data is an effective tool in
setting individual student goals, since the attainment of these individual goals has
greater significance and can hold much more promise than school-wide goals.
Instructional leaders must be savvy and effective in being bale to facilitate
two-way communications with both internal and external publics thus ensuring
meaningful communication with all members of the school community. Internal
publics are stakeholders known as students, teachers and staff; parents, businesses,
community leaders and organizations would comprise the external publics. Students,
the most important internal public, are pivotal to increased engagement by their
parents. They are often an overlooked group because many school leaders fail to
know how to communicate with them. Other internal publics can play a significant
role in positive school-community relation’s plans. Effective instructional leaders
extend their appreciation for the effort and work of the internal publics and build
positive relationships by being visible on a regular, consistent basis (Flore, D., 1998)
The external public is not a homogeneous group. Their roles range from
simply being taxpayers to families without children in schools. George Pawlas
(1995) suggests that key communicators be identified within each group; they are

71
defined as “opinion leaders”, who influence the directions and actions of the various
community organizations. The most significant external public is the parents. The
research bears out that parent involvement is a critical factor in the success of
students (Benson, Buckley, & Elliott, 1980; Epstein, 1992; Rious & Berla, 1993;
Whitaker & Fiore, 2001). Therefore, it is important to engage them as much as
possible in the school’s decision-making processes.
Managing the Instructional Program
Emerging supervisory and evaluative practices emphasize the following
practices:
1. Training for administrators as well as teachers in supervision,
mentoring and coaching
2. Sensitivity to the process of professional growth and continuous
improvement
3. Training in observation and reflection on practice in teacher
preparation programs
4. Integration of supervision with staff development, curriculum
development, and school improvement systems
5. Improved professional practice both in and outside the classroom
6. Continuous improvement as part of every educator’s daily life
7. Focus on group processes in classrooms rather than a one-on-one
supervisory experience
8. Collegial assistance among educators, parents, and students

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9. Use of terms such as a colleague consultation and coaching to
describe collaboration among professionals helping each other to
improve practice
Monitoring student progress is at the core of instructional leadership.
Instructional leaders are tasked with shifting their schools from a culture of internal
accountability, i.e., grades, attendance and qualitative data, to one of external
accountability, i.e., standardized tests, exit exams, quantitative data (Halvorson,
Grigg, Pritchett & Thomas, 2005). Emerging theories such as the Data-Driven
Instructional Systems (DDIS) model provides a framework to describe what
practices leaders use to develop their schools’ capacity to use data for instructional
decisions. An emerging theory incorporated within the DDIS is Distributed
Leadership theory, where instructional leaders create the conditions and the
expectation of shared leadership tasks. Organizational theory, an inherent component
of DDIS provides the frame for translating summative testing into formative
information for modifications in instructional programs. One example of this model
at sites would include data teams, representative of the school community, where
each member is assigned clear responsibilities.
Instructional Leader Role in Improving Mathematics Achievement
To make changes that improve the teaching and learning of
mathematics and science, the principal as instructional leader must
understand and actively participate in the learning process. Rice, R. &
Islas, M., NASSP Bulletin Vol. 85 No. 623, 2001)

73
Studies such as the TIMMS and NAEP document the challenges of American
students in meeting proficient levels in math achievement. The reports generated
from these two assessments specifically identify the gap in areas of knowledge for
the tested students. This information holds enormous implications for teaching and
learning environments. “The linchpin and keystone for a successful reform effort is
the school principal” (Rice & Islas, 2001). He suggests that the principal must
understand and actively participate in the teaching and learning process in order to
make the necessary changes within the environment. Elmore (2000) as cited by Rice
& Islas, 2001) suggests that the “chances for sustainable change increases
dramatically when strong, visionary leadership exists effective leaders help
overcome difficult challenges to achieve excellence for all students” (268). Rice and
Islas suggest,
Improving students’ mathematics and science skills requires a
principal to be engaged primarily as an instructional leader to ensure
that reaching is focused on essential content. The instructional leader
will recognize and support improvements in curriculum, teacher
preparations, teacher recruitment and assignment, and professional
development to help students achieve their highest potential and
regain competitiveness among their peers internationally.

To make a real difference in student achievement, a principal must
focus the entire school around a vision and mission based on
improving teaching and learning. The principal must lead faculty and
staff through a review of the school and student achievement data.
The data analysis should indicate areas for improvement, especially
the alignment of content standards, curriculum, teaching materials,
and instructional practice. From this analysis, the principal and
faculty can embark on a continuous plan of improvement by engaging
in action research (Calhoun, 1994).

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Instructional Leader as a Content Expert
Consistent with current research on instructional leadership, it is the
expectation that principal is expected to be the instructional leader. In fact,
(Newman, King and Young (2000) found that school capacity is the crucial variable
affecting instructional quality and corresponding student achievement and at the
heart of school capacity are the principals focused on the development of the
teachers’ knowledge and skills, professional community, program coherence, and
technical resources. Anecdotally, however, it is important to also realize that often
assistant principals of curriculum and instructional serve as instructional leaders in
many school systems as well. Knowledge of the instructional programs of a district
is the keystone to guiding teachers through its implementation. However, good
knowledge of instruction is not enough to lead schools in the cycle of continuous
improvement. “The principal also needs special capabilities of leadership – recruiting
loyalty to the common task of teaching a specific group of children, knowing
individual teachers well enough to suggest particular ways of improving particular
aspects of their teaching performance, creating a culture in which deep knowledge of
instruction and learning serves as the foundation for an interdependent professional
community” (Fink & Resnick, 2001).

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CHAPTER THREE

RESEARCH METHODOLOGY

Introduction

This study examines the factors that positively influenced the mathematics
performance of students in one high school. This chapter contains detailed
descriptions of the research methodology employed, of the instrument development
process, of the determination and rationale of the population and study sample, of the
data collection methods, and of the methods used for analyzing the data.
A research team of eleven doctoral students at the University of Southern
California (USC), Rossier School of Education, Dr. David Marsh, Committee Chair,
conducted a qualitative case study research of urban high schools with indicators of
positive student achievement in mathematics. This study was one of eleven and
purposed to identify policies, elements of school design and mathematics program
design, specific leadership actions, and role of the school leader in shaping and
directing the school improvement effort that fostered student achievement in
mathematics. Specifically, the study extensively examined how one high school
realized improvement in Algebra I scores over a three-year period from 2002-2005.

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Importance of the Study

The following research questions parmatized and guided this study:
1. What was the pattern of mathematics achievement for various students
at the school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seemed relevant to improved mathematics achievement at the
school?
3. What change process did the school use to enhance the math program
and strategies to assist students in mathematics?
4. To what extent was strong instructional leadership important in
improving a) the mathematic programs/strategies and B) mathematics
achievement among students?
5. How did leaders in the school resolve the dilemmas about instructional
leadership?
Qualitative Research Strategy: The Case Study
Gall et al (1996) state three purposes for a case study: (1) to produce detailed
descriptions of a phenomenon, (2) to develop possible explanations for it, and (3) to
evaluate the phenomenon. The purpose of this analytical case study, conducted using
qualitative methods was to examine the factors that contributed to the phenomenon,
e.g., increased student math achievement. Based on this purpose, use of qualitative
methods for this study was warranted as they are structured to provide “well-

77
grounded, rich descriptions and explanations of processes in identifiable local
contexts” (Huberman & Miles, 1994, p.1). The emergent design aspects of
qualitative research are congruent with the data collection process used in this study,
as they provide the researcher with the latitude to delve into the “multiple meaning
and interpretations” of the participants and not be locked in to assumptions
established “a priori” (Creswell, 2003, p. 198), allowing the researcher to develop
possible multiple explanations for the phenomenon observed.
Yin (1981, 1992) defines the case study as follows: The case study
method…is an empirical inquiry that investigates a contemporary phenomenon
within its real-life context are not clearly evident and in which multiple sources of
evidence are used. The multiple sources of evidence gained through the data
collection process allow the researcher to critically evaluate the phenomenon using
data triangulated from survey results, interviews and document analysis. Patton
(2002) explains the increased validity of the inquiry though triangulated methods,
“…analyzing data using multiple methods allows inquiry into a research question
with an arsenal of methods that have non-overlapping weaknesses in addition to their
complementary strengths (Brewer and Hunter 1989:17 as cited in Patton, 2002).
Therefore, a systematic case study was selected as the most appropriate and effective
approach to be utilized; which “provides depth, detail, and individual meaning”
(Patton, 2002, p.16).
One public high school in Southern California was selected based on the
established criteria for this study. In order to maintain confidentiality and anonymity,

78
pseudonyms were used throughout this study when referring to the district and
school name and interviewees; however, the information was based on factual
evidence. Instruments developed for this study followed current research literature,
were aligned to the research questions, and were used to provide greater reliability of
the data collection process for the cohort of researchers involved in this
investigation. Conceptual frameworks were generated to provide the organizing
structure to capture the salient information through a common lens shared by all the
researchers in this cohort. As aforementioned, use of triangulation increased the
validity of the findings based on surveys, interviews and document analysis.
Sample and Population
Purposive sampling was used in selecting eligible high schools that met the
criteria for study 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 high school selected for the study was chosen 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 50% 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

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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 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 subsequently research improvement in
CST in Algebra 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%; the statewide rank set at 6 or higher, the sample was
limited to only 28 schools in southern California.
5. The second iteration included adjusting the parameters to an enrollment of no
less than 1200; a minority population of 50% or more and a statewide rank of

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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 number of
students scoring in the bottom two performance bands, e.g., Far Below Basic
(FBB) and Below Basic (BB) bands by 3% and increased the number of
students scoring in the top two performance bands by 5%, the school would
have an overall improvement score of 8%.
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.
b. Evidenced an increase in the number of students who scored in the
bottom two performance bands.

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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 District
Firmly nestled in the northeastern end of the suburban San Gabriel Valley,
bounded by the San Gabriel Mountains and the bustle of the interstate,
approximately fifteen miles southeast of Los Angeles, White Oak Tree Unified
School District is part of a middle-class community. The community is well
established with many generations remaining; there is stability. The district is
comprised of mainly “working class” families with an average family income of
$37,000 and where many of the student’s family members are employed by local
industry. The White Oak Tree Unified School District serves approximately 6,600
students at its five K-5 elementary schools, one 6-8 intermediate school, one 9-12
comprehensive high school, one continuation high school, as well as K-12 alternative
education programs. The White Oak Tree Unified School District mission statement
is: We will prepare students as life-long learners to succeed academically,
intellectually, socially, emotionally and culturally.
White Oak Tree Unified School District touts an 85-year legacy of supporting
all students, pre-K through the twelfth grade. The district vision is: We are

82
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 has a rich
history and works in a collaborative manner with the community to support the
students and the entire school district. The Mission of the White Oak Tree Unified
School District is to empower students to be lifelong learners:

Each student will:
Achieve self-worth
Become a productive citizen
Demonstrate social responsibility
Use technology as a tool
Conquer the demand of a changing world

The District in its commitment to excellence will provide:
Leadership with vision
Quality teachers and support personnel
Effective learning environments

Selected School
White Oak Tree High School has an enrollment of 2,142 students and is the
largest school in the district, receiving all the students from the three middle schools.
The school reflects the diversity of the city with the Hispanic enrollment
representing 45% of the school population, 31% Caucasian, 5.2% Asian, 4% African
American, 3% Filipino, Pacific Islanders, American Indians or Alaska Native
comprise less than ½ of 1% and 11.8% specify “other” respectively. More than 3%
of the students are English Learners (ELLs), with Spanish being the dominant second
language. Approximately 17% of the students at White Oak Tree High School are

83
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
approximately 1%, one of the lowest in the San Gabriel Valley.
Student Achievement
The motto for White Oak Tree High School is, “Quality Education Today for
a Better Tomorrow”. This is commitment to ensuring a quality education is
demonstrated in there consistent growth on their API scores, the school has increased
there API scores 63 points over the last six years with a baseline score of 654 in the
year 2000 and an API score of 717 in 2006. 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
705 705 702

School Participants
The administrative team at White Oak Tree High School is comprised of a
Principal and three Assistant Principals. For the purposes of this study the Principal
and the Assistant Principals participated in the interviews. In addition to the
administration teacher leaders, math teachers and other subject area teachers were
interviewed or completed a questionnaire.
As a means of collecting data, the researcher facilitated structured interviews.
The researcher conducted one to three interviews with each identified interviewee in

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an effort to gain in-depth information and understanding. The interviews were
conducted at the school site and were based upon interviews and item response
questionnaires 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 way of addressing
individual or cultural biases that can potentially influence the validity and reliability
of the study. In addition to interviews and questionnaires, document analysis
provided 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 number of sections, who taught what classes and the average class
size. This allowed for patterns and validations of perceptions that were presented in
the interviews and questionnaires.
The following individuals participated in the study and provided valuable
information as it relates to the research questions being examined for this study.
Administrator A. Administrator A was the last interview conducted for this
study. The sitting Principal at White Oak Tree High School, who had been there for
the past 12 years, was transitioning to Director of Secondary Education at the district
office at the time of this study. His background included teaching Civics at White
Oak Tree High School for six years prior to attaining the Principalship, and teaching
history and reading at the junior high school prior to that time. He was a History and
Philosophy major. In our initial communication, he referred me to Administrator B
the point of contact for the study. Administrator A was very clear in communicating

85
the vital role of Administrator B in the facilitation and implementation of the school
vision and the improved student achievement. The interview was structured using the
Key Leader Interview Guide (Appendix A).
Administrator B. Currently in her twelfth year in this role, she has served in
several capacities at White Oak Tree High School, including tenure as an English
teacher, department chair, and International Baccalaureate Programme Coordinator.
Administrators B was interviewed twice, once at the beginning of the study using the
Key Leader Interview Guide, and then as a follow-up after all of the teachers were
interviewed.
Counselor: Upon specific recommendations made by Administration A, one
of the four counselors was selected to be interviewed. This counselor transitioned to
his current role as 11
th
grade counselor in 2000, having served as a teacher on the
staff since 1994. He holds a single-subject business credential with a supplemental
authorization in mathematics.
Leadership Team. Eight teacher leaders were purposefully selected with
assistance from Administrator B to be interviewed. The lead teachers interviewed for
this study represented the four core areas of English (Asst. Department Chair),
History (Department Chair), Mathematics (Department Chair and Assistant
Department Chair) and Science (Department Co-Chair), as well as the Special
Education (Department Chair), Western Association of Schools and Colleges
(WASC) Chair, and Advancement Via Individual Determination (AVID)
Coordinator. In addition, the district mathematics coach who also serves as a

86
mathematics teacher was interviewed. All teacher leaders were selected to participate
in the study based on their leadership roles at the school providing instructional
support across the curriculum to further the school’s visions and aims for student
achievement.
Math Teachers. The entire mathematics department, consisting of thirteen
teachers were involved in the study; they completed the Math Teacher
Questionnaires (Appendix C) and participated in the teacher interviews. The
experience of teachers within the math department ranges from less than three years
of experience to two teachers in this department who have been at White Oak Tree
High School for over twenty years each, with the majority having tenure for an
average of five years. Three of the five Algebra I teachers have less than five years
of experience in the teaching profession. The gender balance is split approximately
60% female and 40% male. All teachers are fully credentialed in mathematics.
Non-Math Teachers. Fifty-three of the non-mathematics teachers were given
the Teacher Questionnaire (Appendix D) to complete. This included all teachers in
the three non-math core areas, English, Social Studies and Science, as well as
Special Education, foreign language, electives, physical education and Special
Assignments. The purpose of involving all teachers across the curriculum was to
gain a broader perspective of the school’s policies and programs that may have
contributed to student achievement.

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Instrumentation
The instrumentation for this study was developed during the summer of 2006
by an eleven-member doctorial research study team. All members of the team were
Ed. D. candidates at the University of Southern California, under the leadership of
Dr. David Marsh, Ph.D., Associate Dean of Academic Programs. The research team
worked during the summer of 2006 to refine the instruments prior to beginning the
data collection process. The impetus for refining the process was to gain greater
fidelity to the research questions upon which the conceptual frameworks were based.
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 to which they
were aligned. (See following page):

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Table 2: Relationship or Data Collection Instruments to Research Questions

Research Question
Instrument 1 2 3 4 5
School Profile X X
Key Leader
Interview Guide
X X X X
Teacher Interview
Guide
X X X X
Math Teacher
Questionnaire
X X X X
Non-Math Teacher
Questionnaire
X X X X

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 process of developing
data collection instruments, which included questions that were associated with each
of the instruments.
Frameworks for Instrument Design
Five conceptual frameworks parameterized the data collection in this study.
Conceptual Framework 1 (CF1), Conceptual Framework 2 (CF2), Conceptual
Framework 3 (CF3), Conceptual Framework 4 (CF4), and Conceptual Framework 5
(CF5) were developed to describe, examine and provide a lens through which to

89
focus the context-based research. Descriptions of the conceptual frameworks and
associated data collection instruments are provided below. There is no one-to-one
correlation between the five conceptual frameworks and the five research questions
as the conceptual frameworks were design to frame research questions two through
five.
There is no formal conceptual framework for research question one. The first
research question asked, “What was the pattern of mathematics achievement for
various students at the school?” This question was aimed at examining the data used
to determine patterns of math achievement for the various subgroups of students and
to generate a school profile. The school profile provided the structure for this
research question, in that it provided a template for the analysis of primary source
documents. Review of these primary source documents provided the initial peek at
trying to understand the organizational factors that contributed to student
achievement. Examples of primary source documents include the master schedule,
teacher assignments, CBEDS Report, School Accountability Report Card (SARC),
and Western Association of Schools and Colleges (WASC) report. Review and
analysis of these documents provided the salient background information and
increased researcher credibility upon beginning the interview process.
Conceptual Framework 1 and 2. School Design Model and Math Program
Design
Research question two asked, “What policy initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math achievement

90
at the school? This question was designed to foster an understanding of what factors
contributed to the consistent increased math achievement at the school during the
three-year time frame of the study. After much discussion, our thematic dissertation
group decided to develop two different frameworks to structure the analysis of the
data collected for the second research question. There is some overlap between CF1
and CF2; however, the decision was based on our desire to isolate the tangible and
specific influences of the mathematics program on student achievement, as apart
from other influences that may exist from the school design model.
CF1 described effective school designs utilizing basic elements of Marsh and
Codding’s school design model. It is separated into four primary sections with
subsections represented in Figure 1. (See following page):

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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

The framework for school design integrates the four foundational areas of
curriculum, student performance assessments, learning activities and school culture.
The Curriculum foundation begins with the “end in mind”, which are student
outcomes and incorporates some of the theory about how students learn and
construct knowledge. Student Performance Assessments capture the primary
conceptual and problem-solving skills, which the research supports as being
underrepresented in the common curriculum and overlooked in the standards-based
histrionics. Learning Activities incorporate aspects of social psychology and how
students interact with others in pursuit of knowledge and making meaning of
learning in a social context. White Oak Tree High School fully integrated AVID to

92
support the school culture and learning activities advancing student achievement.
Finally, the school culture looks at those organizational factors that promote a
healthy teaching and learning environment. Aspects such as quality of interactions
between students and staff and the consistent focus of the ongoing professional
developments for teachers are key indicators when examining those factors that
enhance the teaching and learning environment, and reinforce the standards. The four
instruments used to gather information to answer this question were the Key Leader
Interview Guide, Teacher Interview Guide, Math Teacher Questionnaire, and Non-
Math Teacher Questionnaire.
CF2, the second framework used to analyze the second research question
addresses the elements of effective math programs and is reflected in Figure 2. (See
following page):

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Figure 2 - Framework for Effective Math Programs

Based on extensive research, effective model math programs incorporate the
following components: Curriculum Design, Standards Based Instruction, and
Classroom Practices. Curriculum design reiterates student outcomes, incorporates
learning theory, however, the importance of the scope and sequencing is especially
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

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critical when examining the mathematics curriculum and is highlighted in this
framework. Standards Based Instruction incorporates the student performance
assessments with emphasis on the alignment to standards. High levels of student
engagement, culturally relevant pedagogy, rich instructional environment, and
effective and coherent lesson design and instructional delivery would overlay onto
the School Design Framework in the Learning Activities Component. The four
instruments used to gather information to answer this question were the Key Leader
Interview Guide, Teacher Interview Guide, Math Teacher Questionnaire, and Non-
Math Teacher Questionnaire.
Conceptual Framework 3. The third research question three asked, “What
change process did the school undergo e to enhance the math program and associated
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. This question included analysis of the
Bolman and Deal, Reframing Organizations (2003) four frames used to categorize
those factors that influenced the organization in its efforts to improve student
achievement into: (1) structural, (2) human resources, (3) political, and (4) symbolic.
Utilization of the frame that offered the most cogent and coherent perspective of the
change agent or catalyst towards improved math achievement was the desired goal.
(Table 3). Ultimately, applying different frames to a situation will lead to different
strategies; conversely, viewing an organizational challenge through all four frames
will provide for a sound, overall perspective of the complexity of the situation. The

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effective instructional leader must develop the skill to navigate this 4-quadrant
landscape for the success and growth of all members of the school community. The
frames are a useful way to approach leadership from multiple perspectives that are
dependent on the circumstances dependent.

Table 3 – Bolman and Deal’s Four Frames
Structural Frame Human Resources
Frame
Political Frame Symbolic Frame
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

The Structural Framework. Through the structural frame, the leader tries to
create and implement a process or structure appropriate to the situation or
circumstance. There is emphasis on the task, logic and facts and providing clear
structure and lines of authority.
The Human Resource Framework. The human resource frame fosters greater
responsiveness to the people in the organization. There is emphasis on staff

96
empowerment and an overall feeling that supporting the human resource is the most
important role of the organization.
The Political Framework. Within the political frame, the leader understands
the political reality of the organization and negotiates differences skillfully. There is
emphasis on equitable allocation of resources, effective management of conflict, and
brokering of compromises in and among the power bases of constituencies.
The Symbolic Framework. There is emphasis on the traditions and common
values in the symbolic frame. Vision, mission and inspiration are key components of
this frame. There is emphasis on ceremony, ritual and commitment to the common
purpose.
Conceptual Framework 4. 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 in the improvement of math
achievement and what were the strategies utilized. CF4 is separated into five themes
(Table 4): 1) Vision for Learning; 2) Supervision and monitoring of instruction; 3)
Community and Political; 4) Culture of Teaching and Learning; and 5) Data Driven
Decision Making Analysis. (See following page):

97
Table 4- Instructional Leadership Framework
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

Table 4 reflects the intellectual framework that was utilized in the study as it
supports and delineates concepts associated with instructional leadership.
Instructional leadership continues to be redefined for the past 20 years. Research has

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found that effective schools usually had principals who stressed the importance of
instructional leadership and emphasized academic standards (Brookover and Lezotte,
1982). Moreover, instructional leadership are those actions a principal takes, or
delegates to others, to promote growth in student learning (Flath, 1989). In this
study, The Educational Testing Service (ETS) publication, “A Framework for School
Leaders: Linking the ISLLC Standards to Practice” provided the intellectual
background theory to articulate the goal or standards for instructional leaders
practice and implementation. The five standards or corresponding themes for an
educational leader are as follows:
1. Promotes the success of all students by facilitating the development,
articulation, implementation, and stewardship of a vision of learning that is
shared and supported by the school community,
2. Promotes the success of all students by advocating, nurturing, and sustaining
a school culture and instructional program conducive to student learning and
staff professional growth,
3. Promotes the success of all students by ensuring management of the
organization, operations, and resources for a safe, efficient, and effective
learning environment.
4. Collaborates with families and community members, responding to diverse
community interests and needs, and mobilizing community resources,
5. Acts with integrity, fairness, and in an ethical manner, and

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6. Understands, responds to, and influences the larger political, social,
economic, legal, and cultural context.
The four instruments used to gather information to answer this question were the
Key Leader Interview Guide, Teacher Interview Guide, Math Teacher Questionnaire,
and Non-Math Teacher Questionnaire.
Conceptual Framework 5. The fifth research question asked, “How did instructional
leaders respond in academic areas in which they were not experts?” The goal of this
question was to assess the instructional leader’s expertise level in math and its
impact on their ability to support the teachers in the instructional math program. This
framework was bifurcated into two distinct components. First, an assessment tool, a
flow chart, was created to allow the investigator to ascertain the instructional leader’s
level of math expertise. This assessment tool is a modified version of the “highly
qualified teacher” (HQT) rubrics under the NCLB legislation guidelines, specifically
used to determine the instructor’s level of subject matter competencies in the content
area in which they teach. This modified version is detailed in Figure 3. The output
determines the instructional leader’s designation of a high, medium or low expertise
level. (See following page):

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Figure 3: Assessment of Principal’s Expertise in Math
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
Has Principal
minored in or
taught math?
Yes No
Medium
Expertise
Low
Expertise
Step
3
Step 2

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Secondly, twelve of the most prevailing research-based strategies on leadership
actions were compiled and listed with the corresponding references, i.e.,
Approach/Source to categorize responses about specific actions implemented to
improve 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 Cope
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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The four instruments used to gather information to answer this question were the
Key Leader Interview Guide, Teacher Interview Guide, Math Teacher Questionnaire,
and Non-Math Teacher Questionnaire.

Data Collection Instruments
The four data collection instruments, Key Leader Interview Guide, Teacher
Interview Guide, Math Teacher Questionnaire and the non-Math Teacher
Questionnaire were created after the five conceptual frameworks were developed.
There was no formal data collection instrument generated to answer research
question one. Extensive document analysis was required to identify the pattern of
mathematics achievement for the students at the school. These instruments support
research questions two through five as indicated in Table 2: Relationship of Data
Collection Instruments to Research Questions and are aligned with the five
conceptual frameworks to provide a management system for the organization,
synthesis and parameterization of the data collected to guide the reporting in Chapter
4. The first research question required the development of a school profile based on
the results of an in-depth and triangulated document analysis process. Guiding
questions were asked during the structured interviews using the interview guides
allowing for germane and succinct data to be collected for further analysis.
Instrument 2: Key Leader Interview Guide. Structured interviews were
conducted with the school principal, assistant principal of curriculum and instruction,
one counselor and leadership team members using this instrument. The Key Leader

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Interview Guide does not initially establish background information from the
interviewees; this researcher started each interview with the first two questions from
the Teacher Interview Guide. These first two questions from the Teacher Interview
Guide served to obtain the individual participant information about their current
position, educational background, years of experience, and any specialized training.
This instrument was developed to facilitate the data collection relevant to research
questions two through five. The questions in the Key Leader Interview Guide are
organized explicitly by the research questions and are grouped in the following way:
Research Question Two has four questions related to policy initiatives, curriculum
and instruction and other related conditions to math achievement; Research Question
Three has four questions related to the change process; Research Question Four has
five questions covering issues specifically related to instructional leadership; and
Research Question Five has two questions that are answered through the lens of the
12-Item Strategy Matrix.
Specifically designed for 60- minute data collection semi-structured
(Creswell, 1998) interviews among administrators and leadership team members, the
Key Leader Interview Guide primary and secondary questions allowed this
researcher to obtain the interviewees perceptions and attributes about those factors
they believed to contribute to improved math performance of their students. This also
provided the latitude qualitative researchers need to probe any emergent themes that
resulted from the interviews. The interview with the assistant principal of curriculum
and instruction was broader in focus and required three sessions in order to identify

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areas of further inquiry, clarify any gaps in information resulting from math teacher
interviews and during the interviews with other members of the leadership team.
Instrument 3: Teacher Interview Guide. Semi-structured interviews were
conducted using the Teacher Interview Guide with all of the math teachers, except
for the two math department chairs and the math coach that were interviewed using
the Key Leader Interview Guide. This instrument consists of seven interview
questions that align with and obtain information relating to research questions two
through five. This interview protocol was consistent with the Key Leader Interview
protocol, but designed for no more than a 40-minute data collection interview
process. The questions gathered feedback about perceptions and attributes from the
math teacher’s perspective about the math performance of their students. This
process also provided the latitude qualitative researchers need to probe any emergent
themes that resulted from the interviews. The interviews with the math teachers who
teach Algebra I were a little broader in focus, as they were able to provide more
specialized background information relating to specific policies, school design, the
math program, changes, and instructional leadership elements that influenced greater
math achievement by their students, particularly in Algebra I.
School Profile Analysis
This instrument was developed to create a school profile that is both
comprehensive and accurately portrays the uniqueness of the study site. The
information gathered provided the researcher contextual information and an
overview of the school’s instructional journey. Data collected was organized into

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three primary areas: demographics, student academic performance and general
school information. The California Department of Education website provided rich
demographic data about both students and teachers organized through the School
Accountability Report Card (SARC). Information gathered regarding the students
included overall enrollment, enrollment by ethnicity, achievement by ethnicity,
course enrollment patterns, graduation and drop-out rates, socio-economic
information (free and/or reduced lunch percentages), English Learner (EL)
percentages, and A-G completions rates. This information allowed for analysis of
patterns of student achievement. Teacher information included HQT status, number
of teachers and years in teaching, course assignments, and education levels. This
information gave the researcher insight into some of the leadership and management
philosophy of the administration. The SARC also provided curriculum and
instruction information, textbook names and editions, supplemental materials that
provide the researcher information to effectively probe during the interview. The
school performance longitudinal data included the Academic Performance Index
(API) scores; the passing rates for the California High School Exit Exam (CAHSEE),
standardized CST test scores. Taken together, all three data foci provided the
researcher essential background knowledge to further ground the study.
Instrument 4: Math Teacher Questionnaire. All math teachers were asked to
complete this survey called the Math Teacher Questionnaire. This survey consisted
of a brief introduction, directions for completing the survey, an assurance of
confidentiality and 50 items, which the cohort estimated would take no more than

106
thirty minutes to complete. The Math Teacher Questionnaire was intended to
measure participant perceptions about the improvement in student achievement in
math attributable to: RQ2: policy initiatives, curriculum, instruction and other related
conditions; RQ3: elements of the change process; RQ4: instructional leadership
actions; and RQ5: how instructional leaders resolved dilemmas based on the 12-Item
Strategy Matrix. The questionnaire was grouped in the following way: Questions 1-
13 related to RQ2; Questions 14-29 related to RQ3; Questions 30-42 related to RQ4;
and Questions 43-50 related to RQ5. The statements were presented on a five-point
Likert scale (ranging from 1 -5) to allow the participants to circle their level of
agreement for each statement (Appendix C). The level of agreement for each point
on the scale was: 1) Disagree Strongly; 2) Disagree Somewhat; 3) Neutral; 4) Agree
Somewhat; and 5) Strongly Agree. This instrument was developed collectively by
the cohort group, which ensured the alignment between research questions and the
conceptual frameworks.
Instrument 5: Non-Math Teacher Questionnaire. Selected non-math
certificated teaching personnel in English, Science, Social Studies, Special
Education, Foreign Language and Elective departments were asked to complete the
Non-Math Teacher Questionnaire. This survey consisted of a brief introduction,
directions for completing the survey, an assurance of confidentiality and 30 items,
which the cohort estimated would take no more than twenty minutes to complete.
This instrument was intended to measure participant perceptions that taught in
subjects other than math to participate in the study and to share their ideas and

107
perceptions as to those factors that have contributed to improved student
achievement in math through the lens of research questions two through five. The
questionnaire was grouped in the following way: Questions 1-10 related to RQ2;
Questions 11-16 related to RQ3; Questions 17-22 related to RQ4; and Questions 23-
30 related to RQ5. The statements were presented on a five-point Likert scale
(ranging from 1 -5) to allow the participants to circle their level of agreement for
each statement (Appendix D). The level of agreement for each point on the scale
was: 1) Disagree Strongly; 2) Disagree Somewhat; 3) Neutral; 4) Agree Somewhat;
and 5) Strongly Agree. This instrument was developed collectively by the eleven-
member cohort group, which ensured the alignment between research questions and
the conceptual frameworks. (Table 2).

Data Collection
The school data for this study was collected over a three-month period from
November 2006 through January 2007. The data was collected in three primary
phases to allow for a more thorough comparison of documents, surveys and
interview notes. According to Yin (2003) “[t]he use of multiple sources of evidence
in case studies allows the investigator to address a broader range of historical,
attitudinal, and behavioral issues” (p. 98). All participants were afforded the
opportunity to review the transcribed notes from their respective interviews to ensure
an accurate reflection of their intended message. Multiple phases of activity allowed
for the researcher to follow-up on any emergent themes that surfaced. In this typical

108
case sampling (Patton, p. 236) strategy of purposeful sampling design, White Oak
Tree High School was selected because the criterion data showed it was an
“illustrative” and not “definitive” example and careful analysis of the information is
required to illuminate those key issues that can be considered by other cases to
address the issue of mathematics achievement in diverse environments. These salient
points or key issues emerge in different ways through different methods.
Triangulation of the data through multiple phases of data collection increases the
reliability and credibility of the data.
Schools that met the criteria were identified, provided an overview of the
study, and invited to participate in the study. Schools that accepted the invitation
were studied for their positive gains in student achievement in mathematics. For this
particular study, the 11-member research team was given permission to submit one
IRB proposal for the series of related studies under the leadership of Dr. David
Marsh. This process increased the consistency of the IRB application process, as the
instruments, conceptual frameworks, data collection process and methodologies were
consistent throughout all eleven case-studied for this 11-member cohort. The
Institutional Review Board (IRB) application was completed and submitted in
August 2006. The purpose of the IRB was to protect the participants of the study
from any harm as a result of the methods used in the study. The IRB closely
examined the methodologies, instruments and procedures for data collection
proposed for the study.

109
In the fall of 2006, after clearance from the IRB, the cohort group members
contacted the schools and districts selected for study. Site and district administrators
were contacted, informed about the details of the study and forwarded a request for a
signed, informed consent.
For this study, the first phase of data collection included an invitation by the
assistant principal of curriculum and instruction to meet the entire mathematics
department at a department meeting and provide a very brief overview of the study.
The researcher addressed the math department during this meeting by introducing
herself and described the purpose of the study. The math department chairs and math
coach were specifically introduced at this meeting. The math teachers were informed
that the Math Teacher Questionnaires would be placed in all of their staff mailboxes
and that the subsequent interviews would be scheduled with the entire math
department over the next two months. The surveys were numerically coded and they
were informed that the surveys were voluntary and that their responses would be
confidential and anonymous. All interviewees were reminded about confidentiality
and anonymity as well.
At the first meeting with the assistant principal of curriculum and instruction,
the researcher collected documents from the school such as the Single School Plan,
WASC Visit Preparation Notes, Master Schedule, CBEDS Information,
disaggregated longitudinal CST data, and interdisciplinary CAHSEE data and
information. This added to the documents that had been collected from the California
Department of Education (CDE) website. During this meeting, the AP provided

110
guidance and information about key leaders on campus, an overview of the
instructional programs in general, the math programs specifically, and school wide
cultural factors affecting the school’s academic progress. Also during this meeting,
the researcher was invited to observe an on-site planning meeting of the math
teachers who teach at least one section of Algebra or Algebraic Applications. The
Math Teacher Questionnaires and non-Math Teacher Questionnaires were placed in
manila envelopes marked by a number that correlated to the name of the teacher
known only to the researcher and placed in the teacher’s individual school
mailboxes. The envelope contained instructions about the due date and drop-off
instructions, and most importantly, a reiteration about the confidentiality of the
“voluntary” responses. They were given five-day window to complete and return the
survey in the enclosed manila envelope to the principal’s secretary. This first data
collection phase consisted of reviewing documents and website information before
coming onto the campus. The researcher collected and analyzed pertinent
information and documents from the school prior to conducting interviews such as
school student demographics (ethnicity, language proficiency, SES status), patterns
of achievement by subgroups (Algebra CST scores, AP enrollment and passing
rates). This contextual knowledge provided the researcher with greater opportunities
to probe further and with purpose during the subsequent interview process. The
researcher provided a copy of both the Math Teacher Questionnaire and the Non-
Math Teacher Questionnaire to both the site Principal and Assistant Principal for
their records.

111
The second phase of data collection began with accepting an invitation to
observe an on-site planning meeting of the math teachers who teach at least one
section of Algebra or Algebraic Applications. Four of the five possible teachers that
fit these criteria were in attendance. The goal of that meeting was to revise the end of
semester final examinations. The first round of interviews began at the conclusion of
that planning meeting with two of the math teachers using the Teacher Interview
Guide which outline key areas of focus that were directly aligned with the research
questions. The researcher studied Conceptual Frameworks 1 – 4 to prepare for these
interviews. The first round of interviews was held over a 4 (non-consecutive) day
period at the school site during the school day at either the teacher’s conference
period or lunch time, whichever they preferred. Twelve math teachers (including the
math coach and department chairpersons) were interviewed during this period based
on their teaching or leadership role at the school site. One of the math teachers
provided written answers to the interview questions, as she was part-time and unable
to avail herself for a structured interview. Purposeful sampling was used to ensure
that the participants were involved leaders at the school site and had background
knowledge about the school culture, background and history of achievement. This
second round of interviews 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. In addition, completed teacher questionnaires were collected
and the data from these questionnaires was compiled into a database to be utilized in
analysis the responses.

112
The third phase of data collection also took place at the school site over a
four-day period to conduct interviews. The researcher conducted a second round of
interviews, which included the principal, assistant principal, a counselor and five
non-math classroom teachers. The teacher participants were stratified randomly
selected from teacher leader criteria to ensure a representative sample. The five
stratified randomly chosen leadership team members were department chairs from
each of the other three core subject areas, one special education teacher and one
program coordinator. The researcher used both the Key Leader Interview Guide and
Teacher Interview Guide. In preparation for the interviews, the researcher used
Conceptual Framework 5 as a visual model of the research based strategies and
approaches for the interviewees to focus the responses for research question five.
During the teacher interviews, participants were informed that their participation was
voluntary and they could elect to not answer an interview question or withdraw from
the study at any time.
The researcher also conducted a second interview with the assistant principal
to ask any clarifying questions, provide context to any emergent themes from the
teacher interviews and to ask any final questions not addressed during the first two
phases of the data collection. In this final phase the assistant principal was
encouraged to share any final thoughts, comments or ask questions.
This study incorporated both the interview guide and the standardized open-
ended interview approach to qualitative data collection. Using The Key Leader
Interview Guide and Teacher Interview Guide made the interviewing of a number of

113
different people more systematic and comprehensive by delimiting the issues in
advance, i.e., alignment with the research questions (Patton, 2002). Additionally,
conducting standardized-open ended interviews using the exact instruments as the
other interviewers, i.e, the cohort members in the study, minimized the variation
among other interviewers, kept the interviews focused and time efficient and the data
easier to analyze (Patton, 2002). All interviews were conducted at the school site,
during school hours that were preferable to the interviewee with the principal and
assistant principal’s consent. The researcher always reiterated the purpose of the
study and prefaced the interview with an explanation of the interview guides. At the
conclusion of the interview, participants were reassured of their confidentiality and
anonymity of responses within the study. The researcher audio taped most of the
interviews and took notes during all of the interviews with the participants, except
for one special case interview. One teacher was unable to participate in a face-to-face
interview, so she typed her answers to the Teacher Interview Guide questions and
submitted them to the researcher. Participants were given the opportunity to obtain
copies of the researcher’s notes and transcribed notes to verify accuracy.
Data Analysis
The purpose of the study was to understand the factors that positively
influenced the math achievement at White Oak Tree High School. It described the
actions one school had taken to increase student achievement in mathematics. The
study explored the elements of school design, math program design, the change
process and instructional leadership in relation to the five conceptual frameworks

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and the five research questions, which served as a guide for data collection and
analysis as well as the keystone to explain the findings of the exploration.
The 22 interviews were transcribed and then coded according to one of the
five research questions. Data from the researcher notes and transcribed interviews
were analyzed to discover common themes and perceptions regarding 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 math
program design, the change process, the strength of the instructional leadership, and
the instructional leader’s response strategies in areas of limited subject area
knowledge. The five research questions and five conceptual frameworks addressed
the purpose of this study and served as the foundation for data collection, analysis,
and representation of the findings. The data was grouped and codified into a
spreadsheet/database for comparison and best practices used within the classroom
and the role of the school leader in shaping and directing the school’s improvement
efforts. Five research questions were developed by a cohort to assist in framing and
completing the study. Additionally, data collection instruments that are 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 were 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.
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 efforts 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.
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

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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 White Oak Tree 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
Exhaustive studies have been generated about the poor academic
performance of American high school students, specifically in mathematics. A
national focus generated by a Nation at Risk as well as the international rankings of
TIMMS have galvanized both politicians and educators to enact sweeping legislation
and reforms. State and national efforts have resulted in standardized curriculum and
assessments, delivered in restructured school settings, taught by more credential-
appropriate teachers, implemented innovative researched-based programs and
strategies, instructional programs led and monitored by the new breed of
instructional leader utilizing an arsenal of data-driven decision-making; yet,
performance and achievement gaps persist and prevail despite our best reform
efforts. These altered educational environments have failed to produce consistent,
systematic and sustainable student achievement. However, selective successes have
been registered and are worthy of further study.
The purpose of this study is to examine the conditions that fostered
mathematics achievement at one high school. Specifically, the study examines the
impact of policy initiatives at the federal, state and district levels, the school design
model, the math program design and best practices utilized, and specific actions of
the instructional leader in shaping and directing school improvement efforts that

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realized an increase improvement in student Algebra I scores over a three-year
period from 2002-2005.
The five research questions were aligned with both the four conceptual
frameworks, which identified the themes associated with each of the research
questions and data collection instruments. The four data collection instruments, Key
Leader Interview Guide, Teacher Interview Guide, Math Teacher Questionnaire, and
non-Math Teacher Questionnaire, were developed by a research team of eleven
doctoral students at the University of Southern California (USC), Rossier School of
Education, under the direction of Dr. David Marsh to obtain cogent, relevant
responses for data collection mapped back to the conceptual frameworks. Using
triangulation methods, source documents were analyzed, interviews were transcribed
and coded and entered into a spreadsheet for comparison, and survey data was
indexed and entered into spreadsheet. This tripartite model provided increased
validity as patterns emerged that allowed a cross-indexing of the research questions,
conceptual frameworks, and survey data. The five research questions serve to
organize this chapter and will be used to present the findings.

Research Question 1: What was the pattern of mathematics achievement for various
students at the school?
Analysis of accountability source documents provided the foundational
context for the study while simultaneously defining the first leg for triangulating and
verifying the data collected, leading to increased validity of the findings. Review of

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source documents such as the School Accountability Report Card (SARC),
Standardized Testing and Reporting (STAR) Report, California Basic Educational
Data System (CBEDS) report, California High School Exit Exam (CAHSEE) results,
master schedule, Western Association of Schools and Colleges (WASC) Report, and
Distinguished School Application provided rich data sets for examination and
comparison to identify the patterns of student achievement at White Oak Tree High
School. Through informal meetings and email communications with Administrators
A and B, and the WASC Chairperson, this researcher was able to substantiate the
accuracy of the data provided in the source documents.
White Oak Tree High School is a suburban school with urban school issues
of student math achievement. It has had stable enrollment increasing by
approximately 250 students over the last 10 years. The demographics have fluctuated
slightly with annual increased percentages of Hispanic students, representing slightly
less than 50% of the overall student population. The next largest sub-groups are
white students representing approximately 31% of the total school population.
African-American and Asian student groups comprise between four and five percent
of the school population. English Learners (ELLs) comprise only three-percent of the
students enrolled. WOTHS had met the Average Yearly Progress (AYP) in all areas
for the last three years. The Academic Performance Index (API) fell by three-points
in 2003-04 and 2004-05, but increased by 15 points in 2005-06. The following
segment examines patterns of achievement at WOTHS from the school year
immediately before the period of study (2001-2002) through the year immediately

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following the period of study (2005-2006) to identify trends and dramatic shifts in
achievement.
Patterns of Achievement
The No Child Left Behind Act defines a subgroup as significant when the
percentage of students in a specific group is at least 10% of the student population or
is comprised of more than 100 students. African-American, Asian and English
Learner student groups are thus not considered “numerically significant” in the
calculation of the Academic Performance Index (API). WOTHS’s significant
subgroups include Hispanic, white and socio-economically disadvantaged students.
Even though African-American and Asian students’ achievement data is not
calculated in terms of the API, there is data available to make some comparisons
between all subgroups. The data that follows will provide an overall picture and
demonstrated patterns of achievement for each of the subgroups at WOTHS,
organized and presented as follows: California Mathematics Standards Test (CSTs),
Algebra CSTs, API Sub-groups, CAHSEE Math Pass Rates, IB/AP Exam rates, A-G
Completion rates and a Report Card Analysis. Not all of the data represents positive
growth.
California Standards Test (CST)
Over the last four years, White Oak Tree High School has experienced
significantly lower overall math percentage scores at the proficient and advanced
levels on the California Standards Test than the California state averages. There was
a consistent decrease in math scores at the proficient or advanced levels from 2001-

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2002 through 2003-2004. The results in 2004-2005 showed a four-percent increase
from the previous year, yet remained flat at that same level through 2005-2006,
concurrent with a three-percent drop for the California state averages.
Disaggregating the CST scores by race and ethnicity indicated an alarming trend of
underachievement by some groups of students.
There appears to be no significant growth in the percent of students achieving
at the proficient or advanced levels of mathematics among all student groups from
2002 – 2006. Scores for all students fluctuated greatly during this period. Table 6
illustrates a decline for all groups of students from 2003-2004, except for African
American students, whose scores remained flat. During 2002-2006, two groups of
students experienced a net loss, one group remained flat, and two group’s
demonstrated increases at the proficiency and advanced performance bands. African-
American students fell from 13% to 4%, and Hispanic or Latino students fell from
13% to 12%. White student scores remained flat at 20%, and Filipino and Asian
students enjoyed increases of 17% to 20% and 36% to 40%, respectively. Overall
Asian students are the highest performing while African-American students are the
lowest performing. The Filipino and Asian groups consistently score the highest of
the subgroups; however, no group is higher than the 3
rd
quartile. (See following
page):

122
Table 6: Sub-Groups Achieving at the Proficient or Advanced Level in Math
Race/Ethnic
Group
2002 2003 2004 2005 2006
African
American
13 5 5 6 4
Asian 36 38 34 41 40
Filipino 17 20 12 16 20
Latino 13 13 7 11 12
White 20 21 15 19 20
Socio-
economically
Disadvantaged
19 13 7 12 11

Algebra CST
There are similar patterns of proficient and advanced levels of achievement in
Algebra I as found in the overall mathematics scores. WOTHS Algebra I scores have
fluctuated greatly from 2002-2006 mirroring similar patterns of student achievement
at the California state level except for the 2005 – 2006 school year when they
experienced a decrease in scores simultaneous with an increase in the California state
scores. WOTHS has exceeded the California state average on the CST in Algebra
three of the last five years. However, 2005-2006 WOTHS percentage scores were
significantly lower than the California state average by 9 percentage points. There
was a net ten-percent gain in the number of students moving from the Below Basic
(BB) and Far Below Basic (FBB) performance bands on the CST in Algebra over the
period of 2002-2005.

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Table 7: Comparison of the Percentage of Students Scoring Proficient or Above

CST: Algebra I
2002 2003 2004 2005 2006
California State
Average
35 21 18 19 23
WOTHS 19 13 6 13 14

API Subgroups
API scores rose by 57-points from 2002-2006. There were large increases in
scores from school years 2001-2002 to 2002-2003 with the largest increase occurring
from 2004-2005 to 2005-2006. There was a decline in all subgroups from 2003-
2004, however, all groups experienced increases from 2004-2005. English Learners
increased significantly from 2004-2005, but decreased significantly from 2005-2006,
with an overall decrease of 63% during 2002-2006. Consequently, there is not
enough data to make comparisons between racial/ethnic groups at White Oak Tree
High School. White students scored higher than Hispanic/Latino students every year
except 2004. The Hispanic/Latino population has had small incremental increases
without any great fluctuations on growth scores. A dip occurred in 2004-2005 for
both groups. The Hispanic/Latino subgroup mirrored the school-wide API growth
and non-growth. The White subgroup had two slight decreases followed by a
significant increase in 2005-2006. Both groups have made moderate improvements
score wise, during the 2002-2006 period; in both base and growth API scores even
though the growth numbers would be considered unstable. As stated, there is not

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enough data to make comparisons for racial/ethnic groups at White Oak Tree High
School. There appears to be no significant change in the subgroups from 2002-2006
except for English Learners. There are English as a Second Language (ESL) classes,
but no sheltered classes in any other discipline. Overall, there was an increase in
students scoring proficient or advanced on the Algebra I, Geometry, and Algebra II
CST.
California High School Exit Exam (CAHSEE)
The California state passing average for the class of 2006 is 89.3 percent.
However, these state figures illustrate another troubling statistic. The achievement
gap persists and represents another challenge in our educational system. Latest
figures show that while a total of 96.5 percent of white students and 94.6 percent of
Asian students in the class of 2006 have passed the exam, only 82.7 percent of
economically disadvantaged students, 82.5 percent of Hispanic and 81.1 percent of
African American students have passed the test (California School Boards
Association, 2006). At White Oak Tree High School, overall, the pass rate on the
CAHSEE remains approximately 78% for meeting the requirement during the
sophomore census with another 15% of the students passing either the ELA or
Mathematics sections. Within the subgroups, African American, students with
Disabilities, Hispanic/Latinos and socio-economic disadvantaged continue to
score below the school’s overall passing rate on both the mathematics and English
language sections of the CAHSEE.

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Table 8: Percent of Students Passing CAHSEE in Mathematics by Ethnicity

WOTHS
Overall
African
American
Asian Filipino Latino White
2001 93 No data 92 No data 97 100
2002 60 43 83 92 51 65
2003 49 38 68 63 44 55
2004 84 53 100 79 80 90
2005 70 45 95 69 69 75
2006 69 40 97 69 66 76

International Baccalaureate (IB) and Advanced Placement (AP) Exams
White Oak Tree High School implemented the IB Diploma program over 10
years ago, having the distinction of being the first high school in Los Angeles
County to offer this program to its students. The IB Diploma Programme is a
rigorous two-year curriculum program of study for high school students. This
program prepares students for the university and encourages them to: (1) ask
challenging questions, (2) learn how to learn, (3) develop a strong sense of their own
identify and culture, and (4) develop the ability to communicate with and understand
people from other countries and cultures. The IB Diploma is widely recognized by
the world’s leading universities (www.ibo.org). The curriculum consists of six
subjects selected from six subject groups: (1) Language A1, (2) Language A2, (3)
Individuals and societies, (4) experimental sciences, (5) mathematics and computer
science, (6) the arts. Usually, three subjects are studied at the higher level (HL) and

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the remaining three at a standard level (SL). All three parts of the core of the IB
Diploma Programme—extended essay, theory of knowledge and creativity, action
and service—are compulsory and are central to the philosophy of the Diploma
Programme.
The fifth group of the IB Diplomas Programme, the mathematics and computer
science group consists of four levels of math courses and an elective computer
science course. To earn an IB Diploma, a candidate must pass at least one SL or HL
mathematics course (www.ibo.org). The core of the SL content include number and
algebra, functions and equations, circular functions and trigonometry, vector
geometry, matrices and transformation, statistics, probability and calculus. In
addition to the aforementioned core content, HL candidates choose additional topics
in further statistics, or sets, relations and groups, or discrete mathematics or analysis
and approximation, or Euclidean geometry and conic sections.
White Oak Tree High School has greater curriculum emphasis on International
Baccalaureate (IB) courses rather then Advanced Placement (AP) courses with many
designated at dual AP/IB courses. However, most students elect to take the IB course
exams. Since 1996, the number of students taking International Baccalaureate (IB)
exams has shown a steady increase. In 1996, students took 104 IB exams and 47
Advanced Placement (AP) exams. A decade later, WOTHS students took 301 IB
exams and 249 AP exams. For the 2005-2006 school year, the pass rate for IB exams
was 65% and the pass rate for AP exams was 51%. The overall IB Diploma pass rate
as reported by the International Baccalaureate Organization (IBO), was about 80

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percent in 2005. WOTHS had a 15% lower passing rate than the IBO average for
that same year. AP Enrollment in AP and IB mathematics has had slight increases in
four of the past five years. The passing rates on these exams have increased twice
and decreased twice during this same period, with the most recent year showing a
decrease from a 66% to a 41% pass rate on AP math exams. The increase in math
exam participation coincides with the inclusion of AP Statistics, and IB HL, and the
deletion of standard level math. The number of IB diploma candidates has also
increased from 8 in 1996 to 17 in 2006 with all 17 receiving IB diplomas. The pass
rate for diplomas has been within the range from a low of 68 % to the high of 100%
and the number of candidates from a low of 8 to a high of 19 in the past six years.
University of California/California State University Courses (A-G)
The increased emphasis on academics is reflected in the number of students
completing the minimum University of California (UC)/California State University
(CSU) A-G requirements. In 1996, 45.8% of the seniors completed these
requirements. This percentage steadily increased each year reaching 55.9% in 2000,
but experienced a sharp decline in 2001 when only 30.6% completed the UC A-G
requirements possibly due to a change in reporting procedures. However, the
percentages increased over the next two years to 34.2% in 2003 and to 48.5% in
2004. In the two years following, A-G completion rates decreased to 39.81% and
increased to 41.66% in 2005 – 2006. One of the primary reasons for the failure to
complete the A-G requirements is an incomplete mathematics sequence of three
years of high school mathematics with grades of C or better. In accordance with the

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UC/CSU Admissions Policies, the school does not count any grade of C- or lower
in a course as completion of a college entrance requirement
(www.cpec.ca.gov/Accountability/AtoGReport.ASP).Table 9 illustrates the
aforementioned percentages.
Table 9: Percent of Graduating Students Meeting College A-G Requirements

Percent of WOTHS Meeting College Entrance Requirements
2002 31
2003 21.6
2004 34.7
2005 41.2
2006 41.6

Report Card Analysis
Percentages of students earning Ds and Fs have stayed relatively static over
the last four school years. After a high of 8% of the students receiving Fs in the Fall
2005, a large decrease is shown in the spring semester ending June 2006. (See
following page):

129

Table 10: Report Card Analysis

Semester # of D’s Percent # of F’s Percent
Fall 2002 1340 11.8 757 6.7
Spring 2003 1328 12.5 764 7.2
Fall 2003 1513 12.8 754 6.4
Spring 2004 1332 11.8 672 6.0
Fall 2004 1508 12.1 861 6.9
Spring 2005 1428 12.2 829 7.1
Fall 2005 1473 12.1 971 8.0
Spring 2006 1213 10.7 741 6.6

Summary
There are diverse patterns of student math achievement at White Oak Tree
High School. Some groups of students are experiencing a wide range of success in
their high school mathematics education. Asian students, and to a lesser degree,
white students have performed at the proficient and advanced levels on the CST tests
on a consistent basis for the past five years. Over one-third of all Asian students are
passing these tests at the proficient and advanced levels; white student’s passing
rates are between 15 and 20 percent at these same levels. African American students
are at the bottom of the achievement gap in both the CST scores and CAHSEE
passing rates. African American student CST scores have ranged from 13 to 4
percent passing rates at the proficient and advanced levels over the past five years.
CAHSEE passing rates in math for these students have ranged from 38% - 53% from

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2002 – 2005. Hispanic students are achieving at higher rates than their African
American peers posting CST scores that ranged from seven to thirteen percent from
2002-2005 at the proficient and advanced levels. Hispanic student CAHSEE passing
rates in math have ranged from 44% to 80% during this same period. Asian and
White students are enrolled in IB and AP classes at more than five times the rate of
African American and Hispanic students. Conversely, African American and
Hispanic students are enrolled in Algebra support classes at nearly five times the rate
of White students.

Research Question 2: What policy initiatives, as well as curriculum and instruction
and related conditions seem to be related to improvement mathematics achievement
in the school?
Federal and state accountability systems have dominated public education
since the late 1990s. Policies based on these systems represent broad efforts to
improve public education systems through standards-based curriculum, instruction
and assessment. The purpose of this section is to understand how the accountability
policies and related conditions are related to increased student achievement in
mathematics. The following instruments, aligned with Conceptual Framework 2
(CF2) and Conceptual Framework 3 (CF3), were used to facilitate data collection for
this research question: Key Leader Interview Guide, Teacher Interview Guide, Math
Teacher Survey, and Non-Math Teacher Survey. The qualitative and quantitative
data gathered to address this second research question was organized and presented

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as follows: information/perceptions about existing policies and school response,
description of the school design model, description of the math program design, and
concluded with respondents’ results to the Math Teacher Questionnaire for items 1-
13 and Non-Math Teacher Questionnaire for items 1-10.
Existing Policies and School Response
No Child Left Behind (NCLB)
Educators at White Oak Tree High School weakly attributed No Child Left
Behind Act (NCLB, 2001) and its essential components of Adequate Yearly Progress
(AYP) and Highly-Qualified Teacher (HQT), to efforts to improve student
achievement in mathematics. In terms of AYP, Lead Math Teacher B felt, “NCLB is
a noble idea with merit”, but doesn’t feel as though it has had anything to do with
what he and his colleagues do in their classes. He spoke of understanding the point-
of-view of administrators, district officials and the community, but failed to see the
connection of this policy to his work in the classroom. He believed just covering the
standards is only the “minimum” needed for students to thrive and be successful
overall. He is a 25-plus year veteran in education who has served many roles at the
site including assistant principal but returned to the classroom for personal reasons.
Administrator B agreed with the NCLB philosophically, but thought it unrealistic in
its aim of having all students meeting the target proficiency goal by 2014. However,
she continued to encourage her staff to put the statistical issues aside and remember
that it is the school goal to “take every child and get them as far as we can every
single year”, regardless of the AYP goal. Lead Math Teacher A, a 25-plus year

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veteran teacher, who has held the position of Department Chair for almost fifteen
years, was familiar with NCLB only through its HQT certificated teacher
requirements. She did not believe that this policy precipitated many changes in the
math department for at most, if not all, math teachers, were already “teaching
appropriately”, meaning fully credentialed in math or completing a supplemental
credential in math subjects. White Oak Tree High School has reduced the number of
non-credential teachers from 14 in 2003-2004 to 0 in 2005-2006.
Overall, the math teachers at White Oak Tree High School viewed the NCLB
policy with a high degree of neutrality in terms of its effect on efforts to improve
student achievement. This is consistent with the math teacher response rate average
of 3.05 for Math Teacher Questionnaire items 1, 10 and 12, which explicitly sought
feedback about NCLB. As previously stated, The Math Teacher Questionnaire items
are presented on a five-point Likert scale, ranging from 1-5. The level of agreement
for Neutral is 3. The non-math teachers felt similarly about this issue with a response
rate average of 3.20 on item 1, on the Non-Math Teacher Questionnaire.
Standardized Testing and API
There were clustered responses at both ends of, as well as along the
perceptual continuum about the effect of standardized testing and API on student
achievement in math. At one end of the continuum, Lead Math Teacher C believed
unequivocally that the decision-makers were “very big on testing”, and consequently
this teacher believed that a great deal of the instructional policies were born in
response to the state testing initiatives, e.g., California Standards Test (CST) and the

133
California High School Exit Exam (CAHSEE). This perception is juxtaposed against
a response from Lead Math Teacher B who believed that standardized testing has
“influenced efforts to improve student achievement because it has raised awareness”
only.
Administrator A reported that the California State Standards tests (CST) and
API definitely affected the schools efforts to improve student achievement. He spoke
of implementing changes in the instructional program that started with teacher and
administration analysis of grades after every grade report, and reviewed benchmark
exam score patterns. He stated, “…we kept looking at those two indicators and
hoped that it would change”. A detailed analysis of patterns in these formative
performance data, i.e., student grade reports and benchmark exams, compared to
CST results revealed a strong positive correlation between the two. The
administration team decided that changes in the instructional program, at the
classroom level, were needed to increase student achievement in math.
Lead Math Teacher B felt as though CST scores have had an impact on
efforts to improve math achievement, primarily because of the heightened awareness
about testing and its implications. However, he also felt that by preparing students
adequately for the standards test by teaching all of the standards, not just those
covered on the CST, students are adequately prepared for SAT, CAHSEE, IB and
ACT examinations. He also felt it is was a disservice to students to only prepare
them for the CST by covering the limited material on that test, as opposed to all of
the concepts found in the textbook for that subject.

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California High School Exit Exam (CAHSEE)
White Oak Tree High School has measurably higher pass rates on the
California High School Exit Exam (CAHSEE) in both mathematics and English
Language Arts than the California state scores. The English and mathematics
departments aligned their courses and benchmark exams with the state standards and
implemented writing and math skills in the curriculum. Even with this success, there
continues to be a focused effort to provide additional support to students in the other
core content areas of science and social sciences. Science and Social Science
teachers are provided with both the Language Arts Blueprint and Mathematics
Blueprint for the CAHSEE and encouraged to identify strategies and ways to
integrate items from the Blueprints into their lesson plans. Additionally, after-school
intervention programs are offered so students have additional opportunities to
receive support in order to pass the CAHSEE exams.
District and Site Policies
White Oak Tree Unified School District emphasized the significance of math
by changing the graduation requirement for math from two years to three years in
2002. This change of policy was a recommendation developed and approved by the
White Oak Tree High School Leadership team as part of the ongoing analysis of
achievement data, research and unique needs of the community according to
Administrator A. The WOTHS leadership team grappled with issues such as, “What
do our students need to know and be able to do upon graduation? ”, and “How can
we (the school) best align our graduation requirements with our school Expected

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School Learning Results (ESLR’s) or student outcomes? ”. The effect of this district
policy change reinforced the significance of a solid mathematics education as part of
the minimum preparation in mathematics a student needed upon graduation for
entrance into secondary education, vocational training or the workplace. White Oak
Tree High School responded with major design changes to the Algebra I scope and
sequence, associated changes to the master schedule and the implementation of a
Math Skills class to support the changes in the Algebra course.
It is a site policy that every freshman takes Algebra at White Oak Tree High
School. Even though over 90% of the of the eighth graders take Algebra I at the
middle school, they all take it again during their freshman year at the high school. It
does not matter if the 8
th
grade students passed with a “C” or better or they failed the
Algebra class, they are enrolled in the Algebra I course as freshmen.
Prior to 2002, the Algebra I curriculum at WOTHS was a two-year course
sequence arranged as Algebra A and Algebra B classes. In response to the modified
district graduation policy, and as a result of ongoing analysis of student achievement
data under their current two-year configuration, WOTHS implemented a one-year
Algebra I CP course. It took two years to phase out the old Algebra AB sequence as
to allow students who had completed the first year of the course, Algebra A, the
opportunity to complete the second year of the Algebra course, Algebra B. The 2006
seniors were the last class to graduate under the old two-year mathematics policy.
The Algebra A course content covered the first six chapters of the Algebra I textbook
which covers algebraic concepts up to inequalities, and Algebra B covered the last

136
five to six chapters of the textbook. According to Math Teacher J, Algebra B is really
the “high school portion” of the Algebra course and the concepts taught in Algebra
A, should be taught at the middle school level. Administrator A acknowledged,
“another positive outcome of the change from a two-to-one year Algebra course was
an automatic “bump” in scores on the CSTs in Algebra”. Schools with two-year
Algebra programs get penalized because their students do not participate in the
appropriate grade-level standards tests (www.cde.ca.gov).
The Algebra I CP course was faster paced and consequently more demanding
than the previous configuration. Instead of taking one whole year to cover the first
six chapters of content, teachers were tasked with moving their students along at
about six chapters of the Algebra I textbook by the end of the first semester. There
were a large percentage of students that failed the first semester of Algebra I CP;
these students were in the Below Basic and Far Below Basic performance bands
according the STAR reports. “students cannot be just thrown into the faster paced,
Algebra I CP course without support, so we implemented a math support class”,
acknowledged Administrator A. Prior to the implementation of the Math Skills
support class, most of these failing students from the first semester were simply kept
in the class only to experience similar failure after the second semester. Five years
ago, the first configuration of the Math Skills support class was designed as a one-
semester intervention class where students were un-enrolled from the year-long
Algebra I CP course if they received a failing grade at the end of the first semester,
and subsequently enrolled in the Math Skills support class for the second semester.

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This solution required regular adjustments to the master schedule depending on how
many students experienced failure at the Algebra level. The curriculum of the Math
Skills class provided re-teaching and reinforcement of the basic skills students
needed in order to be successful in Algebra I CP when they were re-enrolled in the
class either during Summer School or in the fall semester.
For the past two years, the Math Skills class was implemented as a support
class that runs concurrently with the Algebra I CP course for the whole year, not just
for a semester when the student failed. Multiple measures are used to determine
which students need the additional skill building and support that are co-enrolled in
the Math Skills concurrent with their Algebra course. The goal of the Math Skills
support class is to “back up” the Algebra content and feed in the background skills as
appropriate for the student so they may experience greater success in the course.
According to Lead Math Teacher C, “we saw a lot of kids having success in Algebra
last year that had not seen success before.”
School Design
Curriculum
White Oak Tree High School is an International Baccalaureate (IB) school.
IB provides a holistic and global educational experience for the learners. The most
rigorous classes offered in the master schedule are IB and dual IB/AP courses. As an
IB school, there is an expectation that they will produce increasing numbers of
students taking the college preparatory IB HL math and the AP Calculus courses.
While WOTHS experienced increasing numbers of students enrolled in these

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courses, review of the data showed they were not producing as many students as they
thought they should be producing in these higher math courses. Analysis of multiple
years of data also revealed the primary reason most students at WOTHS did not meet
their A-G requirements was because they lacked success in the mastery of algebra
concepts. Students failed to master the algebraic concepts and skills at the level
required to access the A-G course sequence of college preparatory courses.
Consequently, the student demand for these higher math courses was low and at the
time of data collection there was only one scheduled class of IB Math HL, two
scheduled classes of AP Calculus, and two scheduled classes of IB Math Studies in
the master schedule representing little less than 10% of all math classes. However
the need for more algebra courses was high. Consequently, Algebra classes comprise
the largest percentage of math courses in the master schedule. More than 18 sections
are offered which represent approximately 30% of all math courses available to the
students at WOTHS. Administrator B shared, “Algebra is the gatekeeper
course…kids that do not grasp the concepts and skills in Algebra will not make their
A-G requirements”. Administrators at WOTHS organized the math department to
emphasize the priority of the algebra curriculum as a pathway to reaching the schools
greater IB goals. To provide greater opportunities for students to have time on task,
WOTHS has organized the structure of the day into seven periods that provide
73.170 instructional minutes in all grades exceeding the California state requirement
of 64, 800 instructional minutes by over 8,000.
A key element of the White Oak Tree high school design is the adoption of the

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Advancement Via Individual Determination (AVID) Program elective classes and
the implementation of the program’s support strategies across the curriculum. AVID
is considered a high school education reform method. The goal of AVID is to
motivate and prepare underachieving students to attend college. Students take
college-prep curriculum and are provided with a system of social supports that give
them explicit instruction in the "hidden curriculum" of school, as well as explicating
connections between high school and college (www.crede.org/tools/glossary.html).
Students are concurrently enrolled in a year long academic grade-level elective class
designed for academically average students who would benefit from one-hour of
support per day during the school day. Emphasis on standards based instruction and
the idea of constantly doing a spiraling curriculum was the response of Administrator
B when asked, “how does the school design contribute to math achievement in
Algebra?”. The AVID program supports standards based instruction. WOTHS has
maintained between five and six sections of AVID over the past five years.
Currently, there are five sections of AVID in the master schedule; two 9
th
grade, two
10
th
grade, one 11
th
grade and one 12
th
grade AVID elective classes are available to
students that meet the recruitment criteria and participate in the interview process.
“We embraced AVID philosophies across the board…SQ4R, Cornell Notes. We’re
really working in the area of math to get teachers to understand that if kids can write,
speak and verbalize math we know from research there’s a higher chance of overall
success in math” stated Administrator B. Students that participate in AVID have
higher percentages of participation in ACT or SAT testing, enrollment in AP or IB

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courses, and greater A-G completion rates than the overall WOTHS school-wide
population for the last five years.
Student Performance Assessments
White Oak Tree High School used end-of-semester teacher-created
assessments as their benchmark examinations. These teacher-created benchmarks
were aligned with the adopted textbook chapters that were to be covered during each
of the semesters of Algebra I CP, according to the course outline. Each of the twelve
objectives of the Algebra I CP course was mapped to the appropriate California State
Standards for each concept listed. Supportive administration provided a release day
in November 2006 for the algebra teachers to collaborate. This researcher had the
opportunity to spend the day listening to the conversations of these teachers. Four of
the five algebra teachers used this time to revise the benchmark exam, align the
questions on the benchmark exam with the standards covered by each chapter in the
Algebra I text, and edited the timeline and pacing plan for consistent delivery of
content among these four teachers. Administrator B shared, “we’ve had the fortune
of being able to design ourselves and revise as we realized we needed more or less
information in certain areas and also as the standards and the blueprints changed”.
During the period of study, 2002-2005, White Oak Tree High School was phasing
out a two-year Algebra AB course, Algebra A and Algebra B. During the data
collection, it was determined that the current end-of-semester benchmark was used
as an end-of-course examination for Algebra A to determine eligibility for
enrollment in Algebra B, also a one-year course. The resulting benchmark exam, also

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known as the end-of-semester exam, was a 60-item, mostly multiple-choice format;
including three true false and word problems, each. Other assessments included end-
of-chapter quizzes and tests. The student performance data from the benchmark or
end-of-semester exams are analyzed at the first level to determine how the student
are doing, then at the next level the teachers are trying to determine what they
themselves think they are doing well and identify areas for improvement. The third
level requires teachers to reflect on what they think they are doing that might not be
working and trying to figure out how to fix the problems is extremely important to
the administrators. Collaboratively, through the use of data, teachers regularly
attempt to identify the student conceptual gaps and skill deficits in order to provide
more targeted support for their students.
School Culture
The culture of White Oak Tree high school could be defined as an
organization committed to the “cycle of continuous improvement”. Through ongoing
and extensive data analysis, administrators have identified the AVID program
support as a contributor towards student achievement in math as well as other
subjects. Comparative data between the students enrolled in the WOTHS AVID
program has confirmed that these students are meeting the accountability indicators
of CST and CAHSEE passing rates at a significantly higher rate than their WOTHS
non-AVID peers. AVID teachers personally encourage, guide and coach their
students into going to college through teaching them the necessary skills of note-
taking, strategies for learning the core content, and test-taking strategies. There is

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some school-wide benefit as the non-AVID students enrolled in these AVID trained
teachers’ subject-specific classes receive the benefit of also learning these skills and
strategies. AVID trained teachers are a component of the informal professional
development plan. AVID trained teachers at WOTHS have provided staff
development on the Cornell Note-Taking system, Socratic Seminars, and inquiry and
collaboration strategies to non-AVID teachers for integration and use in their own
classes. There was particular emphasis on the use of Cornell Notes in the math
classrooms. Administrator A shared, “…we had conversations with the math
teachers and said, “yes, you can use Cornell Notes in math class” and this is how you
do it”. At WOTHS, the AVID teachers’ classrooms are filled with representations of
a college going culture. College pennants and mascot flags line the walls, A-G
posters hang on the doors to greet students as they enter, and a panoply of college
research display boards provide the illusion of a freshman dorm at any recognizable
college in the United States. To varying degrees, the math teachers’ classrooms
provided multiple representations of mathematical concepts. Learning Activities
Learning activities have been identified in Conceptual Framework 1 (CF1) as
those classroom based actions that challenge students to think, are collaborative and
enable students to solve problems. The premise of the AVID design model is to
transform the classroom into a rich bastion of inquiry and learning where students
collaborate, push each other’s thinking and create a collective culture of student
success and achievement while maintaining a family-like culture in the classroom

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where all students hold each other accountable for adhering to the expectations and
tenets of the AVID methodologies.
Mathematics Program Design
Math Skills Class Background
The curriculum utilized in the Math Skills Class was based on the objectives
of the Increasing Understanding of Mathematics (ITUM) Project, Focus on Algebra
Institute, funded through a grant by the state of California whose goals were to:
1) Increase our understanding of the mathematical concepts and skills we teach,
2) Design and implement instruction based on the algebra mathematics standards
with attention to English Language Development (ELD) goals and strategies, 3)
Develop our skills of representing mathematical ideas in multiple ways, 4) Develop
our skills in providing explanations of mathematics and structure them according to
the audience we are addressing, 5) Develop a cadre of mathematics coaches to work
with us in our classrooms, 6) Reflect on our classroom practice and make informed
decisions regarding mathematics and ELD, 7) Read and discuss current research
addressing the teaching and learning of Algebra by all students, 8) Use data to
inform our practice, 9) Create portfolios of approaches to successful teaching of
Algebra to all students, and 10) Become part of a growing, dynamic community of
professionals dedicated to addressing the needs of all students learning algebra.
Lead Math Teacher C was the representative for the White Oak Tree Unified
School District and member of the consortium of teacher leaders from three other
districts and the Center for Education and Equity in Mathematics, Science, and

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Technology (CEEMaST) at the College of Science at the California State
Polytechnic University, Pomona that participated in this project. Participation
included rigorous professional development for several years. In addition, Lead Math
Teacher C was the sole teacher of this curriculum in the Math Skills Class for the
first year of implementation. During subsequent years, a few more teachers became
involved and participated in the professional development and sporadically
implemented the ITUM lessons and instructional strategies. However, there are only
two or three teachers currently using the ITUM lessons and strategies at the site.
Upon completion of the Math Skills class, Lead Math Teacher C stated, “my
objective for these students is that they would be successful when re-enrolling back
into the Algebra class and be able to pass the California High School Exit Exam
(CAHSEE) the following year”.
Mathematics Curriculum
The ITUM project has a bifurcated approach. One of the approaches is really
to increase the teachers understanding of mathematics. Lead Teacher C stated,
“…because we found that teachers don’t really understand what they are doing
besides the traditional algebra. Here’s how you teach it, but they don’t really know
why or what they are doing”. Two of the math teachers report they are learning “the
why” and “the what” by working lessons that take discovery, inquiry-based lessons
and hands-on lessons back into the classroom. In this kind of classroom learning
environment, students are encouraged to ask questions and discover in their own
curious way, and not just have the teacher give answers to them. The philosophical

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basis for the ITUM program is conceptual understanding. It is entirely inquiry-based.
The curriculum sequence progresses from the concrete Algebra block, to the semi-
concrete draw the picture (multiple representations), to the abstract. Integrated within
the program is an emphasis on analogies, compare and contrast, and writing. In
particular, writing in the mathematics classroom is a strong component of the ITUM
program.
Standards-Based Instruction
The ITUM program falls under the auspices of the California Mathematics
Project (CMP), one of nine subject matter disciplines under the California Subject
Matter Project (CSMP). The CSMP is supported by the State of California and
administered by the University of California (http://csmp.ucop.edu/cmp/). The goals
of the CMP Project are: 1) Develop and enhance teachers’ content knowledge and
instructional strategies aligned with California Board of Education adopted
California Mathematics Content Standards and Framework, 2) Expand the statewide
opportunities for professional development in mathematics by developing a network
of teacher leaders who are capable of assuming leadership roles in their profession,
and 3) Improve the mathematical achievement of student in high need and Program
Improvement (PI) schools though the development of partnerships between these
schools and CMP regional sites. The aforementioned consortium of teachers
referenced in this study is a regional example of such a partnership. The ITUM
program was designed to meet the needs of both teachers of Algebra and learners of

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Algebra, and matched the California Mathematics Content Standards. Using a
standards-based program was consistent with WOTHS Action Plan for Mathematics.
Classroom Practices
Lead Math Teacher C shared some of the feedback from students about how
they felt upon completing the one semester of the Math Skills Class as evidence of
effective classroom practices. She asked students to complete an evaluation about
their experiences in the class. One young lady shared “I thought I was stupid and
couldn’t do this, now I understand.” This kind of feedback was interpreted as an
indication of the use of effective classroom practices that engaged the students. As
Lead Math Teacher C reflected upon the growth and achievement of those students
enrolled in her Math Skills Class, she proudly shared a little story about one of her
female students, “…and a little girl, Marisa, who sits here and was just woefully lost
and now she’s volunteering to solve equations at the board and she’s graphing”. This
kind of feedback was also formally reflected in student evaluations forwarded to the
administration as evidence of the need to maintain this type of course. Lead Teacher
C explained, “I gave evaluations from the kids to them [administration] because they
[administration] were considering removing these classes from the master schedule.”
National and state policies such as No Child Left Behind (NCLB), California
Standards Tests (CST), and the California High School Exit (CAHSEE) graduation
requirements were influential in focusing the leadership conversations around
mathematics achievement to varying degrees at White Oak Tree High School. The
White Oak Tree district policy that changed the graduation requirements for

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mathematics precipitated many of the school design changes to the Algebra I scope
and sequence, the master schedule and finally, the implementation of Algebra
support curriculum. These factors fostered the conditions that seem to be related to
improved mathematics achievement in Algebra I. The school design model was
instituted to respond to the increasing federal and state indicators of accountability.
The school leadership realized that the school could only focus on and impact those
factors related to student achievement that occurred inside of the classroom.
Consequently, they decided to focus on the two programs in place, the International
Baccalaureate (IB) Programme and the Advancement Via Individual Determination
(AVID) program and they focused on math achievement, particularly in Algebra.
According to Administrator A, they used AVID and IB as the organizing principles
because they are both extremely comprehensive and framework-oriented. WOTHS
identified lack of student success in Algebra as the critical barrier to increasing
academic achievement and success for their students. As well, through data analysis,
the leadership team had identified lack of student success in Algebra as the number
one barrier to A-G completion. Administrator A stated, “…that’s why Algebra is so
important because everybody recognizes that it’s an introductory course”.
The findings in this section and for this research question reflect a lack of
consensus concerning what policy initiatives and conditions related to curriculum
and instructional program design had an effect on improved mathematics
achievement between and among administrators, math teachers and non-math
teachers at White Oak Tree High School. While the heavy system of accountability

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of the No Child Left Behind policy is fully acknowledged, some math teacher
leaders did not think it impacted their practices at the classroom level; they felt they
had always taught and continue to teach the material in the textbooks.

Research Question 3: What change process did the school use to enhance its math
program and strategies to assist students in math?
The purpose of this section is to understand the change process as it relates to
improved math achievement at White Oak Tree High School. Through Conceptual
Framework 4, four leadership frames are presented to help the reader view the
organizational changes from multiple perspectives. The four frames that comprise
this framework are structural, human resource, political and symbolic (Bolman and
Deal 2003). This question was designed to understand how the leadership style,
philosophy, strengths and challenges could influence organizational change. The
following instruments, aligned with the Conceptual Framework (CF4), were used to
facilitate the data collection for this research question: Key Leader Interview Guide,
Teacher Interview Guide, Math Teacher Questionnaire and non-Math Teacher
Questionnaire. The qualitative and quantitative data collected to answer the third
research question was interpreted through the four frames and the findings were
organized and presented in a frame-by-frame analysis supported by responses to
Math Teacher Questionnaire Items, 14-29 and the Non-Math Teacher Questionnaire
Items 11-16.

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Frame Analysis
Structural Frame
As WOTHS strove to increase student achievement in mathematics, particularly,
Algebra I, their change process and associated efforts were primarily concentrated
within the structural frame. Key vocabulary that exists in the structural frame is
organization, authority, rules, goals, rationale, restructuring, analysis, policy and
tasks. There were three major components of the change process in the structural
frame, as evidenced by the findings and are presented as follows: district policy
change to the graduation requirement in mathematics, site-based change to the
Algebra I scope and sequence, and the implementation of a Math Skills Algebra
support class.
Change in District Math Graduation Requirements
White Oak Tree Unified School District changed its graduation requirements
for mathematics from two-years to three-years. The additional year of math added to
the graduation requirements were recommendations developed and approved by the
White Oak Tree High School Leadership Team as part of their ongoing analysis of
achievement data, research, and the unique needs of the community. Much
discussion within the Leadership Team took place before this recommendation
emerged as policy about what their students needed to know and be able to perform
upon graduation and how the school could best align their graduation requirements
with their school Expected School-wide Learning Results (ESLRs). Many math
teachers regard this as an example of bottom-up decision-making. Lead Math

150
Teacher A stated that…” it was a site decision [not top down] to change from a two-
year math graduation requirement to a three-year math graduation requirement”.
Even though it was board policy, the site initiated the changes, rather than the board
initiating the policy change.

While the impetus for changes to the graduation requirements came from the
site, the process to enact the change went through the Education Services
department, and then onto the Superintendent's Cabinet and finally to the Governing
Board for approval. The changes began as part of the school's action plan, and then
were put into place after the district and Governing Board approval process had
taken place. The class of 2001 was the last graduating class subject to the two-year
math requirement.
Change from 2-year Algebra AB Course(s) to 1-year Algebra 1 CP Course

The change in the graduation requirement from a two-year to three-year math
requirement and the patterns of student achievement evidenced through data analysis
were the keystones that precipitated the change in the Algebra Course sequence from
a two-year Algebra AB course, where Algebra A was taken for one full year and
Algebra B was taken in the second year, to a one-year Algebra I College Preparatory
or Algebra I CP course, to effect student math achievement at WOTHS. Analysis of
student results from California Standards Tests (CST), benchmark examinations, and
grades, as well as their overall impact on the API necessitated the structural school

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design changes the administration thought necessary to increase student achievement
in mathematics.
Administrator A: …
CST’s and API and grades—we did a grade analysis after every grade
report to see what our percentage was because that’s perhaps an even more
significant one because that’s what the kids see. And benchmark
performance - we kept looking at those results and kept hoping that it
would change… We figured out what we could address inside the
classroom and what our emphasis was, and so we told teachers, we don’t
have the resources to do everything so we’re going to focus on two things.
We’re going to focus on programs in place, AVID and IB, and we’re going
to focus on math.

In addition to the overall impact on the API scores, there was a negative
impact on the percentage of students meeting the University of California/California
State University entrance requirements, commonly known as A-G requirements
(http://www.ucop.edu/a-gGuide/ag/a-g/math_reqs.html). Under the A-G system,
students must meet the minimum three years of mathematics with four years
recommended. Most students were failing to meet the minimum requirements
because of mathematics.
Administrator B:
We also had multiple years of data about Algebra A and Algebra B and we
were not achieving what we thought would be the original goal of getting
more students A-to-F qualified through Algebra A and Algebra B. In fact, our
A-to-F rate was falling. And now it’s A-to-G; the UC/CSU requirements. So,
we kept on looking and I went and I pulled some years-ago grade sheets on
the percentage of kids who passed Algebra when we only had Algebra CP
versus the percentage of kids who passed Algebra A and Algebra B and
found out that it was actually lower with Algebra A and Algebra B.

With the realization that providing more time in Algebra by spreading it out over two
years did not have the intended effect, WOTHS phased out Algebra A and Algebra B

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over a two –year process. Not all members of the math department agreed with the
decision to phase out the two-year Algebra A and Algebra B course. Lead Math
Teacher B questioned, “I would like to know, just statistically, what impact did the
phasing out of our AB and instituting a full Algebra I CP, in that transition of
curriculum, what impact did that have on the API? I would really like to know that”.
Implementation of Math Skills Algebra Support Class
Historically, the trends and patterns in the data indicated incoming 9
th
grade
students were arriving with consistently lower levels of mathematics proficiency.
And consequently, it was no surprise that they were experiencing a high degree of
failure in the Algebra I class. A system of support had to be implemented to increase
their likelihood of success. The school implemented a Math Skills class to provide
support for those students that were not passing Algebra A or Algebra B.
Administrator A stated, “We knew the kids coming in, and if we just put them out in
an Algebra class, in a standard Algebra class, the state-required Algebra class, we
know they’re not going to be successful so we have to create something that can
support them and that’s where the Math Skills class came from”. For the first three
years of implementation, this class was considered an intervention class, not just a
support class because students were actually pulled out of Algebra. Students who
failed the first semester of Algebra A or Algebra B were un-enrolled from that
Algebra class at the end of the first semester, and subsequently enrolled in a Math
Skills class for the second semester. Students were encouraged to re-take the Algebra
A or Algebra B course in the summer or re-enroll in the fall. The Math Skills class

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did not yield math credit, but rather elective credit. Administrator B stated, “If the
kid didn’t pass the first semester of Algebra A they needed to be enrolled in the Math
Skills class. So that the next time they took Algebra A they would have a better
chance of passing. And we did the same thing with Algebra B”. There was lack of
consensus by the math department teachers that placing students of all levels in a
one-year Algebra class was the best way to support all students. According to Math
Teacher J, “I think I hated to see it [two-year algebra] go; I really did. I think we’re
going to see a backlash because it means lumping every single ability in one
classroom”.
This support configuration was in place from 2001-2005. The District
Mathematics Coach/Teacher taught the Math Skills classes, which focused on
helping students learn basic math skills. There was disagreement as to whether the
curriculum, for the Math Skills class was appropriate to help students meet the
Algebra standards upon re-enrolling in Algebra A or B. Starting in the school year
2005 - 2006, incoming 9
th
grade students identified as having low mathematics skills
were co-enrolled in a math support class concurrent with their Algebra I CP course.
This is the second year of this configuration. The master schedule was modified so
that the same teacher that taught the Algebra class taught the concurrent Math Skills
class. Those students that needed the additional support in the Math Skills class
would have the benefit of being with the same Algebra teacher. The goal of this
configuration was to create a seamless flow and not a demarcation between the two
classes so that it would feel just like one extended class to students. Administrator A

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felt that they did not quite make this goal: “So the kids sometimes felt like they were
taking two separate courses and it was not supposed to feel like two separate courses.
They should have felt like it was one [class] is helping them succeed in the other”.
The administration felt they have improved the Math Skills concurrent system this
year by increasing the number of participating teachers.
Human Resource Frame
Key teaching assignments, teacher leader empowerment, and the use of the
district personnel evaluation policy has positively influenced mathematics
achievement at White Oak Tree High School. Key vocabulary in this frame includes
the right fit, meaningful, satisfying, best and service.
Teacher Assignments
Current research reveals a sobering statistic that the most needy students
often get the most inexperienced teachers when what they require are the most
experienced in terms of content-knowledge, pedagogy and classroom management
(EdTrust, 2006). At White Oak Tree high school, the most experienced teachers were
not necessarily placed in Algebra classes with the most “needy” students.
Administrator A shared,
“Well, it wasn’t just an issue of the most experienced. It was the issue
of you having a desire to teach that subject. It can cause more damage
to take a teacher who is very good at Calculus and try and put them in
an environment where it’s not their skill because there is a whole
relationship piece that goes along with just the “math skills”, so it’s
not just about the experience”.

Administrators spoke about the affective domain piece of teaching math skills and
the ideal teacher having the “right personality” and “right fit” for teaching that level

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of mathematics content and that level of mathematics student. The affective domain
relates to the emotional component of learning. It emphasizes a feeling, tone, an
emotion, or a degree of acceptance or rejection. There are five levels in the affective
domain: Receiving (Being aware of or attending to something in the environment);
Responding (Showing some new behaviors as a result of experience); Valuing
(Showing some definite involvement or commitment); Organization (Integrating a
new value into one’s general set of values, giving it some ranking among one’s
general priorities); and Characterization by Value (Acting consistently with the new
value). In addition, administration and math teachers agree that one of the essential
skills needed to teach Algebra is the ability to translate abstract concepts into
concrete kinds of things that kids can touch and feel. In addition to the experience in
content-knowledge and pedagogy, the administration believes that it has to be
personally motivating to the teacher to want to teach basic math skills to high school
students. The observation of Administrator A is, “the longer teachers teach math in
the abstract, the more difficult it is to make the transition into teaching concrete
learners”.
When this researcher asked about the relatively low number of years of
teaching experience by four of the five Algebra teachers, Administrator B responded,
We have, I will be honest, we have brought in people and if in the
first two years they do not meet a standard that we think is
appropriate, we have no fear of letting them go which has sometimes
made it really hard on us. But, it is better to let a teacher go than to
have questionable teaching practices…If I do not see significant
improvement going on and I see what I consider mediocrity
continuing, if I don’t see a connection to the school, if I do not see a

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connection to the students, if I don’t see a connection to the
department, why would I keep that particular teacher.

The feeling is that it is better for the school community to recruit and hire someone
else who is willing to participate and ingrain themselves in what is important in the
math. Algebra Teacher A is in their second year of teaching at WOTHS and fourth
year overall. Algebra Teacher C is in their fourth year of teaching at WOTHS and
has 12 years of previous high school math experience. Algebra Teacher G is in their
first year of teaching, however substituted for five years in another district. Algebra
Teacher I is in their third year of teaching at WOTHS. Algebra Teacher J is in their
third year at WOTHS and has five years of previous 9
th
grade teaching experience.
Lead Math Teacher B shared, “I think the fact that we’ve had a change of fourteen
math teachers in four years, we deserve an “A” for handling that changeover and still
see an increase in scores. We need a medal of honor for that.” There is a similar
philosophy about teacher assignment in areas other than math. Administration looks
at personality and how teachers interact with the kids when making strategic
program–based teaching assignment. According to Administrator B, “When you’re
doing special programs and that kind of stuff, when you an AVID program, when
you do an IB program, when you do a freshman intervention program, when you do
any kind of specialized program those teachers have to have certain skills, certain
personality components, they have to want to, and be willing to do, that extra little
bit”. Administrators don’t allow teachers to create their own schedules because they

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work a master schedule based on student demands not teacher’s decisions about what
they want to teach.
Political Frame
Key vocabularies that describe this frame are coalition, interests, perceptions,
reality, values, beliefs, information, resources, conflict, power, bargaining,
negotiation, jockeying, competing, and stakeholders.
The district decision to change the graduation requirement from two-to-three
years in mathematics was a political one. There was spirited negotiation between the
governance board and the school leadership team because some physical fitness
(P.E.) classes had to be cancelled in order to create space in the master schedule for
the additional math sections. There were implications for hiring practices as there
were two P.E. teachers that were impacted as a result of that decision. Administrator
A remarked, “We had to do some things with hiring practices so that was a sell in the
community…sound easy? It wasn’t as easy when we started getting into it but there
were lots of politics involved”. Allocation of resources was another area of conflict
and competition. The decision to allocate our resources only to IB, AVID and
mathematics and not to spend money in other areas of the instructional program was
a political decision that generated some friction among teachers and administration.
According to Administrator A, “So if you come to me, a social studies teacher, and
you want go to a workshop, I’m sorry…because we’re going to focus on AVID, IB
and math. Math teachers went to the Palm Springs Math Conference”. Teachers
eventually came to realize that IB, AVID and math was the school-wide issue. The

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administration had to communicate with upset teachers that did not understand why
their particular subject-area was not being funded for professional development,
supplemental programs, etc. The administrators had to communicate the rationale
behind the priorities of IB, AVID and math. They communicated about issues of
poor student performance in mathematics by using data, issues of how math
achievement affected the overall rating and ranking of the school, issues of the
importance of math as a gateway to success in higher-level courses, and finally,
issues of higher A-G course completion and higher college readiness percentages.
They explained to the teachers that an as IB school, it was critically important to
reputation to garner higher math student scores. Administrator A shared, “The IB
coordinator was upset because we took some IB resources and put them in math.
Administrator A also shared, “So I think just fact things get done to the degree that
you pay attention to. It’s not necessarily actions, but it’s a matter of emphasis and
priorities”.
Symbolic Frame
Key vocabulary for this frame is symbols, hope, perception, ceremony,
rituals, and culture. The change process was not manifested through the elements
that define the symbolic frame; most of the change process was evident with the
structural frame. The administration mandated that the mathematics curricular area,
and IB and AVID programs would be the focus areas upon which the school design
would be built. The schools resources were allocated toward supporting these three
defined areas. White Oak Tree high school administrators communicated general

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messages to the overall staff, and specific messages within the IB, AVID and math
departments, about the goals, targets, policies and procedures to be implemented to
support student achievement efforts. There was an expectation that all of the teachers
would abide by the implemented policies and procedures and work collaboratively
towards increased student achievement.
There appeared to be a perception that the recognition and rewards for
positive student performance occurred intrinsically. As Lead Math Teacher B shared,
“motivation [to do a good job] has got to be intrinsic…there is not much recognition
here. No, there just isn’t… the recognition is intrinsic”. This perspective is
inconsistent with the Non-Math Teachers Questionnaire item 12 response with a
score of 3.84 indicating these teachers “somewhat agree” the school has focused on
motivating students, and celebrating successes.
Summary of Questionnaire Results
There were marked differences between the math teachers and non-math
teachers’ responses on items associated with this research question. Approximately
sixty-six percent of non-math teachers responses were, “agree somewhat”, to the
questionnaire items related to the change process. Conversely, only 18% of the
responses were “agree somewhat” by the math teachers on their questionnaire items
relating to the change process; whereas seventy-five percent of their responses were
“neutral”. The only area of agreement between these two groups was “disagree
somewhat” on the issue of professional development playing a key role in increasing
student achievement in math.

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Summary
The change processes within the structural and political frames enhanced the
math program and strategies ultimately increasing student achievement in
mathematics at White Oak Tree High School. The structural policy change of
increasing the district graduation policies from two-years to three-years
demonstrated a commitment by the White Oak Tree Unified School District as well
as at the high school to align the graduation requirements with Expected School-
wide Learning Results (ESLRs) as well as to increase the percentage of college-
ready A-G students. The change in district graduation requirements in math
precipitated the change in the Algebra course scope and sequence from a two-year
Algebra AB course to a one-year Algebra I CP course. The change of this course
scope was also substantiated through on-going comparative analysis of achievement
levels of students enrolled in Algebra AB with students enrolled in Algebra I CP.
WOTHS restructured its master schedule to implement a Math Skills Algebra
Support class to supplement the student’s basic skills to increase their likelihood of
their success in the faster paced, one-year Algebra I CP course. The rationale was
that students were not successfully completing Algebra AB, spread out over two
years, and in fact, the school’s student API scores were being impacted because
students could not be administered the Algebra CST test until the end of the Algebra
B, or 2
nd
year in Algebra. The school’s decision to focus on IB, AVID and math was
accompanied by allocation of resources towards only those three initiatives.
Restructuring the master schedule to insert additional math sections, meant sections

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of other courses had to be removed, In addition, the administration had to navigate
and balance the political landscape wrought with unhappy teachers in other
departments and the heads of other programs that did not receive resources for things
such as professional development, conference attendance, and collaboration time
within the school day.

Research Question 4: To what extent was strong, instructional Leadership important
in improving (a) the math programs and strategies, and (b) math achievement among
students?
The extent of instructional leadership and its importance in improving the
math programs and strategies, and the degree of student math achievement that
occurred as a result, were uncovered utilizing the Key Leader Interview Guide,
Teacher Interview Guide, Math Teacher Questionnaire, and non-Math Teacher
Questionnaire. Conceptual Framework 4 provided a framework for identifying the
roles leaders played and issues related to the development of a professional learning
community at WOTHS. Consistent with the framework, this researcher focused on
understanding how the instructional leadership implemented the vision for learning,
supervised and monitored the instructional program, interacted with diverse
community and political stakeholders, fostered the culture of teaching and learning,
and used data-driven decision making to inform instruction for greater student
achievement. The qualitative and quantitative data gathered to address the fourth

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research question was organized and presented according to subsections of the
Conceptual Framework 4.
There were markedly different perceptions about the extent to which there
was strong instructional leadership in improving math programs, strategies and math
achievement among students between the math teachers and non-math teachers.
Approximately sixty-six percent of the responses by math teachers to the items that
align with research question 4,“To what extent was strong instructional leadership
important in improving the math programs, strategies and math achievement among
students?” fell within the neutral range. Of the twelve items on the Math Teacher
Questionnaire correlated to this research question, nine of the responses were
“neutral” and two of the responses were “disagreed somewhat”. Math teachers did
agree that the math achievement goals and measures were clearly articulated and
easy to understand. This researcher interpreted the overall response on these
questions, as meaning the math teachers did not perceive that the instructional
leadership was very important or influential in improving the math programs or math
achievement. Non-math teachers somewhat agreed that the instructional leadership
was instrumental in gaining community support, establish and maintain a respect for
cultural diversity, used data-driven information to make decisions and felt students
and staff were valued and their successes celebrated.
Roles
The principal perceived the administration team’s role as the creators of the
conditions that fostered collaboration amongst the leadership team that yielded sound

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instructional program design improvements. The principal along with the assistant
principal of curriculum and instruction felt they had the ability to forecast the
outcome of making very purposeful, design changes in how WOTHS implemented
their Algebra course. They recognized immediately that changing from a two-year to
a one-year Algebra I course would generate “an automatic bump in scores” because
the school would no longer be penalized because the Algebra A, or first year,
Algebra students did not take the Algebra CST; students would take the Algebra
CST at the end of the second year, or Algebra B course. Schools API scores and
students are penalized when students do not participate in their grade level/course
level standards examination. Students are penalized as their score levels are
automatically lowered by one band, e.g., Basic drops to Below Basic. Student scores
are a factor of the API scores; so lowered student scores negatively impact the
schools as well.

Vision for Learning
The vision for learning is the first element of the Instructional Leadership
framework and seeks to help identify how the instructional leaders at White Oak
Tree high school develop, articulate, and implement the vision for learning that is
shared and supported by the school community. The White Oak Tree High School
Vision Statement reads,
Through providing multi-faceted opportunities, the community of
White Oak Tree High School believes in making this school a place
where all students are able to pursue their dream, goals, and desires,

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now and in the future. In a safe, harmonious environment where all
involved recognize the worth of each person, students are challenged,
inspired, and encouraged to do their best and to take advantage of the
opportunities available to them. Students feel safe, worthwhile, and
respected, and at the same time respect others. Students know that
those who are involved in their education truly care about them and
the quality of their education. These supporters include parents,
teachers, staff, administrators and community members. By providing
a rigorous and challenging curriculum with a multitude of learning
situations for the varied learning styles, and by joining these with
activities which connect studies and disciplines, the school provides
students with relevant learning experiences which connect to life
situations. Students graduate from White Oak Tree High School
academically, emotionally, physically, and socially capable of
functioning as productive lifelong learners in a global society and of
facing the challenges of the twenty-first century. Therefore, students,
site personnel, parents, community members, district administration,
and the Governing Board strive to ensure that the district’s mission
statement the State content standards, and the expected school-wide
learning results are accomplished.

This developed vision is communicated to all of the stakeholders at meetings,
through notices and weekly bulletins. Evidence of the administration’s commitment
to communicating the vision is reflected in the WASC report. The vision for learning
at White Oak Tree high school is also embedded in the cultural milieu of teaching
and learning evidenced by this excerpt from the vision statement, “…by providing a
rigorous and challenging curriculum with a multitude of learning situations for the
varied learning styles…”. The administrators believe the school design model that
encompasses programs and opportunities such as the International Baccalaureate
(IB) and AVID programs, as well as the Math Skills class that reinforces the
Algebraic skills to prepare students for the rigors of the gateway Algebra course, are
exemplars of the implementation of the vision. The vision is monitored and

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evaluated by using the California Content Standards and relating these directly to the
California Standards of the Teaching Profession (CSTPs). The administration
strongly believes in the use of data analysis for monitoring and evaluating the
effectiveness of instructional program implementation.
Supervision and Monitoring of Instruction
This element of the effective Instructional Leadership framework addresses
the observation and monitoring of the instructional program, and the constructive
feedback in a timely manner to the teachers from the administration. According to
Hessel & Holloway (2002) effective leaders observe classrooms on a daily or weekly
basis, make appropriate allocations of resources to ensure successful teaching and
learning, and hire and supervise personnel that support the learning goals and vision
of the school. The leadership at White Oak Tree high school strongly believes in
standards-based curriculum and instruction, student engagement and the import of
teachers collaborating on their practices and providing support to each other through
informal conversation. This is evidenced by a. informal observation system, which
includes the assignment of a partner teacher within the departments for new teachers
and staff. Partner teachers’ check-in with their designated new teachers at least a
couple of times per week. It did not appear that the partner teacher–peer system of
support was clearly articulated to the new teachers. For example, a first year math
teacher had thought that a 4
th
year math teacher and a veteran math teacher were
assigned as buddies based on their classroom proximity to the new teachers.

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There is little evidence to support that the administration is actively involved in
direct classroom observation and monitoring of the math instructional program in the
classrooms, except in the case of new teachers. Math Teacher J compared the
observation of their instruction during their first two years at WOTHS to their
experience at a former school, “…here it is nice because at the other school, the
administration was just a revolving door. Here, administrator B was the first person
who had come in and really, really watched what I was doing and actually had pieces
of good advice for me that I found definitely very helpful”. The budgetary policy
regarding allocation of resources to support the implementation of the math
programs is reflected in a statement in the WASC report, “the supplies, equipment,
materials, textbooks, supplemental materials, technology, conferences, personnel
time, college tutors and other resources are designated as needed to accomplish the
steps in the mathematics department action plan will be allotted from the school’s
site budget, federal and state categorical funds and other identified monies.”
According to Administrator B, “We have brought in people and if in the first two
years they do not meet a standard that we think is appropriate, we have no fear of
letting them go which sometimes made it really hard on us. But, it is better to let a
teacher go than to have questionable teaching practices.” An outcome of the pursuit
of building a highly qualified math department has been significant turnover. There
were only two math teachers that were there ten years ago. However, many new
hires came from a wide range of experiences and backgrounds. The math department
at WOTHS is balanced in terms of years of math teaching experience and age

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diversity; some teachers have three to five years, others have eight to fifteen years
and a couple of teachers with over twenty years of teaching.
There is limited evidence of structured math department collaboration time other
than monthly lunch meetings. At the monthly lunch meetings, the department chair is
tasked with recording minutes of the meeting, encouraging the sharing of any
conference or professional development attended, soliciting reflections about
successful classroom practices and reviewing and analyzing assessment data.
According to Administrator A, “The Math department meets regularly, usually it’s
during lunch. A lot of it is just informal. A lot of it is mentoring, “buddying” and
hooking up with other teachers.”
Professional development opportunities are limited to the IB and ITUM program
teachers. According to Math Lead Teacher A, “Professional development is limited
because there’s no money. I know the intervention teachers are required to go
because that program requires professional development”. In an effort to build a high
quality math department, there has been significant turnover in the math staff. The
administration had very strict policies on hiring qualified math teachers. Currently,
there is only one math teacher with a supplemental math credential, which limits
their ability to teach any subject higher than Algebra. If interns had to be hired,
careful consideration was made as to ensuring they were in a credential program that
did good supervision. The significant turnover did not result in all new teachers.
Experienced teachers from private schools that had just recently received their

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credentials and other districts were added to the math teaching staff. This is a direct
result of the significant turnover in the math department

Community and Political
This component of the Instructional Leadership Framework addresses how
the effective leader collaborates engages and responds to the diverse community
interests, needs and mobilization of resources. While there is no evidence of the
impact of the community and political on math achievement, White Oak Tree high
school provides opportunities for parents to become involved with school activities
through the school site council, and booster clubs. Opportunities for parent
conferences are held in September, October and March. Meetings are scheduled
several times each year for parents of the International Baccalaureate Program (IB),
Gifted and Talented Education (GATE), English as a Second Language, Business
Academy, and Advancement Via Individual Determination (AVID) students.
Culture of Teaching and Learning
This element of the framework seeks to identify how the instructional leader
fosters a culture of teaching and learning to improve student mathematics
achievement. Specifically, how do effective instructional leaders advocate, nurture
and sustain a positive school culture and sound instructional program while
negotiating the diverse needs of the school community. There is evidence that the
culture of teaching and learning at White Oak Tree high school is a key element in
their aim of continuous improvement. This is evidenced by the philosophy of

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Administrator B, “No one thing solves all problems. Good teaching involves
multiple approaches, which ultimately means you are using multiple techniques,
more than one program. You may have one program as you focus, but you will
supplement it with elements from other things.” Teachers are encouraged to build
their instructional delivery based on the curriculum standards and the use of data to
identify student needs. Administrators feel you have to give adequate time to
implement a program. There is evidence of valuing students and staff.
Data Driven Decision Making Analysis
Data-driven decision-making is a component of the WOTHS school design
model and an essential component of the school’s efforts to improve student
achievement in math. One administrator stated, “ I think the school administration
and the staff have embraced data-driven decision-making”. The administration
doesn’t think the WOTHS school community are experts at using data, but they are
getting used to looking at data and it has subsequently evolved to be a normal part of
the conversation around student achievement. Administrator B reported already
receiving a number of requests for the grade printouts for the end of the semester
grades. One administrator shared, “Data-decision-making, looking at how kids are
doing; then trying to say what you’re doing that you think you are doing well and
seeing if you can improve it”. Analysis of test data from final and summative exams
is used to “measure the effectiveness of the teaching, the effectiveness of the
teachers…this is a tool for them to use to improve their practices, to figure out where
the kids need help, to figure where the gaps in the program are, my rule of thumb is

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you want to look at each period and you want to look for questions where less than
70% of the students have gotten it correct” according to one administrator, essential
questions are asked that help teachers analyze what is going on in within that period,
or is the data consistent across the department. One administration shared,
It’s not just looking at cumulative date, you need to look sometimes
within that period because we found that …there were a couple of
skills that it didn’t seem to make any difference which class the kids
were in, which teacher they were with. Everybody was missing out.
That then becomes a department-wide issue that has to be addressed.
But if in one teacher’s section, for example, if I’m in with Teacher X
and my kids are the only ones missing this particular standard then
it’s about teacher and you start asking a question. One, was it taught?
Two, when was it taught? Was it taught to some type of level of
mastery or was it just dumped in at the last minute or was it skipped
over? So then you start looking at those. Then you have a department-
wide level, or course-wide level, because our benchmarks are based
on course. So you have a course-wide level of analysis. You have a
teacher level of analysis. And then you get down to the specific class
period level of analysis. And then you can get so far as looking at
which kids might be missing certain ones. Are there any kinds of
groupings that start flowing out? Or, is the kid just low across the
board?

This type of analysis would provide the data “signposts” that Schmoker (1996)
speaks about, “for signposts to be trusted as valid and reliable, they must be
constructed collaboratively”. Using data to drive the discussions about student
performance and achievement enable the WOTHS administration and teachers to
confirm what is working well and to reveal the gaps between the current reality and
the goals of improving student achievement in mathematics.
Command and control devices are evident in changes in structure and
changes in organizational routines (Hess, F. M., 2005). It was evident that WOTHS

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instructional leadership established the policies, routines and structures within the
organization, and that the primary two-member administrative team also established
the guides of acceptable behavior, i.e., expectations within the organization through
the supervision and monitoring of instruction. However, the supervision and
monitoring of math instruction appears to happen more as a result of data analysis
and subsequent inquiry, rather than through direct classroom observation for tenured
teachers. It is evident that the math teachers and non-math teachers perception of the
culture of teaching and learning at WOTHS, which is embedded within Standards-
Based Instruction (SBI), is the most significant contributor to improved math
achievement.

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

Dilemmas about Instructional Leadership
Principals and other on-site instructional leaders have the overwhelming task
of supervising and monitoring all of the curriculum areas and instructional programs
at a school site. However, the minimum eligibility requirement for the position of
principal or other administrator is the possession of a California State Administrative
Services Credential; only candidates that possess a teaching credential are even
eligible to apply for an Administrative Services Credential. As such, training for the
principalship does not result in being “highly qualified” in all academic areas nor are

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they required to be subject-area experts in all areas they supervise. What the research
does say about principals and their effect on student achievement is that, “when
teachers perceive their principals as strong instructional leaders, students achieve
more” (Andrews & Soder, 1987; Heck, Larson, & Marcoulides, 1990; Heck,
Marcoulides, & Lang, 1991). This research question seeks to answer what
instructional leaders do to increase mathematics achievement at their sites, when
they, in fact, do not possess the content knowledge or pedagogical background in
mathematics.
Twelve of the most salient research-based strategies that instructional leaders
use to overcome a lack of subject matter competency were presented to key leaders,
math teachers and non-math teachers using Conceptual Framework 5 (CF5). For this
study, data was collected on which of the twelve strategies referenced in CF5 were
used by the instructional leadership to compensate for their lack of expertise in
mathematics. Another component of CF5 is the assessment of the principal’s
expertise in math, based on the Federal NCLB definition of highly qualified (HQ).
Through answers to the following three questions, this assessment determined the
expertise level of the two-administrator instructional leadership team comprised of
principal and/assistant principal. The three questions asked were, (1) “Is the Principal
highly-qualified teacher compliant (HQT) in mathematics?” (2) “Does the Principal
have a credential or major in mathematics?” and (3) “Has the Principal minored in or
taught mathematics?” According to the assessment, both of the administrators at
White Oak Tree High School are rated as having “low expertise” in mathematics.

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The Key Leader Interview Guide, Teacher Interview Guide, Math Teacher
Questionnaire, and non-Math Teacher Questionnaire were used to ascertain “How
did the instructional leaders overcome obstacles they faced in response to the
dilemmas about mathematics achievement?” Data was collected and analyzed from
the following WOTHS staff members: principal, assistant principal, district
mathematics coach/teacher, mathematics department chair, and assistant
mathematics department chair, all core area department chairs including special
education, and the AVID program Coordinator.
Instructional Leadership Qualifications
The principal, Mr. Forever is not a highly qualified teacher (HQT) in
mathematics. In addition to a Life Administrative Services Credential, he holds a
Life Single Subject Teaching Credential in History issued by the California State
Commission of Teacher Credentialing. Mr. Forever has been the principal at White
Oak Tree high school for the last 12 years. He received his degrees in History and
Philosophy from the University of California at Riverside. His teaching career began
as a junior high history and reading teacher. He also was the Associated Student
Body (ASB) advisor at that level. Mr. Forever taught civics at White Oak Tree high
school for six years before becoming the principal.
The assistant principal of curriculum and instruction, Mrs. French is also not
a highly qualified teacher (HQT) in mathematics. In addition to a Clear
Administrative Services Credential and a Life Standard Secondary Teaching
Credential, she holds a Clear Specialist Instruction Credential (Reading), a Life

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Standard Secondary Teaching Credential (History, English, Speech) and a Life
Standard Elementary Teaching Credential (Humanities, History) all issued by the
California State Commission of Teacher Credentialing. Mrs. French has been the
assistant principal of curriculum and instruction at White Oak Tree high school for
the past 12 years. Prior to that position, she was an IB English teacher and English
Department Chairperson. Mrs. French has been in the district since 1971 and at the
high school since 1975. She received her degrees in English and History from the
California State University, Los Angeles.
Strategies emphasized as a response to dilemmas
In response to not being an expert in mathematics pedagogy, instructional
leaders at White Oak Tree high school identified emphasis on quality instruction,
raised expectations, strategic teacher assignments, revised course scope and
sequence, and the emphasis on interventions for lower performing students as
strategies they implemented to improve student achievement in mathematics.
“Emphasis on quality instruction has got to be at the top of the list” according
to Administrator A. There was strong belief that the emphasis on quality instruction
contributed to improved mathematics achievement by math teacher leaders. One
teacher leader offered, “…it [quality instruction] is the intended goal…and hoped
that quality instruction would be reinforced through the evaluation process”. Over
60% of both math and non-math teachers agree somewhat that the school leaders
emphasize the importance of quality instruction as a primary mission of the school.
The school community perceived standards-based instruction (SBI) as defining

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quality instruction. Responses from both math and non-math teachers strongly
agreed that teachers are teaching standards-based instructional (SBI) lessons. The
perception by administrators and Lead Math Teacher C is that the ITUM program is
an example of quality instruction.
Administrator A stated, “Raising the graduation requirement from two to
three years and getting rid of two-year Algebra was a strong example of raised
expectations for our students”. There is a sense of raised expectations overall,
however, not all math teachers believe that all students can reach a high level of
rigor. There is some disagreement among the teachers about the effect of the
changed district math requirements from two to three years. Particularly, some math
teachers are concerned about the impact of the “one-size-fits-all” algebra class. Math
Teacher J stated, “…lumping all ability levels in the classroom, from the low to the
very high is not very effective and we’re losing the kids in the middle”.
“Strategic teacher assignments is really critical because it’s just not about
experience, it’s about a match. Teachers are not allowed to create their own
schedules because the master schedule is designed to accommodate the student’s
needs first; then we try and find the match of teachers to the demands and needs for
courses, explained Administrator A. The philosophy of teacher assignments as
shared by Administrator B, “…when you do any kind of specialized program those
teachers have to have certain skills, certain personality components, they to want to,
and be willing to do, that little extra bit”. Math teacher leaders concur that there are
strategic teacher assignments of experienced teachers with struggling students.

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As a result of the change from a two-year Algebra I course to a one-year
Algebra I CP course, explicit changes had to be made to the course scope and
sequence of the Algebra curriculum. This researcher had the opportunity to observe a
“release day” meeting of the Algebra teachers as they re-aligned the first semester
summative examination, also referred to as the benchmark examination, with the
Algebra I course scope and sequence. The Math Skills class curriculum was
developed based on the ITUM program philosophy and components of inquiry,
problem-solving, and conceptual understanding and connections. As previously
mentioned, the students were taken out of Algebra completely, enrolled in the math
skills class, and re-enrolled in Algebra either in the summer or fall. Lead Teacher C
commented, “…the math curriculum was written to provide the foundational skills
necessary to be successful in the Algebra A class and subsequently pass the
CAHSEE”.
The implementation of the Math Skills class was in response to the needs of
those failing students. For the first two years of implementation of the Math Skills
class, failing students were un-enrolled from Algebra A at the end of the first
semester and enrolled in the Math Skills class for the second semester. The goal was
to bolster their skills and get them ready to re-take Algebra A, either in the summer
or for most of these students, in the fall. For the past two years, students who were
unsuccessful in Algebra were not taken out of algebra, but rather co-enrolled in
support class that ran concurrent with their Algebra. The support class curriculum
was also based on the ITUM program components. Lead Teacher C explained,

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“…last year it was a support class for the Algebra student, a full year, not just at the

semester when they failed. So we tried to back up the Algebra and feed in the skills
as we went”.
The two instructional leaders at White Oak Tree High School, the principal
and assistant principal, emphasized quality Standards-Based Instruction (SBI), raised
expectations through the increase in graduation requirements for mathematics,
making strategic teaching assignments, revised Algebra course scope and sequence,
and emphasized interventions for lower performing students by implementing a
Math Skills Algebra Support class, as strategies they used to improve student
achievement in mathematics. However, the findings support the revised Algebra
course scope and sequence and Math Skills Support intervention class as the most
influential in impacting student math achievement. By implementing a one-year
Algebra I CP course, the students were automatically eligible to take the Algebra
CST the first year, versus having to wait until the 2
nd
year of Algebra and being
penalized on the their API scores. Struggling students were eligible to enroll in the
Math Skills Algebra Support class to receive reinforcement of the basic skills
necessary to successfully complete the Algebra subject. Through data analysis and
inquiry, the math skills class configuration changed from a true pullout, 1-semester
intervention class to a yearlong, concurrent enrollment with their Algebra class. The
additional support has increased the student pass rates on both the CST and the

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CAHSEE exams. As well, there have been modest increases on the college-ready A-
G completion rates.

Discussion
The findings in this chapter were ascertained by an analysis of data,
synthesized, organized and presented by the research questions. It was evident that
there had been many on-going discussions at White Oak Tree High School focused
on how to increase student Algebra achievement. WOTHS had an instructional
improvement plan that generated some positive results. This organizational structural
change was both multi-faceted in its approach and complementary to the district
vision for student achievement. There were three marked themes that emerged in the
study of WOTHS’s increased achievement in Algebra.
Theme One: Change in Graduation Requirements from two to three years of
Mathematics
The WOTHS Leadership Team, functioning as a Professional Learning
Community (PLC) made recommendations to the White Oak Tree Unified School
District Governing Board based on their ongoing analysis of achievement data,
research and the unique needs of the teaching and learning environment at WOTHS.
Much discussion came forward from the leadership team concerning what their
students needed to know and be able to perform upon graduation and how could they
best align their graduation requirements with the Expected School-wide Learning
Results (ESLRs), also referred to as student outcomes. The leadership teams’ review

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of research strengthened their belief that their students needed a stronger background
in mathematics to be able to access post-secondary, vocational and apprenticeship
opportunities. Multiple years of data analysis showed that the primary reason
students were not meeting their A-G sequence of courses, the four-year college and
university eligibility requirements, because of lack of success in mathematics
courses. And, as they looked further back into the students’ transcript records, the
leadership team discovered that their math difficulties started in the Algebra year of
the students’ math course-taking sequence. Algebra is considered the “gateway”
course and as such failure to grasp the concepts and skills decreased the students’
likelihood of enrollment or success in higher-level math courses.
WOTHS is an authorized International Baccalaureate (IB) school, and as such
would be considered a high-performing school. Politically, the situation was
exacerbated by the perception of educational community concerns because “year
after year, their math scores were dismal”, and they were not producing as many
students in IB Higher Level (HL) math and Advanced Placement (AP) Calculus, as
they thought they should be producing.
Thus, the structural change process began with the district governance
accepting the recommendations of the White Oak Tree High School Leadership team
and instituting a policy change to increase the graduation requirements from two to
three years in mathematics. An increase in the number of mathematics courses
mandated for graduation required a focus on the math department with implications
for strategic teaching assignments, professional development, and other resources to

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support the implementation of the policy. Politically, this policy change necessitated
a prioritization of resources to support the successful implementation. In an
environment of limited resources, the administration had to place emphasis on those
instructional elements that would support the students with the increased
expectations in math. Consequently, an administration decision was made to allocate
resources to IB, the flagship program at the school site, to AVID, an instructional
elective program designed to support academically-average students identified as
having the potential to access the rigor of the A-G college preparatory track, and
towards mathematics achievement, specifically Algebra, in order to increase the CST
scores and provide a more rigorous math experience for students to prepare them for
postsecondary, vocational and apprenticeship opportunities upon graduation from
high school. Perhaps one of the biggest concerns about raising graduation
requirements was that such policies would cause more students to drop out of high
school. However, research has shown that, everything else being equal, schools that
push students to take tougher academic courses actually have lower dropout rates
(Achieve, 2006)

Theme Two: Implementation of a Math Skills Algebra Intervention and Support
Class
The implementation of the math skills class appears to have contributed
towards increased achievement in Algebra. Through discussion and analysis of
student achievement data in algebra, the leadership team determined that the idea of

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providing more time in the two-year Algebra AB course sequence was not
necessarily helping students be more successful in that course. The data reviewed
illuminated a pattern of Algebra A repetition by many freshman students. Students
were re-enrolling multiple times in Algebra A because of consistent failure during
the first semester of the course. The administration conjectured whether the solution
was to provide different instructional methodology and/or to utilize a different
support system. Their decision was to implement a math skills class as an
intervention class to help students acquire and reinforce basic skills necessary to be
successful in Algebra A. The policy was if the student did not pass Algebra A during
the first semester, they were enrolled in the Math Skills class during the second
semester instead of just repeating the first semester of Algebra A again. The school
enacted the same policy with the unsuccessful Algebra B students. The explicit
objectives of the math skills class was to increase the students’ chances of passing
the Algebra class upon re-enrollment in the summer or fall and to prepare the
students to pass the CAHSEE during their sophomore year.
Under the first configuration of the math skills class as a pullout intervention
class, it was taught by the district math coach/teacher who was the lead for the
district in the ITUM Algebra Project initiative out of the California State Polytechnic,
Pomona grant program. The district math coach/teacher had previously taught high-
level mathematics at both the private and public school, but expressed a passion for
and an interest in, helping struggling students. This coach/teacher developed the
curriculum for the math skills class which was based solely on the foundational

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tenets of the ITUM program which is designed as a conceptual, inquiry-based,
constructivist, discovery-learning, Algebra skill building program to help teachers
help students move from the concrete to the abstract Algebra through multiple
representations of equations, graphing and writing.
The second configuration of the math skills class was implemented as a result
of the changed scope and sequence of Algebra from a two-year Algebra AB course
to a one-year Algebra 1 CP course. Under this structure, the math skills class
operates as a one-year Algebra support class where students were concurrently
enrolled in both the Algebra 1 CP course and the math skills class. For the past two
years, the math skills class has been run as a support program. The district math
coach/teacher and one other math teacher in the department wrote the curriculum and
both teach the class. The other co-writer and co-teacher, Math Teacher K also
teaches the IB Math Studies and AP Statistics courses. According to the curriculum
developers, the curriculum was not based on the Algebra book or other existing
instructional materials. The objective of the math skills concurrent class was to
instruct and reinforce the algebra sub-skills and background skills, while at the same
working on the algebra concepts and “feeding in” the skills being taught in the
Algebra course. Issues arose around the pacing, articulation with the Algebra
teachers and not having what the administrators describe as a “clear-cut” curriculum.
It is evident that there is a lack of consensus about what curriculum or
program should be used in the math skills class. Last year, the University of
California at Los Angeles (UCLA) introduced an Algebra Readiness Course.

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Currently, the Algebra Readiness course is being used in Algebra classes to
supplement the Algebra curriculum and is being used in Math Teacher K’s math
skills classes. There is administrative concern about the heavy emphasis on
worksheets in the Algebra Readiness course. However, teachers using the Algebra
readiness course report greater ease of use because it provides a bit more structure
than the teacher-created curriculum. Math Teacher K reported it is very paper-
intensive, but is glad that the teachers do not have to create everything, however
admits it needs some of the manipulatives and other conceptual elements connected
to it.
White Oak Tree High School is undergoing action research as they seek to
identify the most effective structure and curriculum for their math skills class. They
are committed to this journey as they feel their students are getting better prepared
rather than just enrolling them in Algebra and having them become embroiled in a
cycle of failure.
Theme Three: Change from two-year Algebra AB to one-year Algebra I CP
The change in the mathematics graduation policy from two to three years
precipitated leadership team conversations about revising the scope and sequence of
the Algebra I course. The configuration of the two-year Algebra course for the past
several years looked like students taking one-year of Algebra A and the second-year
taking Algebra B. Under the old graduation requirement, successful completion of
both Algebra A and Algebra B would satisfy the two-year graduation requirement
for mathematics. Math teachers had differing opinions and perspectives about

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implementing a one-year Algebra and there was lack of consensus about whether it
would impact student achievement positively or would it have more of a negative
effect because of the faster pace. According to the teachers, one of the benefits of a
two-year Algebra I course included having the time to more fully develop the
concepts in Chapters 1-6 in Algebra A and chapter 7-12 in Algebra B in the algebra
textbook. In a top-down approach, the administration decided to phase out the two-
year Algebra AB course over two years in order to allow students who had
completed Algebra A the opportunity to complete Algebra B and meet the California
state and district Algebra course requirement, and institute the Algebra CP course.
Analysis of data by the administration had provided insight that many years
ago when the school only offered the one-year Algebra I CP course, there were a
couple of years when the failure rate was the same as the Algebra AB course, and
many more years when there was less of a failure rate than the Algebra AB course.
The administration decided if they were going to “take at hit” on the CST scores
anyway, then they were going to give their freshmen students the “best shot” to be
successful in Algebra during their freshman year. WOTHS was being penalized on
the school Algebra CST scores because the Algebra A students were ineligible to
take the Algebra CST during that first year in the course, and had to wait until their
sophomore year to be eligible to take the Algebra CST. The penalties are a result of a
mandate by NCLB for students and schools when students take an assessment out of
grade level standard, the student scores are automatically lowered by one
performance band level, i.e., students that score at the Basic performance level

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would automatically receive a lower ranking of Below Basic level. Consequently,
beginning that first year of the implementation of the Algebra I CP course, students
were eligible to take the Algebra CST effectively giving White Oak Tree High
School an automatic bump in their CST scores. In addition, further evidence was
found for the justification of the implementation of an Algebra I CP course. Analysis
of the student failure rate in Geometry for students who were enrolled in the Algebra
AB compared to students enrolled in the Algebra I CP demonstrated a higher failure
rate by those students enrolled in the Algebra AB course. Upon interview of several
of these failing Geometry students by the administration, the most common response
was, “it [the class] moved too fast”.
By implementing these structural changes to the Algebra course scope and
sequence, WOTHS raised the level of expectation for their students. It appears
students want raised expectations. Results of a survey performed by Achieve, Inc.
reported as many as 40 percent of high school graduates are not prepared for their
future endeavors whether it is within the realm of academia or out in the workforce.
Additional feedback from surveyed students was they [the students] would have
preferred to face high expectations in high school, with 62 percent of college
students and 72 percent of non-students indicating that they would have taken at least
one more difficult course. The three themes highlighted in this study represent a
structural and political change process that led to improved math achievement at a
high school that overall considers itself a high-performing school. The first theme
relates to increasing the rigor and expectations for graduation that will better prepare

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students for a productive life after high school. In this case, the school wanted to
align its priorities for student outcomes with the graduation requirements. The
second theme highlights s a school community involved in action research (Stringer,
1999) to solve the complex problem of determining the most effective curriculum to
be implemented in their math skills class. Through the cycle of trial, feedback, and
trial, WOTHS continues to search for solutions. In conclusion, theme three
illuminates structural changes based on data to inform the school algebra curriculum
design.
The preceding review of the literature and the findings of this qualitative case
study at White Oak Tree High School provided evidence that through data-driven
decision-making, structural policy changes were enacted that raised the level of rigor
and expectations for their students. The district and high school site worked in
tandem to communicate a clear message about the vision for their students upon
graduation to be prepared for various postsecondary choices in the form of increased
graduation requirements in mathematics. Through an inquiry-based philosophy as a
response to longitudinal data analysis, WOTHS changed the configuration of their
Algebra I scope and sequence resulting in raised student achievement scores.
Implementation of a math skills class supported students with basic skills to access
the Algebra course content, as well some students received additional support
through enrollment in the AVID program. These combined efforts results in
increased student achievement in Algebra. While the leadership at WOTHS
communicated the vision for student achievement, there is a culture of teaching and

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learning that is embedded in SBI. The administration’s ability to resolve dilemmas
regarding instructional leadership created a school culture that seemingly resulted in
increase student achievement in mathematics.

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CHAPTER FIVE:
Summary, Conclusions, and Implications

Summary of Background

The overall academic performance of America’s high school students has
been low for several decades as reported by the educational community, the media
and concerned public. Reports such as A Nation at Risk have catapulted the
indicators of America’s public education deficiencies onto the world stage.
Assessments such as the Third International Mathematics and Science Study
(TIMMS) confirmed the fact that America’s high school students are not performing
up to the level of their international counterparts in mathematics, triggering both
national embarrassment and fear about the competitiveness of America in the global
arena. Even on national measurement indicators such as the National Assessment of
Educational Progress (NAEP), American students demonstrate low achievement as
well, with less than one-third scoring at the proficient or advanced levels. Within the
nation, achievement gaps persist amongst African-American and Hispanic students
in comparison to their white and Asian peers. Moreover, as student’s progress
through the public schools, their achievement levels decline and this trend represents
a growing challenge to maintaining an informed national citizenry.
The performance gap in mathematics presents a critical problem for our
students, particularly in urban settings. Mathematics in general, and Algebra more
specifically, is considered the “gateway” to postsecondary education, vocational

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training, and apprenticeship program opportunities. The U.S. Department of Labor
has identified a high correlation between individual future earning power and math
skills. They find that individuals with lower skills in math have a lower average
income (Stiff, 2006). In the job market, workers who have strong mathematics
background are more likely to be employed and generally earn more than workers
with lower achievement even if they have not gone to college. In urban areas, it is
critical to have a trained workforce able to provide economic stability to those
communities.
There have been concerted efforts at both the state and national levels to
improve mathematics achievement in high schools by focusing on state standards,
improving curriculum and instruction, preparing better teachers, and relating reform
efforts. These efforts have resulted in innovative research-based school designs or
organizational models. Small Learning Communities (SLCs) and Professional
Learning Communities (PLCs) as a foundation for professional development are
considered the two most prevalent comprehensive school reform models. Although
issues such as teacher quality, standards-based instruction (SBI) and professional
development have been identified as having an impact on student achievement, much
of the existing research confirms that leadership is second only to classroom
instruction among all school-related factors that contribute to student learning.
Instructional leadership has become the “dominant paradigm” in public education.
Instructional leadership plays a central role in shifting the emphasis of the traditional
business of school, i.e., managing more directly the instructional components, such

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as the vision for learning, the supervision and monitoring of instruction, the
community and political aspects, the culture of teaching and learning and the use of
data-driven decision-making.
District and school leaders are on a continuous search for the most optimum
recipe of personnel, curriculum, research-based instructional materials, strategies,
and best practices to improve student achievement. Mere identification of the
aforementioned ingredients is not enough to translate into successful
implementation; consequently, more needs to be known about the related conditions
that foster student achievement. Mathematics continues to be the most challenging
subject area in meeting the accountability requirements prescribed by the No Child
Left Behind Act. More needs to be known about how various policies, programs and
instructional leaders actions combine to successfully navigate the school community
milieu to effectively impact student achievement in mathematics.
Purpose of the Study

The purpose of the study was to examine the conditions that fostered student
mathematics achievement in high schools. This study examined how the school
design and response to federal, state and local policy initiatives, related to curriculum
and instruction effected efforts toward increasing student achievement in
mathematics. This study investigated how instructional leaders navigated the change
process and implemented school-based programs for mathematics. The study
explored the extent to which instructional leadership was important in improving the

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math programs and how the instructional leaders responded when they lacked strong
pedagogical content knowledge in mathematics.
The research questions that paramatized and guided this study were:
1. What was the pattern of mathematics achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seemed relevant to improved mathematics achievement at the
school?
3. What change process did the school use to enhance the math program and
strategies to assist students in mathematics?
4. To what extent was strong instructional leadership important in improving
a) the mathematic programs/strategies and b) mathematics achievement
among students?
5. How did leaders in the school resolve the dilemmas about instructional
leadership?

Methodology

The study used a qualitative and quantitative case study approach that utilized
document analysis, interviews, and questionnaires to form conclusions about the role
and actions of the instructional leaders towards improved student mathematics
achievement at one high school. Qualitative insights were gained through key leader,
math teacher and non-math teacher interviews, using interview guides, about their

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experiences and beliefs about the mathematics program and the role of the
instructional leader. This experiential perspective data was organized through the
lenses of the five conceptual frameworks. Quantitative data were collected from the
Math Teacher Questionnaire and non-Math Teacher Questionnaire instruments and
was tabulated. This data provided insight by measuring the strength of responses
organized by each of the research questions. Common themes arose through the
analysis and examination of both qualitative and quantitative data. Through data
triangulation, both sets of data were combined with document analysis and review,
which allowed the researcher to test for consistency among and between the three
sources, with the goal to increase internal validity of the study.

Conceptual Frameworks

Five conceptual frameworks parameterized the data collection for this study.
The frameworks were aligned with research questions 2 through 5. There was no
framework for the first research question. Two conceptual frameworks, Conceptual
Framework 1 (CF1) and Conceptual Framework 2 (CF2) were developed to answer
the second research question. CF1 described research-based effective school design
utilizing basic elements of the Marsh & Codding (2002) school design model. CF2
addresses the research-based elements of effective math programs. Conceptual
Framework 3 (CF3) utilized the four frames, structural, human resources, political,
and symbolic, to describe the instructional leaders’ actions within the frames as they
navigated the change process. The underlying assumptions of the frames are

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grounded from Reframing Organizations (Bolman and Deal, 2003). CF3 was
organized to collect data on the third research question. Conceptual Framework 4
(CF4) was developed based on the intellectual background theory of the Interstate
School Leaders Licensure Consortium (ISLLC) standards or goals for effective
instructional leaders (Hessel & Holloway, 2002; Johnson, 2002). CF4 was developed
to respond to the fourth research question. The fifth conceptual framework (CF5)
was bifurcated into two components and used to answer the fifth research question.
The first is an assessment tool, adapted from the No Child Left Behind (NCLB)
highly qualified teacher (HQT) assessment to determine the instructional leader’s
level of math expertise as low, middle or high. The second component is a list of the
most prevailing strategies instructional leaders use to respond in academic areas
where they are not experts.
Sampling

Purposeful sampling was used for the selection of the high school that was
analyzed in this study. The parameters defining the selection of the high school
included that it had demonstrated an improvement in Algebra I student achievement
as measured by California Standards Test (CST) scores, and that it had greater than
1200 students and 50% of those students were from traditionally ethnic minority
groups. Factors that limited the selection of the school site included that it have an
Academic Performance Index (API) of at least 600 and a California state rank of at
least 5, as well as a stability of leadership demonstrated by the presence of the same
principal for at least the last three years.

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Instrumentation, Data Collection and Data Analysis

The instrumentation for this study was developed during the summer of 2006
by an eleven-member doctorial research study team. All members of the team were
Ed. D. candidates at the University of Southern California, under the leadership of
Dr. David Marsh, Ph.D., Associate Dean of Academic Programs. During the summer
of 2006, the research team developed the instruments used in the study guided by
five conceptual frameworks that were also developed for the study. Each of the five
conceptual frameworks corresponds to research questions 2-5, with two of the
conceptual frameworks being used to collect data to answer the second research
question. For the study, data was collected, organized and analyzed using the
following instruments:
1. School Profile. This document set the parameters and criteria for school
selection for the study.
2. Key Leader Interview Guide. This guide contained a list of questions to be
organized around research questions two – five to be asked in semi-structured
interviews with the school principal, assistant principal of curriculum and
instruction, a counselor, and leadership team members. The interview guide
delimited the topics (research questions) and provided a systematic and
uniform way of aligning responses to the research questions and frameworks
among all members of the research team.
3. Teacher Interview Guide. This guide contained a list of questions to be used
during semi-structured interviews with math teachers. The interview guide

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contained eight questions that helped establish the interviewees’ background
and organize their responses around the five research questions. The
interview guide provided a systematic and uniform way of aligning responses
to the research questions among all members of the research team.
4. Math Teacher Questionnaire. This 50-item questionnaire was based on the
five research questions and was intended to measure math teachers’
knowledge and perspective about the improvement in student mathematics
achievement attributable to: RQ2: policy initiatives, curriculum, instruction
and other related conditions; RQ3: elements of the change process; RQ4:
instructional leadership actions; and RQ5: how instructional leaders resolved
dilemmas based on the 12-Item Strategy Matrix.
5. Non-Math Teacher Questionnaire. This 30-item questionnaire was based on
the five research questions and was intended to measure non-math teachers’
knowledge and perspective about the improvement in student mathematics
achievement attributable to: RQ2: policy initiatives, curriculum, instruction
and other related conditions; RQ3: elements of the change process; RQ4:
instructional leadership actions; and RQ5: how instructional leaders resolved
dilemmas based on the 12-Item Strategy Matrix.
6. Document Review Guide. Adapted from Olsen (2005), this researcher used
this instrument to align school documents to the research questions developed
in the study.

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Summary of Findings

This study looked at the ways in which White Oak Tree High School’s
responded to California State policies and District policies and the implementation of
a math skills intervention class to support Algebra achievement. In conjunction with
the instructional design improvements, leadership actions within the structural and
political frames to undergo the change process are examined along with how
instructional leaders supervise and monitor instruction and make decisions based on
data are presented. Finally, how the instructional leaders responded to compensate
for their low expertise in mathematics were presented through the lens of research-
based strategies that ultimately created the conditions that fostered increased
mathematics achievement at the site. The findings and conclusions for each of the
five research questions were revealed through analysis of the data collected in this
study. These findings, organized by research question are reviewed below.
Research Question One
The first research question asked, “What was the pattern of mathematics
achievement for various students at the school? Through analysis of student
achievement data, the following patterns emerged.
1. In 2005, there was a significant increase in the percentage of students
moving from Below Basic (BB) and Far Below Basic (FBB)
performance bands into Basic (B) performance band in Algebra
2. Between 2002-2005, there was zero-percent of students moving into
Proficient and Advanced performance bands in Algebra

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3. There is a significant achievement gap between Asian and White
students compared to Latino students on CST scores and CAHSEE
pass rates
4. There is an extremely significant achievement gap between African
American students and all other student groups on CST scores and
CAHSEE pass rates
Research Question Two
The second research question asked, “What policy initiatives as well as
curriculum, instruction and related conditions seemed relevant to improved
mathematics achievement at the school? Two conceptual frameworks guided data
collection and analysis. Conceptual Framework 1, the research-based school design,
which had four sections: (1) Curriculum; (2) School Culture; (3) Student
Performance Assessments; and (4) Learning Activities and Conceptual Framework
2, research-based descriptors of effective math programs, which had three sections:
(1) Curriculum design; (2) Standards Based Instruction; and (3) Classroom practices,
were both utilized to frame and organize the data collection. Key leader interviews,
teacher interviews, the Math Teacher Questionnaire, the non-Math Teacher
Questionnaire, and school documents were the primary sources of data for this
question. The data from this question reflected that the key areas were the policy
initiatives of the California Standards Test (CST), California High School Exit Exam
(CAHSEE) and district graduation. Additional learning activities, standards-based

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instruction and assessments, and the Math Skills intervention class curriculum design
were identified as critical.
Creating awareness, communicating, supporting, and focusing on algebra
student achievement was a key priority. The administration understood the need to
constantly analyze data that would guide student achievement on the Algebra CST
and the CAHSEE exam. The leadership team members, math teachers and non-math
teachers who were all interviewed “somewhat agreed” that the CAHSEE graduation
requirement had contributed to the school’s efforts to improve student achievement.
The district changed the graduation requirements in mathematics, requiring three
years instead of two years that precipitated a change in the Algebra course scope and
sequence. However, there was a consistent neutral response from both math and
non-math teachers whether board policies had contributed to math achievement at
the school.
Programs such as AVID strongly contributed to the school culture and
learning activities components of the school design, and both math and non-math
teachers perceived that the school’s master schedule was built based on student
needs. In the AVID class, students are required to collaborate, solve problems and
through the process of inquiry-based Socratic tutorials with college tutors, perform
critical reading, writing, and mathematical tasks to support their work in their core
content classes.
The leadership team members, math teachers and non-math teachers
interviewed all strongly agreed that teachers at White Oak Tree high school teach

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standards-based lessons and that the school has successfully implemented common
assessments that support increased student achievement. Evidence showed that the
common assessments administered were standards-aligned textbook/chapter-based,
teacher-created, end-of-semester summative exams. There was some concern by the
District math coach/teacher about the reliability of such exams as the teachers relied
on the textbooks as the curriculum and as such they may not have been creating
“good” tests that measured the standards and concepts assessed or intending to be.
The original math skills class curriculum was developed by the District math
coach/teacher using many of the strategies found in the Increasing Teachers
Understanding of Mathematics (ITUM) Focus on Algebra Institute program. The
district coach is the lead teacher of the program at White Oak Tree high school. Most
of the students enrolled in the math skills classes are at the far-below basic (FBB)
and below-basic (BB) performance bands on the CST, and lacked the basic skills
necessary to be successful in Algebra. The ITUM program is philosophically
conceptual, inquiry-based, constructivist, and provides hands-on type of teaching and
learning. The district math coach/teacher reported students made significant gains
based on the pre-test and post-test in the math skills class.
Research Question Three
The third research question asked, “What change process did the school use
to enhance the math program and strategies to assist students in mathematics?”
Conceptual Framework 3 guided the data collection and analysis, which had four
sections: (1) the structural frame (emphasis on top down hierarchies, rules, policies

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and procedures, specialized tasks, and goals and objectives); (2) the human resources
frame (emphasis on employees as partners and family, people of the organization,
and productivity through group effort); (3) the political frame (emphasis on power,
bargaining, competition for limited resources, and negotiations); and (4) the
symbolic frame (emphasis on vision, belief and faith, stories, and culture). Key
leader interviews, teacher interviews, the Math Questionnaire, and the non-Math
Questionnaire were the primary sources of data for this question. The data from this
question demonstrated that the change process was evidenced primarily in the
structural frame and the political frame.
The change process began when the Governance Board of the White Oak
Tree Unified School District changed the graduation policy. An additional year of
mathematics instruction was added to the district’s graduation requirements,
increasing the number of years of mathematics education requirement from two to
three years. The recommendation for this more rigorous graduation requirement
originated from the White Oak Tree high school Leadership Team, as a result of
ongoing analysis of achievement data, research and the unique needs of their
community. Prior to the recommendation to the Governing Board, the WOTHS
Leadership Team grappled with what their students needed to know and be able to
do upon graduation and how the school could best align their graduation
requirements with the Expected School Learning Results (ESLRs), also known as
student outcomes. As a result of efforts to foster a culture of teaching and learning,
administration realized they had limited resources, and therefore had to prioritize

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areas of focus. The decision was made to focus on programs in place, International
Baccalaureate (IB) and Advancement Via Individual Determination (AVID), and to
focus on mathematics achievement. Administrators felt they had to bargain with
teachers, by sharing the data that showed mathematics was the most unsuccessful
subject-area, and therefore had to have school-wide focus and appropriate allocation
of resources, in order to effectively manage conflict.
The increased graduation requirement in mathematics was the initial catalyst
to revise the Algebra course scope and sequence at White Oak Tree high school.
Before the change, the high school had implemented a two-year Algebra AB course
for the past several years. However, analysis of achievement data showed that
slowing down the Algebra curriculum by spreading it over two years was not making
a significant change in the student passing rates in Algebra nor did it facilitate the
goal of increasing the number of students enrolling in colleges and universities. The
non-compelling data on Algebra passing rates, coupled with the penalties received
on the California Standards Test (CST) because the students were not allowed to the
Algebra I CST during their first year of Algebra, Algebra A, led the administration to
change the two-year Algebra AB course to a one-year Algebra I College Preparatory
(CP) course. There was lack of consensus on changing the Algebra course. Therefore
a top-down approach was used to adopt and implement the one-year Algebra I CP
course.
The Math Skills intervention class was implemented to provide support to a
significant percentage of freshmen students that were unsuccessful in the first

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semester of the Algebra I CP course. The majority of these freshmen were
categorized at the Far Below Basic (FBB) and Below Basic (BB) performance bands
based on their 8
th
grade CST scores. There have been two configurations of the Math
Skills class. Initially, it began as a 2
nd
semester elective class where students were
un-enrolled from the Algebra course and enrolled in the Math Skills class and
provided basic skills to prepare them to re-enroll in the Algebra I CP course during
summer school or in the fall of next school year. The math curriculum used for this
class was the Increasing Teachers’ Understanding of Math (ITUM) Algebra Project
and was taught by the District math coach/teacher who has been a member of the
ITUM Consortium since its inception. For the past two years, the second
configuration of the Math Skills class was implemented as a concurrent support class
where students were identified and co-enrolled in Algebra I CP and the Math Skills
support class. The goal of the concurrent support class was to align the Math Skills
curriculum with the Algebra I CP class and weave in the skills, as students needed
them, to access the rigor and pace of the Algebra I CP class. These classes were
taught by two teachers, the district math coach/teacher and one other ITUM trained
teacher using the ITUM curriculum.
Research Question Four
The fourth question asked, “To what extent was strong instructional
leadership important in improving A) the mathematic programs/strategies and B)
mathematics achievement among students?” Conceptual Framework 4 guided the
data collection and analysis, which had five sections: (1) vision for learning; (2)

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supervision and monitoring of instruction; (3) community and political; (4) culture of
teaching and learning; and (5) data driven decision-making analysis. Key leader
interviews, teacher interviews, the Math Questionnaire, and the non-Math
Questionnaire were the primary sources of data for this question. The data from this
question demonstrated a strong utilization of data driven decision-making and
facilitating the supervision and monitoring of instruction.
Administrators at White Oak Tree high school are strong implementers of
data-driven decision-making and it is an essential component of the school design.
Through consistent inquiry and analysis of data, the administration used a top-down
approach to set school-wide priorities consistent with their belief that if students did
not have a strong enough understanding of Algebra concepts, as demonstrated by
passing Algebra successfully, they would automatically eliminate themselves from
opportunities in post-secondary or trade schools and apprenticeship programs. The
teachers have slowly adopted the culture of data analysis where they more regularly
engage in conversations about their student performance through the use of data. The
data from both questionnaires reflect that both the math and non-math teachers agree
somewhat that that the school leaders used data-driven information to address
problems and issues related to student achievement.
Prior to the NCLB highly qualified accountability requirements, it was the
policy at WOTHS to only hire teachers for the mathematics department that held
math credentials or who were enrolled in an intern program with strong university
supervision. Administrators performed regular classroom observations and provided

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feedback to new teachers during their first two years in the classroom. Peer support
is perceived by the administration as an effective component of the observation and
monitoring of the instructional program at White Oak Tree high school. New math
teachers are assigned a partner teacher that provides a system of informal support for
them. Math teachers somewhat disagreed that they received coaching or mentoring
from instructional leaders or peer coaches. There has been significant turnover in the
math department over the last few years, as the administration is reluctant to take
risks in making a teacher permanent personnel, who has exhibited classroom
management challenges or an inability to connect with the students during the first
two years. The math teachers agree that the math achievement goals and measures
were clearly articulated and understood. However, the overall perception of the math
teachers is either neutral or somewhat disagreed that strong instructional leadership
was important towards improving the math programs and strategies or student
achievement. Non-math teachers had less neutrality and more positive perceptions
about the overall instructional leadership.
Research Question Five
The fifth research question asked, “How did leaders in the school resolve the
dilemmas about instructional leadership? Conceptual Framework 5 guided the data
collection and analysis, which had two components. The first component was used to
assess the instructional leaders’ level of expertise in the mathematics subject area.
The second component was a list of the most prevalent research-based strategies
utilized by instructional leaders to overcome lack of expertise in any content area to

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include: (1) delegate leadership to assistant with greater expertise; (2) empower
department chair; (3) bring in outside expertise; (4) emphasize inquiry and problem-
solving; (5) emphasize quality instruction; (6) emphasize strategies to engage
students in the learning process; (7) emphasize articulation with feeder schools; (8)
emphasize raised expectations; (9) emphasize strategic teacher assignments; (10)
emphasize revised course scope and sequence; (11) emphasize interventions for
lower performing students; and (12) emphasize professional development. Key
leader interviews, teacher interviews, the Math Questionnaire, and the non-Math
Questionnaire were the primary sources of data for this question. The data from this
question showed the leaders’ response to their low levels of math expertise by
emphasizing quality instruction, emphasizing raised expectations, emphasizing
strategic teacher assignments, emphasizing a revised course scope and sequence, and
emphasizing interventions for lower performing students.
The majority of respondents felt that the overarching goal that was clearly
articulated was the expectation that all teachers provide quality instruction.
Instructional quality became the focus of all school efforts and the foundation for all
learning activities. There is a commonly held belief at White Oak Tree high school
that standards-based instruction is synonymous with quality instruction; thus
teaching the concepts within the standards-based aligned textbooks would be
considered providing quality instruction. Both math and non-math teachers
somewhat agreed that the school leader’s emphasize the importance of quality
instruction as a primary mission of the school.

206
Raised expectations were evident in the increased graduation requirement
from two-years to three-years of mathematics. The overall perception by
administrators was that getting rid of the two-year Algebra AB course and replacing
it with the one-year Algebra I CP course was the most profound example of raised
expectations. Student achievement data indicates an increase in students moving
from the far below basic (FBB) and below basic (BB) performance bands into the
basic (B) band. Both math and non-math teachers somewhat agreed that the site
leaders emphasize having raised expectations for student achievement, particularly,
in mathematics.
Strategic teacher assignments were not just based on the experience of the
teacher. The administration felt that teachers have to have certain skills to work with
specific groups of students and within specialized programs as there is a lot of
interdependency with other teachers and aspects of the program, Teaching
assignments are made based on the administrator perception of the right fit for the
groups of students or particular instructional program. There is a lack of consensus
among math and non-math teachers with respect to their perceptions about strategic
teaching assignments. Math teachers felt very neutral about whether teacher
assignments in the math department were made strategically and with the student in
mind. Conversely, the non-math teachers felt that overall the teacher assignments
were made strategically and with the student in mind.
The Algebra course scope and sequence was changed from a two-year
Algebra AB course to a one-year Algebra I CP course. The first semester of Algebra

207
I AP covers approximately the first six chapters in the Algebra book. The second
semester covers chapters 7-12. Students take the Algebra CST during their
enrollment in the Algebra I CP course, instead of the student and the school being
penalized, as was the case when students were enrolled in Algebra A and were
ineligible to take the Algebra CST that first year.
The Math Skills class was implemented as an intervention for lower
performing students in Algebra I. It was initially designed as an intervention elective
class which students were enrolled in as their math class, if they were unsuccessful
during their first semester of Algebra. Students received basic algebra skill building
with the goal of the student being successful upon being re-enrolled in algebra either
in the summer or in the fall. The Math Skills class was re-configured as an Algebra
support class in which students were enrolled concurrent with their Algebra class.
The objective of this class was to weave in the skills the students needed in order to
access the rigor and pace of their Algebra class. The same teacher that taught the
Algebra class would also teach the Math Skills class.
Conclusion
Through analysis and triangulation of the qualitative and quantitative data
collected, several findings have emerged that confirm the importance of a deliberate
and focused approach to improving student achievement. White Oak Tree High
School has demonstrated consistent elements of a school adhering to the cycle of
continuous improvement, by integrating the federal and state accountability systems,
with a balance of providing a holistic, well-rounded learning experience for all of

208
their students. According to the Frank Barnes from the Annenburg Institute for
School Reform,
The continuous cycle of improvement involves “completing the self-
study process and make it into a cycle, plan when and how to evaluate
the impact of your actions on school practice and student outcomes. You
should plan to examine, at regular intervals, whether school practice has
really changed and whether student achievement has really improved.
This will take you back to the beginning of a new cycle – revisiting your
original student-achievement goals, establishing new student-
achievement goals, and developing new essential questions, based on
learning from the previous cycle”.

Through the process of regular data analysis and inquiry, the administration
consistently questioned the “Whys” and “Hows” of ensuring an equitable, standards-
based teaching and learning environment at WOTHS.
WOTHS is a comprehensive high school is located in the suburbs but is
experiencing many of the same issues that beset schools located in the metropolitan
cities. It operates on a traditional calendar and seven-day period instructional day.
The IB and AVID programs and standards-based instruction (SBI) effectively define
their school design model. There is an explicit focus on mathematics, as they have
identified that the primary reason students do not meet the college preparatory A-G
requirements is their lack of success in the Algebra course. The administration
strongly believes that Algebra is a gatekeeper course and therefore has modified the
master schedule to provide math skills intervention classes to support the revised
scope and sequence to support the structural change from a two-year Algebra AB
course to a one-year Algebra I CP course. The AVID program provides the support
for students enrolled in an elective through which the students receive two hours of

209
Socratic tutorials and an additional 3 hours of class time to learn strategies to
increase their reading, writing, math and collaboration skills, thereby effectively
increasing their success in their rigorous courses.
The math skills intervention and support class uses instructional elements
from the ITUM Focus on Algebra Project program offered through a grant with the
California Polytechnic University, Pomona and The Center for Education and Equity
in Mathematics, Science, and Technology (CEEMaST). The ITUM Algebra project
incorporates conceptual, inquiry-based and constructivist strategies to teach algebraic
skills. The analysis of the findings suggested that some areas played a key role in the
increased student mathematics achievement in Algebra. The math skills class was
initially designed as an intervention class where students were enrolled instead of
their second semester of Algebra. It now serves as a support class where students are
co-enrolled along with their Algebra class. The district math coach/teacher was the
primary teacher for this class during the period of study. The district math
coach/teacher has over twenty years of experience teaching mathematics and is the
lead teacher for the district in the ITUM grant project.
There is lack of consensus about the extent to which instructional leadership
was important in improving math programs and strategies, and improving student
achievement. However, there is consistent agreement between both math and non-
math teachers that math achievement goals and measures were clearly articulated and
easily understood, and that the school’s leaders emphasized the importance of quality
instructions as the primary mission of the school. What is evident is that the

210
instructional leaders used data-driven decision-making to address problems and
issues related to student achievement and that is confirmed by the leadership team
and teachers interviewed.
Overall White Oak Tree High School has confirmed that by using analysis of
data to identify and target areas of student needs, by providing interventions for
lower performing students, by emphasizing quality instruction and, by raising
expectations for their students, has led to increased student achievement. As the
instructional leadership continue on the cycle of continuous improvement, White
Oak Tree High School is committed to continued data analysis to determine the most
effective curriculum and instructional methods to be utilized in the math skills
algebra support class, to increased professional development offerings in the math
department, to establish a vertical articulation system with the middle school math
department, and to greater utilization of AVID strategies school-wide across the
curriculum.
Implications
Implications for Further Research
Baaed on the findings in this study, the following recommendations are made
regarding future research in this area:
1. Student achievement data was slightly higher in a one-year Algebra I CP
course than a two-year Algebra AB course. Longitudinal research would be
advised to determine the most effective Algebra scope and sequence at the
high school level, especially with struggling and at-risk students.

211
2. The implementation of an Algebra support class is critical to the support of
struggling Algebra students. Further research is needed to determine the best
configuration of such a course, and examine the advantages/disadvantages of
the support class as an intervention class (pull-out of Algebra), as a
concurrent class (co-enrollment in Algebra), or another undiscovered
configuration.
3. Instructional support programs e.g., AVID, incorporate teaching and learning
strategies to increase student achievement in core subjects. Further research
is advised to determine what components of the AVID program and
associated teaching strategies, directly impact student achievement rates in
mathematics, specifically, the Algebra I course.
4. Survey questions developed for multiple instruments used to glean answers
to the same research questions, must be clear, concise and aligned.
Implications for practice
Baaed on the finding in this study, the following recommendations are made
regarding implications for practice in this area:
1. The effectiveness of the math skills intervention class curriculum should be
measured. One version of the curriculum was based on the ITUM Algebra
project. Another version was based on another program. Students enrolled in
these intervention classes should be tracked as a cohort to determine the
effectiveness of the intervention as determined by their performance on
standardized exams, e.g., CSTs, CAHSEE, SATs.

212
2. It would be of interest to study the impact on student achievement if a
mathematics department operated as a professional learning community and
given structured time, both as a whole department and other times as same-
subject subcommittee, to collaborate around issues such as analysis of
student achievement data, best practices, and ensure alignment with pacing
plans and schedules.
3. It would be of interest to study student achievement if benchmark
assessments were administered quarterly, and teachers had the opportunity
to make mid-semester corrections. This additional piece of data would
provide the opportunity to identify critical instructional gaps in the teaching
and learning environment.
4. The implementation of the “top-down” approach inherent within in the
structural frame for implementing the instructional program. It would be of
value to study the effect on student mathematics achievement if the
instructional leadership utilized a strategy of empowered department chair
and/or mathematics coach (Gabriel, 2005).

213

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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?

229
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

230
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

231
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

232

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?

233

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

234
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

235
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

236
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

237
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

238
50. Teacher assignments in the math department are made strategically and with
student need in mind.
1 2 3 4 5

239

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

240
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

241
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

242
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

243

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 Poor student mathematics achievement in American public schools, as determined by national and international rankings in math has resulted in tremendous public and political pressure to reform our public educational systems. Current federal and state accountability policies and systems have been focused on this issue consistently for almost the last two decades. A plethora of school reforms have been scattered across the public education landscape in response to the myriad needs of our students and stakeholders. However, despite heroic efforts and financial maneuvers, student achievement wanes and the gaps persist between white and Asian students and students of color. The new paradigm of school management, instructional leadership, has dominated the conversations and several configurations of school designs, curriculum and instructional modifications have been pursued with the goal of finding just the right recipe for student success. The purpose of this study is to examine the conditions that fostered mathematics achievement at one high school. Specifically the study examines school design, school and classroom policies, conditions and best practices that enabled the improvement in student achievement, and the role of the instructional leader in shaping and directing the reform efforts in improving student achievement in mathematics. The study also aimed to increase our understanding of how instructional leadership impacted the creation of a culture for mathematics achievement when the instructional leaders lacked strong, pedagogical in mathematics as a subject area.

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Asset Metadata

Creator Smith, Jennifer Denise (author)

Core Title High school math reform and the role of policy, practice and instructional leadership on math achievement: a case study of White Oak Tree High School

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 08/08/2007

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), USA (countries)

Language English

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

Creator Email cv1335@earthlink.net

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m775

Unique identifier UC1483615

Identifier etd-Smith-20070808 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-545657 (legacy record id),usctheses-m775 (legacy record id)

Legacy Identifier etd-Smith-20070808.pdf

Dmrecord 545657

Document Type Dissertation

Rights Smith, Jennifer Denise

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