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Secondary math reform and the role of policy, practice, and instructional leadership on math achievement

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Secondary math reform and the role of policy, practice, and instructional leadership on math achievement

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SECONDARY MATH REFORM AND THE ROLE OF POLICY, PRACTICE
AND INSTRUCTIONAL LEADERSHIP ON MATH ACHIEVEMENT: A CASE
STUDY OF VALLEY HIGH SCHOOL

by

Staci Lynn Erlandson

_____________________________________________________

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

May 2008

Copyright 2008 Staci Lynn Erlandson
ii
DEDICATION
This dissertation is dedicated to my family. You all have guided me and
inspired me in my educational journey. You have all taught me to be change in the
world and use the power of my thoughts and words to make a difference. Mom, I
dedicate this to you first and foremost for all that you have created for me. Thank
you for being such a source of wisdom and motivation for me. I am eternally grateful
to you and all of your amazing support.
This dissertation is also dedicated to my grandmother and grandfather, Mrs.
and Mr. Aline and John Hays. Nana I know you are especially proud of this
accomplishment and Papa continues to send his spirit of love and perseverance
through my educational journey. You both are the strength of my soul and I love you
very much.
I would also like to dedicate this dissertation to my aunts, Kathy Dummond
and Jennfier Grimes. You both have supported my efforts of continued education.
My aunts are so proud of me and all of my accomplishments. You both are such
strength in my life.
This dissertation is also dedicated to my incredible godparents, Cathie
Bustamante, Diana Stanton, and Bill Bustamante. The three of you are my biggest
cheerleaders. Thank you for your support, encouragement, and praise. I have learned
so much from all of you and thank you dearly.
And finally, but in no way last, I want to thank my husband, Mr. Daniel
Block. You are my best friend and such an inspiration to me. Thank you for your
iii
untiring love, patience, understanding, support, and humor to encourage me to make
my education a priority at times. I look forward to our life together with many
adventures and successes in our future together. As partners we will continue to
challenge each other, learn from each other, support each other and share laughter for
many, many years to come. I love you, honey.
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. They have motivated and encouraged me countless times
throughout my educational career. I would like to acknowledge my patient and
masterful editor, Dr. Shantanu Duttaahmed who pushed and challenged me with my
thoughts and writing.
To my endlessly supportive mom, who is an inspiration to me professionally and
personally, I have learned the most from you, Mom. You have been my greatest
teacher! I am so thankful for my new extended family that came to celebrate at the
graduation and festivities; your love and support are incredible.
I would like to thank my colleagues from the Santa Monica-Malibu Unified
School District and Castaic Union School District. I want to especially thank Denise
Davis, Jennetta Thomas, Jennifer Lynch, Lorie Alexander, Esperanza (Hope)
Radcliffe, Patricia Cairns, and especially Dr. Molly Millard. Your friendship and
love is greater than anyone could hope for within life.
I also would like to acknowledge the knowledge and support I received as an
undergraduate at University of California at Berkeley. The education I received in
Berkeley was the most impacting experiences of my life. I thank the students, faculty
and campus for infusing a desire to pursue a career in education and policy and make
me a life-long learner. Dr. Pedro Noguera, your lectures and courses were and still
v
are the foundation of my beliefs for improving our nation’s education system. I want
to thank my favorite fellow “bear,” Ms. Courtney Powers for her support, spirit and
encouragement to pursue my doctorate.
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. Marsh thank you for your
constant support, patience and encouragement through all of my wonderful life
experiences over the past year.
I want to thank Dr. Jennifer Smith, Dr. Meg Abrahamson, Dr. Merrill Irving,
Dr. Kimberly Tresvant, Dr. Roger Rice, Dr. Khunghae Schwartz, and Consuelo
Hernandez for sharing ideas, support, frustrations, and ultimately success in our
journey as students together over the past three years Thank you for your
contributions to this life changing and powerful process.
vi
TABLE OF CONTENTS
DEDICATION ………………………………………………………… ii
ACKNOWLEDGMENTS ……………………………………………. iv
LIST OF TABLES …………………………………………………… vii
LIST OF FIGURES ………………………………………………….. ix
ABSTRACT …………………………………………………………. x
CHAPTER ONE: Overview of the Study …………………………… 1
CHAPTER TWO: Review of the Literature ………………………… 31
CHAPTER THREE: Research Methodology ……………………….. 69
CHAPTER FOUR: The Findings and Analysis …………………….. 109
CHAPTER FIVE: Summary, Conclusions and Implications ………. 198
REFERENCES ……………………………………………………… 236
APPENDICES ………………………………………………………. 250
vii
LIST OF TABLES
Table 1: API Scores for four years …………………………………………….. 79

Table 2: Relationship of Data Collection Instruments to Research Questions …. 86

Table 3 – Bolman and Deal’s Four Frames ……………………………………. 90

Table 4 – Strategies to Overcome a Lack of Subject Matter Competency …….. 99

Table 5: Comparison of Percentage of Students Scoring at and
Above Proficiency on CST: Algebra I ………………………………………… 113

Table 6: Change in Percentage of Students Scoring at and Above
Proficiency on CST: Algebra I ………………………………………………… 113

Table 7: Valley High School’s API Scores for three years ……………………. 114

Table 8: Valley High School’s API Base and Growth Data …………………… 117

Table 9: API Growth Score Comparison of White and Hispanic
Students ………………………………………………………………………… 118

Table 10: Mathematics CST Percentage of Proficient or Advanced
Students by Race and Ethnicity ………………………………………………… 119

Table 11: Algebra I CST Percentage of Proficient or Advanced
Students by Race or Ethnicity …………………………………………………. 120

Table 12: Algebra I CST Percentage of Proficient or Advanced
Students by Gender ……………………………………………………………. 121

Table 13: Mathematics CST Percentage of Proficient or Advanced
Students by Gender ……………………………………………………………. 122

Table 14: Mathematics CST Percentage of Proficient or Advanced
Students by Subgroup …………………………………………………………. 123

Table 15: API Growth Score Socio-economically Disadvantaged
Students ……………………………………………………………………….. 124

Table 16: Percentage of Students Passing CAHSEE Mathematics
Section by Student Subgroup …………………………………………………. 126
viii

Table 17: Number of AP exam test takers at Valley High School ………… 127

Table 18: Comparison of AP Exam pass rates between State
average and VHS ………………………………………………………….. 127

Table 19: Percentage of VHS Graduates completing the University of
California (UC) a-g requirements and/or the California State
University (CSU) requirements …………………………………………… 128

Table 20: Comparison of Valley High School (VHS) and State Scores
for SAT Exam …………………………………………………………….. 129
ix

LIST OF FIGURES
Figure 1: Framework for Effective School Design …………………….. 88

Figure 2: Effective Math Programs …………………………………….. 89
Figure 3: Instructional Leadership Framework ………………………… 96
Figure 4: Assessment of Principal’s Expertise in Math ………………… 98
x
ABSTRACT
Poor student mathematics achievement in American public schools, as
determined by national and international rankings in math has resulted in 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 tremendous amount of school reforms have occurred
effecting both students and stakeholders. However, despite dramatic, time-
consuming, and costly efforts, 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 urban 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 knowledge in
mathematics as a subject area.
1
CHAPTER ONE
Overview of the Study

Over the past fifty years, the United States Public Education System has been
continually criticized for the poor performance of students. At every level of
American society there are intense debates over how to improve the quality of public
education. Yet, student achievement still remains poor and at an unacceptable level
for a great number of students in our public school system. Nationally, achievement
gaps increased due to disparities related to students’ ethnic and socioeconomic
backgrounds.
In 1983, the fears of Americans, regarding the poor performance of our
public school system, were confirmed when the National Commission on
Excellence published its landmark report, A Nation at Risk. The Commission,
selected by the Reagan-Bush administration, was charged with investigating the state
of public education in the United States. Released amidst a great deal of media
attention, A Nation at Risk painted a dismal picture of the academic proficiency of
American students, stating that “declines in educational performance are in large part
the result of disturbing inadequacies in the way the educational process itself is often
conducted” (National Commission on Educational Excellence, 1983, p.1).
Mathematic achievement in the United States has become more important
than ever because American students still fall behind students in other nations in this
area. National and international comparisons have found that mathematic
2
achievement levels of American students fall far behind those students of other
developed nations (National Center for Education Statistics, 2000).
Mathematics is the key element in a student’s education that provides the
pathway for their future careers. Students that have a strong grasp on mathematics
concepts and deduction have an advantage in both academics and in the job market.
Mathematics achievement is critical at all grade levels in a child’s education, but it
has been found to be the most important in understanding and mastering Algebra by
the 8
th
grade. The achievement of 8
th
and 9
th
grade Algebra is a critical point in
mathematics education. Achievement at this grade level allows for students to take
rigorous high school mathematics and science courses, which are the keys to college
entrance and success in the work force. However, most 8th and 9th graders lag so
far behind in their math courses that they are at a disadvantage when preparing for
college. Students who take rigorous mathematics and science courses are much more
likely to go to college than those who do not.
A Nation at Risk exposed the public school system as a “failure,” which did
lead to some school reform efforts. The failure of the American public schools was
highlighted in the Third International Mathematics Science Study (TIMSS) in 1995.
The TIMSS study found that as American students progressed through the public
education system, their academic competitiveness with international students
decreased. According to TIMSS 1995, students in the 12
th
grade scored significantly
lower in math and science than did their foreign counterparts (National Center for
Education Statistics, 2000).
3
Achievement gaps persist between American high school students and their
international peers. While America continues to raise standards to prepare students
for international competition, students are unable to meet the standards set
nationally. Since the publication of A Nation at Risk, Mathematic achievement has
increased. However, internationally, according to Third International Mathematics
and Science Study (TIMMS 1999), “the scores of both our overall student population
tested on general mathematics and science knowledge , and of the more advanced
students tested in mathematics and physics, were well below the international
average” (Forgione,1998). Even with the elimination of Japan and other Asian
countries, which tend to score highest in international comparisons, United States
twelth grade students were outperformed by 14 countries, and outperformed two
countries (Forgione, 1998).
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 on to college. A national survey found that
by age 30, high school graduates who had not furthered their education but had
scored in the top quartile on the mathematics portion of the Armed Services
Vocational Aptitude Battery (ASVAB) earned 38 percent more per hour than high
school graduates who had not gone to college and had scored in the bottom quartile
of the mathematic portion of the ASVAB.
Today our nation’s public education system is failing to equip our children
with the essential mathematical skills required in an increasingly competitive global
4
economy. Nearly three-quarters of our nation’s 4
th
and 8
th
graders and nearly four-
fifths of our 12
th
graders are scoring at levels below “proficient” in mathematics and
science for their grades (National Center for Education Statistics, 2002).
International mathematics and science assessments demonstrate that as U.S. students
progress through their educational tenure, they score progressively worse than do
students in the rest of the developed world. Furthermore, national and international
benchmarks confirm that minority students and students from low-income families
perform particularly poorly in relation to other U.S. and international students
(National Center for Education Statistics, 2002).
In 2001 the National Research Council’s Mathematics Learning Study
Committee reported that one area in which the research evidence is consistent and
raises compelling concerns is the weaknesses in the mathematical performance of
American students. State, national, and international assessments conducted over the
past 30 years indicate that, although U.S. students may not fare badly when asked to
perform straightforward computational procedures, they tend to have a limited
understanding of basic mathematical concepts (National Research Council, 2001).
The committee also found that American students are also notably deficient in their
ability to apply mathematical skills to solve even simple problems. Although
performance in mathematics is generally low, there are signs from national
assessments that it has been improving over the last decade (National Research
Council, 2001).
5
It is imperative that students graduate from high school with a solid
mathematics background in order to be prepared and viable for the job market and/or
college. The continual rise in technology in the global economy requires more and
more workers finding they need to have strong backgrounds in mathematics.
Rigorous mathematics preparation is also important to students intending to go to a
two- or four-year college or university. Two-year colleges require all students to gain
an understanding of intermediate Algebra prior to high school graduation. Four-year
colleges and universities typically require more high school mathematics preparation
for admission, Typical state four-year colleges and universities require students to
take Advanced Placement mathematics courses while in high school.
The recent and continual advances in technology have fueled the demand for
a more highly skilled labor force, transforming a high school education into a
minimum requirement for entry into the labor market. The impact of technology in
our society’s job market make it even more imperative that all students are
graduating with a high school diploma. Because high school completion has become
a requirement for accessing additional education, training, or entering the labor
force, the economic consequences of leaving high school without a diploma are
severe. On average, dropouts are more likely to be unemployed than students who
complete high school and to earn less money when they secure work. Therefore,
secondary schools today are faced with the challenge of increasing curricular rigor to
strengthen the knowledge base of high school graduates and motivating students to
understand the connection.
6
Many of these minority students are concentrated in high poverty urban
schools. For the minority students attending these schools high concentrations of
students with low mathematical proficiency at the end of the eighth grade have
serious consequences. The ability to succeed in college preparatory mathematics
courses in high school has been linked to success in post-secondary schooling and to
life-long opportunities for success (Pelavin & Kane, 1990). In nearly all of the
nation’s states there is a 30 to 50 percentage point difference between White students
and the largest minority group in the percent of students scoring at basic on the 8th
grade NAEP exam (Blank & Langesen, 1999).
Solid mastery of mathematic computation skills is imperative for all students
to be academically successful. Loveless and Coughlan’s “Improving Achievement in
Math and Science: The Arithmetic Gap” explain how computation skills are critical
for American students to master from the early grade levels in order to confidently
reach proficiency in Algebra and higher mathematics. Learning mathematics is an
incremental process and basic computation skills are necessary to advance in
mathematics and the sciences. Eighth graders who cannot do basic arithmetic with
ease, who cannot find the right answer quickly and confidently without a calculator,
will be hampered in their efforts to learn algebra and geometry in high school.
Without some proficiency in algebra, students will have little grasp of calculus,
physics, or chemistry and little chance of succeeding in college mathematics and
science courses (Loveless and Coughlan, 2004). Loveless and Coughlan further
explain that computation skills are also an increasingly important predictor of adult
7
earnings. In Murnane, Willett, and Levy's study of cognitive skills as a predictor of
future earnings, “The Growing Importance of Cognitive Skills in Wage
Determination,” they observe that a high school senior's mastery of skills taught in
American schools no later than the 8th grade is an increasingly important
determinant of subsequent wages. (Murname et al., 1995)
Mastering computation skills at an early age can also promote equity in math
achievement. The declining arithmetic achievement in the United States also raises
concern about racial equity. The achievement gap in computation skills between
black and white students narrowed in the 1980s but began to widen in the 1990s
(Lee, 2002). Lee’s “Racial and Ethnic Achievement Gap Trends: Reversing the
Progress toward Equity?” uses the National Assessment of Educational Progress
(NAEP) data to show that the Black-White racial achievement gap narrowed
substantially in the 70s and 80s but that the gap stopped narrowing further and even
widened in the 90s. According to NAEP from 1990 to 1999 white 9-year-olds'
performance on division problems dropped one-tenth of a percentage point, whereas
their black counterparts' performance fell by 6 percentage points. Furthermore,
thirteen-year-old white students fell 2.1 percentage points on fractions compared
with a drop of 4 percentage points for black students. An increasing disparity is the
seventeen-year-olds' struggle with fractions, in which white students' performance
fell nearly 18 percentage points, whereas that of black 17-year-olds decreased by
33.6 percentage points (National Center for Education Statistics, 2003).
8
The quality of mathematics and science achievement of students in America
has been a major area of concern for the last fifty years. Over that time, the federal
government launched and participated in a variety of attempts to promote
mathematics and science education. State and national efforts to improve math
achievement in high schools have included reforms that focus on state standards,
improved curriculum, standards-based instruction, and highly qualified teachers.
These reform efforts have dramatically improved mathematic achievement in many
secondary schools. Recently there has been more challenging learning standards and
higher stakes accountability systems for all schools and students, with the
accountability system of No Child Left Behind Act of 2001. These standards-based
reform efforts have created the movement towards smaller learning communities in
large and over-crowded secondary school sites.
Comprehensive secondary school reforms within mathematics have been on
America’s educational agenda for more than 30 years now. The quality of
mathematic education in public schools offered to all children had reached a level of
state and national concern that has not diminished. The country’s policymakers and
government have remained committed to public education as was demonstrated by
national campaign for standards’ based educational reform and No Child Left Behind
Act of 2001.
Many possible explanations have been offered to explain why our nation is
failing to help our students achieve in mathematics. Plausible causes include weak
and unfocused mathematic curriculums (Schmidt et al 1999), unequal opportunities
9
to learn challenging mathematics (Raudenbush, Fotiu & Cheong 1998), shortages of
skilled, trained, and knowledgeable mathematics teachers (National Commission on
Mathematics and Science Teaching, 2000), under-motivated students (Bishop 1999),
For each one of these possible causes American public schools have implemented
comprehensive secondary school reforms that relate to mathematic content,
curriculum and instruction.
The accountability systems of No Child Left Behind have forced states to
write and adopt academic content standards to improve the quality and continuity of
education provided to students. Statewide academic standards provide goal posts for
teaching and learning across all of a state’s public schools. These standards also
drive myriad other education policies. Standards determine the content and emphasis
of tests used to track pupil achievement and school performance; they influence the
writing, publication, and selection of textbooks; and they form the core of teacher
education programs. The quality of a state’s K-12 academic standards holds far-
reaching consequences for the education of its citizens, because of the federal No
Child Left Behind Act. The entire accountability edifice rests upon these state
academic standards.
In the fall of 1989, standard-based goals were published by the National
Council of Teachers of Mathematics (NCTM) (Schoenfeld, 2004). In so doing, the
goal was to set standards and benchmarks for students in all grades. Standards
would become the foundation of instruction and a measure of accountability.
10
Preliminary studies indicate a positive relationship between state
implementation of standards, assessments and accountability systems, and gains on
NAEP. A moderate positive relationship between states’ overall embrace of
standards-based education and gains in student math achievement. With the
implementation of standards, states have adopted stronger accountability systems. In
turn, strong accountability systems have had a clear positive impact on student
achievement (Olson, 2006).
Over the past ten years, high schools have recognized the need to change
their methods and operations to enhance instruction. In the early 1990s, the
comprehensive school reform (CSR) movement began and adopted both top-down
and bottom-up methods to remedy targeted areas such as instructional content and
methods, scheduling requirements, school culture, and staffing needs (Kilgore,
2005).
Many states used a wide range of incentives to spur change and improvement
in schools. Schools were held accountable through the coupling of student
performance with rewards, i.e., monetary incentives, public recognition, relief from
regulation; and sanctions, i.e., loss of accreditation, state intervention, takeovers and
reconstitution (Elmore & Fuhrman, 2001; Zradicka & Holman, 2000). The
consequences for poor performance varied among states depending upon the level of
local authority in relation to state authority, the state’s willingness to intervene at
low-performing schools, and the state’s capacity to effectively assist these schools.
11
Darling-Hammond (1999) wrote that having relevant data that is easy to
understand for teachers will bring about much needed accountability. By analyzing
results from year to year is important to the long-term effects of the reform
(Schmoker, 1999). Data will provide information on how to adjust and intervene
when needed. Data-driven decision making is what districts and school sites use to
improve the quality of instruction, professional development, and also intervention
programs that are necessary for the academic achievement of struggling students.
Professional development efforts in mathematics have had a positive impact on
systemic reform efforts when used as a strategy to improve student achievement
(Taylor-Anderson, Brown, & Lopez-Ferrao, 2003).
Other significant factors that impact students’ mathematic achievement
include: time, class size, professional development, and research-based instructional
strategies. There are many findings that correlate positive results with time and
learning. The amount of time students are in class and finding a school schedule that
is conducive to learning is a constant topic of debate. The University of Illinois-
Chicago found a high correlation between the amount of time spent at school and
student learning. Researchers claim that while time is an important factor for
learning to take place, students must be exposed to a highly engaging curriculum
(Sadowski, 1998). Changes to the organizational structure of the school, i.e., block
scheduling and year-long calendars, affected student learning. Walberg (1987)
consistently found a positive relationship between alternative scheduling and student
achievement. This positive relationship was attributed to increased instructional time,
12
i.e. block scheduling, or with increased opportunities for teacher collaboration, i.e.
“banking instructional minutes.”
Daily scheduling issues in high schools are examined closely to assure
students are getting the greatest educational benefit. Block scheduling has been a
popular reform that challenged school districts to allocate more classroom time for
students in the most critical classes- Mathematics and English Language Arts.
Researchers have found that block scheduling increased graduation rates, lowered
discipline referrals, and improved dropout rates (Queen, 2000).
Quality instruction has a profound effect on a student’s achievement
(Marzano, Pickering & Pollock, 2001). Although, socioeconomic status, race,
school scheduling, and class size have a demonstrated an impact on student
achievement, the benefit of a quality teacher was found to be the strongest predictor
of student performance (Ferguson, 1999). Quality teachers are created by on-going
and meaningful professional development opportunities available to teachers in order
to improve their instruction. High-quality, research-based professional development
is essential for improving instruction in ways that will impact all students’ learning
(Marzano, Pickering, Pollock, 2001). Students who attended class with high quality
teaching learn more and have been found to average 23 percent higher on
standardized tests versus those students who attend school with poor teacher quality
(Marzano, Pickering & Pollock, 2001). While effective teachers are able to raise
student achievement with all socioeconomic and ethnic sub-groups, ineffective
teaching results in students with lower scores on standardized tests (Marzano,
13
Pickering & Pollock, 2001). National Commission on Teaching and America’s
Future (Darling- Hammond, 1996, p. 102) recommended the following:
Our schools need to be redesigned so that they honor teaching, respect
learning, and teach for understanding. To be able to direct their energies
around a common purpose, schools need to adopt shared standards for
student learning that become the basis for common efforts of teachers,
parents, and the community. Then, schools must structure their work so that
teachers can work more intensively with students and with each other and can
have greater influence over the design of the learning experiences their
students encounter.

New curriculum frameworks were implemented across the country and
within the NCLB guidelines districts and states are encouraged to implement a
comprehensive school reform effort that includes one of the many research-based
designs( McCombs, Quait 2002). These school reforms include a comprehensive
design with aligned components; effective researched-based methods and strategies;
professional development; measurable goals and benchmarks; support within the
school; parental and community involvement; external technical support and
assistance; evaluation strategies and the coordination of resources.
Many innovative school designs are created to improve student achievement
and quality of education in secondary schools. The effort and commitment to
improving student achievement and reducing the pervasive achievement gap in our
secondary schools has brought innovative design models which create the most
optimum learning environment and instructional program for diverse learners in our
urban schools. Refrom efforts include the implementation of : Small Learning
14
Community (SLC), the Community for Learning program (CFL) (Wang, 1998) and
the Professional Learning Community (PLC) (DuFour, 2003).
Many secondary schools modify the traditional high school structure to better
meet the needs of students. One major modification is the introduction of SLCs:
SLCs are small learning communities such as career academies or school-
within a school, break students up into subgroups to provide them an
environment where students are able to develop closer relationships with
teachers and peers. SLCs such as career academies emphasize the
relationship between academies and the workplace and have been shown to
decrease dropout rates and improve work attendance and job performance
(Pluker, Zapf and Spradin, p. 5, 2004).

With new policy initiatives from national and state educational entities, the
creation of new school designs, local capacity must be empowered and allowed in
order to achieve national goals set forth in mathematics. However, in an attempt to
find research articles, material and curriculum that schools have used to improve
mathematics programs and strategies on the high school level-- there are none.
There exist no methods, strategies or theories as to how to improve mathematics
instruction on the secondary level. School leaders and teachers must use the state
standards and state-approved textbooks in combination with academic rigor to
improve mathematics achievement.
The SLC’s purpose is to personalize the instructional program by
reorganizing larger high schools into smaller communities of learners. This effort has
been met with mixed results. The reform model of CFL is a model that is focused on
setting high standards for student achievement in the context of building and
maintaining positive self-perceptions. The instruction is developed in tandem with
15
the characteristics of the individual student and his/her learning needs within the
context of the school and the larger community.
Within the dynamics of attempted school reform and design there are many
factors that play an important and influential role in the academic achievement of
students. One predictor of student success is the culture of the organization. Research
has demonstrated that a positive and healthy inclusive cultural climate in a school is
link to student success and the opposite is true as well, in that negative learning
environments have a detrimental impact on students (van der Westhuizen, Mosoge,
Swanepoel, Coetsee, 2005). The leadership of the school ultimately creates a
collaborative school culture on student learning. The leaders’ leadership skills are an
essential and S/he must build the capacity of all stakeholders in the school site and
community. Remarkable leaders possess solid knowledge and understanding of
policy and initiatives that are guiding the school reform. To embark on this aspect of
school reform requires that support is offered to meet the individual needs and that
models that increase the awareness of what “best practices’ the school is embracing
through its reform effort is fundamental to the improvement of student learning;
everyone must know the vision of where they are going and why (Leithwood, Louis,
Anderson, Kyle 2004).
Educational leadership is key in the context of new policy, initiatives, and
designs. The Interstate School Leadership Licensure Consortium (ISLLC) has
researched and combined the standards-based oriented age and developed six key
elements that facilitate the contemporary visions of school leadership. These
16
elements are: 1.) Facilitating shared vision, 2.) Sustaining a school culture
conducive to student and staff learning, 3.) Managing the organization for a safe,
efficient, and effective learning environment, 4.) Collaborating with families and
community members, 5.) Acting with integrity, fairness, and in an ethical manner,
and 6.) Influencing the larger political, social, economic, legal, and cultural context.
These standards are now the guide in principal preparation programs and its origins
where found in practicing effective principals (Lashway, 2003).
Instructional leaders of standards-based high accountability schools are no
longer able to shoulder all the schools’ instructional responsibility. Effective leaders
are able to provide, “coherent instructional vision, rigorous standards, use of data to
make decisions, emphasis on professional development, the creation of learning
communities, and the clear demonstration-through behavior as well as words-that
principal is fully engaged with classroom instruction (Lashway, p 5, 2003). School
leaders are change agents:
A change agent is a person who leads a change project or business-wide
initiative by defining, researching, planning, building business support and
carefully selecting volunteers to be part of that change. A change agent must
have the vision to state the facts based on data, even if the consequences are
associated with unpleasantness” (Bhardwaj, 2003).

Effective school leaders create collaborative learning communities. Leaders are able
to sharpen their own skills, develop teacher leadership, find resources to support
professional community growth, give teachers the confidence to grow, and manage
the leadership agenda systemically.
17
Effective leaders are the moral center of the education community. They
are able to listen to the voices of teachers, parents, and students. They balance
accountability against responsibility. They protect the educational community’s
“lifeworld”. “The “lifeworld” consists of the values, beliefs, and purposes that knit
the school community together and give significance to everyday activities”
(Lashway, p.8, 2003).
Lastly, effective leaders respond to challenges. They constantly scan the
environment for new ideas, tools and solutions, and reflect on the implications. They
attend to the learning of all members of the education community. They explore
current practices, beliefs, and assumptions that serve as a basis for posing inquiry
questions. “These questions are signposts in the hunt for evidence and the struggle
with dissonance. Dissonance is tackled in dialogue, thereby lowering defenses and
increasing shared understanding” (Lashway, p. 9, 2003).
The characteristics that the leaders need to have are described by Fullan
(2001) as five core competencies;
• Broader moral purpose- Leaders must have the capacity to inspire
and motivate people to accomplish the challenges inherent in urban
school reform. They must have the skills to work with a broad group
of contingencies in a consistent, fair and equitable manner when
implementing the reform.
• Keeping up with and understanding the change process- The leader
must be familiar with and comprehend the change process and
18
dynamics of change; approaching challenges with creative processes.
Through the change process the leader must have the capacity to
reculture the community in a safe environment in an effort to keep
moving forward with change.
• Cultivating relationships- The leaders must have the capacity to
establish and support good relationships across all of the unique and
diverse groups of the school environment; fostering a community
spirit.
• Sharing of knowledge- This must be a core value of the leader;
sharing of knowledge and information creates a more inclusive effort
where people are informed, engaged and active participants. The
leader must establish protocols and procedures to facilitate this.
• Creating coherence- A common challenge for the urban school leader
which offers so much diversity is bringing everyone together as a
collaborative group that can work as a group with a coherent vision
and action plan.
It is found in research that school reform efforts do not happen over night,
they take many years to create and foster. In order for an effective leader to make a
real impact in school reform it takes many years of consistent effort to create
sustainable changes and improvement in student achievement and learning (Murphy
& Datnow, 2003; Borman et. al., 2002). Strong school leaders need time to foster
and create a school climate with a vision that fosters student achievement.
19
Statement of the Problem
Many of California’s urban secondary schools have significantly lower
academic performance in the area of mathematics. Focused attention on increasing
mathematic achievement by national and state agencies through policy initiatives and
published accountability reports such as Annual Yearly Progress (AYP), the Annual
Performance Index (API) and high school exit exams has pressured school districts
to implement standards-based education where the ultimate goal is to elevate
students’ mathematics competency. School districts are compelled to implement
standards and best practices to meet the standards set forth. However, in regards to
urban schools, which differ based on diversity, social-economics, perspectives and
culture as compared to their suburban counterparts, must discover and implement
best practices that will positively impact their student body. It is critical to
understand how schools that are demonstrating mathematics academic success have
reformed their schools to promote such successes for their students. It is important to
understand what are the best practices being implemented and utilized at these high
achieving school sites. It is necessary to learn what is the role of the leader in the
reform process as well as the school design models.
Curriculum committees, universities, field experts, and textbook publishing
companies have provided curriculum aligned with state standards and the High
School Exit Examination. Districts have allotted special funds and positions for
“math experts” and states have funded after-school programs to assist students who
are not faring well in mathematics. Despite these various efforts and choices
20
presented to districts, no one program has been packaged as the panacea for all ills
and designed to “fit all”. This is evident in the continual dismal mathematics scores
posted annually. Discernment in adapting a mathematics program or moving the
school culture and people to achieve a higher standard in mathematics is an essential
element that has been a great challenge in the school districts. It is yet to be known if
the curriculum framework or the instructional leadership of a school are the guiding
source towards increased student achievement in mathematics.
Effective instructional leadership is viewed as critical to a school’s success.
Having the ability to communicate a vision, build internal capacity, create an
atmosphere that includes academic rigor and carry out the duties effectively is
seemingly lacking when it comes to mathematics achievement. School-based
administrators and district leadership alike, continue to struggle in defining the
characteristics that, in the context of improving math performance for students,
create good instructional mathematical leadership. Several issues seem to be
especially relevant to instructional leadership in this setting. Leaders often do not
have strong pedagogical content knowledge in mathematics education; yet need to
carry out functions related to fiscal, personnel, organizational leadership, data
analysis, and review, etc. Little is known about how leaders work effectively in this
context to raise student achieevment within mathematics.Therefore it is necessary to
look at how educational leaders can effectively guide their faculty to increased and
sustained student achievement and improved instructional strategies.
21
Purpose of the Study
The purpose of this study was to conduct a case study of one secondary
school’s efforts at a mathematics reform design and implementation. It examines
factors that positively influenced the math performance of secondary students. This
study investigated a school’s math achievement as a result of policy initiatives in
standards-based curriculum and instruction. This study investigated the high school’s
elements of design; factors that shaped the district design for mathematics reform;
strategies educational leaders used to implement the instructional reform; the extent
to which the reform was implemented; and how effective the reform has been in
affecting teaching and learning practices. The focus was on the school site’s
administrative and leadership roles in the mathematics reform process. The study
incorporated an understanding of how instructional leaders, who lack strong
pedagogical content knowledge in mathematics education, were able to impact
significant mathematics achievement at the school site.
Research Questions
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement at the
school?
3. What change process did the school use to enhance the math program
and strategies to assist students in math?
22
4. To what extent was strong instructional leadership important in
improving A) the math programs/strategies and B) math achievement
among students?
5. How did leaders in the school resolve the dilemmas about
instructional leadership?
Importance of the Study
School District leaders, school site leadership, state policy makers, classroom
teachers and educational researchers will benefit from this study as it will make an
affirmative contribution to the existing body of knowledge on the subject of
mathematics achievement, curricula development and teaching methodology.
School districts and individual schools will benefit from the opportunity to examine
their own organization, curriculum and teaching practices and evaluate them in light
of the most effective practices in mathematics instruction.
This study will be of importance in contributing to the limited research
currently available on the school district’s role and effectiveness in mathematics
reform efforts. School district leaders will acquire a broader understanding of how to
increase mathematics achievement at school sites. While this study is focused on a
single school, it was designed to illustrate a mathematics reform effort. District
officials will establish how teaching pedagogies; mathematics curricula, school
organization and intervention programs are most effective at improving and
enhancing mathematics instruction and achievement. The study will inform district
practitioners and policy makers about the successes and the pitfalls to consider in
23
providing instructional practices, reorganization or mathematics curricula and related
programs.
School leaders will find the information useful as they implement change at
their school site. Practitioners will have a context for their own needs as they
compare how to organize their personnel, curriculum and courses that will foster
optimum mathematics instruction and achievement. Having an unbiased report of
information provides leaders the opportunity to incorporate successful strategies and
to plan for potential setbacks. This study will provide knowledge as to how to
effectively and efficiently lead mathematics instruction without having the
mathematics specialization required to instruct mathematics. ) Leaders will gain a
better understanding of mathematics programs, curriculum and teaching practices
that will promote mathematic achievement on their school sites. The study will
provide practitioners with successful practices in mathematics instruction and
curriculum that can be implemented on their sites.
State policy makers will find the study useful as they are able to understand
the process school sites must undertake to transform mandates into meaningful
classroom practices. A school site’s reflection on mathematics reform strategies may
assist lawmakers to set policy if they see the progress and problems districts face
when finding creative solutions to meet the needs of all students while implementing
standards-based reforms.
The study will allow classroom teachers to find effective instructional
practices for implementation in their classrooms. They will find this a study to be
24
useful in providing strategies and best practices to improve mathematics
achievement for their students. Teachers will understand how their educational
leaders can support them in a similar mathematics reform at their school site.
Limitations
The following is a list of limitations of the study and findings:
1. The study was limited by the number of high schools in California’s
Los Angeles Ventura or Orange counties.
2. The study is not a longitudinal; data is collected in a short time frame.
3. The participants possible biases and willingness to participate in the
study.
4. The researchers biases and interpretation of the data collected through
the interview and literature review.
Delimitations
The following parameters served as delimitations of the study;
1. Only schools in Southern California’s Los Angeles, Orange, or
Ventura counties for this study.
2. School sites were chosen by their steady improvement in student
mathematic achievement as demonstrated by API, AYP and Algebraic
achievement.
3. One school was utilized for the study, which limits the sample size.
4. The study was based on the data and study of one secondary urban
school which impacts the generalizability of the findings.
25
5. The school was selected based on specific criteria of improved math
achievement.
6. The study was a qualitative case study, which impacts the ability to
draw a definitive cause and effect relationships in the findings.
Assumptions
The following assumptions were considered to be understood in the study;
1. The instrumentations used were designed and utilized were effective
in eliciting and providing the information sought.
2. The respondents were honest with their answers on the questionnaires
3. California Standards Test (CST) and the California High School Exit
Exam are valid predictors of student’s skills and thus the schools math
program.
Definition of Terms
For the purpose of this study, the following terms are operationally defined
below:
The Academic Performance Index (API): The API is the cornerstone of the
Public Schools Accountability Act (PSAA). The API ranks school performance, sets
growth targets, and provides similar-school comparisons. The API is a single
number on a scale of 200 to 1,000, indicating how well a school has performed
academically the previous school year (California Department of Education, 2001).
Adequate Yearly Progress (AYP): AYP is an individual state's measure of
yearly progress toward achieving state academic standards. "Adequate Yearly
26
Progress" is the minimum level of improvement that states, school districts and
schools must achieve each year.
Achievement gap: denotes differences in the academic achievement in of a
particular group of students. (Bridging the Great Divide (2002): Broadening
Perspectives on Closing the Achievement. North Central Regional Educational
Laboratory (NCREL).
Assessment: The processes used to collect information about student progress
toward educational goals. The form varies with what is being assessed and the
purposes for which the results will be used. Secondary Periodic Assessments
measure student proficiency toward California Content Standards for the explicit
purpose of improving teaching and learning (LAUSD, 2005).
Benchmark: Formative uniform measure of student progress relative to
standards. Standards-aligned assessments and assignments provide information
about progress toward the end target (California Department of Education, 2001).
Best Practices: A best practice is a technique or methodology that, through
experience and research, has proven to reliably lead to a desired result. Target Teach,
SearchVB.com Needham, MA.
California High School Exit Examination (CAHSEE): A graduation
requirement, authorized by state law in 1999, which requires California public
students, beginning with the graduating class of 2004, to pass the CAHSEE in order
to receive a high school diploma. The CAHSEEl covers the curricular areas of
reading, writing, and mathematics and is aligned with the state content standards
27
adopted by the State Board of Education (California Department of Education,
2001).
California Standards Test (CST): Pupil achievement by grade level, as
measured by the Standards Testing and Reporting (STAR). (California Department
of Education).
Content Standards: Stated expectations of what students should know and be
able to do in particular subjects and grade levels. They define not only what is
expected of students, but also what schools should teach (LAUSD, 2005).
Cultural Capital: Forms of knowledge; skill; education; any advantages a
person has which give them a higher status in society, including high expectations.
Parents provide children with cultural capital, the attitudes and knowledge that
creates an educational system that is a comfortable and familiar place in which they
can succeed easily (Bourdieu, 1986).
Cultural 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 ( Hayes, Elaine. (n.d.) The Forms of Capital).
Cultural Deficit Theory - Assumes that some students cannot achieve at high
levels because of deficits inherent in their race, ethnicity, language, or culture.
Data-driven decision making: The process of utilizing multiple indicators to
make decisions about student placements, curriculum and instruction based on the
analysis of classroom data and standardized test data. (Massell, 2000).
28
Highly Qualified Teacher: The definition of "highly qualified" in the law
requires that public elementary and secondary school teachers have obtained full
state certification or passed the state teacher licensing examination; hold a license to
teach in the state; and have not had a certificate or license requirement waived under
emergency, temporary or provisional.
Highly Qualified Teacher: A Highly Qualified Teacher (HQT) as defined by
No Child Left Behind (NCLB) as a teacher who has an appropriate credential to teach
in the area(s) assigned and who has demonstrated subject matter competency through
various acceptable State teacher licensing examination or through a highly objective
uniform state standard of evaluation (HOUSSE) (NCLB, Title IX, section 9101).
Instructional Leadership: An influence that guided the activities designed to
impart knowledge or skills to students (Olsen, 2005).
Leadership: "Leadership is a process of influence leading to the achievement
of desired purposes. Successful leaders develop a vision for their school based on
their personal and professional values [and goals]. They articulate this vision through
their actions and words; they seek to ensure that their staff and other stakeholders
share the vision. The philosophy, structures and activities of the school are geared
towards the achievement of this shared vision." (School Leadership Concepts and
Evidence, spring 2003).
Master Schedule: This is a construct that reflects the format of the school
day. The following elements are included in and are specified by the master
schedule; the length of each instructional period, when and how frequently courses
29
are offered, which teachers are assigned to teach specific courses and grouping of
students.
National Assessment of Educational Progress (NAEP): The NAEP is an
ongoing, national assessment of what America’s students in grades four, eight, and
twelve know and can do in various academic subject areas. NAEP is administered
by the National Center for Education Statistics of the U.S. Department of Education.
One NAEP component provides states with a measure of their students’ academic
performance over time and a comparison of the results to 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). Reference-Shulman, L. ( 1987).
Knowledge and teaching: Foundations of the new reform. Harvard Educational
Review, 57(1), 1-22.
Performance Bands: Bands that identify levels of student achievement based
on a demonstrated degree of mastery of specified content standards. California has
identified five performance levels for its statewide standards based assessments:
Advanced, Proficient, Basic, Below Basic, and Far Below Basic (California
Department of Education, 2001).
30
Sanctions: The consequences imposed for not meeting expected performance
outcomes in accountability systems (Olsen, 2005).
Social Capital: The central premise of social capital is that social networks
have value. Social capital refers to the collective value of all "social networks" [who
people know] and the inclinations that arise from these networks to do things for
each other ["norms of reciprocity"].
Organization of the Study
This dissertation is organized in five chapters. Chapter One is organized as
the introduction of the study and includes; the statement of the problem, the purpose
of the study, the significance of the study, the research questions, limitations of the
study, the delimitations, the assumptions and the operational definitions of terms to
be used in the study. Chapter Two is the review of relevant literature addressing the
current status of secondary urban school performance in math, best practices used by
teachers, the role of the Principal as an agent of change and secondary school reform
efforts. The focus of Chapter Three is to outline the methodology used for the study
and the instrumentations that are used to gather information including the sampling
criteria and selection process of participants. The overall findings of the study are
presented in Chapter Four with a discussion and analytical perspective. The final
Chapter Five provides a summary of the study and offers recommendations and
potential implications based on the findings. The references and appendices are
included at the end of the five chapters.
31
CHAPTER TWO
Review of the Literature

There are many concerns about student achievement in the United States
when comparing the performance levels of US students to their international peers
and the quality of instruction in public education. The concerns over student
achievement in the United States, both in terms of the performance levels in the past
as well as the performances reported from other nations, constantly drive national
education reforms here.
These concerns were reinforced in 1983 with the publication of A Nation at
Risk, which contained recommendations for changes needed in the quality of
mathematics instruction. In an era of accountability these reform efforts were
indoctrinated from the political milestones of A Nation at Risk, the TIMSS report,
and NAEP, which invested in keeping the pressure on educational reform in the
United States and has driven school districts and local leaders to invest in
tremendous educational reform efforts to improve the academic achievement of
students and the quality of instruction.
Student performance trends among minority students in the United States
fluctuated in the 1970’s and 1980’s. Although the gap appeared to be closing at a
steady pace between White, African American, and Latino students, in the 1990’s the
gap began to widen once again (NCES, 2001). Looking at student performance data
32
provided schools and districts across the country with an opportunity to face a
growing problem in need of a solution.
A Nation at Risk: The Imperative for Educational Reform, was issued in 1983
by the National Commission of Excellence in Education to help inform the United
States about the status of public education. The report noted that, “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.” (National Commission on
Excellence in Education, 1983, p. 5) This open call to elected officials, educators,
parents, and students urged Americans to reform the public school system because it
was “in urgent need of improvement.” A Nation at Risk provided many grim
statistics regarding the increasing illiteracy rates among American students. Further,
the report claimed that the achievement gap was growing among minority students
(Education Week, 2004).
The report urged Americans to focus its attention on educational reform and
simultaneously encouraged legislators to take an active role in improving the
nation’s schools. In their eighteen month study of America’s decline in public
education A Nation at Risk identified a variety of key statistics including student and
adult literacy rates and student achievement on standardized assessment measures.
Specifically, the report found 23 million American adults were functionally illiterate
as measured by the simplest tests of reading, writing, and comprehension. Further
results showed that thirteen percent of all 17-year-olds in the United States could
have been classified as functionally illiterate. Amongst minority youth, the statistic
33
soared to forty percent. Finally, the average achievement of high school students on
standardized tests was even lower than that of 26 years ago (NCEE, 1983).
A Nation at Risk had a strong impact on how the public, politicians, and the
media now envisioned the quality and performance of United States public education
system. The United States Department of Education had been monitoring student
performance data through its Office of Educational Research and Improvement
(OERI) since 1867 (Vinovskis, 1996; NCES, 2002). Before now, this data was not a
subject of public scrutiny but, the panic over student achievement propelled research
institutions into providing legislators, educators, and the public with more detailed
data on the status of student achievement through other international and national
assessments.
The report punctuated the important message that “we have, in effect, been
committing an act of unthinking, unilateral disarmament,” (p. 5). The report had in
effect made Americans begin to question progress being made in education. There
was a general feeling that the American educational system was actually regressing
(Cuban & Tyack, 1995). The publication of A Nation at Risk provided
recommendations for changes needed in the structure and operation of public
schools.
Our nation is at risk. Our once unchallenged preeminence in commerce,
industry, science, and technological innovation is being overtaken by
competitors throughout the world. This report is concerned with only one of
the many causes and dimensions of the problem, but it is the one that
undergirds American prosperity, security, and civility. We report to the
American people that while we can take justifiable pride in what our schools
and colleges have historically accomplished and contributed to the United
34
States and the well-being of its people, the educational foundations of our
society are presently being eroded by a rising tide of mediocrity that threatens
our very future as a Nation and a people. (National Commission on
Excellence in Education, p. 1)

In response to the widening achievement gap in the 1980’s, the National
Commission on Excellence in Education was commissioned to study education and
reported that the American school system was failing to educate American children.
From the research contained in the report, the standardized test scores in the United
States reflected that students were not meeting grade level standards and were not
making progress. The report claimed that many colleges and universities in effect
had to spend more resources to provide basic mathematics and English courses
because of the lack of achievement in high school graduates. Also, American
companies were impaired because young people in the work force did not have basic
problem solving skills that were achieved from mastery of Algebraic thinking. The
report called attention to the fact that in comparison to countries such as Japan,
Germany, and Korea, the United States was losing its position as a global economic
leader and immediate attention must be directed at student achievement.
Although A Nation at Risk was sufficient to cast a negative shadow on
education throughout the 1990’s, a newer study, the Third International Mathematics
and Science Study (TIMSS) was interpreted as evidence of the ineffectiveness of
United States education.
35
Trends in International Mathematics and Science
American students have participated in eight major international achievement
studies in science and mathematics since the 1960s. The first of the eight major
studies was in the 1960s, the First International Mathematics Study and the First
International Science Study which involved students from over 15 countries. Then
the next study was in the 1980s, the Second International Mathematics Study and the
Second International Science Study evaluated students from 13 different countries.
In 1988, the international assessment of achievement in mathematics and science
was combined into the First International Assessment of Educational Progress given
to 13-year old students from six countries. The studies found that overall United
States students progressed poorly against their international peers on these
assessments. But, the findings from these reports were in effect disregarded due to
technical procedures and differences in sample populations (National Center for
Educational Statistics [NCES], 1992).
In 1995 a consortium of international research experts developed a valid
international assessment, the Third International Mathematics and Science Study
(TIMSS). In 1995 the TIMSS was administered to students from 41 countries across
a variety of grade levels. As product of the International Association for the
Evaluation of Educational Achievement, TIMSS is known as the most
comprehensive international study of mathematics and science (NCES, 2001, 2002).
Data were collected from U.S. students in the fourth, eighth and twelfth grades and
then compared to students internationally. TIMSS utilized a variety of methods to
36
measure enrollment and analyze the results. The findings confirmed that the student
sample from the United States was comparable to other participating countries. The
assessment was now statistically reliable, yet the results remained relatively the
same, with American students performing poorly (TIMSS International Study
Center, 1997).
The results from the 1995 TIMSS math assessment showed that while
students in fourth grade performed well in science and were above the international
average in mathematics, there was a sharp decline in the scores of middle school and
high school students. U.S. students in the eighth and twelfth grades performed lower
than their international student counterparts. The 1995 TIMSS found that American
seniors were third from last in mathematics and fifth from the last in science when
compared to 21 other countries. This monumental data verified that as students were
making headway through the educational system in the U.S., but they were not
maintaining their position internationally.
In 1999, the Third International Mathematics and Science Study Repeat
(TIMSS 1999) was given to eighth-grade students around the world. Comparisons
could now be made internationally and within cohort groups. The most disturbing
result of this data were that U.S. students now in eighth grade, that had performed
above average four years earlier, had made no progress in either math or science
(NCES, 2001, 2002). The results were that the mathematics performance of the U.S.
eighth-graders in 1999 was lower than it was for this cohort as fourth-graders in
1995. In comparison, most of the 16 participating countries did not show any
37
significant change in mathematics performance between the four years. The TIMSS
1999 analysis of sub-groups by race indicated no change for White or Hispanic
students in math or science, and very small gains for Black students in math only.
Basically TIMSS 1999 found that the overall mathematics and science scores for the
United States students decreased even lower than their international counterpart
students.
The most recent results of the Trends in Mathematics and Science Study
2003 (TIMSS 2003) were very promising for American fourth and eighth-grade
students. TIMSS 2003 involved fourth-grade students from 26 countries and eighth-
grade students from 48 countries. TIMSS 2003 assessed the mathematics and science
achievement of half a million students at either the fourth- or eighth-grade levels. In
the TIMSS 2003, America's fourth- and eighth-grade students significantly
outperformed many of their international peers, scoring well above the international
average in both mathematics and science. In addition, the report found promising
results that U.S. eighth-graders improved their scores compared to previous years
(1999 and 1995), with gains across most student groups, including boys, girls, and
minority students. Scores for U.S. fourth graders remained static in mathematics and
science.
U.S. Secretary of Education Rod Paige expressed optimism with the TIMSS
results, "Eighth-grade results from TIMSS confirm what we have seen domestically
that there is a greater emphasis on higher standards in the classroom leads to
improved performance and a smaller achievement gap. However, the results also
38
show that we have further to go, particularly in earlier grades, toward establishing a
culture of excellence and achievement at all grade levels" (U.S. Department of
Education, 2004). Paige noted that the TIMSS tests are closely linked to the curricula
of the participating countries. "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 that every student in every school has a real opportunity to learn"
(U.S. Department of Education, 2004).
TIMSS 2003 results along with the international assessment, Program for
International Student Achievement (PISA), which showed America's 15-year-olds
performing below the international average in mathematics literacy and problem-
solving (U.S. Department of Education, 2004). The results of these international
comparisons confirmed even more so that efforts to prepare all of our students for a
future that has never been more competitive and challenging. It is imperative that
students must graduate from high school ready to succeed in college and in life.
The report on the U.S. TIMSS results, Highlights From the Trends in
International Mathematics and Science Study 2003, released by the Education
Department's National Center for Education Statistics (NCES) in the Institute of
Education Sciences, found that in 2003, U.S. eighth-graders improved their average
mathematics and science performances compared to 1995. The growth in
achievement occurred primarily between 1995 and 1999 in mathematics, and
between 1999 and 2003 in science. Moreover, the available data suggested that the
performance of U.S. eighth-graders in both mathematics and science was higher in
39
2003 than in 1995 relative to the 21 other countries that participated in the study
(TIMSS, 2003). There were no measurable findings detected in the average
mathematics and science scores of U.S. fourth-graders between 1995 and 2003.
Moreover, the data suggests that the performance of U.S. fourth-graders in both
mathematics and science was lower in 2003 than in 1995 relative to the 14 other
countries that participated in the studies (TIMSS, 2003).
When looking at the sub-groups, U.S. Black fourth-graders and eighth-
graders and Hispanic eighth-graders improved remarkably in both mathematics and
science between 1995 and 2003 (TIMSS, 2003). As a result, the gap in achievement
between White and Black fourth-and eighth-grade students in the United States
narrowed between 1995 and 2003 in both mathematics and science. The gap in
achievement between Black and Hispanic fourth-graders also narrowed in science
over the same period. In releasing the U.S. findings, Grover Whitehurst, Director of
the Institute for Education Sciences, said, "international assessments such as TIMSS
provide important information about education in the United States and in other
industrialized nations, and an external perspective on U.S. performance. For
example, TIMSS not only shows that U.S. eighth-graders are making strides in
mathematics and science when measured against their prior performance, but that
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).
40
National Assessment of Educational Progress
The National Assessment of Educational Progress (NAEP, the “Nation’s
Report Card,” provides valuable statistics on long-term student performance trends
on assessments in reading, mathematics, and science and serves as America’s
monitoring system for student achievement. research into the factors that cause the
discrepancies needed to be completed. Under the No Child Left Behind Act of
2001, NAEP became a required assessment to ensure that state accountability
systems accurately measured student performance. The accountability of NAEP
provided reliable measurement of changes in national achievement over time and
highlighted the gaps in achievement between different subgroups of the student
population.
According to NAEP the trend in mathematics confirmed decreasing scores in
the 1970’s, followed by increases in the 1980’s and early 1990’s, eventually
resulting in similar scores between 1991 and 1999. When looking at the longitudinal
data of different subgroups, the scores of white students continued to increase
gradually, while continually remaining higher than the scores of Hispanic and
African-American peers. According to NAEP the scores of the Hispanic and African
American students demonstrated a modest net increase between 1971 and 1999
(NCES, 2000c).
In 1999 NAEP published their annual report on the ‘Condition of Education’
(NCES, 1999). According to the mathematic findings White students had higher
average mathematics scores than their black and Hispanic peers. The gap between
41
white and black students in mathematics narrowed between 1973 and 1999 in each
age group. However, there was some widening in 1986 with the 13 year old age
group and in 1990 with the 17 year old age group (NCES, 1999). The conclusions
drawn from the NAEP study confirmed that nationally there is an academic
achievement gap, whereas White students continue to outperform both African-
Americans and Hispanic sub-groups.
In nearly all of the nation’s states there is a 30 to 50 percentage point
difference between White students and the largest minority group in the percent of
students scoring at basic on the 8th grade NAEP exam (Blank & Langesen, 1999).
Many of these minority students are concentrated in high poverty urban schools. For
the minority students attending these schools high concentrations of students with
low mathematical proficiency at the end of the eighth grade have serious
consequences. The ability to succeed in college preparatory mathematics courses in
high school has been linked to success in post-secondary schooling and to life-long
opportunities for success (Pelavin & Kane, 1990).
According to Haycock, Jerald, and Huang (2001), minority students showed
improvement over the decade, however, the gaps that separated them from White
students remained significantly wide so that twelfth grade minority students were
about four years behind white students. A thirteen year-old white student read at
grade level, while an African American or Latino student would reach that reading
level four grade levels later (Haycock et al., 2001; SIG, 2004). These findings
provided additional evidence of the need to reform American education (Elmore,
42
1997). Although policymakers frequently devoted special attention to the education
of disadvantaged students, most states have not been successful in reducing the
achievement gap between white and minority students (Barton, 2001; Hanushek,
1997). Although there is disappointment with student achievement amongst the sub
groups, NAEP also indicated that the achievement gap appeared to close at some age
levels while progress in others was stalled.
California’s NAEP scores remained significantly lower than the average
national scores and were the lowest in comparison with the five most populous
states, even when students’ family backgrounds were controlled to account for the
higher percentage of minority students in California (Arkes et. al., 2005). In 2003,
NAEP assessed over 14,000 Californian students in the fourth or eighth grades. On
average California’s Reading and Mathematics scores were below the national
average. From 1992 to 2003, California increased the percentage of fourth-grade
students scoring at or above the basic achievement level in mathematics from 34%
up to 42%. Gains were not made in the eighth grade, with 34% at or above the basic
level—the same percentage in 1990 as in 2003 (Flores, 2003).
The Student Achievement Gap
There are many implications and causes of the achievement gap in the United
States. Darling-Hammond (1996), Haycock (2001), and Resnick (1999) have
addressed the factors responsible for the growing achievement gap in the United
States. Socioeconomic status and race are frequently blamed for low student
achievement (Haycock, 2001). Yet much research indicates that the gap begins
43
before the child enters kindergarten. It is clearly not the genetic make-up of children
that is causing the achievement gap, but the experiences that the child has in their
first few years of life (Whitmire, 1997). Many children of color are not being
exposed to the fundamental aspects of life, which include attending some form of
preschool, parents reading to them at home, and exploration of the world around
them.
Public education is currently immersed in reform efforts mitigated by an era
of accountability and high-stakes standardized testing. Despite these reform efforts
over the past thirty years, there continues to be academic achievement gaps amongst
different groups of students. The gaps in achievement appear by income and by race
and ethnicity. According to NAEP large percentages of low-income Black, Hispanic,
and Native American students are at the low end of the achievement ladder, and
large percentages of middle- and high-income White and Asian students are at the
top of the achievement ladder. The College Board’s National Task Force on Minority
Achievement (1999) offers compelling evidence about the persistent gaps between
Black, Hispanic, and Native American students and their White and Asian
counterparts that begin in elementary school and continue through the postsecondary
levels of education:
The gaps are found among these groups regardless of socioeconomic level.
At second and third grade, Black, Hispanic, and Native American youngsters
are scoring much lower than their White and Asian counterparts are. Blacks,
Hispanics, and Native American 12
th
graders made up only about 1 in 10 of
those students scoring at the Proficient level on the 1996 NAEP math test.
Achievement gaps are evident in the Advanced Placement and SAT exams.
Although college-going rates are increasing for all groups, Blacks, Hispanic,
44
and Native American students earn much lower grades than so White and
Asian students with similar admission test scores (College Board’s National
Task Force on Minority Achievement, 1999).

There are some promising indicators that show increasing numbers of
students of all backgrounds taking college preparatory courses and Advanced
Placement and college entrance exams. This encouraging data must be supported by
systems that provide not only access, but also appropriate preparation and resources
for success.
The Importance of Mathematics in Schooling
Solid mastery of mathematic computation skills is imperative for all students
to be academically successful. Loveless and Coughlan’s “Improving Achievement in
Math and Science: The Arithmetic Gap” explain how computation skills are critical
for American students to master from the early grade levels in order to confidently
reach proficiency in Algebra and higher mathematics. Learning mathematics is an
incremental process and basic computation skills are necessary to advance in
mathematics and the sciences. Eighth graders who cannot do basic arithmetic with
ease, who cannot find the right answer quickly and confidently without a calculator,
will be hampered in their efforts to learn algebra and geometry in high school.
Without some proficiency in algebra, students will have little grasp of calculus,
physics, or chemistry and little chance of succeeding in college mathematics and
science courses (Loveless and Coughlan, 2004). Loveless and Coughlan further
explain that computation skills are also an increasingly important predictor of adult
earnings. In Murnane, Willett, and Levy's study of cognitive skills as a predictor of
45
future earnings, “The Growing Importance of Cognitive Skills in Wage
Determination,” they observe that a high school senior's mastery of skills taught in
American schools no later than the 8th grade is an increasingly important
determinant of subsequent wages. (Murname et al., 1995)
Mastering computation skills at an early age can also promote equity in math
achievement. The declining arithmetic achievement in the United States also raises
concern about racial equity. The achievement gap in computation skills between
black and white students narrowed in the 1980s but began to widen in the 1990s
(Lee, 2002). Lee’s “Racial and Ethnic Achievement Gap Trends: Reversing the
Progress toward Equity?” uses the National Assessment of Educational Progress
(NAEP) data to show that the Black-White racial achievement gap narrowed
substantially in the 70s and 80s but that the gap stopped narrowing further and even
widened in the 90s. According to NAEP from 1990 to 1999 white 9-year-olds'
performance on division problems dropped one-tenth of a percentage point, whereas
their black counterparts' performance fell by 6 percentage points. Furthermore,
thirteen-year-old white students fell 2.1 percentage points on fractions compared
with a drop of 4 percentage points for black students. An increasing disparity is the
seventeen-year-olds' struggle with fractions, in which white students' performance
fell nearly 18 percentage points, whereas that of black 17-year-olds decreased by
33.6 percentage points (National Center for Education Statistics, 2003).
It is imperative that students graduate from high school with a solid
mathematics background in order to be prepared and viable for the job market and/or
46
college. The continual rise in technology in the global economy requires more and
more workers finding they need to have strong backgrounds in mathematics.
Rigorous mathematics preparation is also important to have a strong background in
mathematics. Rigorous mathematics preparation is also important to students
intending to go to a two- or four-year college or university. Two-year colleges
require all students to gain an understanding of intermediate Algebra prior to high
school graduation. Four-year colleges and universities typically require more high
school mathematics preparation for admission, Typical state four-year colleges and
universities require students to take Advanced Placement mathematics courses while
in high school.
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 on to college. A national survey found that
by age 30, high school graduates who had not furthered their education but had
scored in the top quartile on the mathematics portion of the Armed Services
Vocational Aptitude Battery (ASVAB) earned 38 percent more per hour than high
school graduates who had not gone to college and had scored in the bottom quartile
of the mathematic portion of the ASVAB.
Reform Efforts to Improvement Mathematic Achievement
The quality of mathematics and science achievement of students in America
has been a major area of concern for the last fifty years. Over that time, the federal
government launched and participated in a variety of attempts to promote
47
mathematics and science education. State and national efforts to improve math
achievement in high schools have included reforms that focus on state standards,
improved curriculum, standards-based instruction, and highly qualified teachers.
These reform efforts have dramatically improved mathematics achievement in many
secondary schools. Recently there has been more challenging learning standards and
higher stakes accountability systems for all schools and students, with the
accountability system of No Child Left Behind Act of 2001. These standards-based
reform efforts have created the movement towards smaller learning communities in
large and over-crowded secondary school sites.
Comprehensive secondary school reforms within mathematics have been on
America’s educational agenda for more than 30 years now. The quality of
mathematic education in public schools offered to all children had reached a level of
state and national concern that has not diminished. The country’s policymakers and
government have remained committed to public education as was demonstrated by
national campaign for standards’ based educational reform and No Child Left Behind
Act of 2001.
There are many significant educational reform efforts that have improved
student mathematic achievement in high schools. One of the outcomes from the 1983
A Nation at Risk publication was national systemic reform. This occurred as the
United States began to understand the need for curriculum standards as is common in
other countries (Anderson, B., Brown, C., & Lopez-Ferrao, J., 2003). These reform
efforts were two-fold: first, they created high expectations for the quality of learning
48
and instruction for all students, and second, they maintained an accountability system
to improve the quality of instruction and high student achievement. Researchers
agree that one of the important obstacles to high student achievement in the United
States is our low expectations for students, not just students who are poor and come
form minority backgrounds, but most of our students (Codding and Tucker, 1998).
In the Fall of 1989, mathematic standard-based goals were published by the
National Council of Teachers of Mathematics (NCTM) (Schoenfeld, 2004). Its goal
was to set mathematics standards and benchmarks for students in all grades.
Standards would become the foundation of instruction and a measure of
accountability. The development of statewide academic standards focused attention
on a consistent understanding of student learning, now measured in relation to the
standards and not in subjective student-to-student comparisons (Codding & Tucker,
1998; Hoppe, Kirst, & Massell, 1997; Jamenetz, 2001).
President Clinton’s Goals 2000 program labeled the reform movement as a
‘system’ or ‘standards based reform’ (Fuhrman, 1994). The goal was to assure
students had a number of standards they were to learn at each grade level. Each state
identified exactly what their content standards would be for each subject area and
each grade level. The standards were to provide a more productive system of
accountability for student learning (Darling-Hammond, 1999). As of 2001, every
state but one had content standards in at least one subject area and 44 states had
content standards in the four core subjects of Language Arts, Mathematics, Science,
and Social Studies (Hirsch et al, 2001). Standards formed the central core of
49
systemic reform designed to improve instruction, yet content standards alone did not
produce gains in student performance. They were only one piece in the puzzle that
also encompassed performance standards, assessment, accountability, professional
development, resource allocation, and intervention to support struggling students and
schools (American Association of Educational Research, 2000; ECS, 2000b).
Many possible explanations have been offered to understand why our nation
is “failing” to help our students achieve in mathematics. Plausible causes include
weak and unfocused mathematic curriculums (Schmidt et al 1999), unequal
opportunities to learn challenging mathematics (Raudenbush, Fotiu & Cheong 1998),
shortages of skilled, trained, and knowledgeable mathematics teachers (National
Commission on Mathematics and Science Teaching, 2000), under-motivated
students (Bishop 1999), For each one of these possible causes American public
schools have implemented comprehensive secondary school reforms that relate to
mathematic content, curriculum and instruction.
The accountability systems of No Child Left Behind have forced states to
write and adopt academic content standards to improve the quality and continuity of
education provided to students. Statewide academic standards provide goal posts for
teaching and learning across all of a state’s public schools. These standards also
drive myriad other education policies. Standards determine the content and emphasis
of tests used to track pupil achievement and school performance; they influence the
writing, publication, and selection of textbooks; and they form the core of teacher
education programs. The quality of a state’s K-12 academic standards holds far-
50
reaching consequences for the education of its citizens, because of the federal No
Child Left Behind Act. The entire accountability edifice rests upon these state
academic standards.
After creating the state academic content standards, policy makers created a
form of accountability to monitor the academic progress nationally. States
implemented assessment programs to determine students’ progress towards meeting
standards. The alignment of these tests to standards varied from state to state, with
34 states assessing all four core areas in 2001 (Hirsch et al., 2001). No Child Left
Behind (NCLB), the educational initiative that began with President George W.
Bush, called for increased accountability for schools and districts through state
standardized tests. This initiative worked to make student data on standardized tests
more relevant and has set a nationwide goal for all students to become proficient by
the year 2014. The creation of content standards and curriculum frameworks that
spiral and adjust from grade level to grade level highlights the entire process (NCES,
2000).
Although accountability systems have been around for decades, standards-
based accountability differed from previous systems in that it focused on outcomes,
not inputs (EdSource, 2000). Standards-based accountability focused the actions of
entire educational system directly on teaching and learning (Elmore & Fuhrman,
2001). Alignment between secondary schools and postsecondary institutions can
help define what students need to know to be successful. This curricular alignment
51
can help prepare students for success in college or the workplace by ensuring they
have attained the necessary skills.
Many states used a wide range of incentives to spur change and improvement
in schools. Schools were held accountable through the coupling of student
performance with rewards, i.e., monetary incentives, public recognition, relief from
regulation; and sanctions, i.e., loss of accreditation, state intervention, takeovers and
reconstitution (Elmore & Fuhrman, 2001; Zradicka & Holman, 2000). The
consequences for poor performance varied among states depending upon the level of
local authority in relation to state authority, the state’s willingness to intervene at
low-performing schools, and the state’s capacity to effectively assist these schools.
New national and state educational policy initiatives have empowered local
capacity to achieve the national goals set forth in mathematics. However, in an
attempt to find research articles, material and curriculum that schools have used to
improve mathematics programs at a secondary school level, one finds, is limited.
There are no methods, strategies or theories as to how to improve mathematics
instruction on the secondary level. School leaders and teachers must use the state
standards and state-approved textbooks in combination with academic rigor to
improve mathematics achievement. The leadership team at school sites are
visionaries attempting to improve the quality of mathematic instruction and student
achievement.
Darling-Hammond (1999) wrote that having relevant data that is easy to
understand for teachers will bring about much needed accountability. By analyzing
52
results from year to year is important to the long-term effects of the reform
(Schmoker, 1999). Data will provide information on how to adjust and intervene
when needed. Data-driven decision making is what districts and school sites use to
improve the quality of instruction, professional development, and also intervention
programs that are necessary for the academic achievement of struggling students.
Professional development efforts in mathematics have had a positive impact on
systemic reform efforts when used as a strategy to improve student achievement
(Taylor-Anderson, Brown, & Lopez-Ferrao, 2003).
Other significant factors that impact students’ mathematic achievement
include: time, class size, professional development, and research-based instructional
strategies. There are many findings that correlate positive results with time and
learning. The amount of time students are in class and finding a school schedule that
is conducive to learning is a constant topic of debate. The University of Illinois-
Chicago found a high correlation between the amount of time spent at school and
student learning. Researchers claim that while time is an important factor for
learning to take place, students must be exposed to a highly engaging curriculum
(Sadowski, 1998). Changes to the organizational structure of the school, i.e., block
scheduling and year-long calendars, effected student learning. Walberg (1987)
consistently found a positive relationship between alternative scheduling and student
achievement. This positive relationship was attributed to increased instructional time,
i.e. block scheduling, or with increased opportunities for teacher collaboration, i.e.
“banking instructional minutes.”
53
Daily scheduling issues in high schools are examined closely to assure
students are getting the greatest educational benefit. Block scheduling has been a
popular reform that challenged school districts to allocate more classroom time for
students in the most critical classes- Mathematics and English Language Arts.
Researchers have found that block scheduling increased graduation rates, lowered
discipline referrals, and improved dropout rates (Queen, 2000).
The benefits of smaller class sizes were the focus of the Student/Teachers
Achievement Ratio research project in Tennessee (Queen, 2000). This study
collected fourteen years of data based on 11,000 students to analyze the effect of
class size on student achievement. At the end of the third grade, the children in
smaller classes were four months ahead of the other children. Queen (2000) found
that class size has a significant change on student achievement if students are
provided with direct instruction and other effective teaching strategies.
In addition to new school designs, many states have adopted innovative math
programs. Since 1983, the "University of Chicago School Mathematics Project
(UCSMP)," funded by Amoco, General Electric, and the Carnegie Corporation, has
developed a six-year secondary mathematics curriculum. This curriculum
encompasses a broad scope of content and emphasizes real-world applications within
mathematics instruction. In focusing on both procedural and conceptual knowledge,
student understanding is developed in four domains: skills, concepts, applications,
and representations.
54
Another state reform effort that incorporates improving mathematics
instruction and student learning is the Oregon State University Calculus Curriculum
Project. This program has developed a curriculum that uses super-calculators (e.g.,
HP-48SX) and emphasizes multiple representations of functions, graphical
interpretations, conceptual understanding, real-world applications, mathematical
modeling, and the intelligent use of technology with full awareness of its limitations.
The use of technology for the students provides opportunities students need to be
successful in a growing technological world of careers.
Many secondary schools modify the traditional high school structure to better
meet the needs of students. One major modification is the introduction of SLCs:
SLCs are small learning communities such as career academies or school-
within a school, break students up into subgroups to provide them an
environment where students are able to develop closer relationships with
teachers and peers. SLCs such as career academies emphasize the
relationship between academies and the workplace and have been shown to
decrease dropout rates and improve work attendance and job performance
(Pluker, Zapf and Spradin, p. 5, 2004).

The SLC’s purpose is to personalize the instructional program by
reorganizing larger high schools into smaller communities of learners. This effort has
been met with mixed results. The reform model of CFL is a model that is focused on
setting high standards for student achievement in the context of building and
maintaining positive self-perceptions. The instruction is developed in tandem with
the characteristics of the individual student and his/her learning needs within the
context of the school and the larger community.
55
The school reform and design there are many factors that play an important
and influential role in the academic achievement of students. One predictor of
student success is the culture of the organization. Research has demonstrated that a
positive and healthy inclusive cultural climate in a school is linked to student success
and the opposite is true as well, in that negative learning environments have a
detrimental impact on students (van der Westhuizen, Mosoge, Swanepoel, Coetsee,
2005).
The leadership of the school ultimately creates a collaborative school culture
on student learning. The leadership skills are an essential and leaders must build the
capacity of all stakeholders in the school site and community. Remarkable leaders
possess solid knowledge and understanding of policy and initiatives that are guiding
the school reform. They also possess strong pedagogical content knowledge, which
allows them to improve the quality of instruction. To embark on this aspect of school
reform requires that support is offered to meet the individual needs and that models
that increase the awareness of what “best practices’ the school is embracing through
its reform effort is fundamental to the improvement of student learning; everyone
must know the vision of where they are going and why (Leithwood, Louis,
Anderson, Kyle 2004).
Role of Leadership
It is the leader who demonstrates a willingness to extend themselves beyond
the boundaries of expectations that are quite often the effective leaders; these are “
the non-compliers” (Meier, 1995). To achieve the objectives of moving all kids
56
forward and improving achievement they must challenge the status quo of our
educational institutions and have convictions that are such that they are willing to
challenge the day to day behaviors of our teachers, students and administration
(Wagner & Kegan, 2005, pg 14 ).
It is still a belief that the Principal is the instructional leader not the merely
the manager of their school. This is often a goal that is unrealized on a day to day
basis as the functions of the school Principal can become mired in the more mundane
activities as addressing concerns and relationships with the parents and the
community, handling the many crisis’s that are part of a regular school day all of
which takes them away from the classroom (Fink & Resnick ,pg 1).
The characteristics that the leaders need to have are described by Fullan
(2001) as five core competencies;
• Broader moral purpose- Leaders must have the capacity to inspire
and motivate people to accomplish the challenges inherent in urban
school reform. They must have the skills to work with a broad group
of contingencies in a consistent, fair and equitable manner when
implementing the reform.
• Keeping up with and understanding the change process- The leader
must be familiar with and comprehend the change process and
dynamics of change; approaching challenges with creative processes.
Through the change process the leader must have the capacity to
57
reculture the community in a safe environment in an effort to keep
moving forward with change.
• Cultivating relationships- The leaders must have the capacity to
establish and support good relationships across all of the unique and
diverse groups of the school environment; fostering a community
spirit.
• Sharing of knowledge- This must be a core value of the leader;
sharing of knowledge and information creates a more inclusive effort
where people are informed, engaged and active participants. The
leader must establish protocols and procedures to facilitate this.
• Creating coherence- A common challenge for the urban school leader
which offers so much diversity is bringing everyone together as a
collaborative group that can work as a group with a coherent vision
and action plan.
Educational leadership is key in the context of new policy, initiatives, and
designs. The Interstate School Leadership Licensure Consortium (ISLLC) has
researched and combined the standards-based oriented age and developed six key
elements that facilitate the contemporary visions of school leadership. These
elements are: 1.) Facilitating shared vision, 2.) Sustaining a school culture
conducive to student and staff learning, 3.) Managing the organization for a safe,
efficient, and effective learning environment, 4.) Collaborating with families and
community members, 5.) Acting with integrity, fairness, and in an ethical manner,
58
and 6.) Influencing the larger political, social, economic, legal, and cultural context.
These standards are now the guide in principal preparation programs and its origins
where found in practicing effective principals (Lashway, 2003).
Instructional leaders of standards-based high accountability schools are no
longer able to shoulder all the schools’ instructional responsibility. Effective leaders
are able to provide, “coherent instructional vision, rigorous standards, use of data to
make decisions, emphasis on professional development, the creation of learning
communities, and the clear demonstration-through behavior as well as words-that
principal is fully engaged with classroom instruction (Lashway, p 5, 2003). School
leaders are change agents:
A change agent is a person who leads a change project or business-wide
initiative by defining, researching, planning, building business support and
carefully selecting volunteers to be part of that change. A change agent must
have the vision to state the facts based on data, even if the consequences are
associated with unpleasantness” (Bhardwaj, 2003).

Effective school leaders create collaborative learning communities. Leaders are able
to sharpen their own skills, develop teacher leadership, find resources to support
professional community growth, give teachers the confidence to grow, and manage
the leadership agenda systemically.
The instructional leader is able to foster and cultivate this environment
through genuine personal warmth and authentic interest in supporting the total
student not just the academic aspects of the student (Cotton, 2003 pg 8).
It is the leader who demonstrates a willingness to extend themselves beyond
the boundaries of expectations that are quite often the effective leaders; these are
59
“the non-compliers” (Meier, 1995). To achieve the objectives of moving all kids
forward in their achievement they must challenge the status quo of our educational
institutions and have convictions that are such that they are willing to challenge the
day to day behaviors and belief structures of our teachers, students and community
(Wagner & Kegan, 2005).
The instructional leader must be secure and certain of their convictions and
belief in what their vision is for the school and how this will transform a school
through improved instruction and school culture that results in student achievement.
Effective leaders are the moral center of the education community. They are able to
listen to the voices of teachers, parents, and students. They balance accountability
against responsibility. They protect the educational community’s “lifeworld”. “The
“lifeworld” consists of the values, beliefs, and purposes that knit the school
community together and give significance to everyday activities” (Lashway, p.8,
2003). The facts indicate that the role of the instructional leader extends to creating
an environment that is not only rich in academia but one in which the school leader
has the capacity to keep many balls in the air creating a learning environment with
agreed upon standards for student behavior and as such providing a learning
environment that is safe, orderly and effective.
Effective leaders also respond to challenges. They constantly scan the
environment for new ideas, tools and solutions, and reflect on the implications. They
attend to the learning of all members of the education community. They explore
current practices, beliefs, and assumptions that serve as a basis for posing inquiry
60
questions. “These questions are signposts in the hunt for evidence and the struggle
with dissonance. Dissonance is tackled in dialogue, thereby lowering defenses and
increasing shared understanding” (Lashway, p. 9, 2003).
Strong leaders are able to provide quality instruction by offering professional
development that is organized around the collective participation of teachers, focused
on active learning activities where teachers applied their new learning, and
coherently linked teachers' professional knowledge with state and district standards
and assessments. The professional development needs to be based on the five
following principles:
• Organized around collective problem solving
• Included follow-up support
• Used information on student outcomes, instruction, and lessons
• Focused on understanding theories underlying knowledge and skills
to be learned
• Connected to the overall school change process
The Effect of Dynamic Leaders
Dynamic educational leaders are those who can create and maintain quality
instruction in classrooms. Quality instruction has a profound effect on a student’s
achievement (Marzano, Pickering & Pollock, 2001). Marzano’s Classroom
Instruction that Works includes a meta-analysis of the research conducted on the
effectiveness of nine instructional strategies, along with a thorough description of the
nine instructional strategies, with suggestions for the practical application of each.
61
There are studies on instructional strategies used in K-12 classrooms, which
demonstrate the positive impact of nine instructional strategies on student
achievement as measured by standardized test scores.
Although, socioeconomic status, race, school scheduling, and class size have
a demonstrated an impact on student achievement, the benefit of a quality teacher
was found to be the strongest predictor of student performance (Ferguson, 1999).
Quality teachers are created by on-going and meaningful professional
development opportunities available to teachers in order to improve their instruction.
High-quality, research-based professional development is essential for improving
instruction in ways that will impact all students’ learning (Marzano, Pickering,
Pollock, 2001). Students who attended class with high quality teaching learn more
and have been found to average 23 percent higher on standardized tests versus those
students who attend school with poor teacher quality (Marzano, Pickering & Pollock,
2001). While effective teachers are able to raise student achievement with all
socioeconomic and ethnic sub-groups, ineffective teaching results in students with
lower scores on standardized tests (Marzano, Pickering & Pollock, 2001).
National Commission on Teaching and America’s Future (Darling-
Hammond, 1996, p. 102) recommended the following.
Our schools need to be redesigned so that they honor teaching, respect
learning, and teach for understanding. To be able to direct their energies around a
common purpose, schools need to adopt shared standards for student learning that
become the basis for common efforts of teachers, parents, and the community. Then,
62
schools must structure their work so that teachers can work more intensively with
students and with each other and can have greater influence over the design of the
learning experiences their students encounter.
Burney (1997) found that the major influences on teachers’ instructional
practices were demonstrated from participation in curriculum-specific professional
development, collaboration with peers, support from leadership, and time during the
workday to address the issues of instruction. Effective professional development
training is curriculum-specific, connected to pedagogy, and extended in time. The
educational leader provides meaningful professional development activities that are
based on analyses of standards and actual student performance and engaging to
teachers and addressed their needs as learners. People learned best through active
involvement and reflection on what they learned (Resnick, 1999). With strong
professional development teachers are able to reflect upon their practice and refine
their instruction to best meet the needs of their students.
Along with professional development, another powerful form of teacher
learning came from educational leaders providing a professional learning community
(Darling-Hammond & McLaughlin, 1995). There are five important characteristics
of learning communities (Elmore, 2000). 1. Shared values and vision that enables a
staff to maintain a consistent focus on improving teaching and learning. 2. Collective
learning and the search for new research-based strategies to positively impact the
educational core. 3. Shared leadership empowered staff that assumes new roles and
63
shared power. 4. Supportive conditions improved teaching and learning. 5. Shared
personal practice facilitated collective responsibility for student learning and success.
One of the most important obstacles to improve student achievement in the
United States is overcoming teachers’ low expectations for students. Research
suggests that low expectations are not just students who are poor and come form
minority backgrounds but most of American students. In order to increase United
States’ educational and economical position in the world, the National Commission
on Educational Excellence recommended raising the expectations for teaching,
teacher education, and performance standards. Many educational leaders are using
Resnick’s cognitive constructivism teaching to improve their quality of instruction
and simultaneously raise their expectations for students.
Cognitive constructivism was a fundamental premise in standards-based
reform. Hall and Resnick (2000) articulated the research-based components of the
blended cognitive constructivist position required for effective instruction that
allowed all students to reach high standards. “Principles of Learning” guide quality
instruction and curriculum in the following manner.
• The teacher utilized a rigorous, articulated curriculum that progressively
increased students’ understanding of core concepts, without needless
repetition, so that students’ engaged in high-level thinking and active use of
knowledge.
• Within the classroom, the teacher facilitated meaningful dialogue that
reinforced the students’ ability to use and create knowledge.
64
• The teacher clearly communicated learning expectations in the form of content
standards and performance standards, requiring the social assimilation of
those standards.
• Metacognition and the responsibility for personal learning were taught through
scaffolded learning experiences.
• The teacher assumed the role of mentor and coach, modeling new behaviors to
student apprentices who then practiced and reflected on their new learning.
• Everything within the classroom and the school encouraged and supported the
virtue and benefits of increased student effort, including fair and credible
evaluations and recognition of accomplishments.
Massell (2000) identified interpreting and using data as one of four primary
capacity-building strategies used by school districts. Data is used to plan professional
development activities, identify achievement gaps, align curriculum and instruction,
assign and evaluate personnel, and identify students for remedial programs (Massell,
2000). Along with this increased use of data come challenges related to providing
greater understanding of how to use data to improve performance; managing and
understanding an overwhelming amount of data; and, moving teachers from viewing
performance results as a product of curriculum alignment to using data for analysis
of their own instructional strategies (Massell, 2000).
Data-driven decision-making is used to directly inform the development and
practice of instruction. By using formative and summative tests teachers work in
grade-level teams to find out areas of concern in student achievement. Darling-
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Hammond suggests that this new paradigm in public education policy shifts
policymakers' efforts from designing controls to developing capacity among schools
and teachers to be responsible for student learning and to be responsive to student
and community needs and concerns. This new paradigm must include a collective set
of goals for the entire school campus. All stakeholders need to be included in the
decision-making processes to improve the quality of education for all students from
every sub group. The process of change and reform is on going with professional
development, teacher collaboration and self-reflection. By using the strategies that
are in effect and continuing to hold high expectations for all students school sites
continue to make significant gains in student learning.
Blasé and Blasé(2004) promote that schools should be learning environments
for all students and educators and the facilitation of learning and growth should be
the number one responsibility of the educational leader. Instructional leaders can
facilitate empowerment on their campus with reform. Blasé and Blasé propose that
practitioners develop supervisory platform that includes building trust, empowering
teachers and fostering reflection. “The process of reflection, undertaken in an
environment based on trust and seeking the empowerment of participants, constitutes
a powerful potential for improved teaching practice” (p. 277).
Instructional leaders are providing structured professional development that
offered cutting-edge, research-based practices related to what teachers were doing
and provide schools with strategies to improve their practice (Grossman, Thompson,
& Valencia, 2002; Marsh, 2002). In District #2, New York, professional
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development was used as a management strategy for teachers and principals when
mathematics reform was implemented. Teachers were taught to share and reflect on
lessons while principals were taught what to look for in a lesson (Stein, 2003).
Professional development is used as a resource to empower teachers and to
build administrator leadership capacity. Having a combination of diverse individuals
working together toward common goals will support the district’s vision and it
provide the learning community with coherence. A key component of the
professional development is to assess the extent to which teachers use the adopted
district-wide curricula and approaches of the mathematics program, which required
principals to play a strong role in the process. Administrators will attend the same
training as teachers to learn what to look for when they entered classrooms and to
improve their personal instructional leadership skills (Elmore & Burney, 1997).
Darling-Hammond expresses that ambitious learning requires school
structures that provide time for the more complex teaching and relationships that
give serious ongoing assistance to learners. Blasé and Blasé illustrate how successful
principals provided planning time as one major way to encourage the development of
formal instructional and curricular collaboration among teachers Building an
atmosphere and processes of democracy and culture of learning among teachers and
administrators is key to promote a quality professional development ( Blase and
Blase, 2004). Burney (1997) found that the major influences on teachers’
instructional practices were demonstrated from participation in curriculum-specific
professional development, collaboration with peers, support from leadership, and
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time during the workday to address the issues of instruction. With effective
professional development there will be improved student achievement for all
students in the school population. This effective professional development training
needs to be curriculum-specific, connected to pedagogy, and extended in time.
It is found in research that school reform efforts do not happen over night,
they take many years to create and foster. In order for an effective leader to make a
real impact in school reform it takes many years of consistent effort to create
sustainable changes and improvement in student achievement and learning (Murphy
& Datnow, 2003; Borman et. al., 2002). Strong school leaders need time to foster
and create a school climate with a vision that fosters student achievement.
Effective instructional leadership is viewed as critical in a school’s success.
Having the ability to communicate a vision, build internal capacity, create an
atmosphere that includes academic rigor and carry out the duties effectively is
seemingly lacking when it comes to mathematics achievement. School-based
administrators and district leadership alike, continue to struggle in defining the
characteristics that, in the context of improving math performance for students, that
create good instructional mathematical leadership. Several issues seem to be
especially relevant to instructional leadership in this setting. Leaders often do not
have strong pedagogical content knowledge in mathematics education; yet need to
carry out functions related to fiscal, personnel, organizational leadership, data
analysis, and review, etc. Due to the limited amount of research in this area of
secondary mathematic achievement, it is imperative that we address and study this
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issue. In an era of high accountability it is necessary to investigate the role of an
instructional leader in developing a culture of high student achievement in
mathematic achievement.
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CHAPTER THREE
Research Methodology
This chapter outlines the methodology used in this study. It begins with an
overview of the school being researched, followed by a detailed description of the
research design, sampling criterion and process, and methodology used for data
collection and analysis. The study investigates the best practices, organizational
structure and leadership in an urban high school that has produced and maintained
high student achievement results in mathematics for at least three consecutive years.
The study will also research specific programs, curriculum and any policy that
contributed to the improved math results. The purpose of this study is to learn more
about how urban high school leaders successfully bring together policy initiatives
along with the best practices to improve math performance in their schools.
The study’s particular importance has to do with carefully examining how the
school’s leadership marshaled resources that led to improved student achievement
for sustained academic growth. Many school leaders often do not have strong
pedagogical content knowledge in mathematics, therefore this study examines how
these leaders carried out functions related to fiscal management, personnel,
organizational leadership, and data analysis to successfully bring about the growth
they sought in math achievement. A Southern California high school was selected
for this study using the school profile instrument that only identified schools based
on a set criteria, which will be described later in this chapter. Data from student
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achievement, teacher and administrator surveys and questionnaires, and interviews
were used to examine the following research questions:
1. What was the pattern of Math achievement for various students at the
school?
2. What Policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement in the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. How was instructional leadership important in improving a) the math
programs/strategies and b) math achievement among students?
5. How did instructional leaders respond in academic areas in which they
were not experts?
To support the case study a mixed methods approach was utilized to collect
the data to support the study. This included the gathering of quantitative data to
support the descriptions found through the qualitative data collection in the study.
The qualitative approach provided data and information from interviews; and the
analysis of documents and artifacts of the school were cross referenced as a means of
gathering findings.
Conceptual frameworks were used to provide context for the reader and
support the analytical style used in this study. Evidence found in document analysis
was cross- referenced with interview and questionnaire findings wherever possible.
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Triangulation was used to verify and support findings. This entire case study process
is intended to add to the reliability of the findings made in the study. All information
about the school and participants is factual, but pseudonyms were used in all cases to
protect anonymity and maintain confidentiality.
Sampling Criteria and Process
This case study’s goal is to identify urban high schools that serve
economically disadvantaged and cultural diverse student populations with program
and leadership features of excellence in mathematics. A purposeful sampling process
was used in order to provide an opportunity to conduct a thorough investigation and
to explore more deeply the processes related to the research questions of this study.
Selected schools were chosen through a purposeful sampling developed by the
research team and principal investigator using 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
6. Leadership stability as defined by a Principal being at the school for at least
three years during the time the improvement was made.
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Research team members reviewed the list of schools that were identified
based on the criteria above. The eleven members in the cohort group led by Dr.
David Marsh, Associate Dean of USC’s Rossier School of Education, worked
together to develop the sampling criteria, and then to identify schools in southern
California that met those criteria. The research team began meeting as a collaborative
cohort model in January of 2006. The team worked together to research questions
and the relevant academic literature was discussed in preparation for this study. The
team continued to meet through the summer of 2006 and into the beginning of the
2006-2007 academic year at which time individual researchers commenced their
detailed studies at their chosen sites.
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 (see Appendix B).
3. Knowing that the group would need to research improvement in CST in
Algebra in a later step and that many schools would not have demonstrated
improvement, the group set a goal of a sample size of no less than 100
schools in the southern California region.
4. Preliminary efforts to use more stringent requirements did not yield a
sufficient sample so adjustments had to be made. For example, when the
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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
5 or higher. The sample population then rose to a satisfactory level of 110
schools in the southern California region.
6. Students in the group were then assigned to research 10 schools each by
looking up and recording CST scores in Algebra I for the years 2003, 2004
and 2005 onto a common spreadsheet which one person in the group
compiled.
7. The group then assigned an absolute value to the improvements made in two
areas. First, decreasing the number of students scoring in the bottom two
performance bands; and second, increasing the number of students scoring in
the top two performance ands. These totals were added to indicate an overall
level of improvement. For example, if a school decreased the numbers of
students scoring in the bottom two performance bands by 3% 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:
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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.
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.
A flyer was distributed to all potential participants of this study, which
included a detailed description of the research procedures, purpose of the study and
also indicated that participation in the study would remain anonymous and was
entirely voluntary. A recruitment letter approved by the university’s Institutional
Review Board (IRB) was sent directly to potential participants following the
distribution of the initial flyer. Recruitment letters for teachers were placed in their
individual mailboxes, and clearly stated that participation in the study was
completely voluntary. Teachers returned a signed letter indicating whether or not
they desired to be part of this study without any involvement from their principal or
any other superior. A returned signed letter denoted agreement to participate thus no
further consent letters were necessary.
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The subjects involved in this study were limited to teachers, administrators,
and some support staff. Subjects in the teacher category were identified for
participation based on their response to the recruitment letter given to them early in
the process. The subjects consisted of all math teachers and other teachers who
appeared to have a leadership role at the school. If and when the educational
professional agreed, S/he was provided with a recruitment letter specifying the
purpose and process for the study.
All site administrators and key teacher leaders were interviewed using the
interview guide attached as Appendix C. The school site’s math instructors were
asked to complete a 48 item teacher questionnaire (See Appendix D). The results
from the teacher questionaires provided the researcher with data about teacher
perceptions and classroom experiences related to issues of the research questions
being studied. All teachers at the school site who were not math teachers completed
a shorter questionnaire designed to get their impressions about school-wide factors
that might be linked to the research questions.
Participation was completely voluntary and all participants were assured that
due efforts would be made to ensure confidentiality and anonymity. Participants that
were interviewed were scheduled for at least one interview, while some key leaders
were interviewed more than once for follow up and additional questions related to
leadership and providing staff development and support. All interviews were held on
campus and in an environment that ensured confidentiality.
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As the Principal Investigator I visited the school research site 10 times during
September 2006 and March 2007. Each visit to the site lasted approximately seven
hours. The visits included interviews and other research activities related to this
study. The Principal Investigator, Co-Investigators and Graduate Student Research
Assistant met formally at least monthly to evaluate and discuss research findings
gathered at individual research sites. There were ongoing meetings that also took
place between the Principal Investigator and Co-Investigators to insure that deadlines
were met while following the protocols of effective research. This combination of
investigation, collaboration and discussion provided adequate time to conduct and
complete the research at each of the high school sites selected for this study.
Selected School Profile
The high school that was selected for this study is Valley High School in the
Valley Unified School District. Valley High School is located in the San Fernando
Valley in Los Angeles County in Southern California. The district is approximately
20 miles from the beach, 30 miles from the local mountains and approximately 10
miles north of the city of Los Angeles. The community is a well established
community with many generations remaining; there is stability. The district is
comprised of mainly “working class” families.
The Valley Unified School District mission is that “in partnership with
parents, families, students, and community, the district guarantees the effective use
of all available resources to create, provide, and support quality instructional
programs, services, and environments. Every student will develop the skills,
77
knowledge, attitudes, and behaviors in order to be a responsible, productive citizen
and a lifelong learner in a diverse and changing global society.”
Valley High School is a comprehensive high school. Originally, Valley High
was a junior high school from 1928-1947. It became a high school in 1948. The high
school has a population of approximately 2340 students in grades 9 through 12.
There are 105 faculty members, 5 administrators, and a support staff of 52, including
4 counselors, secretaries, nurses, teaching assistants, custodians, cafeteria workers,
and campus supervisors. The school operated under a single principal model until
1998. From 1998-2001, the school operated under the co-principal model, with three
assistant principals. In the fall of 2001, Valley High) returned to the single principal
model with four assistant principals.
One of the features that is unique about Valley High School, and which some
believe is a major component of its success, is the connection staff members have
with the school and community. Several of the teachers and staff live in the city, and
12 graduated from Valley High. Approximately 43% of the faculty have earned a
master's degree or higher, and approximately 20 members of the faculty are bilingual
(English-Spanish) and 43 are certified with CLAD or SB 1969 training.
The official four-year graduation rate for Valley High students is 98.4%.
Twenty percent of the senior class of 2003 completed the a-g requirements for
entrance into the University of California . The students have gained entrance into
MIT, Harvard, Stanford, Occidental, University of Southern California , and most of
the University of California schools and various California State Universities. About
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45% of Valley High School students continue on to a post-secondary education. The
school has decreased its drop out rate each year for the past five years and currently
the drop out rate is 3.8%.
The ethnic composition of the students closely resembles the community at
large: 53% White, 38% Latino, 7% Asian/Pacific Islander, and 2% African-
American. Approximately 10% of the students are English Language Learners
(ELL), which is much below the county average.
Valley High School provides several unique educational programs. During
the 2003-04 school year the Freshman Village was inaugurated on the second floor
of the new administration building. There are 22 classrooms, which comprise the
village where ninth graders take 95% of their classes. The goal of the Freshman
Village is to provide a smooth transition for students into high school and to give
them a sense of belonging. Valley High School features a strong Business Academy
that provides job shadowing, apprenticeships and project based learning. The Multi-
Media Communication Arts Academy features broadcast journalism, video-
production, photography, journalism, screenwriting, and web page design. The
school has a renowned performing arts program with instrumental and vocal music,
dance, and drama. Many extra-curricular opportunities exist such as Mock Trial,
Odyssey of the Mind, and Academic Decathlon.
The philosophy of Valley High School is to provide encouragement and
support to assist students to achieve at high levels. This educational philosophy is
reflected by their Academic Performance Index of 742. Valley High School’s
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mission statement is that they seek to create a learning environment where students
succeed academically, socially, and vocationally. The result of their mission is to
see that students at Valley High distinguish themselves by their superior conduct and
character. Students are held to the highest standards not only in their academic
pursuits, but also on the athletic field as well as in their social interactions.
Academic integrity, appropriate speech, and punctuality are the established goals,
which the students must strive towards.
Valley High School’s mission is to prepare students for academic, vocational
and personal success as active citizens in a democracy. It is a school that is
supportive and responsive to the needs of our students; the community provides
positive role models for our students and has high expectations for excellence.
Student Achievement
Valley High School’s commitment to ensuring a quality education is
demonstrated in the consistent growth on their API scores, the school has increased
their API scores 72 points over the last four years with a baseline score of 670 and an
API score of 742 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 four years

2003 2004 2005 2006
670 717 737 742

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The school profile (Appendix A) contains most of the demographic and
student performance data that lead to the final selection of the research sites. The
first section of the school profile centers on demographic indicators such as school
size, ethnic breakdown, percent of students receiving free or reduced lunch and other
subgroup data as defined by AYP. The California Basic Education Data System
(CBEDS), and the School Accountability Report Card (SARC) were sources used to
find important data. The next part of the school profile focused on the human
resources available at the school, which provides valuable information on the
average years of experience of the teaching staff, compliance with NCLB highly
qualified teacher standards and the number of years each teacher has been employed
by the school. Administrator data is also part of the school profile and centers on the
number of years the leader has been a school site administrator, the number of years
at the high school, and background experience in math.
The final section of the school profile deals with data on student
performance. Data was located on the California Department of Education’s
Website, College Board reports, SARC, and the school’s master schedule. Student
performance data includes graduation rate, percent of student scoring proficient in
math, percent of students taking the College Board SAT exam, the percent of
students meeting A-G college entrance requirements and other student achievement
data. All of the data collected in the school profile is relevant to the literature related
to school reform and effective math programs.
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Participants in the Study
The literature on instructional leadership and effective math programs
identifies instructional leaders not just as school principals, but as other
administrators or teachers who emerge to take on the role of leading a successful
program. Participants that volunteered to participate in the study were rich sources
of information relative to the research questions being examined.
The following individuals participated in the study and provided valuable
information as it relates to the research questions being examined for this study:
The administrative team at Valley High School is comprised of a Principal,
three Assistant Principals and four Guidance Counselors. For the study the Principal,
the Assistant Principals, and Guidance Counselors participated in the interviews. In
addition to the mathematics teacher leaders, math teachers and other subject area
teachers were interviewed or completed a questionnaire.
As a means of collecting data structured interviews were facilitated by the
researcher. The researcher conducted one to three interviews with each identified
interviewee in an effort to gain in-depth information and understanding. The
interviews were conducted at the school site and were based upon the Case Study
Guide which had its foundation in current educational research. The study was
conducted in a manner that provided for triangulation of data from multiple sources.
This is important when conducting qualitative case studies as a means of addressing
individual or cultural biases that can influence the validity and reliability of the
study. In addition to interviews and questionnaires, document analysis provided
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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.
Site Administrators. The school site principal serves as the primary
instructional leader on a high school campus. For the purposes of this study the
principal was interviewed on more than one occasion in an effort to collect detailed
information and perceptions about how the school achieved improvement in
mathematics. The principal relies tremendously on his or her assistant principals to
carry out the day to day logistics of program implementation, staff development, and
curriculum/instruction. Assistant principals were interviewed and were the subjects
of surveys in order to help determine the degree to which implementation and staff
development matched policy. The assistant principals also provided a bridge
between the vision for curriculum and instruction provided by the principal, as well
as staff development opportunities and the pedagogical practices carried out in the
classroom.
The school Principal completed the survey and the interview (s). The
Principal was very clear in communicating the vital role that the Assistant Principal’s
play in the facilitation of the school vision and the consequent improvement in
student achievement. As such the Assistant Principals were interviewed to both gain
additional information and to assess the degree of continuity between the different
administrators.
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Teacher Leaders Teacher leadership is a key component in this study and
several teacher leaders participated in the study including (a) the mathematics
department chair, (b) leadership team members, (c) resource teachers, and (d) data
coaches. It also included the other teachers that are part of the site leadership team.
They were selected to participate in the study based on their roles at the school
providing instructional support for the math department and leadership for the other
core content areas.
Math Teachers Classroom math teachers are the keys to successful
implementation of educational policy and are in the best position to have a feel for
how well practice is meeting expectations. Classroom math teachers were
interviewed in order to learn about their practice and perceptions related to the
instructional program at the school, staff development provided and administrative
support given to them in order to improve their instruction.
Twenty Four of the 29 math teachers participated in the study; all 24 math
teachers completed the survey and 16 of them were interviewed. The collective
teaching experience of the math department ranges from very new, with only one
year of experience, to veteran status for four teachers who have been at the school
for the past 25 years. The majority of the teachers have been with the school for five
to seven years. The ethnic make-up of the math department corresponds with the
student representation. The department is comprised of two Asian, nineteen
Caucasian and eight Latino teachers. The math department teaching staff is 15%
female and 75% male. Of the twenty-nine teachers in the department, 28 are fully
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credentialed in math and one is in an internship program working towards this
objective.
Teachers All core teachers (71 in total) were given a questionnaire to
complete; this questionnaire was different from the one given to the other participant
groups. Of the surveys 70% were completed and returned to the researcher. The
purpose of involving all teachers across the school was to gain a broader perspective
of the school and strategies, programs and policies that have been implemented over
the past three years that the teachers perceive as having positively influenced the
math achievement of the students at Valley High School.
The study utilized mixed measures to conduct research on the school site.
Research was conducted in a manner that allowed for triangulation of data from
multiple sources. Triangulation is especially important in qualitative case studies
where individual or cultural biases can present challenges to validity and reliability.
The purpose of involving all teachers across the school was to gain a broader
perspective of the school and strategies, programs and policies that have
implemented over the past three years that the teachers perceive as having positively
influenced the math achievement of the students at Valley High School. Additional
interviews were conducted with teachers who were selected randomly from different
content areas across the school. The purpose of this was to learn about their practices
and perceptions on a deeper level and to understand how they believed these related
to the instructional program.
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Instrumentation
The instrumentation used in this study was developed collaboratively by
eleven members of a dissertation cohort at the University of Southern California.
These Doctoral candidates met regularly during the Spring and Summer of 2006 in a
research seminar led by Dr. David Marsh, Associate Dean of Academic Programs
and Professor of education at the Rossier School of Education. The class
collaboration included open-ended discussions of the topics to be covered in the
study and how best to gain the data necessary to address the research questions noted
above. Four data collection instruments were developed by the research team in
order to collect data and to interpret it by way of the conceptual frameworks. The
conceptual frameworks were created as a foundation for research and the
overarching principles found in the academic literature that have proven to improve
student achievement at a secondary level. The school profile, teacher interview
guide, key leader interview guide and teacher questionnaire were the research tools
employed to gather and interpret the data. The collaboration also included working to
identify the relationship between the research questions and the data collection
instruments to ensure maximum efficiency in the data collection process.
Table 2 depicts the relationships between the various data collection
instruments used in the study and the research questions examined. The teacher
questionnaire (Appendix D) consists of 48 questions using a five point Likert scale.
The questionnaire is divided into four sections each addressing research questions
two, three, four and five. The questions in this instrumentation tool ask teachers to
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rate the school’s effectiveness based on their own perceptions of school-wide
practices, policy initiatives and the school’s math program and leadership.

Table 2: Relationship of Data Collection Instruments to Research Questions
Instrument Research Question
1 2 3 4 5
School Profile X X
Key Leader Interview X X X X
Teacher Interview X X X X
Teacher Questionnaire X X X X

Conceptual Frameworks
The research team members collaborated to develop instruments through a
process grounded in conceptual frameworks that identified key components of the
major themes associated with the research questions. Four frameworks were
developed, each guided the process of developing data collection instruments and
appropriate questions associated with each instrument. The frameworks assisted in
maximizing efficiency in the data collection and analysis process.
Framework for Research Question 1: School Profile of Student Achievement Data
Research Question One asks about the pattern of mathematic achievement for
various students at the school. The school profile detailed above served as the
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framework for research question one in that it provided a template for identifying
areas of student achievement in math where quantifiable data was available for
analysis. Appendix E includes the relevant achievement data that was used in the
researcher’s efforts to identify the pattern of student achievement in math at the site.
Frameworks for Research Question 2: Effective Math Programs and School Design
Research Question 2 asked about the policy initiatives, curriculum and
instruction and related conditions that are related to improved math achievement in
the school. Two separate frameworks were developed to help in the analysis of this
research question. The first is a framework describing effective school design. The
elements of this framework consist of Marsh and Codding’s model of school design .
The School Design conceptual framework is made up of four areas: curriculum,
school culture, learning activities and student performance assessments. The basic
elements are reflected in Figure 1. The framework emphasizes curriculum
foundations built on student-centered approaches and outcomes. School cultures that
enhance effective school design are those that have meaningful interactions between
students and staff, ongoing professional development and enhance learning
opportunities. Small school size is another essential feature of Marsh and Codding’s
design. Learning activities that challenge students to use higher order thinking
skills, solve problems and collaborate are also an integral component of the
framework. Finally, the framework includes student performance assessments
rooted in effective communications, problem solving and which emphasize
conceptual understanding.
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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

Framework for Effective Mathematics Instruction
The second framework deals with the elements of effective math programs
and is depicted in Figure 2. Essential elements included in the framework begin with
a student-centered curriculum that emphasizes conceptual understanding that
ultimately leads to an in-depth mastery of computations and manipulations of
mathematical symbols and procedures as tools in the problem solving process. The
framework also incorporates rigorous, standards-based practices based on content
standards and assessments being closely aligned, along with data-driven decision
making at the site. This framework also depicts how model math programs rely on
coherent and effective classroom pedagogy that includes sound lesson design, makes
89
use of prior knowledge, is culturally relevant, and focuses on on-going assessment.
Effective classroom pedagogy promotes high levels of student engagement.

Figure 2 – Effective Math Programs

Framework for Research Question 3: The Change Process
Research Question 3 asked about the change process used by the school to
enhance its math program and about strategies used to assist students in math. Blasé
and Blasé (2004) emphasize that a primary characteristic of an effective instructional
Effective
Math
Programs
Classroom Practices

 Effective and
coherent lesson
design
 Promotes high
levels of student
engagement
 Makes use of prior
knowledge
 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
 Assessments
aligned to standards
 Student
achievement data
drives instruction
and decision
 Common
performance rubrics
through
collaboration

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leader is the ability to understand and embrace the challenges of change. For
instructional leaders to effectively manage the change process, it is important for
them to posses an intimate knowledge of how the change process works from
individual and organizational points of view.
Bolman and Deal’s Reframing Organizations (2003) provides leaders with an
useful framework for addressing the diverse aspects of complex organizations as
they manage the change process and is detailed in Table 3. The authors do this by
detailing four distinct frames from which to view the operation of their organization:
(a) structural, (b) human resources, (c) political, and (d) symbolic. These four
frames were used to better understand and categorize the site’s efforts to bring about
increased student achievement in math. Such efforts were described in terms of
these distinct areas of practice.

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

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The structural frame emphasizes rules, roles, goals and policies. The
effective leader aligns such elements to the goals of the organization and the
objectives of the change initiative. Common obstacles to effectively change in this
frame include a loss of clarity about one’s role, confusion and chaos. Good
communications and realigning policies to support and clarify roles is an effective
means that leaders can use to overcome these challenges to achieving successful
change.
The human resources frame involves creating a fit between people and
organizations. When these two elements are effectively aligned, organizations thrive
as their employees work with energy and enthusiasm. Thus, organizations are
effective in this area gain a competitive advantage that is created by talented and
motivated employees. The human resources frame also emphasizes individual needs
and relationship building. Without these elements in the workplace, employees tend
to withdraw, become indifferent, passive and apathetic. They also may restrict
output, resist change and otherwise sabotage the organization (Argyris, 1964).
Effective human resource leaders encourage participation and provide psychological
support to all employees.
The political frame emphasizes power, conflict and competition. According
to Bolman and Deal, every significant organizational process is inherently political.
This is true since organizations are comprised of disparate interests competing in an
“arena” for control over power and resources. Effective leaders in today’s public
schools need to be able to deal with diverse constituencies such as labor unions,
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school boards, parent organizations, community groups and classroom teachers.
Each of these groups often have different points of view on issues of importance to
education. Successfully negotiating these differences and forming alliances may
prove critical to a leader’s ability to implement change effectively.
The symbolic frame emphasizes the need for cultural competency. Effective
leaders are those who deal well with rituals, ceremonies, and other ways of building
meaning within the school setting. Effective use of metaphors and stories can be a
powerful way for leaders to address objections and create buy-in and ownership.
Creating rituals to transition to new ways of doing things while working to celebrate
the past may prove effective in overcoming the inertia frequently associated with
today’s public high schools.
Framework for Research Question 4: Instructional Leadership
Research Question 4 asked how instructional leadership had helped to bring
about improved math strategies and programs as well as student achievement in
math. Figure 3 depicts the conceptual frameworks used in this study in support of
concepts associated with instructional leadership. Blasé and Blasé (2004) outlined
three basic components of effective instructional leadership. First, instructional
leadership involves activities that are directly related to classroom instruction and
others that foster necessary foundational elements of school-wide practices that are
conducive to effective classroom instruction. First effective instructional leadership
involves talking with teachers in a collaborative manner in order to build trusting
relationships. This element involves such activities as peer coaching, direct
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observation of instruction and high visibility. This also implies helping build a
culture of inquiry where teachers learn to reflect on their craft. Finally, this element
of effective instructional leadership is also about promoting continued professional
growth for teachers. Inherent in this process is building the climate of trust that is
necessary to encourage risk-taking and innovation.
The role of the instructional school leader is demanding and diverse in terms
of the demands and expectations of what the leader is responsible for engaging in,
facilitating and the leadership they must provide in moving a school forward and
improving student learning. The Educational Testing Services (ETS) published, “A
Framework for School Leaders: Linking the ISLLC Standards to Practice” which
identified standards for what the instructional leader must demonstrate an
understanding for and knowledge of.
The instructional leader must be the “keeper of the vision” of the school and
the larger district for student learning through the daily activities of the school. The
leader’s decisions and actions taken at the school must reflect this understanding as
well and appreciate of how they both directly and indirectly impact student learning.
To ensure the successful implementation of the vision the leader must communicate
with and engage all the stakeholders who are on the site and to those who are part of
the larger school community. In doing so the leader must have the skills needed to
navigate obstacles whether it is individuals or systems that impede the schools
capacity to move the vision forward. This relates back to the frames as defined by
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Bolman and Deal in which the leader must have an understanding of how best to
engage the community in an effort to implement the vision for all students.
The school leader is ultimately responsible for the instructional program at
the school site and as such is responsible for monitoring and supervising the
instruction in the classroom. The instructional leader must develop relationships at
the site that provide for professional conversations regarding daily and weekly
observations in which the leader participates. As result of such observations the
leader must provide the resources, time and professional development opportunities
for the teachers.
A second major element associated with instructional leadership is the
development of Professional Learning Communities (PLCs). Teacher empowerment
through shared governance and democratic leadership are key to this effort. Also
important is the ability to foster increased teacher leadership. This process involves
tapping into the expertise of teachers and building ownership of change initiatives.
Building PLCs also involves modeling effective practice, encouraging collaboration
and focusing on the nature of learning as a continuous process for teachers and
students.
Developing constructivist leaders and learners is the third major component
associated with effective instructional leadership identified by Blasé and Blasé. The
effective instructional leader helps others realize and act upon the social nature of
learning where multiple outcomes are encouraged and where learners construct
meaning from values, beliefs and experiences. Leadership is seen as reciprocal in
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this process and shared experiences are important. Joint visions are articulated and
help shape the direction of learning activities where inquiry is a shared and essential
activity. Finally, action research is encouraged as a means of improving
instructional practices at the site.
The role of the school leader is complicated and involves many different
aspects. In today’s educational setting the leader cannot be simply a manager but
rather must have the capacity to lead with passion and be committed to all students
and their learning. This framework defines essential aspects of instructional
leadership; vision for learning; supervision and monitoring of instruction;
community and politics; culture of teaching and learning; and data driven decision
making are the focal themes in effective instructional leadership. The instructional
leaders whose primary focus is to guide the learning of students in their schools will
not only understand, but practice the behaviors which are associated with these five
themes.
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Figure 3 – Instructional Leadership Framework

97
Framework for Research Question 5: Assessment of Individual Leader’s expertise in
math and Leadership Strategies to Improve Student Achievement
Research Question 5 asked how instructional leaders responded to the
academic areas in which they were not experts. The framework developed to deal
with this question was divided into two distinct components based on the two parts
of the research question. First, an assessment was developed to help determine the
level of expertise the principal had in math. The process was based on the state of
California’s definition of a highly qualified teacher (HQT) under NCLB. This
definition was chosen precisely because the intent of the HQT provisions were aimed
at judging a teacher’s qualification primarily based on subject matter competency.
The assessment involved is detailed in Figure 4 and results in one of three levels of
expertise being assigned to the leader – high, medium, or low.
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Figure 4- Assessment of Principal’s Expertise in Math

Source: NCLB Teacher Resource Guide [electronic version] located at
http://www.cde.ca.gov/nclb/sr/tq/documents/nclbresourceguide.pdf
Assessment of Principal’s Expertise in Math
Step 1
Is the Principal
HQT Compliant?
Yes No
High
Expertise
Step 2
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
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A range of strategies were charted based on school literature and research on
school improvement was developed to assist the investigator in identifying
categories around efforts that were implemented to improve student math
achievement. The second part of this framework is detailed in Table 4.

Table 4 – Strategies to Overcome a Lack of Subject Matter Competency

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Data Collection Instruments
For this study data was collected utilizing five data collection instruments;
School Profile, Key Leader Interview Guide, Teacher Interview Guide, Math
Teacher Questionnaire, General Teacher Questionnaire. The questionnaire was
utilized with teachers and the interview guides were utilized with Key Leaders and
the Math teachers. Each of the instruments was created collaboratively between the
doctorial student team during the summer of 2006. They were developed to ensure
alignment with the individual frameworks.
Instrument 1 - School Profile
The School profile instrument was designed to provide a framework for
better understanding the myriad of characteristics that make up the school
community. The secondary school reform cohort led by Dr. Marsh worked to
identify those elements most likely to provide a comprehensive picture of the school
being studied. Characteristics were also chosen based on practical availability of the
data. Data to be collected was organized into three main areas of concern:
Demographics, student performance, and general school information. Most of the
data collected for this purpose was available on the California Department of
Education’s web site.
Demographic data comprised a large part of the school profile and included
both student and teacher demographic traits. Teacher demographics included total
numbers of teachers; credential and NCLB Highly Qualified status; and years of
experience. Teacher data can yield a wealth of information about the instructional
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program at the school and help shed light on potential strengths and weaknesses in
that area. Data collected for students included ethnicity, English Language Learner
(ELL) status; Free and reduced lunch status; and student enrollment patterns.
Likewise, student demographic data has the unique potential for illuminating the
probable challenges facing the school as it works to improve student achievement.
Student performance data was also an important component in the school
profile. Such data is directly responsive to one of the research questions being
examined in that it can help reveal the academic achievement pattern in the school.
Among the items compiled were the Academic Performance Index scores at the site
for the most recent three years; CAHSEE pass rates; standardized test score data; and
other assessment data such as benchmark assessment data. By examining student
performance data, one can more readily identify areas of curricular strength and
areas that might merit further investigation.
The data described above was collected for the school profile compiled into
Appendix E and is presented in a table broken down into the three areas identified
above.
Instrument 2 – Key Leader Interview Guide
The Key Leader Interview Guide was developed to facilitate the collection of
data relevant to research questions numbers 2 through 5. In particular, key leaders
were interviewed to help determine their perceptions of the factors they believe were
responsible for the observed improvement in student achievement in math. The key
leader interview was developed collectively by the cohort group to ensure alignment
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between proposed questions and conceptual frameworks and specific research
questions. The interview guide assumed an interview of no more than 40 minutes
and included a total of 16 open-ended questions to allow the interviewer the freedom
to explore emergent themes and issues. This semi-structured interview process is
based on Creswell’s protocol (1998). The Key leader interview guide is incorporated
in this study as Appendix C.
Instrument 3 – Teacher Interview Guide
The Teacher Interview Guide was developed to facilitate the collection of
data relevant to research questions numbers 2 through 5. As with key leaders,
teachers were interviewed to help determine their perceptions of the factors they
believed were responsible for the observed improvement in student achievement in
math. The teacher leader interview guide was developed collectively by the cohort
group by ensuring alignment between proposed questions and conceptual
frameworks and specific research questions. The interview guide assumed an
interview of no more than 30 minutes and included a total of 7 open-ended questions
to allow the interviewer the freedom to explore emergent themes and issues. This
semi-structured interview process is based on Creswell’s protocol (1998). The
teacher interview guide is incorporated in this study as Appendix F.
Instrument 4 – Math Teacher Questionnaire
The Math Teacher Questionnaire was developed to facilitate the collection of
data relevant to research questions 2 through 5. As with the interviews, teachers
were asked to complete the questionnaire in order to help the researcher develop an
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understanding of how the staff felt at large about which factors were most
responsible for the observed improvement in student achievement in math. The
teacher questionnaire was developed collectively by the cohort group to ensure
alignment between proposed questions and conceptual frameworks and specific
research questions. The teacher questionnaire used a 5 point Likert scale ranging
from Strongly Agree to Strongly Disagree. It also assumed that it would take no
more than 30 minutes to complete and that the researcher would not have to return
more than once to collect as many questionnaires as possible. The Math Teacher
questionnaire is incorporated in this study as Appendix D.
Instrument 5 – General Teacher Questionnaire
The General teacher questionnaire was developed to include 25 items
providing teachers in subjects other than math with an opportunity to share their
perceptions around school-wide issues. This instrument is attached as Appendix G.
This study used multiple sources of data in an effort to minimize threats to
internal validity. This process of triangulation of data included interviews with key
informants, document analysis, teacher questionnaires as well as direct observation.
This process allowed for the researcher to follow-up on unanswered questions, vague
points, and validation of claims and questioning of multiple parties involved in the
educational effort at the school. In addition, participants reviewed their interview
notes to validate their contents. External validity is beyond the scope of the study,
which used a single, case study methodology. While the findings in this study are
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reasonable given the data collected, via a careful analysis, they are not generalizable
to other settings beyond the comfort level of the reader.
Data Collection
This study collected data over a 4 month period from September 2006
through December 2006. The data was collected in three distinct rounds to allow for
a more thorough comparison of data sets and documents. All participants were
afforded the opportunity to review notes compiled form their respective interviews to
ensure the notes accurately reflect their words and the spirit of their intended
message. In addition, this multiple rounds strategy allowed for the follow up
investigation in later rounds as emergent themes and issues arose from previous
rounds. The reliability of the triangulated data using these methods was thereby
increased.
A key step in the process of data collection was obtaining the approval of the
Institutional Review Board (IRB) prior to the collection of any data. The IRB
process is intended to protect the participants through a close examination of the
methods involved in the study. This examination required the submission of several
documents to the IRB by the researcher. The main document submitted was the
Request of Claim of Exemption for Non-Medical Research, in which, the researcher
described the purpose of the study, the population to be studied, and the
methodology used in the study. For this particular study, Dr. David Marsh submitted
one IRB proposal for the series of related studies being done by members of the
cohort described earlier. This process limited flexibility in some respects, yet
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increased consistency amongst the researcher by requiring the same data collection
instruments and methodologies.
Once the IRB gave final approval for the study to begin, the cohort group
returned to their list of qualified schools and approached the schools selected for
study. Site principals were contacted and informed about the details of the study and
once the site gave approval, data collection started soon thereafter. Participants were
informed of the need to give voluntary consent and informed that they could end
their participation at any time. The questionnaire was voluntary as well and the
researcher made more than one effort to collect those that were submitted.
During the first round of data collection the hope was to gain a broad
overview of the school. As such, the first interview was of the site principal. The
principal interview was designed to provide an opportunity to learn more about key
leaders on campus, instructional programs in general, the math program specifically,
and school-wide cultural factors affecting the school’s academic progress. The
researcher spent time in the classrooms and on campus to get a feel for life at the
school. Key documents such as the school’s master schedule and school site plan
were also gathered during this first round visit. The Teacher Questionnaire was also
distributed during this round with the knowledge that maximizing the number of
questionnaires returned would require a sustained effort over time and allow for
multiple efforts.
The second round of data collection served as an opportunity to follow up on
aspects of the school’s culture and instructional program that had been learned after
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analyzing the data collected during the first round. Key leaders such as assistant
principals, department chairs and teacher leaders were interviewed during the second
round of data collection. In addition, completed teacher questionnaires were
collected and the data from these questionnaires was compiled into a database of
information (see attached Appendix H). Finally, a second interview was held with
the principal to follow-up on items gleaned from both rounds of data collection to
that point.
The third and final round of Data Collection was used to collect any teacher
questionnaires still at the site and to conduct brief interviews consisting of follow up
questions based on questions arising from data collected in earlier efforts. This
process of “filling in the gaps” allowed the researcher to effectively eliminate
guesswork and tie up all the loose ends.
Data Analysis
The purpose of this study was to produce a better understanding of how
effective instructional leadership works to improve student achievement in
mathematics. Specifically, the study explored the various facets of instructional
leadership, the components of instructional effectiveness and the design of the
mathematics curriculum at the site in order to arrive at a reasonable explanation for
the success achieved by the school. Five research questions were developed to assist
in completing this study and data collection instruments were developed that were
aligned to the research questions in an effort to ensure efficiency within the study
and reliability of findings to be made following a review of the data collected.
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Interview notes were taken manually and transcribed to be subsequently
reviewed by the participants. Following this verification, an effort was made by the
researcher to link relevant points made in the interview to aspects of the appropriate
conceptual framework. Copies of interview notes and transcripts were made as
needed to allow for cross filing onto thematic files indexed by the salient points of
the framework. This effort assisted with retrieval of data and in identifying themes
that emerged as more than one person noted a particular dynamic on campus. A
spreadsheet was compiled in which similar thematic concepts would be sorted and
grouped by research question and data collection instrument in order to help in the
identification of patterns in the data and in establishing the relative frequency of a
given response.
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, validation of claims and questioning of multiple parties involved in the
educational effort at the school. In addition, participants reviewed their interview
notes to validate their contents. External validity is beyond the scope of the study
which used a single, case study methodology. While the findings in this study are
reasonable given the data collected, via a careful analysis, they are not generalizable
to other settings beyond the comfort level of the reader.
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Conclusion
The purpose of this chapter was to describe the methodologies used in this
study. This included a detailed description of the sampling criteria, the data
collection instruments, data collection process and data analysis methods. The
procedures used for this study were collectively developed by the students in the
cohort led by Dr. David Marsh and were approved by the IRB of the University of
Southern California. The concepts and methodologies were reviewed by and gained
the approval of the school principal at Valley High School. Data collection was
mainly comprised of teacher and key leader interviews and a teacher questionnaire.
Document analysis was performed and direct observations were made to triangulate
data whenever possible. The findings presented in the next chapter are based on a
thorough analysis of the data collected and will be expressed in terms of the research
questions that have guided this study.
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CHAPTER FOUR
Findings, Analysis, and Discussion
Introduction

The purpose of this study was to examine the conditions that fostered
mathematics achievement at one high school. Specifically, the study examined 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
realized an increase improvement in student Algebra I scores over a three-year
period from 2002-2005.
The following research questions were used to parameterize the case 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 seem to be related 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?
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5. How did leaders in the school resolve the dilemmas about instructional
leadership?
The first part of this chapter will describe and frame the academic
achievement patterns of the students at Valley High School in response to the first
research question: What was the pattern of math achievement for various students at
the school? The second part of this chapter discusses the findings regarding
procedures and policies that have been established and implemented to effectively
improve student achievement in math, responding to research question number two:
What policy initiatives including curriculum, instruction and related conditions seem
to be related to improved math achievement at the school? The third section in this
chapter will discuss the efforts that were implemented so as to have a positive impact
on student achievement in math, answering the third research question: What change
process did the school use to enhance the math program and strategies to assist
students in math? The next section will discuss and analyze the impact of strong
instructional leadership, specifically including the perception of the on site teachers
providing an answer to the fourth research question: To what extent was strong
instructional leadership important in improving A) the math programs/strategies and
B) math achievement among students? The fifth section will be respond to the
findings as they relate to answering the final research question: How did
instructional leaders respond to academic areas in which they are not experts? The
discussion will focus on whether the academic background and knowledge in math
played out at the school site and the subsequent impact of such knowledge. Finally
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the chapter will close with an analysis and discussion of the findings and what they
mean and how they are connected with the research in terms of the role of school
design, the math program and the role of the instructional leader.
Research Question 1: What was the pattern of mathematics achievement for
students?
To respond to this question it was necessary to conduct a review and analysis
of the academic performance of Valley High School over the past three years
utilizing both qualitative and quantitative data which was gathered as a means of
responding to the first research question. The California Standards Test (CST) was
used as the primary indicator of academic performance. To support and provide a
broader picture of the pattern of student academic achievement other indicators were
analyzed, these included: the passing rate of the California High School Exit Exam
(CAHSEE); the percentage of students taking and passing College Board Advanced
Placement (AP) Exams in math and the enrollment patterns of students in higher
level math classes as reported on the CST and school personnel. Other documents,
report and data used to analyze and answer this research question came from the
School Accountability Report Card (SARC), STAR Report, CBEDS report, master
schedule, and WASC Report. These all provided rich data sets for examination and
comparison to determine the patterns of growth and achievement at Valley High
School.
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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). VHS’ 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 VHS, organized and presented
as follows: California Mathematics Standards Test (CSTs), Algebra CSTs, API Sub-
groups, CAHSEE Math Pass Rates, IB/AP Exam rates, and A-G Completion rates.
Not all of the data represents positive growth.
California Standards Test (CST)
Math percentage scores for the last three years at VHS are similar to the
California state average for students achieving at the proficient or advanced levels on
the California Standards Test in Algebra I. Overall, from 2002-2006, there was a
consistent and significant increase in math proficiency at Valley High School. Valley
High School School has continued to have significant improvements in student
achievement on the CST exam. Scores are also disaggregated by the subgroups
race/ethnicity, gender, socioeconomics, language, and disabilities. Comparitively, the
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state Algebra I scores have fluctuated greatly from 2002-2006. In 2004 Valley High
School reached the state average on the CST in Algebra. Then in 2005-2006 Valley
High School’s percentage scores exceeded the state average on the CST in Algebra
by 1 point in 2005 and 3 points in 2006. The change in percentage score during
2002-2006 was significantly higher for Valley High School (+ 20 points) in
comparison to the state average (-12 points).

Table 5: Comparison of Percentage of Students Scoring at and Above Proficiency on
CST: Algebra I

2002 2003 2004 2005 2006
CA State Algebra 1 35% 21% 18% 19% 23%
VHS Algebra I 6% 13% 18% 20% 26%

Table 6: Change in Percentage of Students Scoring at and Above Proficiency on
CST: Algebra I

2005-2006 2002-2006
CA State Algebra 1 +4% -12%
VHS Algebra I +6% +20%
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Academic Progress Index (API)
The philosophy of Valley High School is one of providing encouragement
and support to assist students to achieve at high levels. That Valley High School is
committed to ensuring a quality education is demonstrated by their consistent growth
on their API scores, the school has increased their API scores 72 points over the last
four years with a baseline score of 670 and an API score of 742 in 2005. In addition
to this the school has met its AMO targets each year since the start of the program,
including all their sub groups.

Table 7: Valley High School’s API Scores for three years

2003 2004 2005 2006
670 717 737 742

The Academic Performance Index of 742 reflects the school’s consistent
philosophy to provide encouragement and in assisting students to achieve at high
levels. Valley High School has exceeded its growth target for five consecutive years.
The school's curricular emphasis has been built upon a solid foundation of the
California State Content Standards. According to the administration, special
attention has also been given to meeting the academic needs of all of the students.

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Expected School Wide Learning Results (ESLRs)
According to Key Leader A, increased student achievement has continued to
improve as a result of Valley High School’s Expected School Wide Learning Results
(ESLRS), which consist of:
1. Students will build upon their knowledge and comprehension,
developing the higher order thinking skills of application, analysis
and synthesis, and evaluation.
2. Students will use a variety of media to access, organize, evaluate, and
communicate information.
3. Students will participate in creating an individualized road map for
high school and beyond.
4. Students will be contributing members of a community.
5. Students will show creativity, originality, resourcefulness and
ingenuity in their work.
The Principal has worked with the leadership team to create school wide
learning results that are prominently posted throughout the campus and discussed in
classrooms. The learning results are a clear indicator of the expectations the Principal
has of the standards for learning at Valley High School. According to Key Leader K,
a guidance counselor:
“The Principal is present in the way that our ESLRS (School Wide Learning
Results) for our WASC accredentation have been formulated, reevaluated and
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reformulated then acted upon. ESLRS are on the marque, posted in the classroom,
and they are the framework on which we hang everything else.”
According to Teacher C:
“My Principal has developed standards throughout the school which are
called the ESLRS. The kids have these standards memorized and the Principal will
walk around the school and ask students to recite the ESLRS.”

Racial/Ethnic Groups
The ethnic composition of Valley High School students closely resembles the
community at large: 48% Anglo, 39% Hispanic, 8% Asian/Pacific Islander, and 2%
African-American as reported in the CBEDS information report, dated October,
2006. About 7% of the students are English Language Learners (ELL), which is
well below the county average.
API Subgroups
API scores rose by 72-points from 2003-2006. There is data reported for all
of the school subgroups listed above, however, only subgroups that have more then
100 students are calculated into the API subgroups. For this study, those groups are
Hispanic and White students. Consequently, there is not enough data to make
comparisons between all other racial/ethnic groups at Valley High School. White
students scored higher than Hispanic students every year. As stated, there is not
enough data to make comparisons for all racial/ethnic groups at Valley High School.

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Table 8: Valley High School’s API Base and Growth Data

API Base Data
2002 2003 2004
Percent Tested 99 99 99
API Base Score 670 717 737
Growth Target 7 4 3
Statewide Rank 7 8 8
Similar Schools Rank 8 9 9
API Growth Data
From 2002 to 2003 From 2003 to 2004 From 2004 to 2005
Percent Tested 99 99 100
API Growth Score 714 742 758
Actual Growth 44 25 21

Valley High School's Academic Performance Index (API) continues to grow
significantly each year. The school's API scores were 670 (2002), 717 (2003), and
742 (2004). Since 2002 the API has grown ten percent and in the last five years the
API has improved by ninety-five points. Most significant is that not only has the API
grown, but each sub-group has exceeded its growth target. The significant racial and
ethnic subgroups for Valley High School are Hispanic and White. The API for
Hispanic students has improved twenty percent since 2002 and is currently at 683.
According to Table 9 both Hispanic and White students have been significant
improvements in their API Growth Scores. There is a significant achievement gap
between the White and Hispanic students at Valley High School. White students
score significantly higher on the API Growth Score in comparison to Hispanic
students. White students’ API Growth Score was 748 (2002 to 2003), 776 (2003 to
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2004), and 792 (2004 to 2005), in comparison to Hispanic students who scored 657
(2002 to 2003), 683 (2003 to 2004), and 707 (2004 to 2005).
However the API growth scores for these subgroups proves that as the
growth scores increase the achievement gap remains. The gap of the subgroups show
that there was a discrepancy between White and Hispanic students of 91 points (2002
to 2003), 93 points (2003 to 2004) and 85 points (2004 to 2005). Although the gap
reduced from 91 to 85 points over the three years, there is still a significant
difference in achievement scores between White and Hispanic students. Hispanic
students have increased 117 API growth points from 2002 to 2005. While, White
students have increased 78 API growth points from 2002 to 2005. Overall, both
White and Hispanic students are increasing in academic achievement while an
achievement gap does exist.)

Table 9: API Growth Score Comparison of White and Hispanic Students

API Growth Score
Comparison of White and
Hispanic Students
Actual Growth
2002 to
2003
2003 to
2004
2004 to
2005
2002 to
2003
2003 to
2004
2004 to
2005
2002 to
2005
Hispanic 657 683 707 +63 +28 +26 +117
White 748 776 792 +30 +22 +26 +78
Gap of
Subgroups
-91 -93 -85

119
There appears to be significant growth in the percent of Hispanic and White
students achieving at the proficient or advanced levels of mathematics from 2003 –
2005, and a slight decrease from 2005-2006. Hispanic students improved from 17%
to 24% of students at or above proficiency from 2003 to 2005, while White students
improved from 25% to 33% of students at or above proficiency. While Hispanic
students made significant gains, they are still significantly less percentage of
Hispanic students reaching proficiency in comparison to White, Asian or Filipino
students. The African American students represent 2% of the total student population
at Valley High School and regrettably there is only 21% of this subgroup reaching
proficiency in Mathematics. Overall Asian students are the highest performing while
African-American students are the lowest performing. The Filipino and Asian groups
scored the highest of the subgroups in 2005. (See Table 10)

Table 10: Mathematics CST Percentage of Proficient or Advanced Students by Race
and Ethnicity

2003 2004 2005 2006
African American * * 21 *
Asian * * 46 *
Filipino 36 * 35 *
Hispanic 17 22 24 22
White 25 28 33 27
120
When examining the percentages of students reaching proficiency on the
CST Algebra exam there are similar results among the subgroups. There appears to
be significant growth in the percent of students achieving at the proficient or
advanced levels of mathematics among all student groups from 2003 – 2006. Scores
for Asian, African American, and Filipino students fluctuated during this period,
while Hispanic and White students are made significant and consistent gains. There
was a decline for Filipino students from 36% (2003) to 24%(2004), which was
followed by gains to 27% (2005) and 36% (2006). African-American students made
the most impressive gains from 2003 to 2006. This subgroup improved from 6%
(2003) to 27% (2004), and then fell to 21% (2005) followed by a dramatic gain to
38% (2006). The Asian students fluctuated the most from 29% (2004) and fell to
14% (2005), then drastically increased to 43% (2006). The Filipino, African
American and Asian students scored the highest of the subgroups. (See Table 11)

Table 11: Algebra I CST Percentage of Proficient or Advanced Students by Race or
Ethnicity

2003 2004 2005 2006
African American 6 27 21 38
Asian * 29 14 43
Filipino 36 24 27 36
Hispanic 13 14 18 22
White 12 21 24 26

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Disaggregated Subgroups
Since 2002 Valley High School’s API has grown ten percent and in the last
five years the API has improved by ninety-five points. Most significant is that not
only has the API grown, but each sub-group has exceeded their own growth targets.
Disaggregated subgroup mathematics achievement data include male, female,
English Learners, Economically Disadvantaged, and Students with Disabilities
categories.
During the period from 2003-2006, the percentage of males achieving at
proficient or advanced on Algebra I CST has shown a slow rise in scores. In 2003-
2004 male students were outperforming female students. During 2004-2005 the male
students remained at the 20% proficiency level. Since 2005, female student have
outperformed male students in proficiency. During 2003-2006 the female students
have improved from 14% proficiency to 28% proficiency, in comparison to male
students only improved from 18% proficiency to 25%. Female students have made
significant increases during 2002-2006 and in 2004-2006 they scored higher than the
male students. (See Table 12)

Table 12: Algebra I CST Percentage of Proficient or Advanced Students by Gender

2003 2004 2005 2006
All Students 13 18 20 26
Male 18 20 20 25
Female 14 17 21 28

122
A similar proficiency pattern is discernible when comparing male and female
students on the Mathematics CST from 2003-2006. For both subgroups there have
been an incremental increase in achievement from 2003-2005, while in 2005-2006
both groups had a decrease in proficiency. During 2005-2006 male students
decreased by 2%, while female students decreased by a drastic 8%. Overall, male
students consistently outscored female students during 2003-2006 in proficiency on
Mathematics CST. (See Table 13)

Table 13: Mathematics CST Percentage of Proficient or Advanced Students by
Gender

2003 2004 2005 2006
All Students 21 25 32 26
Male 22 27 32 30
Female 21 24 28 20

Based on the Mathematics CST, English Learners increased significantly
from 2003-2004, but decreased significantly from 2004-2006, with an overall
increase of 2% points during 2002-2006. English Learners are significantly
outperformed in comparison to the total student population. The most dramatic
comparison occurs during 2005 when the data reveals that 32% of the total student
population was proficient, in comparison to 12% of the English Learner population.
(See Table 14)
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There have been small increases in achievement for students with disabilities.
During 2004-2006 this subgroup increased 2% points. Students with disabilities have
the most discrepancy in their percent proficient in comparison to the total student
population.

Table 14: Mathematics CST Percentage of Proficient or Advanced Students by
Subgroup

2003 2004 2005 2006
All Students 21 25 32 26
Econom. Disadvantaged 16 19 20 18
English Learners 9 18 12 11
Students with a Disability * 8 10 10

Improvement is also evidenced for students in the category of Economically
Disadvantaged, whose API increased twelve percent since 2002 and stands at 661.
The API Growth Score demonstrates how there is an overall growth of 69 points for
Economically Disadvantaged students from 2002-2005. There was a significant
increase in API Growth Score for this subgroup in 2002-2004 by an increase of 80
points, then in 2004-2005 there was a lose of eleven points. Overall, there has been
improvement for this subgroup in API Growth Score from 2002-2006 of 69 points.
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Table 15: API Growth Score Socio-economically Disadvantaged Students

API Growth Score
Socio-economically
Disadvantaged Students
Actual Growth
2002 to
2003
2003 to
2004
2004 to
2005
2002 to
2003
2003 to
2004
2004 to
2005
2002 to
2005
Economic.
Disadvan.
641 661 651 +56 +24 -11 +69

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). Valley High School CAHSEE results are a mirror image of the
state CAHSEE results. At Valley High School the pass rate on the Mathematics
section of the CAHSEE for the class of 2006 is 85%. The results show that 93% of
10
th
graders pass it on the first try. The pass rate for 11
th
graders taking the exam is
53% and 62% for 12
th
graders. According to the results there were twenty 12
th

graders who did not pass the Mathematics section of the CAHSEE exam. Within the
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subgroups, Students with Disabilities, Hispanics, African American, and
Economically Disadvantaged continue to score below the school average. The results
show that while a total of 91% of White students and 92% of Asian and Filipino
students have passed the Mathematics section in the class of 2006, only 79% of
African American students. 80% of Hispanic students, 77% of Economically
Disadvantaged students, 50% of English Learner students and 50% of Students
receiving Special Services passed the exam. The achievement gap still persists with
the CAHSEE exam. The stakes and consequences are high for students not passing
the exam, as not passing the CAHSEE by 12
th
grade disqualifies them from receiving
their diploma.
Although there is still an achievement gap among students reaching
proficiency on the CAHSEE exam, the various subgroups have been making
impressive gains for past five years at Valley High School. Table 16 shows the
growth made by the subgroups on the CAHSEE exam from 2002-2006 at Valley
High School. The passing rate significantly improved from 34% in 2002 to 85% in
2006. The most impressive year was 2006 when there was a passing rate of 90% for
the total student population.
126
Table 16: Percentage of Students Passing CAHSEE Mathematics Section by
Student Subgroup

2002 2003 2004 2005 2006 Gains
Total Student Populat. 34 57 90 85 85 +51
African American * 35 85 89 79 +44
Asian * 53 86 97 92 +39
Filipino * 64 100 97 92 +28
Hispanic 27 48 85 76 80 +53
White 44 65 94 92 91 +47
Econom. Disadvant. 26 46 83 65 77 +51
Stud. Receiving Serv. 14 21 47 62 50 +36
English Learners 21 22 65 51 50 +29

Advanced Placement (AP)
The number of students taking Advanced Placement (AP) exams continues to
increase. In the spring of 2004, 237 students took AP exams, while in the spring of
2006, 320 students took AP exams. (See Table 17) Valley High School continues to
increase the amount of AP courses offered, therefore increasing the opportunity for
more students to take AP courses. In spring of 2005 there was an extremely high
rate of students taking and passing AP exams at Valley High School. In the spring
of 2005, 325 students took AP exams and 81% of the 12
th
graders passed their AP
exams. Valley High School has consistently scored above the state average on AP
exam pass rates for the past three years. Between 2004-2005 Valley High School
significantly improved their AP exam pass rate. Valley High School went from
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49% of the 12
th
graders passing the exam in 2004 to 81% of the 12
th
graders passing
the exam in 2005. (See Table 18)

Table 17: Number of AP exam test takers at Valley High School

2004 2005 2006
# of VHS Test Takers 237 325 320

Table 18: Comparison of AP Exam pass rates between State average and VHS

2004 2005 2006
State Gr. 12 43 45 56
State Gr. 11 & 12 20 21 26
VHS Gr. 12 49 81 73
VHS Gr. 11 & 12 23 38 33

University of California/California State University Courses (A-G)
The increased emphasis on academics is reflected in the number of students
completing the University of California (UC) a-g requirements and/or the
California State University (CSU) requirements. In 2001, 11% of the seniors
completed the UC a-g requirements. This percentage steadily increased to 20% of
the seniors completing the UC a-g requirements in 2002 and 2003. The percentage
rose to 38% in 2004 and slightly dipped in 2005 to 37%. In 2006, the percentage
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rose slightly to 38%. (See Table 19) One of the primary reasons for the failure to
complete the a-g requirements is: 1) incomplete mathematics sequence of three
years of high school mathematics with grades of C or better. In accordance with the
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. (SARC Report)

Table 19: Percentage of VHS Graduates completing the University of California
(UC) a-g requirements and/or the California State University (CSU) requirements

2001 2002 2003 2004 2005 2006
% VHS Grads with a-g 11% 20% 20% 38% 37% 38%

SAT I Reasoning Test
Overall, Valley High School has had a steady increase on the SAT I
Reasoning Test from 2003 through 2005, which parallels the state average that has
also had a steady increase during 2003 to 2005. Valley High School made a
significant increase in math in 2003-2004 of 15 points, Valley High School still
remains under the state average on the math section, and it remains consistently
above the state average on the verbal section. There has been a significant increase in
the math section from 2003 to 2005. Valley High was 22 points below the state
average on the math section in 2003 and it is now only 9 points below the state
average in 2005.
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Table 20: Comparison of Valley High School (VHS) and State Scores for SAT Exam

2003 2004 2005
State Verbal 494 496 499
VHS Verbal 508 509 519
State Math 518 519 521
VHS Math 496 511 512

Summary
There are diverse patterns of student math achievement at Valley 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
Mathematics 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 25 and 33 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 were 21 percent
passing rates at the proficient and advanced levels.
CAHSEE passing rates in math for these students have ranged from 34% -
90% from 2002 – 2005. All subgroups have significantly increased their CAHSEE
Mathematics passing rates over the last five years. Hispanic students are achieving at
slightly lower rates than their African American peers posting CST scores that
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ranged from 35% to 89% from 2002-2005 at the proficient and advanced levels.
Hispanic student CAHSEE passing rates in math have ranged from 27% to 85%
during this same period. Asian and White students are enrolled in AP classes at more
than four times the rate of African American and Hispanic students. Conversely,
African American and Hispanic students are enrolled in Algebra support classes at
nearly four times the rate of White students.
The pattern at Valley High School of consistently improved math
achievement in Algebra has been a result of deliberate decisions to support student
learning for all the students. The school leadership and the math department leaders
have responded to the critical need for students to increase their levels of
achievement in an effort to ensure that the students at Valley High are sufficiently
prepared to meet the demands of passing the California High School Exit Exam
(CAHSEE) for graduation and to ensure that all students meet at the minimum
graduation requirement of passing Algebra. This has been a sustained effort for the
Valley High administrative leadership team and Valley High math department for the
past five to six years when the school first began making both systemic and
instructional changes to meet increasing academic expectations.

Research Question 2: What policy initiatives, as well as curriculum and instruction
and related conditions seem to be related to improved math achievement in the
school?
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This question was designed to foster an understanding of what factors
contributed to the consistent increased math achievement at the school. To answer
this research question multiple resources were accessed and analyzed as a means of
triangulating the findings and providing broad perspective and lens in which the
progress was predicated. Two different conceptual frameworks were utilized for this
question, Marsh and Coddings’ Effective School Design (1998) and a Effective Math
Programs conceptual framework which was developed based on findings from
research conducted by a variety of researchers and research to include data from
TIMSS, J.W. Stigler, and Deborah Ball. The following instruments 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 as follows: information, perceptions, and opinions
about existing policies and school response, description of the school design,
description of the math program design, and analyzed 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
All administrators and faculty members at the school suggested that much of
the current local accountability policies could be traced to the No Child Left Behind
Act (NCLB, 2001). NCLB’s components of Adequate Yearly Progress (AYP) and
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Highly-Qualified Teacher (HQT) were explained by educators as significant efforts
that had contributed to improved student achievement in math. As the Assistant
Principal of Guidance and Instruction, Key Leader C has been at Valley H.S. for
only two years, but has seen the importance the administrative team places in the
hiring practices at the school. He believes the hiring practices at Valley High School
are responsible for retaining highly qualified mathematics teachers on their staff,
which in turn has resulted in the increased AYP and API scores for the school. In
terms of NCLB Key Leader C, felt that:
“At Valley High School, the NCLB Act has forced educators and
administrators to look at certain programs, instructional strategies,
and new hires in a whole different way. We have a saying here at
Valley High School, we are not a school to take on a ‘project’ All
teachers need to come in with the motivation and instructional
techniques to teach high school and really perform. NCLB has placed
this additional pressure on schools where you really can’t afford to
take on a ‘project.’ If you have a teacher who can connect with the
kids, then the kids will be receptive to learning from them and they
have the techniques to diversify their instructional strategies then the
kids are going to learn. It translates into good test scores.”

Key Leader D, school counselor at Valley High School for the past eight
years agrees that NCLB makes sure that only the best teachers are hired on our
school site. She also states that NCLB has been responsible for establishing strict
mandates on the level of training and education each teacher must have in order to be
highly qualified. She believes the highly qualified and motivated teachers equal
higher test scores, improved student achievement and the desire for children to learn
more mathematics in high school.
133
The Assistant Principal of Curriculum, Key Leader B adds how NCLB has
set standards for the hiring practices pertaining to credentialed teachers in order to
have highly qualified teachers. She explained,“All of our new hires are now
credentialed in mathematics and more qualified because of NCLB. Before NCLB the
teachers were teaching out of their credential area.” She has been the Assistant
Principal of Instruction for the past nine years. In her opinion, one benefit of NCLB
is the safeguard on hiring highly qualified teachers. She explained how at Valley
High School NCLB’s mandates are interpreted as the need to hire experts in the
specific teaching areas. The administration believes that hiring the best in the field
will drive improved instruction and increase student achievement.
Key Leader A, the Principal of Valley High School, is regarded in every
interview by both the teachers and administration as the key instructional leader at
the school and the driving force behind the school’s continued increase in student
achievement. He has been Principal at Valley for the past eight years, and prior to
that he taught at Valley High School as an AP and General Spanish teacher for 12
years. His dedication to the campus is monumental and his charismatic nature is
clearly evident at each encounter.
The faculty’s interviews questionnaires and observations all place Key
Leader A in high regard as an educational leader that the faculty trusts and follows.
Key Leader A’s perceptions of NCLB make it obvious that the hiring practices are a
priority for him at Valley High School. He believes that the credit for the high
student achievement and improved test scores are all due to the tremendous efforts of
134
his teachers. He explains that he has become an expert in hiring and that he looks to
find experts in respective subject areas to teach the students.
Key Leader A’s perspective on the new hiring policies and practices attests to
the fact that quality of applicants at Valley Unified School District has indeed
improved over the past few years. The seriousness of having a credential or being
enrolled in a credential program has prompted districts to improve hiring practices
and also re-examine current teachers in the district. If someone was not credentialed
to teach the subject area, that S/he may have been teaching for several years, after
NCLB that practice would not be allowed to continue. Key Leader A explained that
it was the accountability measures inherent to NCLB that allowed the district to
‘clean up’ a lot of the old systems that had been habitually put in place. It was the
system of seniority that was in place prior to NCLB that crumbled when the new
accountability system was put in place at Valley Unified School District.
Through the comments of the staff it is evident that a new system of
accountability created by NCLB is in place at Valley High. They all know that
NCLB is about showing material growth that has been made in student achievement
through improved test scores. The conversations on the campus center around data-
driven decision-making and figuring out how to improve and perfect instructional
practices.
As previously stated, all teachers across the school completed a questionnaire
so the researcher could gain a broader perspective of the school and the instructional
strategies, as well as programs and policies that have implemented over the past
135
three years that the teachers perceive as having positively influenced the math
achievement of the students at Valley High School. As previously stated, the
questionnaire items are presented on a five-point Likert scale, ranging from 1-5. The
following score scale is used when analyzing the averages of each question results
from the questionnaires: 1.0 – 1.7 is strongly disagree, 1.8 - 2.5 is disagree
somewhat, 2.6 - 3.3 is neutral, 3.4 – 4.1 agree somewhat, and 4.2 – 5.0 is strongly
agree.
Overall, the math teachers at Valley High School viewed the NCLB policy
with a high degree of neutrality in terms of its effect on efforts to improve student
achievement. Math Teacher Questionnaire item 1, which attained a response rate
average of 2.96, Math Teacher Questionnaire item 10 had a response rate average of
3.04, and Math Teacher Questionnaire item 12 had a response rate average of 3.17.
This is consistent with the math teacher response rate average of approxiamately 3.0
for all Math Teacher Questionnaire items 1, 10, and 12 which explicitly sought
feedback about NCLB. Item 1 asked if the No Child Left Behind Legislation had
promoted increased student achievement at the school. Item 10 asked if the school
had focused on personnel issues including hiring quality teachers and fostering a
positive working environment amongst peers on campus. Item 12 asked if in an
effort to improve instruction on campus, the school had focused on motivating
students and staff as well as celebrating successes. The non-math teachers felt
similarly about this issue with a response rate average of 2.88 on the Non-Math
Teacher Questionnaire item 1.
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Standardized Testing and API
Key Leader A reported that California State Standards tests (CSTs) 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. Key Leader A, the Principal, works with the math department
chair, Key leader E, to create a detailed analysis of patterns in formative performance
data, i.e., student grade reports and benchmark exams, compared to the CST results.
The administrative team decided that changes in the instructional program, at the
classroom level, were needed to increase student achievement in math. The math
department chair is able to provide that support to all teachers in their classroom
instruction. Key Leader E provides math coaching and support to all members of the
math department in order to improve instruction.
Much of the success at Valley High School is attributed to how school
leadership promotes collaboration amongst the staff. Key Leader D, guidance
counselor adds that: “The success on the CAHSEE, state test and API is all a result
of the math department collaborating all the time and refining their practice..”
From interviews with Key Leaders and teachers it is evident that there is a
high degree of collaboration and inquiry among the mathematics teachers at Valley
High School.
Teacher B, a first year math teacher at Valley, explains how the school is set
up to support teachers with mathematic instruction. She explained that there is a
137
focus on high achievement in test scores for all students by providing intervention
classes and support to struggling students. Teacher B offered how there is a
tremendous amount of support from the leadership of the school when improving
teacher instruction. There is time for the department chair to work with teachers to
improve instruction. She went on to describe: “The school Principal is amazing! He
fosters a lot of collaboration amongst the departments. Key Leader A has the math
department chair, Key Leader E, work with math teachers to improve the test scores
and daily math instruction. He goes in their classroom daily to coach teachers and
provide support”
According to Key Leader K, Guidance Counselor: “We have a high degree of
teacher collaboration on our campus. The late start Fridays have been exclusively
been devoted to departmental time where teachers get together to look at how
curriculum is delivered, assessment tools, and things they are trying to encourage in
the classroom.”
Throughout the campus there was a common goal among the teachers in
terms of the ways in which they are using state standards for instruction and there is
constant discussion in department and leadership meetings on data-driven decision
making. Both math and non-math teachers strongly agree that teachers are
implementing standards-based instruction at Valley High School. The Math Teacher
Questionnaire registered a response rate average of 4.7 on item 5 and the Non-Math
Teacher Questionnaire had a response rate average of 4.2 on item 5. A great deal of
the instructional policies at the school have been engendered in response to the state
138
testing initiatives, e.g., California Standards Test (CSTs) and the California High
School Exit Exam (CAHSEE). There is a common perception that the tests drive
instruction on the campus. The tests, such as the common final district assessments,
though they may not be the most conceptual examination, still motivate the faculty.
As Teacher E, a math teacher, stated: “The tests get us all on the same page of what
we need to teach and there are clear expectations.”
California High School Exit Exam
The Principal revealed that the basic requirement of passing the CAHSEE
makes no excuses for students for students to meet the Algebra requirement.. He
stated how the exam has now established a standard, which has been set by the state,
that students must meet the Algebra requirement in order to graduate. He argues that:
The CAHSEE requirement has made it so there is no excuses. The students
can now get a diploma or a certificate of attendance. The students have gotten
math assistance from math department in tutoring, gone in after school for
help to mathematics teachers, taken a summer school, or taken a class at the
adult school in the evening for math achievement on the CAHSEE. It’s told
the kids that there is no excuses anymore, they know that if they want the
diploma they need to do something.

Key Leader F, a guidance counselor, states that Valley High School has
continued to reform after NCLB in order to insure that all students will graduate.
Most Key Leaders interviewed agreed that they are proud of Valley High School’s
high percentage on initial passage rates for the CAHSEE, but they also felt that the
CAHSEE does not test for 9
th
, 10
th
, 11
th
or 12
th
grade state standards.
The Assistant Principal of Instruction and Curriculum, Key Leader B,
illustrated how the CAHSEE requirement was most difficult for the neediest
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students, the Special Education and Englsh Language Learners. She explained that
there is an attitude on campus that these students that struggle the most, need the
most resources and attention. These students are seen as the priority in many cases
as to how to improve instruction and student achievement for the Basic level of
education in order to pass the CAHSEE exam.
Key Leader G, Guidance Counselor, illuminated how serious CAHSEE
passage rates are to Valley High School students and faculty. She explained how
getting all students to pass the CAHSEE is a priority for all faculty on the campus.
She went on to describe that in order to have all students pass the CAHSEE, the
continued group effort of everyone on campus was needed to reach all students.
Math teachers strongly agree that the requirement that students pass the
CAHSEE to earn a high school diploma has contributed to the school’s effort to
improve student achievement. The Math Teacher Questionnaire received a response
rate average of 4.4 on item 2. Teacher D, an Algebra teacher also explained how
Valley High School places student success on the CAHSEE as a priority for all
administrators and teachers. Teacher D is convinced increased student achievement
will continue due to the math interventions, student support classes and tutoring
available to students to pass the CAHSEE exam.
Many teachers and administrators felt the CAHSEE class offered to students
is successful because of the class size. This class is limited to twenty students and in
most cases the classes have between fourteen to sixteen students, which allows for
more attention to each students and personalized instruction. Math Teacher G, who
140
teaches this course, explains: “We have good CAHSEE results, because we have a
CAHSEE class that prepares the kids for the exam. There are less than 20 students in
each CAHSEE class.”
Key Leader H, Guidance Counselor and veteran educator of Valley district
for the past fifteen years, explained the commitment to improving the initial success
rate in student achievement on the CAHSEE. She explained: “Regardless to what
the legislation has been, the philosophy here is that every child needs to be
successful. There is on-going curriculum development in our district and having as
high of an initial success rate on CAHSEE as possible.”
District Policies
All administrators take part in discussions on instructional practices at Valley
Unified School District. Key Leader C. Assistant Principal of Guidance and
Instruction, shared his involvement in meetings to increase math scores this year at
the district level and during this academic year. At these district administrative
meetings the Superintendent has sat down with Assistant Principals of Instruction to
look at data, master schedules, what is being taught, how it is taught, and what
strategies we are using to increase student achievement. Key Leader C felt that: “The
fact that we are having collaborative discussions on this speaks volumes, especially
because it is including teachers that are in the trenches, the classrooms, each day. We
are questioning to implement new strategies to increase mathematic achievement
even more.” Math teachers somewhat agreed , while non-math teachers were neutral
that Board policies in the district have improved student achievement. The Math
141
Teacher Questionnaire received an average response rate of 3.4 on item 3 and the
Non-Math Teacher Questionnaire received an average response rate of 2.9 on item 3.
Teacher J, Algebra teacher for the past seven years at Valley, explained the district
policy for the number of years of mathematics required at Valley High School in
order to graduate. He explained: “The students need to pass two years of math. It’s
unfortunate that it can be Algebra I, but it does set some standard that they have to
do Pre-Algebra. I think we should have Geometry as the standard, because it would
push the kids some more.” Teacher I felt that many students that do well in Algebra
by Sophomore year will naturally go on to higher level math classes. He explained
that the students are aware that more math equals college acceptance.
Valley district reformed educational curriculum and instruction with the
passage of NCLB. The faculty explained how administration was quick to reform to
standards-based instruction. In order for standards-based instruction to happen key
math teacher leaders designed curriculum mapping and pacing plans for all math
teachers.
School Design
Student Performance Assessments
Valley High School uses end-of-semester teacher-created assessments as
their benchmark examinations and common final exams. These benchmarks were
aligned with the adopted textbook chapters that were to be covered during each of
the semesters of Algebra I, according to the course outline.
142
Math teachers strongly agree that Valley High School has successfully
implemented common assessments that promote student achievement. The Math
Teacher Questionnaire received an average response rate of 4.2 on item 4. Key
Leader E, math department chair, developed much of the standards-based
instructional units and common assessments used throughout the district. Teacher E
explained that:
The district policy here is to standardize assessments in mathematics. Right
now we have a standardized math final for every class in all middle and high
schools in the district. It’s a good thing because it sets the standard for the
class and also provides problems that are important for all of us to teach and
make sure the students have mastered. It gives us something to shoot for and
it’s clear expectations for us.

He also went on to explain that benefits of clear expectations when teaching. The
common assessments, curriculum maps, and pacing plans allow teachers to stay in
synch with one another and provide more meaningful conversations about instruction
in the department meetings. The expectations are laid out for all teachers on what
needs to be taught and how it will be assessed at Valley High School.
Curriculum
The curriculum at Valley High School is closely tied to the state standards
and is created around a student-centered approach and outcomes. Teacher A. an
Algebra teacher at Valley for the past ten years, described how there had been a
change in math instruction to standards-based instruction for the past four years. All
textbook adoptions in mathematics need to be standards-based. Teacher A explained:
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Our textbook is designed towards teaching the standards. Standards are
everywhere here at Valley. They are posted in every room. As a math department
most of our instruction, class work and homework is from the textbook. We
periodically have tests related to the specific math standards. The review tests we
give are all driven to help students test well on the CST and review the standards.
When speaking with other math teachers there was a common agreement that the
curriculum at Valley is standards-based instruction.
Most teachers felt the curriculum and text used at Valley was adequate and a
solid textbook for instruction. The only concerns brought up from teachers about the
curriculum is the lack of time and opportunities they have to use manipulatives
during instruction.
School Culture
Valley’s school culture has a visible and supportive administration that
emphasizes high expectations of students in mathematics. Valley High School
provides meaningful relationships between the students and the adults on campus
and extended learning opportunities. Most teacher interviews brought up the
supportive nature they felt from school administration. Teacher C, an Algebra
teacher for the past six years, summarizes:
I constantly see a strong support from administration that goes to build a
culture of students achieving in mathematics specifically. When I observe other
teachers teaching on our campus I see different styles and I see people who teach
similar to me. I see different ideas from different teachers, but I don’t see anything
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coming from the top down that’s really improving the students’ achievement. Except
for the fact that I see supportive administration, the administration builds a school
culture, a culture that cares about the kids and works with the parents.
Teacher C went on to explain that he feels the administration is supportive,
which can be attributed to improved instruction. Having improved instruction then
leads to improved student achievement. He felt that most of the credit for the student
achievement should go to all of the mathematics teachers. He felt:
The student achievement at this school is attributed the hard working
teachers. The teachers on this campus are highly dedicated and are extremely
professional. They each take their job seriously and believe that all of the students
can be successful. I feel student achievement improves each year from the efforts of
the teachers and their high expectations of each other and the students.
Math Department Chair, Key Leader E, also felt high respect and regard for
all teachers in the math department. He also equated high student achievement to the
efforts of the teachers.
According to the administration, Valley High School has undergone a reform
in the school culture. When the Principal was hired eight years ago, he described
pockets of negativity throughout the campus. The negativity among a few of the
faculty members was affecting the entire campus. According to the Principal, the
attitudes of these few faculty members was not helping to improve student
achievement. He also noted that when he had assumed his position as Principal at
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Valley High School, there were some faculty who were not teaching in their
credentialed content area. According to Key Leader A, the Principal:
In order to improve mathematic achievement at Valley High School we had
some personnel changes. We had some folks that were really not that strong
and we need to get rid of to be blunt. Others we needed to make a change on
the level of math that they were teaching. They did not have particular
expertise in the subject matter, even though they thought they did.The
mindset was that if you put in your dues and put in your time you were
protected. I thought, this isn’t about him, this is about the kids. It’s about
what’s not happening. The personnel changes were not personal, they were
just not in the right place. I put them where they needed to be and where they
could service students better than where they are.

So the Principal adopted a strong vision for the school and high expectations
for the faculty members and change happened. Now he feels that Valley High
School promotes a school culture of hard working teachers, collaboration amongst
faculty members, high expectations of students, and the desire to have every student
learn. There are high expectations of all faculty members and even higher
expectations of new hires. All non-tenured teachers must work collaboratively with
other faculty members and the students need to achieve. According to Key Leader A,
the school Principal: “Frankly the way I look at it is that if you are a new math
teacher, you have got a year to prove yourself. And if within that year you show that
you are not coachable, which is key, or willing to grow, then maybe another
environment would be better for you. There are no excuses when it comes to this.”
The school culture went through a change process to improve the quality of
teacher instruction, raise the expectations of new hires and eliminating the blame
factor. According to Key Leader A. the school Principal:
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We also use to have a culture here on campus where faculty wanted to blame
everybody, especially the situation at home. I told the staff we can’t control
these things, but what can we control? What elements can we control about
this child from 8am to 3pm? Let’s talk about that.

According to Key Leader A., the Principal: “The other thing is that we had a
culture that blamed the kids. Some of the staff use to refer to the students as
‘damaged goods.’ As an administration team we said we are not going there and that
will never be a factor of our discussion.”
Math Program Design
Classroom Practices
The classroom practices at Valley High School are aligned to the state
standards in the mathematics department. The teachers are creating a student
centered curriculum that is guided by learner outcomes and ensuring that students are
gaining a conceptual understanding of content that facilitates, the in-depth mastery of
computations and manipulations of mathematical symbols, and procedures as tools to
support the learning of the problem solving processes. According to the
administration and the teachers, the standards dominate mathematics instruction and
curriculum. Teachers use a common syllabi for courses. They teachers explained
how they use common pacing guides and common final assessments. Both the
teachers and the administrators felt that standards based instruction and common
assessments are an integral facet of the mathematics classroom practices. According
to Key Leader C: “All math teachers use common pacing guides, benchmarks and
common assessments throughout the school. They are in the same place, using the
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same material and using the same tests, which I believe helps contribute to the
student achievement.”
Teachers work together to design well developed lessons that make
connections and require students to draw from prior knowledge and encourage
student engagement.
Curriculum Design and Standards based Instruction
Valley High School offers Algebra A, which is first semester Algebra and
Algebra B, which is second semester Algebra. Algebra Readiness is offered to
Freshman as an extra preparation for Algebra.
According to Key Leader B, the Assistant Principal of Curriculum and
Instruction:
Some districts waited for the mandates and see if the standards were going to
go away. Our district jumped on the Standards-based instruction really
quickly. We wrote all of our curriculum on standards. There was a great
emphasis to get standards-based textbooks. So we were out in our common
assessments rather early in comparisons to other school districts.

Teachers felt they were supported by the administration to have time to
collaborate and plan instruction. They felt there was a shared vision of inquiry on the
campus at the department meetings. The last Friday of each month is late start at
Valley High School. This time is allocated to teachers working together in
departments for curriculum planning. According to Key Leader E, the Mathematics
Department Chair: “Collaboration is talked about a lot on our campus. Once a month
we have late starts and the teachers are able to meet together as a department.
Teachers have a chance to discuss how to improve instruction.” Collaboration and
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uniformity is fostered by the administration team at Valley High School. All final
assessments in mathematics classes are the same. Teachers have designed their own
department finals to measure student learning. Teachers sit down as a department
and analyze the scores on all of the finals to make modifications for improved
instruction and teaching practices.
Much of the curriculum designed at Valley High School is from data-driven
decision-making. All of the assessments are analyzed by the entire faculty to
improve instruction and also create new courses. The CAHSEE Support, Algebra
Readiness, and Algebra A/B courses were all designed based on the results from the
student performance on state and district assessments. According to Key Leader A,
the school Principal:
Several years ago the administration team and I created the Principal’s vision
statement and it is now called the shared vision statement. We looked at the key parts
and elements to work on. One of these key elements was mathematics. We started
having honest discussions and looking at the key data in mathematics. It was at that
time that we created the Algebra Readiness class, which worked on the
computational skills of students.
Many of the teachers confirmed in the interviews that the Algebra Readiness
class is successful in improving student achievement.According to Teacher L: “The
Algebra Readiness Program is very successful here at Valley High School. Algebra
Readiness along with Sheltered Math Classes are great ways in which we can
differentiate the instruction for the students at different levels. The Algebra
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Readiness is successful for the students because we work on basic skills in
arthematic with the students.”
The decision to create Algebra Readiness to help prepare students for
Algebra has garnered mixed opinions from faculty members. Some feel it is a great
support to all students enrolled in the course, while others feel that about half of the
students in Algebra Readiness are not motivated to learn. According to Key Leader
C, Assistant Principal of Guidance and Instruction: “Algebra Readiness Class is
offered to Freshmen concurrently with them being in Algebra. So they have a double
period of Algebra and Algebra Readiness. I have found that this gives them that
additional support and students get the extra instruction they need to be successful in
Algebra.”

Summary
The curriculum, at Valley High School is aligned with the California Content
Standards, with their larger goal being defined by NCLB (2001) that all students will
be proficient by 2014 as measured by the CST. To facilitate students improving their
learning and achievement Valley High School uses an Algebra Readiness Class,
which is the instructional program used by Valley High School to assist the school in
realizing its goal of improved student achievement for all students. The course is also
designed to improve student achievement on the CAHSEE Mathematics section.
The leadership and staff at Valley High School acknowledged to varying
degrees the impact of federal, state and local policies. The teachers lesser connection
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to these policies may have been more of a reflection of their lack of knowledge for
the terminology than an indication that they did not identify the impact of such
policies as NCLB, CAHSEE and graduation requirements. Because within the
context of the interviews, there was a greater acknowledgment by the teachers that
such policies had influenced the instructional decisions and subsequent student
performance. Based on administrator interviews the administrative leadership was
more cognizant of the direct implications of state and federal policies on the
decisions made in respond to the guidelines and policies regarding improving student
achievement.
Overall the math teachers are a cohesive department that is united around
common structures, practices and expectations for both the students and the adults.
They clearly identified the design of the master schedule, the practices of curriculum
sharing, department meetings, creating common assessments, mapping out a school
mathematics pacing plan for each course, and the mathematic department chair
adjunct math colleague coaching duties are all critical components of their increase
in achievement.
Research Question 3: What change process did the school use to enhance the
math program and strategies to assist students in mathematics?
This question will examine what processes were established and implemented
as a means of changing the school math performance. The Bolman and Deal,
Reframing Organizations (2003), frames provide a “guide” for understanding the
complexity of organizations. The following instruments were used to facilitate data
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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 third research question was organized and
presented as follows: information, perceptions, and opinions about efforts to improve
mathematics instruction, description of the change process that improved math
achievement, description of the structural, human resource, political, and symbolic
methods used by the key leader, and analyzed with respondents’ results to the Math
Teacher Questionnaire for items 14-29 and Non-Math Teacher Questionnaire for
items 11-16.
The purpose of this question was to develop an understanding of what
processes were established and implemented, and how leaders respond to the
challenges of effecting increased achievement in math through the four frames
(Bolman and Deal, 2003). These frames provide a way to categorize the approach,
response and influence in organizational change and are listed as follows: (1)
structural, (2) human resources, (3) political, and (4) symbolic. The application of
multiple 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 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 depending on the circumstances.
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Structural Frame
School Design
At Valley High School student achievement in mathematics continues to be
an area of great concern. School leadership has increased mathematics achievement
as a priority in the school improvement plan. There have been major efforts from the
administration team to get feedback from all math teachers about areas of concern
with curriculum design and planning, student learning expectations, common
assessments, homework policies and professional development. According to Key
Leader A, school Principal: “Seven years ago we started monthly late start staff
development days where the teachers can meet as a department to dialogue about the
data and to look at student work and have the discussions they need to while
analyzing the work. We have also promoted the lunch time math meetings and have
an administrator there who is involved."
The scheduling of late start at Valley High School has allowed teachers to
collaborate and discuss any areas of curriculum concern. During the late start
department meetings teachers have an opportunity to analyze student work in teams
of teachers, re-evaluate common assessments, plan class instructional activities, and
create common benchmarks of assessment.
According to the Principal: “There is a lot of collaboration with the teachers
and the benchmarks are always used. The syllabus and rubrics are similar from class
to class.” Master scheduling is a delicate operation at Valley High School in which
the “neediest” students take priority when scheduling. The Principal was proud of the
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master scheduling at Valley High School. There are specific guidelines and policy to
follow when scheduling students for courses.
Math teachers strongly agreed that support classes have been included in the
master scheduling to improve student achievement in math. The Math Teacher
Questionnaire received a an average response rate of 4.3 on item 13, which asked is
the master schedule was made for the students’ needs. . Furthermore, both math
teachers and non-math teachers agreed somewhat that the master schedule is built
based on student need. The Math Teacher Questionnaire received a response rate
average of 4.0 on item 6 and the Non-Math Teacher Questionnaire received a
response rate average of 3.6 on item 6. According to Key Leader C. Assistant
Principal of Guidance and Curriculum:
The Math Department Chair is very respected on this campus and has been
here a long time. He is very involved with the master schedule, which teachers are
best at teaching each course and what classes are offered here. He knows which
teachers are nurturing enough to teach the Algebra Readiness course for kids that
need remediation. He is also involved in where the teachers will be located.
The formula for master scheduling symbolically speaks to where the
priorities are at for student achievement at Valley High School. Students who require
the most attention and unique classes are scheduled first. There is an attitude that
attention and careful consideration needs to be taken for special education students,
ELL students and gift and talented students. The focus and priority of master
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scheduling is placed on a minority group of students that has the most unique class
schedule.
Math teachers and non-math teachers agree somewhat that Valley High
School has a clear strategic plan to improve student achievement. The Math Teacher
Questionnaire received an average response rate of 3.4 on item 21 and the Non-Math
Teacher Questionnaire received a response rate average of 3.6 on item 14, which
asked if there was a clear strategic plan to improve student achievement.
Through interviews the faculty and administration explained how they are
aware of the Principal’s vision for increased collaboration. There is a common thread
of commitment to collaboration and teachers working together at Valley High
School.
As an integral leader at Valley High School the Principal takes an approach
to honestly discussing areas of improvement in order to increase student
achievement. As a blunt and assertive leader the Principal has pushed the
mathematics department to reform its current program.
Facilities
Valley High School’s school design is carefully considered to increase
student achievement in mathematics. School administration work together to create a
learning environment that best promotes learning for all students. Consideration is
taken to the placement and location of mathematics classes.
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According to Key Leader C: “The Assistant Principal of Facilities and Assistant
Principal of Instruction work together to make sure the physical environment for the
kids is conducive to learning.”
There was a change in the location of mathematics classes at Valley High
School three years ago. A majority of the math classrooms were in the main building
on the second floor and the remainder of the classes were spread throughout the
campus with a handful of classrooms across the street from the main campus in the
portable classrooms. The leadership team realized that many of the math teachers
were isolated based on the location of their classroom. This isolation discouraged
teachers from planning with each other, as well as working on collaboration and
commonality of instruction. Site leadership committed to improving the school
design by relocating the mathematics department in a common area of the campus.
At Valley High School the mathematics classes are now centrally located in
the main building on the second floor. All math classes, with the exception of one,
are located in the same building and same floor. The site administration agreed that
the location and placement of classrooms can drastically improve collaboration,
student achievement and improved instructional practices.
Class Size Reduction
Another school design change at Valley High School is the implementation
of reduced class sizes in many of the math courses offered. All Freshman math
classes have a maximum of twenty students per class in order to increase student
achievement in mathematics. The Principal explained that the school district helps
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fund this effort to have class size reduction in Freshman classes. According to Key
Leader B, Assistant Principal of Curriculum: “We are committed to 20 to 1 with our
Freshmen students. We keep those ratios down so the kids get the attention they
need.”
This is a huge change in comparison to the other math classes that range from
thirty-three to thirty-five students per class. According to the Freshman math
teachers, the benefits of a reduced class size are monumental. The Mathematic
Department Chair also agreed that class size reduction in Freshman math classes
impacts increased student learning. He explains: “The twenty to one ratio in the
Freshman classes helps give more attention to these students. The students have
more opportunity to learn in smaller classrooms and have their individual needs
met.”
The Math Department chair also felt the class size reduction of the CAHSEE
course has impacted student performance on the CAHSEE exam. He accounts: “Our
CAHSEE class that prepares the kids for the exam is successful because it’s small.
There are less than 20 students in each CAHSEE class. These classes that are so vital
to help prepare students for the requirements to graduate.”
Many teachers and administrators also felt the CAHSEE class offered to
students is successful because of the class size. This class is limited to twenty
students and in most cases the classes have between fourteen to sixteen students,
which allows for more attention to each students and personalized instruction. Math
Teacher G, who teaches this course, accounts: “We have good CAHSEE results,
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because we have a CAHSEE class that prepares the kids for the exam. There are less
than 20 students in each CAHSEE class.”
Human Resource Frame
Teacher Assignments
There has been a significant change in the hiring practices of teachers at
Valley High School for the past eight years. The Principal is highly involved in the
hiring of all teachers at Valley High School and there are always other administrative
team members and teachers within the specific departments who are also present at
the interviews for teachers. In all interviews with Key Leaders at Valley High School
there was a strong unified voice that the hiring of highly qualified math teachers over
the past eight years has been instrumental in increasing student achievement in
mathematics as well as improving math instruction on the campus. According to Key
Leader D, the Math Department Chair: "The Math department has been getting better
and better teachers. As teachers leave we seem to be hiring teachers that have better
teaching skills.”
The vision of the hiring process at Valley High School is from the Principal.
He is aware of how important it is to take the time to recruit and search for the best
teachers available. The Principal is actively involved in going to many recruiting
fairs across the nation to find the most talented math teachers. He notes that a
majority of the faculty is rather young. He has personally hired over 40% of the
teachers that are presently on the faculty.
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According to Key Leader B. Assistant Principal of Curriculum: “Our
Principal is a cheerleader. He is so passionate and so intent on the students having
the best opportunities. He is very infectious! When he interviews the perspective
teachers I see that and they really want to be part of the team, too. I believe student
achievement in mathematics is contributed to the Principal because of his key hires.”
Many administrative and faculty members explained how impressed they
were with the reform in the hiring practices at Valley High School. They explained
how there is more involvement from a team of faculty and administrative members
that work together to hire the best candidates. According to Teacher C: “Our
leadership is huge. The administration is really committed on making sure they hire
all the right people that compliment our math department. Our math chair is involved
in the interviewing of all new hires.”
According to Key Leader H: “Our Principal is very big on hiring good
teachers in math. He is personally involved in all of these hiring decisions.”
According to Key Leader K: Guidance Counselor: “It has been a great
benefit to have experienced math teachers involved in the hiring of new math
teachers. The experienced math teachers are mentors to new teachers in order to
move them along.”
According to Teacher F: “As a human resource leader our Principal will
interview teachers immediately at a Teacher Fair. He has made drastic changes in the
hiring practices at our school site.”
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The administration believes that teachers have a better performance when
their classroom assignments are matched with their expertise level as opposed to just
seniority. As previously mentioned, Valley High School has undergone a reform in
the school culture. According to the Principal, when he assumed his position at
Valley High School there was a huge shake up that needed to take place to improve
some teacher performance. When he started leading at Valley High School there
were some faculty who was not teaching in their credentialed content area.
Political Frame
As a political leader Valley High School’s Principal is able to work with
stakeholders, as well as strategically allocate spending and network to promote his
vision for the school. According to Key Leader B, Assistant Principal of Curriculum:
“Our Principal has made many political changes in terms of how moneys are spent
on campus. Rather than spending money on a new copier, he is in favor of teachers
attending workshops at UCLA or other educational conferences.”
The Principal is a leader that involves all stakeholders in the process of
change on the campus. He listens to everyone and leads with a central vision to
improve instruction and student achievement on the campus. According to the
faculty and administration team the Principal is able to implement change from
listening to others. He is described as a leader that takes the time to here from all of
the stakeholders before making a discussion.
The Principal takes time to get input and help from teachers to improve
instructional practices. While generally in line with this observation, math teachers
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somewhat agreed on Item 18 of the questionnaire that teachers have helped to
develop strategies used at Valley High School to improve the instructional practices.
The Math Teacher Questionnaire received an average response rate of 3.7 on item
18. Furthermore. The math teachers agreed somewhat on Item 35 of the
questionnaire that the school leader provides opportunities for faculty members to
discuss mathematic instruction and also agreed somewhat that the school
instructional leader encouraged faculty members to discuss effective math
instructional strategies.
As a political leader the Principal not only took the time to have one hour
interviews with all of the current math teachers to get their feedback on where they
see areas of growth for the math department, he also took time to understand the
current practices in the department and see where there is and is not commonality in
instruction, expectation and classroom policies.
The Principal is politically involved with the school district in order to
increase allocation and gain political support to improve the school. According to
Key Leader C, Assistant Principal of Guidance and Instruction:
A lot of obstacles we have are financial barriers in what we can offer and
provide. Our Principal has invited the School District Board of Education
members to come on our campus to show the things he has started to do and
have their support. He shows the things we have been doing and always adds
that we hope to do this… Politically, our Principal tries his best to bring the
School Board members on board with the changes that are made and need to
be made at Valley High School.

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The Principal is aware of the political stakeholders that are involved in the
reform process. He works with these stakeholders as an advocate, fundraiser and
spokesperson for Valley High School.
According to Key Leader K, Guidance Counselor: “There is a lot of
acknowlegement of successes. It is always visually rewarded and teachers are
acknowledged for the success. Our Principal always tells the staff that success
happens from the teachers were involved in the process.”
Symbolic Frame
Leadership at Valley High School appears to have a shared vision and
symbolic approach. According to most faculty members the key leader on campus is
the school Principal. Key Leader A has been Principal of Valley High School for the
past eight years. Prior to that he taught at Valley High School for 10 years as an
Advanced Placement Spanish Teacher. Almost all of his career has been at Valley
High School and it is apparent that he is dedicated and personally involved in the
success of the school.
The school Principal has a strong, clear vision for the school for increased
student learning and an approach to education that all students can learn and will
learn at Valley High School. His leadership style is considered charismatic and
infectious by many faculty members. The Principal has intense pride for Valley High
School in terms of the progress made so far, and even higher expectations for where
it needs to be and the future. The members of the administrative team and faculty are
aware of his high expectations for student achievement.
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Key Leader A, school spoke about his vision for leadership at Valley High
School. He felt: “I believe my job is to encourage leadership on this campus. My
belief is that if something happens to me on the way home and not that I am not that
great, but there if there is nor a culture of nurturing leadership and having people
ready to take charge, then I have failed.” The Principal further explained his visions
for shared leadership on the campus and it is evident that he feels the more
involvement you have with others the better the results and outcomes. He is
committed to taking Valley High from “good” to “great.” He feels Valley High
School can reach greatness through collaboration, inquiry and self-betterment.
According to Key Leader E, Guidance Counselor:
We have a culture on this campus with administration, faculty staff, clerical
or whoever that there is an open door with the Principal if there are any
changes they are not happy with. The lines of communication always stay
open on this campus. We present change in a collaborative way. When you
are on this campus you are brothers and sisters in a community.

Summary
Through the questionnaire responses, both from the math teachers and the
“non-math” teachers, and the interviews there was evidence of leadership utilizing
skills, actions, and decisions that connect with differing aspects of the four frames.
Overall the Structural and Human Resource frames are specified through interviews,
review of documents and researcher observation as the most dominate frames having
the most significant impact, both of the other frames fall within these frames. The
response from the teachers and administrators during the interview consistently
reinforced the Principal as the facilitator who put systems in place to move the
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school but that the real change in the math program was coming from the leadership
of the Mathematics Department Chair in terms of instruction and supporting
colleagues with improved instruction and assessments.
The change processes within the Structural and Human Resource frames
enhanced the math program and strategies ultimately increasing student achievement
in mathematics at Valley High School. The major structural policy changes at the
high school are to align the graduation requirements with Expected School-wide
Learning Results (ESLRs), critically design the master schedule based on the needs
of the most “critical” students (EL, SPED and AP students), creation of common
collaboration departmentalized planning time, and the restructuring of the central
location and departmentalization of almost all the math classes. VHS restructured its
master schedule to implement an Algebra Readiness Class to supplement the
student’s basic skills to increase their likelihood of their success in the faster paced,
Algebra course. In addition, the administration made it a priority to recruit and hire
high quality faculty members that best compliment their Mathematics Department
and school vision. The Principal was mentioned numerous times in interviews as a
change agent for transforming the staff through key new teacher hires.
Research Question 4: To what extent was strong instructional leadership
important in improving A) the mathematic programs/strategies and B)
mathematics achievement among students?
This question will examine what the role of the instructional leader is in the
improvement of math achievement and what were the strategies utilized. This
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analysis utilizes The Educational Testing Services (ETS), “A Framework for School
Leaders: Linking the ISLLC Standards to Practice” which defines essentials aspects
of instructional leadership: vision for learning; supervision and monitoring of
instruction; community and politics; culture of teaching and learning; and data driven
decision-making. The following instruments 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 fourth research question was organized and
presented as follows: information, perceptions, and opinions about who the key
leaders are that promoted improved student achievement in math, description of the
roles leaders played in the development of the professional learning community on
the campus, description of how professional growth was supported, description of
how teacher collaboration was fostered, and analyzed with respondents’ results to the
Math Teacher Questionnaire for items 30-42 and Non-Math Teacher Questionnaire
for items 17-22.
Vision for Learning
According to Key Leader J, Guidance Counselor: "Our goal is to sustain or
improve achievement on this campus."
According to Key Leader C, Assistant Principal of Guidance and Instruction:
“My Principal was a teacher here and has grown up through the ranks to become the
Principal. He knows the culture and community here. He knows when someone is
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going to fit. Getting the right teachers here is critical. My Principal is proactive with
the teachers that are not working out here.”
Supervision and Monitoring of Instruction
There has been a significant change process in the evaluation of teachers at
Valley High School. When the Principal came into leadership at Valley High School
he created high expectations of teachers and increased classroom visitations. Prior to
the current Principal there was a school culture where evaluations were not being
done appropriately or at all. Teachers were evaluated without an administrator
coming into their classroom.
According to Key Leader A, school Principal: “When I came on as the
Principal I had frequent visitations to classrooms. That was a shock when I came on
here, because the culture here was that you were visited very infrequently.
Sometimes you weren’t even being visited when you were being evaluated.”
The Principal works with the Mathematics Department Chair in the
evaluation process to give feedback on what type of instruction is happening in the
classroom. By working with the Math Department Chair the Principal hopes to get
coaching for a struggling teacher and also promote a discussion in department
meetings where teachers are sharing and collaborating on their instructional practices
Non-math teachers agreed somewhat on Item 21 of the questionnaire that the
Principal works hard to monitor and supervise instruction in the classroom. The Non-
Math Teacher Questionnaire received an average response rate of 3.4 on item 21,
which asked the dedication of the Principal to monitor and supervise instruction in
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the classroom. The Mathematic Department Chair also explains that he has seen
improvements in teacher instruction through the reformed evaluation process. He
accounts that there is a high standard set for expectations of teachers here at Valley
High School and these standards improve the instructional practices of our
department. According to Key Leader D, the Mathematic Department Chair: “It is
helpful that we have good hiring and evaluation practices here at Valley High
School. The practices have really improved over the past five years with our
Principal taking a more proactive approach to what he expects in the classroom.”
Other faculty and administrative members also discussed the improved hiring
and evaluation procedures at Valley High School. There was consistency in their
accounts that the Principal was instrumental in the change process of the evaluation
process by being more pro-active in the classrooms and holding high expectations
for new hires. According to Key Leader F, Guidance Counselor:
“Our administrative team discusses our expectations of new hire teachers. I know
that the culture at this school is that if the teachers don’t ‘get it,’ then they are not
tenured.”
According to Key Leader A, the school Principal:
We have looked at teacher evaluation much more seriously. Quite frankly, I
have a few short fuse for that. So if that individual, especially if they are a
math teacher and a new hire, is not with the program, isn’t on the bus, or
doesn’t want to get on the bus, and certainly isn’t on the right seat, then we
have made a personnel change.

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Community and Political
The Principal at Valley High School works with community members and
district school board members to gain support to improve the educational practices.
The faculty and administrators explained that Valley High School is in an area of
active community members with high expectations for student performance. Some
believe that these expectations are due to parents having high expectations for their
sons or daughters to attend four-year universities Parents place high expectations on
the school to prepare and encourage their sons or daughters to go on to higher
education. According to Key Leader B, Assistant Principal of Curriculum:
The community has higher expectations now that the students need to go on
to higher level math and anything to help with their acceptance into colleges.
We really try to accommodate that and get those students better prepared and
move further along.

According to Key Leader K: Guidance Counselor: “We have a partnership
with the local community college with the college-prep math class that offered to
Juniors and Seniors. Our Math Department Chair teaches that class with the
community college curriculum, but on our campus.”
Parents are concerned about the academic progress of their son or daughter at
Valley High School. According to staff there is a lot of parental support, which they
feel is a benefit to the teachers and the students. According to Teacher C: “There is a
lot of parental support at this school. Every time I call home to a parent I get a lot of
support and I think that has a lot to be said about the school culture here at Valley
High School.”
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Non-math teachers agreed somewhat on Item 17 of the questionnaire that the
Principal works to gain the support of the community for the school’s academic
efforts. The Non-Math Teacher Questionnaire received an average response rate of
3.6 on item 17. There are many areas, which the administration and teachers would
like to improve at Valley High School, but there is a financial barrier. Politics are
involved when it comes to these barriers at Valley High School. Therefore the
Principal has to work as a political leader by advocating for additional funds and
resources to improve student achievement. According to Key Leader F: “We would
like to have smaller math classes, but the funding is limited from the district. We
would also like to offer math classes to all students during the summer, but currently
they are only offered to students who did poorly in the school year. A lot of obstacles
we have are financial barriers in what we can offer and provide.”
The Principal is an advocate in a variety of political arenas to ensure
additional opportunities that foster student learning. On School Site Council the
Principal works all stakeholders of the community to create the school plan and
allocate additional funding to enrich the quality of education at Valley High School.
According to Key Leader K, Guidance Counselor:
The School Site Council has been active in listening and filtering requests to
enriching the quality of instruction. They paid for math teacher tutoring for
the students to gain additional support. The school site council encompasses a
variety of stakeholders: teachers, parents, administrators and students that are
able to work together and provide additional opportunities to provide learning
opportunities for the students.

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As a political leader Valley High School’s Principal is able to work with
stakeholders, strategically allocate spending and network to promote his vision for
the school. According to Key Leader B, the Assistant Principal of Curriculum: “Our
Principal has made many political changes in terms of how moneys are spent on
campus. Rather than spending money on a new copier, he is in favor of teachers
attending workshops at UCLA or other educational conferences.”
The Principal is politically involved with the school district in order to
increase allocation and gain political support to improve the school. According to
Key Leader C, the Assistant Principal of Guidance and Instruction: “A lot of
obstacles we have are financial barriers in what we can offer and provide. Our
Principal has invited the School District Board of Education members to come on
our campus to show the things he has started to do and have their support.”
The Principal is aware of the political stakeholders that are involved in a
reform process. He works with these stakeholders as an advocate, fundraiser and
spokesperson for Valley High School.
Culture of Teaching and Learning
Valley High School’s leadership promotes a culture of teaching and learning.
Currently one of the Principal’s areas of concern is increasing mathematic student
achievement and teacher instruction. The Principal believes in a lot of professional
development among his faculty in order to improve teaching practices. He is in favor
of teachers attending conferences to get innovative ideas to use at Valley High
School. There is limited funding, but he reports that he has been prioritizing all
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professional development funding in order to improve the culture of teaching and
learning on the campus. Math teachers somewhat agreed that the instructional leader
provides professional development resources that they can use in mathematics
instruction. The Math Teacher Questionnaire received an average response rate of
3.4 on item 32 when faculty was asked how supportive the instructional leader is to
provide professional development.
According to Key Leader D, the Math Department Chair: “Our Principal is
very concerned, as he should be, about the academics of the school. This year he is
doing more workshops for teachers to help them develop more strategies for math
instruction.”
According to Key Leader A, the school Principal: “The district does provide
some professional development for mathematics teachers. The district is supportive
of the fact that we need to provide more staff development in mathematics, have
common interim assessments, and grading policies for math by level.”
The staff describes a philosophy in which everyone is working together to
educate the students at Valley High School and that everyone is responsible for the
performance of the students. There is a culture of teamwork and collaboration in
order to foster the education that takes place at the high school. According to Key
Leader B, the Assistant Principal of Curriculum:
Every summer we get together as a staff and review where with are with our
API and get together collectively to acknowledge our successes and make
goals. We are in the philosophy of colleuegiality that we are all responsible
for our school. We are all responsible for the success and we all need to
work together to improve and move on in student achievement.
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Math teachers agreed somewhat on Item 38 of the questionnaire that the math
achievement goals and measures at Valley High School are clearly articulated and
easy to understand. The Math Teacher Questionnaire received an average response
rate of 4.0 on item 38. In addition, the non-math teachers agree somewhat on Item
20 of the questionnaire that the school leaders use data-driven information to address
issues related to student achievement. The Non-Math Teacher Questionnaire
received an average response rate of 3.5 on item 20 when asked to what degree the
school leaders use data-driven information to address issues related to student
achievement. According to Key Leader K, the Guidance Counselor: “We have to
figure out ways to have people to really feel ownership of what is going on here at
Valley High School. That is what we do as a leadership team here at Valley High
School, we do our best to keep teachers involved and invested into the school and
district”.
The Principal is described as a proactive leader who meets with faculty to
listen to their concerns and input for improvements within the school. By doing this
the leader is able to hear directly from the faculty and engage the teachers in the
change process. According to Key Leader B, the Assistant Principal of Guidance and
Instruction:
We have a principal who is proactive to meet with Department Chairs and
have conversations with teachers. He did an hour long interview with each
individual math teacher to get their feedback. This is vital and critical to the
process. He now knows where each teacher’s frustrations lie and what they
think we need to do to improve.

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The Principal has worked with the leadership team to create school wide
learning results that are prominently posted throughout the campus and discussed in
classrooms. The learning results are clear expectations from the Principal of the
standards for learning at Valley High School. According to Key Leader K, the
Guidance Counselor: “The Principal is present in the way that our ESLRS (School
Wide Learning Results) for our WASC accredentiation have been formulated,
reevaluated and reformulated then acted upon. ESLRS are on the marque, posted in
the classroom, and they are the framework on which we hang everything else.”
According to Teacher C: “My Principal has developed standards throughout
the school which are called the ESLRS. The kids have these standards memorized
and the Principal will walk around the school and ask students to recite the ESLRS.”
There are high expectations set to improve student motivation and
achievement. The faculty is encouraged to collaborate and discuss teaching
strategies. Many faculty and administration members account that the Principal is
responsible for the current vulture of teaching and learning.
According to Key Leader E., the Guidance Counselor: “Valley High School
has a learning climate where students want to do well in their classes, we have a
culture of learning. The teachers are very proactive and will do calls home if the
students aren’t doing well.”
Data Driven Decision Making Analysis
At Valley High School, the Principal uses data-driven decision making to
drive the instruction of the mathematics department. The data was out and openly
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analyzed in conversations with him and also watching faculty and administrative
team meetings. The Principal explains how there is a healthy internal competition
amongst the faculty to improve student achievement, which drives improved
instruction.
The Principal is described as a leader that simplifies the data for the faculty to
interpret areas of concern. According to Key Leader B, the Assistant Principal of
Curriculum: “Our Principal is also really good at analyzing data and seeing where
we are and where we are going. He is able to simplify the results for us and put clear
expectations for the staff of where he want us to be.”
The Principal discusses student data in all Leadership meetings in order to
have honest conversations on how to improve student achievement. According to
Key Leader I: “The Principal is meets with department chairs to make sure everyone
in their department is on the same page with their benchmarks and the expectations
are all the same. In every Leadership meeting they are discussing student data and
figuring out how to solve the problem together.”
In addition the math teachers agree somewhat on Item 43 of the questionnaire
that the Math Department Chair has been entrusted with and is empowered to make
important curricular decisions. The Math Teacher Questionnaire received an average
response rate of 3.4 on item 43 . In comparison non-math teachers had a high degree
of neutrality on Item 22 of the questionnaire that the Principal makes effective use of
the department chairs and relies on their expertise when making important curricular
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decisions. The Non-Math Teacher Questionnaire received an average response rate
of 2.9 on item 22.
According to Teacher M: “Our department chair is the math guru of the
district. He does a good job breaking down all of the data for the teachers and seeing
where we need improvement. He disaggregates the data for both high schools in the
district.”
According to Key Leader A, the school Principal:
We look at data every year. We don’t hide the data and we have the honest
discussions. The discussions go on all the time. The data ranges from grade
frequencies, in which I look at ten week grades and the grade percentages of
As, Bs, Cs, Ds and Fs. We have the discussions as a math department in
which they look at their common finals. The teachers know there is a crisis in
math.

Summary
The role of leadership at Valley High School has been the stimulus for many
structures and practices that have been implemented to support student learning. The
Principal has taken more of a facilitative leadership role and encourages shared
decision-making. The Principal does not assume the role of the instructional leader
but rather has delegated this to those in supportive leadership roles. The Mathematics
Department Chair is most frequently identified by the teachers as the instructional
leader in their department and the most consistent and influential person affecting the
curriculum and instructional strategies. The administration are viewed as the leaders
on a larger scale, as the ones responsible for the school in it’s entirety and as a
resource for support specifically as it pertains to providing necessary resources. It is
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evident that the math teachers and non-math teachers perception of the culture of
teaching and learning at Valley High School, which is embedded within Standards-
Based Instruction (SBI), is the most significant contributor to improved math
achievement. The role of the leader both at the administrative level and the
department level have been essential to the progress and improved achievement in
math.
Command and control devices are evident in changes in structure and
changes in organizational routines (Hess, F. M., 2005). It was evident that the
Principal was a structural and instructional leader who established the policies,
routines and structures within the organization. He also guided the administrative
team to establish the guides of acceptable behavior, i.e., expectations within the
organization through the supervision and monitoring of instruction. The educational
leader was monumental in improving the hiring and evaluation procedures at Valley
High School. There was consistency in the faculty’s accounts that the Principal was
instrumental in the change process of the evaluation process by being more pro-
active in the classrooms and holding high expectations for new hires.
Research Question 5: How did leaders in the school resolve the dilemmas about
instructional leadership?
This question will answer the impact that the Instructional Leaders expertise
or lack of, had in their ability to support the teachers and the instructional math
program. The framework developed to address this question of expertise was divided
into two distinct components predicated on the two different parts of the research
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question. First, an assessment tool, flow chart, was created to allow the investigator
to ascertain the level of expertise in math of the instructional leader. Secondly, this
question will address how the key leader overcame obstacles that were faced to
improve student achievement in mathematics. The following instruments 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 fifth research question was
organized and presented as follows: information, perceptions, and opinions about
obstacles the school face in the implementation of changes related to improvement
achievement in mathematics, description of how site leadership worked to overcome
the obstacles, description of structural, human resource, political, and symbolic
changes implemented by site leadership, and analyzed with respondents’ results to
the Math Teacher Questionnaire for items 43-50 and Non-Math Teacher
Questionnaire for items 23-30.
Principal’s Expertise in Math
Valley High School’s Principal is not a High Qualified Teacher in
Mathematics based on the terms of NCLB. He currently has a Clear Single Subject
Credential in Social Science. He did not major in Math, nor did he minor in Math or
teach Math. Therefore based on the Assessment of the Principal’s Expertise in Math,
Valley High School’s Principal would be an instructional leader with low expertise
in mathematics. There were many strategies the Principal used to overcome obstacles
when faced with improving student achievement in mathematics.
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Strategies Used to Overcome Obstacles that have a High Degree of Success
While there were many obstacles that the Valley High School Principal faced
when improving mathematic achievement, he was able to use specific instructional
leader strategies to overcome these obstacles. Because of the Principal’s low
expertise in math, it is impressive that such significant improvements were reached
in math student achievement. It is necessary to look at what specific strategies the
Principal used to create human resource, political, structural, and symbolic change at
Valley High School. The following are strategies used by the Principal to overcome
obstacles that had a high degree of success.

Strategy 1: Delegate Leadership to Assistant with Greater Expertise
The Principal definitely uses the philosophy of high degree of collaboration
and a moderate degree of delegation at Valley High School. It was apparent that he
encourages leadership opportunities for all faculty members. There is a team
approach to solving problems at Valley High School. The Principal is highly reliant
on other administrators, counselors, and department chairs when making decisions
and implementing change. The reliance on these key leaders is a relationship of
listening and giving feedback to his ideas. While observing a leadership meeting and
interactions with faculty it is apparent that the Principal is a thoughtful leader that
listens to everyone’s point of view before speaking his own. He encourages inquiry
and discussion on how to implement change on the campus. He listens to the ideas
and points of view spoken and then expresses his views.
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The relationship of the Principal, and the Assistant Principal of Guidance and
Instruction and Assistant Principal of Curriculum is very symbiotic. First of all, they
are all on the same page and have very similar views about the school. There is a
shared passion by all of the administrators about the vision of the school and where
the school needs to be. The assistants rely on the vision of the Principal to implement
change and the Principal does delegate responsibilities to the assistants. The
Assistant Principal of Guidance and Instruction works closely with the guidance
counselors, feeder schools, school district office and school community. He is
delegated the responsibility of working with the guidance counselors to discuss
students who are struggling, working as a pathways leader for incoming Freshman
from the middle schools, attending district meetings that incorporate district-wide
curriculum reform, and working with parents and community members to encourage
student achievement. He also attends a majority of the IEPs on the campus.
While the Assistant Principal of Curriculum works closely with the
department chairs and Educational Services Department of the school district. She
attends many of the department meetings late-start and lunch meetings to provide the
administrative perspective. She also works closely with key teachers to develop
common assessments, pacing plans, curriculum guides and lesson designs.
Strategy 2: Empower Department Chair
The Principal also delegates the responsibility of running the faculty
meetings to a department chair. The Principal attends all faculty meetings and creates
the agenda for the meetings, but a key leader is delegated the responsibility of
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running the meeting. During the meetings the Principal sits with the teachers and will
stand up to give his Principal’s report.
The Principal empowers the Math Department chair to improve instruction
and reform the curriculum. There is an intimate relationship with the Principal and
the math department chair. He does delegate the chair to run department meetings,
coach struggling teachers in the math department, create the master schedule,
analyze student data and collaborate in data-driven decision making. Key Leader B,
the Assistant Principal of Curriculum, explained: “I work with department chairs and
the department chair work with the teachers in order to implement something new on
the campus.”
The math department chair is able to provide that support to all teachers in
their classroom instruction. He works as a coach for teachers that are struggling.
Teacher B offered how there is a tremendous amount of support from the leadership
of the school when improving teacher instruction. There is time for the department
chair to work with teachers to improve instruction.
The department chairs are empowered to be integral leaders on the campus to
improve teacher instruction and promote shared leadership. The Principal also
discusses the evaluation process with the math department chair and lets him know
how the math teachers perceive instruction. They work together to focus on student
learning and make standards-based instruction the solution.
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Strategy 3: Emphasize Inquiry and Problem Solving
The Principal encourages inquiry and problem solving in department
meetings and leadership meetings. The teachers are able to participate in shared
inquiry by analyzing student work and discussing teaching practices. The math
department also analyzes the data of the common interim assessments to guide
instruction for future courses.
The Principal is involved in an inquiry process with all math department
teachers. He analyzes how to improve instruction, looks for commonalities and
listens to the teachers’ input. According to Key Leader D, the Math Department
Chair: “Our Principal has taken a more aggressive stance to mathematics on our
campus.”
The Principal explained that the focus in mathematics reform at Valley High
School is improving common interim assessments to guide instruction. There is a
push from the district office to get feedback on the common interim assessments
used at Valley High School. By involving all teachers and the department chair in the
change process he is not only encourages inquiry and problem solving, but he
encourages shared decision-making and collaboration.
Strategy 4: Emphasize Quality Instruction
The Principal has high expectations of teachers and emphasizes the
importance of quality standards-based instruction in the classrooms. There has been
a change process to implement standards-based instruction and also increase
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classroom visitations. Administrators are now actively engaged in classroom
observations to witness learning taking place.
There is a positive professional learning community at Valley High School
that acknowledges the quality of instruction. Teachers are praised and encouraged
for their successes.
Teachers strongly agreed on Item 26 of the questionnaire that the Principals
emphasize the importance of quality instruction as the primary mission of the school.
The Non-Math Teacher Questionnaire received an average response rate of 4.2 on
item 26 . The Principal makes quality instruction the integral component of change at
Valley High School. There are high expectations on what standards should be taught
and how the standards are taught and assessed.
The Principal encourages his staff with praises on their achievements, and
also is not afraid to have honest conversations on areas of growth with teachers.
When students are not learning the concepts he sits down with teachers individually
or in teams to discuss modifications that can be made in the instruction. He works
with the staff look at the data and come up with alternative options and strategies for
success.

Strategy 5: Emphasize Raised Expectations
The Principal has a strong vision for the school and high expectations for the
faculty members. He feels that Valley High School has changed over time due to an
emphasis on raised expectations. It is his belief that now Valley High School
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promotes a school culture of hard working teachers, collaboration amongst faculty
members, high expectations of students, and the desire to have every student learn.
Expectations have been raised for everyone at Valley High School. He feels that a lot
of the change happened when there was an increase of classroom visitations. There
are high expectations of all faculty members and even higher expectations of new
hires. Teacher C explains that he feels administration is supportive, which can be
attributed to improved instruction. According to Teacher C: “I feel student
achievement improves each year from the efforts of the teachers and their high
expectations of each other and the students.”
Many Key Leaders attributed the raised expectations to the vision of the
Principal. They felt that the Principal encourages everyone to raise expectations and
work towards greatness. According to Key Leader G: “At our weekly leadership
team meetings we are reading Good to Great and reflecting on what we are doing on
our campus that is good and what areas we need to improve to take it to greatness.
We take time for an honest discussion to find out how we can improve and what
changes need to be made.”

Strategy 6: Emphasize Strategic Teacher Assignments
The Principal has a high degree of involvement and strategy in the creation of
the master schedule at Valley High School. He has overcome Human Resource and
Political challenges by implementing change with strategic teacher assignments. The
administration believes that teachers have better performance when their classroom
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assignments are matched with their expertise level as opposed to just seniority. As
previously mentioned, Valley High School has undergone a reform in the school
culture.
According the Principal when he became the Principal at Valley High School
there was a huge shake up that needed to take place to improve some teacher
performance. When he assumed his position at Valley High School there were some
faculty members who were not teaching in their credentialed content area. He
worked with the Math Department Chair to implement change and used his expertise
to create the master schedule. They worked together and looked at teachers’
credentials, education background and training to place teachers in the most
appropriate classroom assignments.
So the Principal took on a strong vision for the school and high expectations
for the faculty members and change happened. He feels that Valley High School now
promotes a school culture of hard working teachers, collaboration amongst faculty
members, high expectations of students, and the desire to have every student learn.
There are high expectations of all faculty members and even higher expectations of
new hires. All non-tenured teachers must work collaboratively with other faculty
members and the students need to achieve.

Strategy 7: Emphasize Revised Course Scope and Sequence and/or Curriculum
The Principal emphasizes a high degree of curriculum and course revision at
Valley High School. Much of the curriculum designed at Valley High School is from
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data-driven decision-making. All the assessments are analyzed by faculty to
improve instruction and also create new courses. The CAHSEE Support, Algebra
Readiness, and Algebra A/B courses were all designed from the results of student
performance on state and district assessments.
Teachers and administrators explained how the courses are constantly being
changed based on student results. The courses syllabi and courses offered change
every year in order to best meet the needs of the students and improve student
achievement. According to Key Leader K, the Guidance Counselor: “One thing that
has helped a number of students is when we moved to the four semester Algebra I
model and it helped students tremendously.”
Over the past decade Valley High School’s math program was revised
numerous times. Valley High School math program use to be a Algebra I,
Trigonometry, Algebra II sequence. Then the school reformed to an Integrated Math
with Algebra and Geometry. The school then moved back to the traditional model of
a slower paced Algebra I for the students who needed it to integrate the concepts,
and this has given the students a stronger foundation in Algebra I. The students can
now go onto the higher level math and complete through Algebra II by the end of
high school for college math.

Strategy 8: Emphasize Interventions for Lower Performing Students
While Valley High School faces many of the challenges of a high school,
they do not qualify for, nor receive Title I funds. Consequently, the Supplemental
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Educational Services (SES) mandate under NCLB (2001) is not applicable.
However, the administration and teachers recognized that many of their students
required additional support in Algebra I. Providing support for these lower
performing students has been a priority for the Principal. He is highly involved in
providing interventions for lower performing students at Valley High School. The
administration has math tutoring a priority intervention offered to struggling
students. The CAHSEE Support, Algebra Readiness, and Algebra A/B courses are
all intervention classes designed to support lower performing students.
According to Math Teacher A: “We have tutoring programs at Valley High
School which I believed help student achievement.”
The Principal worked with the School Site Council to find funding to pay all
math teachers to offer math tutoring after school. Each teacher offers math tutoring
after-school at least two days a week. There are about five to fifteen students at each
tutoring session. Many teachers find that math teacher tutoring is the most effective
way to improve student achievement on the campus by providing one-on-one time to
re-teach specific skills to students.

Strategy 9: Emphasize Strategies to Engage Students in the Learning Process
The Principal is aware that most of the mathematic department is not
providing learning opportunities that engage the students in the learning process.
Therefore, he now promotes the staff to use alternative strategies and modalities of
teaching to engage students in the learning process. As the school leader he works
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with the Mathematics Department Chair to encourage the teachers to use alternative
real-world mathematic projects and strategies that engage students in the learning.
The Principal explains that he would prefer to see the math teachers
improving their instruction to look more like his instruction as a Spanish teacher in
the Foreign Language Department. As a Spanish teacher he provided many
opportunities for the students to be engaged in learning and provided a lot of project-
based/inquiry experiences for his students. He realizes the need for increased
manipulatives and conceptual math used in daily instruction to encourage higher-
level thinking. Most importantly he felt that all students graduating from Valley High
School should understand the practicality and application of mathematics. According
to Key Leader A, the school Principal:
One of the things we have talked about recently is that you need to change
the mindset about mathematics for many kids. We need to show them the practicality
and application, especially for the kinestic learner. The Principal went to Japan two
summers ago to observe instruction at seven Japanese high schools. He was
impressed by how the Japanese instill the practicality of mathematics in their
students. He felt they do a great job of showing young people: “this is how math
applies to real life and how you can solve problems.” He feels the Japanese really
apply mathematical principles in their classrooms, they just don’t sit there and stare
at it in a book. According to Key Leader A: “I would like to use the model of foreign
language department with their framework and their project based learning and see it
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incorporated in mathematics. What I am talking about is having them do projects that
meet the visional, auditorial, kinestic, and musically inclined students”.

Strategy 10: Emphasize Articulation with Feeder Schools
The data shows that there is little articulation with Valley High School and
the feeder schools. However, Key Leader C, Assistant Principal of Guidance and
Instruction feels there is a lot of communication between (? the middle and schools)
in terms of curriculum. He believes this is because he is the sole person doing all the
articulation.
According to the data a majority of the articulation takes places with the
Assistant Principal of Guidance and Instruction as the spokesperson for Valley High
School in articulation meetings. He dialogues with the math department and reports
their point of view in articulation meetings with feeder school administrators. Based
on the data there needs to be more articulation directly with teachers from all the
campuses. Articulation can be improved by teachers talking directly to other teachers
about student expectations, key standards taught, student assessment data, teaching
strategies and grading policies

Strategies Not Used by Principal to Overcome Obstacles
There are strategies from Table 4 that the Principal is not using at Valley
High School. These strategies are used in other high school as reform efforts and
have proven to be highly effective when improving math instruction and student
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achievement. It is due to financial barriers that both of these strategies are not fully
implemented at Valley High School. The Principal shared that he would like to
implement these strategies but there is not enough funding to implement these
reforms.

Strategy 11: Bring in Outside Expertise
Valley High School has not brought in an outside expert to improve the math
program. The Principal has not brought in consultants or a math expert to implement
new strategies in math education at Valley High School. The only thing that is
offered is for a small amount of math teachers to attend math conferences each year.
After attending conferences the teachers are required to report what they learned in
the conference at the department meetings. From this strategy some teachers are
sharing math experts ideas with the staff.

Strategy 12: Emphasize Professional Development
Valley High School’s teachers and administrators agree that mathematics
professional growth is very weak, because there is not the necessary money
allocation need for adequate professional development. Currently the faculty does
professional growth among each other at the campus level. Teachers informally work
together to collaborate together and plan lesson.
According to Key Leader A, the school Principal:
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We have not been doing a good job in math professional development. The
bottom line is that I as a leader need to make a conscientious decision of
redistributing our discretionary funds. It is all a matter of making it a priority.
In my opinion we haven’t been doing a good job, but we are going to address
the issue and we are addressing it to try to make it better.

The professional growth has not been as strong as the Principal would like. It
is explained that professional development is now going to be focus for improvement
at Valley High School.

Summary
The administrative leadership, while they are not the math experts on the
Valley High School campus, is able to utilize their leadership expertise to access
strategies that have created an instructional program across the school that is
designed with the student and faculty needs in mind. The administration has
encouraged shared decision-making and increased collaboration amongst the staff.
This ability and willingness to reach out and engage others is not only a reflection of
leadership but also an indication of confidence. The teachers identify the
administration as participating in a facilitator capacity. These key leaders
acknowledge the expertise of others to support and improve the math instructional
program. The Principal emphasized quality Standards-Based Instruction (SBI),
raised expectations through the increase in graduation requirements for mathematics,
making strategic teaching assignments, increased collaboration with teacher inquiry
to design courses, and emphasized interventions for lower performing students by
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implementing an Algebra Readiness course and tutoring for all students in
mathematics, as strategies they used to improve student achievement in mathematics.
Analysis and Discussion
The findings in this chapter were determined 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 Valley High School focused on how to
increase student Algebra achievement over the past five years. VHS had an
instructional improvement plan that generated many positive and impacting results.
This organizational structural change was both multi-faceted in its approach and
complementary to the district vision for student achievement. Although there were
many factors that contributed to increased math achievement at VHS, there were
three themes that emerged as the foundations that have ultimately created the
conditions for improved math achievement at Valley High School.
Theme One: Shared Leadership and Decision-Making
The Principal has encouraged the Leadership Team to figure out ways to
create ownership of what is going on at Valley High School. The Principal kept
teachers involved and invested into the school and district. He made sure everyone
has felt they are really making a positive difference and change for the students,
regardless of what subject area they are teaching. There has been a philosophy
created on the campus in which everyone is working together to educate the students
at Valley High School and that everyone is responsible for the performance of the
students. There is a culture of teamwork and collaboration in order to foster the
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education that takes place at the high school. There are high expectations set to
improve student motivation and achievement. The faculty is encouraged to
collaborate and discuss teaching strategies.
The math achievement as reflected by the standardized state assessment
results show that the student math achievement at Valley High has increased
consistently the past five years, with some years reflecting substantial growth and
others more modest improvement. According to Fink and Resnick (2001)
instructional leadership ensures a sufficient knowledge of the instructional program
that is utilized by the school and more specifically the departments. This knowledge
allows for the Instructional Leader to facilitate the improvement of the mathematics
program.
Valley High’s leadership, while not math content experts themselves,
demonstrated that through action and decisions that reflected an understanding of the
math program, they were able to implement the systems and structures necessary to
fully implement and improve student achievement. The Principal had the skills and
the confidence as a leader to engage key personnel within the math department that
did have content expertise with regard to the implementation of policies, designing
the instructional program and changes that would ultimately influence the math
achievement. His leadership style has served as a source of empowerment and
insight for the math leaders in the math department. The Principal stepped back from
the overall day to day instructional leadership, instructional decisions and
implementation of the math instructional program giving much authority to the
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Mathematics department chair. This provided the opportunity for the Mathematics
department chair to assume more active and essential roles in the success of the
students and improved math achievement. The ability and insight of the Principal to
delegate instructional authority afforded him the ability to support other needs of the
school community. There is an intimate relationship with the Principal and the math
department chair, which has allowed the Principal to delegate the chair to run
department meetings, coach struggling teachers in the math department, create the
master schedule, analyze student data and collaborate in data-driven decision
making. The department chairs have been empowered to be integral leaders on the
campus to improve teacher instruction and promote shared leadership.
The leadership at Valley High School fostered and created a shared vision for
student achievement within the math department. They, specifically the Principal,
were able to accomplish this by developing a school culture that was focused on
teaching and learning as reflected in the collaboration of the teachers using data as a
means of making instructional decisions and fostering the underlying tenet of this
effort; a learning community that is student focused but respectful of the need to
support and provide opportunity for teachers to develop as professionals. The
Principal has involved all stakeholders in the process of change on the campus. He
listened to everyone and leads with a central vision to improve instruction and
student achievement on the campus. The Principal not only took the time to have one
hour interviews with all of the current math teachers to get their feedback on where
they see areas of growth for the math department, but he also took time to understand
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the current practices in the department and see where there is and is not commonality
in instruction, expectation and classroom policies.
The Principal’s vision focused on shared leadership on the campus and feels
the more involvement you have with others the better the results and outcomes. He
committed to taking Valley High from “good” to “great” and felt Valley High School
can reach greatness through collaboration, inquiry and self-betterment. Teachers also
agreed there was a shared vision of inquiry on the campus in the department
meetings. The scheduled collaboration time allowed teachers to work together in
departments for curriculum planning.
The Principal has been the catalyst for the many changes that were made to
improve the overall math program and department at Valley High School. He
certainly has served as the leader of the school sharing the instructional leadership
with those who have the expertise and she taking a more Facilitative Leadership
position as a means of engaging the school in a change process. He utilized his years
as a professional educator to access resources to support the math department. He
communicated clear directions, high expectations and his knowledge of the
importance of relationships as a means of attaining instructional goals. As a means of
meeting goals he sought to ensure that he was engaging the right people in and out of
the classroom.
Theme Two: Strategic Hiring Practices
At Valley High School, the NCLB Act has forced educators and
administrators to look at certain programs, instructional strategies, and new hires in a
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new and strategic way. The expectation of NCLB and Valley High School’s
leadership team has been that all teachers need to come in with the motivation and
instructional techniques to teach well and encourage high student achievement.
Valley High School’s Principal felt that by hiring the best teachers in the field would
drive improved instruction and increase student achievement. Therefore there have
been more serious practices and selection criteria with the hiring of teachers. The
accountability of the NCLB has allowed Valley High School to ‘clean up’ a lot old
systems that were unconsciously put in place by previous administration. Previously
the site was running under a system of seniority, which did not allow for much
collaboration, consistency and departmentalization of instruction, assessment and
curriculum. Prior to NCLB and the new administration there were teachers hired on
an emergency credential and many senior teachers were teaching subjects they were
not credentialed to teach. This system crumbled when the new accountability system
with NCLB and new administration was put in place at Valley Unified School
District.
For the past eight years the Principal has been highly involved in all of the
hiring of teachers at Valley High School. He made sure there are always other
administration team members, the department chair, and teachers within the specific
department at the interviews for teachers. There has been a strong unified voice that
the hiring of highly qualified math teachers over the past eight years has been
monumental to increase student achievement in mathematics and improve math
instruction on the campus.
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The vision of the hiring process at Valley High School has been from the
Principal. He was aware of how important it was to take the time to recruit and
search for the best teachers available. The Principal was actively involved in going to
many recruiting fairs across the nation to find the most talented math teachers. He
has personally hired over 40% of the teachers that are presently on the faculty.
The response from the teachers and administrators consistently reinforced the
Principal was a facilitator who put systems in place to move the school and create
new systems for hiring at Valley High School. The hiring practices at Valley High
School have influenced the retaining of highly qualified mathematics teachers on
their staff, which in turn has resulted in increased teacher collaboration, improved
instructional strategies and ultimately, increased student achievement.
Theme Three: Teacher Collaboration and Shared Inquiry
Teacher collaboration played has been a critical and essential design element
of the Valley High Schools to improve math performance. Due to the leadership
from both the administration and the math department structures and systems were
created that support teachers and the instructional program. As well, administration
and the math department leadership increased accountability of the teachers while
acknowledging teachers and the importance of them engaging in reflective thinking
and collaborative conversations as professionals with the knowledge and skills to
improve student achievement.
The implementation of the curriculum sharing, collaboration, creating
common assessments, designing course pacing calendars, and department meetings
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created dialogue and an increased focus on how to improve student learning. This
collaboration facilitated a change of practice. The teachers with the support and
leadership of the Mathematics department chair were unwrapping standards,
discussing concepts and engaging in analytical conversations about instructional
practices that the prior to the collaboration was not occurring.
Increased collaboration was also fostered by the relocation of the math
classrooms to a central location. The site administration moved the location and
placement of classrooms, which drastically improved collaboration, student
achievement and improved instructional practices. The accessibility to one another’s
classrooms was monumental in creating change in instruction and also created
increased commonality amongst teachers. Teachers were then able to visit other
math classrooms more readily and also use common resources from teachers to
improve instruction.
The ability to create a more “open door” policy that forced teachers from the
comfort of isolation and independence in their own classroom appears to have been a
critical aspect that changed the culture and dynamic of the math department chair
they interacted as a department and utilized these different structures as a tool for
their own professional development which is rooted in the concept of teacher
collaboration. The Mathematics department chair has the opportunity to coach other
teachers with their instruction by facilitating model lesson design and lesson inquiry
sessions.
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Teacher collaboration has also been fostered through student data discussions
at department meetings. With NCLB Valley High School concentrated on increasing
test scores and student achievement, which allowed the conversations on Valley
High School campus to lie around data-driven decision-making and figuring out how
to improve and perfect instructional practices. Valley High School used data-driven
decision making to drive the instruction of the mathematics department and increase
common lesson design, analyze student work, improve instructional strategies, and
common course assessments.
Much of the success at Valley High School has been attributed to how school
leadership promotes collaboration amongst the staff. There has been an increased
focus on the state standards being taught in the math classes and providing
intervention for the struggling students. Much of the curriculum designed at Valley
High School has been from data-driven decision-making. The assessments were
analyzed by all faculty to improve instruction and also create new courses. The
CAHSEE Support, Algebra Readiness, and Algebra A/B courses were all designed
from the teacher and administration conversations regarding the results of student
performance on state and district assessments. These new courses were created to
improve student achievement in mathematics and support students that were
struggling.
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CHAPTER FIVE
SUMMARY, CONCLUSIONS, AND IMPLICATIONS

Summary of Background
There is great concern about how many of California’s urban secondary
school students continue to have poor performance on mathematics standardized
assessments. Focused attention on increasing mathematic achievement by national
and state agencies through policy initiatives and published accountability reports
such as Annual Yearly Progress (AYP), the Annual Performance Index (API) and
high school exit exams has pressured school districts to implement standards-based
education where the ultimate goal is to elevate students’ mathematics competency.
School districts are compelled to implement standards and best practices to
meet the standards set forth. However, urban schools, which differ based on issues
of diversity, social-economics, perspectives and culture, schools must discover and
implement best practices that will positively impact their student body. It is critical
to understand how schools that are demonstrating mathematic academic success have
reformed their schools to promote significant rates of success for their students. It is
important to understand what are the best practices being implemented and utilized
at these high achieving school sites. It is necessary to learn what is the role of the
leader in the reform process and school design models.
Curriculum committees, universities, field experts, and textbook publishing
companies have provided curriculum aligned with state standards and the High
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School Exit Examination. Districts have allotted special funds and positions for
“math experts” and states have funded after-school programs to assist students who
are not faring well in mathematics. Despite efforts and choices presented to districts,
one program is not packaged to “fit all”. This is evident in the continual dismal
mathematics scores posted annually. Discernment in adapting a mathematics
program or moving a culture and people to achieve a higher standard in mathematics
is an essential element that has been challenging for school districts.
Effective instructional leadership is viewed as critical in a school’s success.
Having the ability to communicate a vision, build internal capacity, create an
atmosphere that includes academic rigor and carry out such leadership duties
effectively is seemingly lacking when it comes to mathematics achievement.
School-based administrators and district leadership alike, continue to struggle in
defining the characteristics that, in the context of improving math performance for
students, create good instructional leadership in mathematics. Several issues seem to
be especially relevant to instructional leadership in this setting. Leaders often do not
have strong pedagogical content knowledge in mathematics education; yet need to
carry out functions related to fiscal, personnel, organizational leadership, data
analysis, and review, etc. Little is known about how leaders work effectively in this
context.
Purpose of the Study
The purpose of this study was to conduct a case study of one secondary
school’s efforts towards a mathematics reform design and implementation. It
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examines factors that positively influence the math performance of secondary
students. This study investigated a school’s math achievement as a result of policy
initiatives in standards-based curriculum and instruction. This study investigated the
high school’s elements of design for the study; factors that shaped the district design
for mathematics reform; strategies educational leaders used to implement the
instructional reform; the extent to which the reform was implemented; and how
effective the reform has been in affecting teaching and learning practices. The focus
was on the school site’s administrative and leadership roles in the mathematics
reform process. The study incorporated an understanding of how instructional
leaders, who lack strong pedagogical content knowledge in mathematics education,
were able to impact significant mathematics achievement at the school site.
The research questions were:
1. What was the pattern of math achievement for various students at the school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement at the school?
3. What change process did the school use to enhance the math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in improving A)
the math programs/strategies and B) math achievement among students?
5. How did leaders in the school resolve the dilemmas about instructional
leadership?
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Methodology
To support the case study a mixed methods approach was utilized to collect
the data to support the study. This included the gathering of quantitative data to
support the descriptions found through the qualitative data collection in the study.
The qualitative approach provided data and information from interviews; and the
analysis of documents and artifacts of the school were cross referenced as a means of
gathering findings.
For the purposes of this case study one public high school based on an
established criteria was selected, information about the school and participants is
factual. But to maintain confidentiality and protect the anonymity of the participants
and the school, pseudonyms were used throughout the study. The instruments that
were developed for the study were created using current educational research
practices with the purpose of eliciting relevant responses that related to the research
questions. To support the analytical style which was utilized in the study, conceptual
frameworks were used so as to provide a context for the reader. The data was
validated through triangulation, which meant that analyses of all documents were
cross referenced with the interview and questionnaire results whenever possible.
Conceptual frameworks were used to provide context for the reader and
support the analytical style used in this study. Evidence found in document analysis
was cross- referenced with interview and questionnaire findings wherever possible.
Triangulation was used to verify and support findings. This entire case study process
is intended to add to the reliability of the findings made in the study.
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Data Collection and Analysis
The goal of this case study is to identify urban high schools that serve
economically disadvantaged and culturally diverse student populations with program
and leadership features that have proven to be efficacious in improving student
achievement in mathematics. A purposeful sampling process was used in order to
provide an opportunity to conduct a thorough investigation and to explore more
deeply the processes related to the research questions of this study. Selected schools
were chosen through a purposeful sampling developed by the research team and
Principal investigator using 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
6. Leadership stability as defined by a Principal being at the school for at least
three years during the time the improvement was made.
Research team members reviewed the list of schools that were identified
based on the criteria above. 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. The research team began meeting in a
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collaborative cohort model in January of 2006. The team worked together to
research questions and relevant academic literature was discussed in preparation for
this study. The team continued to meet through the summer of 2006 and into the
beginning of the 2006-2007 academic year at which time individual researchers
commenced their detailed studies at their chosen sites.
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 (see Appendix B).
3. Knowing that the group would need to research improvement in CST in
Algebra in a later step and that many schools would not have demonstrated
improvement, the group set a goal of a sample size of no less than 100
schools in the southern California region.
4. Preliminary efforts to use more stringent requirements did not yield a
sufficient sample so adjustments had to be made. For example, when the
student enrollment parameter was set to 1500; the percentage of minority
students was set at 65%; 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 research group were then assigned to research 10 schools each
by looking up and recording CST scores in Algebra I for the years 2003,
2004 and 2005 onto a common spreadsheet which one person in the group
compiled.
7. The group then assigned an absolute value to the improvements made in two
areas. First, decreasing the number of students scoring in the bottom two
performance bands; and second, increasing the number of students scoring in
the top two performance ands. These totals were added to indicate an overall
level of improvement. For example, if a school decreased the numbers of
students scoring in the bottom two performance bands by 3% 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.
c. Failed to evidence an overall improvement score as calculated in the
example detailed in number 7 above.
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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.
A flyer was distributed to all potential participants of this study, which
included a detailed description of the research procedures, purpose of the study and
also indicated that participation in the study would remain anonymous and was
entirely voluntary. A recruitment letter approved by the university’s Institutional
Review Board (IRB) was sent directly to potential participants following the
distribution of the initial flyer. Recruitment letters for teachers were placed in their
individual mailboxes, and clearly stated that participation in the study was
completely voluntary. Teachers returned a signed letter indicating whether or not
they desire to be part of this study without any involvement from their Principal or
any other superior. A returned signed letter denoted agreement to participate thus no
further consent letters were necessary.
The subjects involved in this study were limited to teachers, administrators,
and some support staff. Subjects in the teacher category were identified for
participation based on their response to the recruitment letter given to them early in
the process. The subjects consisted of all math teachers and other teachers who
appeared to have a leadership role at the school. If and when the educational
professional agreed, he or she was provided with a recruitment letter specifying the
purpose and process for the study.
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All site administrators and key teacher leaders were interviewed using the
interview guide attached as Appendix C. The school site’s math instructors were
asked to complete a 48 item teacher questionnaire (See Appendix D). The results
from the teacher questionnaires provided the researcher with data about teacher
perceptions and classroom experiences related to issues of the research questions
being studied. All teachers at the school site who were not math teachers completed
a shorter questionnaire designed to get their impressions about school-wide factors
that might be linked to the research questions.
Participation was completely voluntary and all participants were assured that
due efforts would be made to ensure confidentiality and anonymity. Participants that
were interviewed were scheduled for at least one interview, while some key leaders
were interviewed more than once for follow up and additional questions related to
leadership and providing staff development and support. All interviews were held on
campus and in an environment that ensured confidentiality.
The Principal Investigator, Dr. Marsh, and Co-Investigators working on this
study visited research sites between 8 – 10 times consisting of approximately seven
hours per visit from September 2006 until March 2007. The visits included
interviews and other research activities related to this study. The Principal
Investigator, Co-Investigators and Graduate Student Research Assistant met formally
at least monthly to evaluate and discuss research finding gathered at individual
research sites. There were ongoing meetings that also took place between the
Principal Investigator and Co-Investigators to insure that deadlines were met while
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following the protocols of effective research. This combination of investigation,
collaboration and discussion provided adequate time to conduct and complete the
research at each of the high school sites selected for this study.
Summary of Findings
Research Question 1
Research question one was intended to identify patterns of math achievement
at the school and asked, “What was the pattern of math achievement for various
students at the school?” The school profile was developed as a template that allowed
for the identification of student math achievement and the organizational factors that
may have contributed to the improved math achievement. To respond to this question
it was necessary to conduct a review and analysis on the academic performance of
the Valley High School over the past three years utilizing both qualitative and
quantitative data, which was gathered as a means of responding to the first research
question. The California Standards Test (CST) was used as the primary indicator of
academic performance. To support and provide a broader picture of the pattern of
student academic achievement other indicators were analyzed these included; the
passing rate of the California High School Exit Exam (CAHSEE); the percentage of
students taking and passing College Board Advanced Placement (AP) Exams in math
and the enrollment patterns of students in higher level math classes as reported on
the CST and school personnel. Other documents, report and data used to analyze and
answer this research question came from the School Accountability Report Card
(SARC), STAR Report, CBEDS report, master schedule, and WASC Report. These
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all provided rich data sets for examination and comparison to determine the patterns
of growth and achievement at Valley High School.
There are diverse patterns of student math achievement at Valley 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
Mathematics tests on a consistent basis for the past five years. All subgroups have
significantly increased their CAHSEE Mathematics passing rates over the last five
years. Hispanic students are achieving at slightly lower rates than their African
American peers posting CST scores that ranged from 35% to 89% from 2002-2005 at
the proficient and advanced levels. Hispanic student CAHSEE passing rates in math
have ranged from 27% to 85% during this same period. Asian and White students are
enrolled in AP classes at more than four times the rate of African American and
Hispanic students.
The pattern at Valley High School of consistently improved math
achievement in Algebra has been a result of deliberate decisions to support student
learning for all the students. The school leadership and the math department leaders
have responded to the critical need for students to increase their levels of
achievement in an effort to ensure that the students at Valley High are sufficiently
prepared to meet the demands of passing the California High School Exit Exam
(CAHSEE) for graduation and to ensure that all students meet at the minimum
graduation requirement of passing Algebra.
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Research Question 2
The second research question asked, “What policy initiatives as well
curriculum, instruction and related conditions seem to be related to improved math
achievement at the school site?” To answer this research question multiple resources
were accessed and analyzed as a means of triangulating the findings and providing
broad perspective and lens in which the progress was predicated. Two different
conceptual frameworks were utilized for this question, Marsh and Coddings’
Effective School Design (1998) and a Effective Math Programs conceptual
framework which was developed based on findings from research conducted by a
variety of researchers and research to include data from TIMSS, J.W. Stigler, and
Deborah Ball. The following instruments were used to facilitate the data collection;
Leadership Interview Guide, Teacher Interview Guide, Math Teacher Questionnaire,
Non-Math Teacher Questionnaire and the review of school provided documents.
At Valley High School, the NCLB Act has forced educators and
administrators to look at certain programs, instructional strategies, and new hires in a
whole different way. There were more serious practices in the hiring of teachers. The
leadership team created a new accountability system that promoted hiring the most
highly qualified teachers and ensure that the current faculty was also highly
qualified. It is evident that NCLB created a new system of accountability that is
place, which was about showing growth made in student achievement and improved
test scores.
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The curriculum, at Valley High School is aligned with the California Content
Standards, with their larger goal being defined by NCLB (2001) that all students will
be proficient by 2014 as measured by the CST. To facilitate students improving their
learning and achievement Valley High School uses an Algebra Readiness Class,
which is the instructional program used by Valley High School to assist the school in
realizing its goal of improved student achievement for all students. The course is also
designed to improve student achievement on the CAHSEE Mathematics section.
Valley High School used data-driven decision-making and to figure out how to
improve and perfect instructional practices. Along with data-driven decision making
there was a common thread of teacher collaboration throughout the campus. The
leadership and staff at Valley High School acknowledged to varying degrees the
impact of federal, state and local policies. The teachers lesser connection to these
policies may have been more of a reflection of their lack of knowledge for the
terminology than an indication that they did not identify the impact of such policies
as NCLB, CAHSEE and graduation requirements. Because within the context of the
interviews, there was a greater acknowledgment by the teachers that such policies
had influenced the instructional decisions and subsequent student performance.
Based on administrator interviews the administrative leadership was more cognizant
of the direct implications of state and federal policies on the decisions made in
respond to the guidelines and policies regarding improving student achievement.
District policies were mandated that promoted increased student achievement
at Valley High School. Freshmen and Sophomores needed to pass two years of math.
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There was been class-size reduction in all Freshman math classes to help facilitate
learning and provide the best environment for the students to be successful.
There has been a sustained effort for the Valley High administrative
leadership team and Valley High math department for the past five to six years when
the school first began making both systemic and instructional changes to meet
increasing academic expectations. As increased student achievement continues to
improve, there is a correlation with the high expectations of Valley High School’s
leadership team. Valley High School’s Leadership Team created Expected School
Wide Learning Results (ESLRS) to promote academic achievement and create a
shared vision for students and faculty. The Principal has worked with the leadership
team to create school wide learning results that are prominently posted throughout
the campus and discussed in classrooms. The learning results are clear expectations
from the Principal of the standards for learning at Valley High School.
Much of the success at Valley High School has been attributed to how school
leadership promotes collaboration amongst the staff. There was a lot focus on the
state standards being taught in the math classes and providing intervention for the
struggling students. Administration has worked with the staff to use collaboration
time to design standards-based instruction, common assessments and pacing plans.
There is a standard now set by the state that students must meet the Algebra
requirement and pass the CAHSEE in order to graduate. The staff and students have
responded to the new policy and now Valley High School has 93% pass rates for
English and Math for the CAHSEE. The CAHSEE requirement was most difficult
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for the Special Education and English Language Learners. Therefore, there was an
attitude on campus that these students that struggle the most, need the most resources
and attention. These students were seen as the priority in many cases as to how to
improve instruction and student achievement for the Basic level of education in order
to pass the CAHSEE exam. The most qualified teachers were placed in with these
students and the master schedule was written with those students in mind first.
Valley High School made sure those teachers had their students and schedules in
first.
Overall the math teachers are a cohesive department that is united around
common structures, practices and expectations for both the students and the adults.
They clearly identified the design of the master schedule, the practices of curriculum
sharing, department meetings, creating common assessments, mapping out a school
mathematics pacing plan for each course, and the mathematic department chair
adjunct math colleague coaching duties are all critical components of their increase
in achievement.
The CAHSEE Support, Algebra Readiness, and Algebra A/B courses were all
designed from the results of student performance on state and district assessments.
These new courses were created to improve student achievement in mathematics and
support students that were struggling. Regardless to what the legislation has been,
the philosophy at Valley High School is that every child needs to be successful.
There was on-going curriculum development to improve the quality of instruction.
The priority at Valley High was getting all students to graduate.
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Research Question 3
The third research question asked, “What change process did the school use
to enhance the math program and strategies to assist students in mathematics?” To
answer this question there was an examination of what processes were established
and implemented as a means of changing the school math performance. The Bolman
and Deal, Reframing Organizations (2003), frames provide a “guide” for
understanding the complexity of organizations. The following instruments 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 third research question was
organized and presented as follows: information, perceptions, and opinions about
efforts to improve mathematics instruction, description of the change process that
improved math achievement, description of the structural, human resource, political,
and symbolic methods used by the key leader, and analyzed with respondents’ results
to the questionnaires.
The findings identified that the Structural and the Human Resource Frame are
the most influential and dominant in the implementation of any change towards
improved student achievement in math, and to a lesser degree the political and
symbolic frames. The administrative leadership clearly approaches leadership and
change from both of these two frames. The structures and systems that are in place to
support teaching and learning at Valley involved the administrative team as those
responsible for creating a structure that supports this effort. The response from the
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teachers and administrators during the interview consistently reinforced the Principal
as the facilitator who put systems in place to move the school but that the real change
in the math program was coming from the leadership of the Mathematics Department
Chair in terms of instruction and supporting colleagues with improved instruction
and assessments.
The change processes within the Structural and Human Resource frames
enhanced the math program and strategies ultimately increasing student achievement
in mathematics at Valley High School. The major structural policy changes at the
high school are to align the graduation requirements with Expected School-wide
Learning Results (ESLRs), critically design the master schedule based on the needs
of the most “critical” students (EL, SPED and AP students), creation of common
collaboration departmentalized planning time, and the restructuring of the central
location and departmentalization of almost all the math classes. VHS restructured its
master schedule to implement an Algebra Readiness Class to supplement the
student’s basic skills to increase their likelihood of their success in the faster paced,
Algebra course.
There has been a significant change process in the evaluation of teachers at
Valley High School. When the Principal came into leadership at Valley High School
he created high expectations of teachers and increased classroom visitations. The
Principal worked with the Mathematics Department Chair in the evaluation process
to give feedback on what type of instruction is happening in the classroom. By
working with the Math Department Chair the Principal provided coaching for a
215
struggling teacher and also promoted a discussion in department meetings where
teachers are sharing and collaborating in their instructional practices. In addition, the
administration made it a priority to recruit and hire high quality faculty members that
best compliment their Mathematics Department and school vision. The Principal was
mentioned numerous times in interviews as a change agent for transforming the staff
through key new teacher hires.
The scheduling of late start once a month at Valley High School has allowed
teachers to collaborate, analyze instruction and student data, and discuss any areas of
curriculum concern in department meetings. During the late start department
meetings teachers had an opportunity to analyze student work in teams of teachers,
re-evaluate common assessments, plan class instructional activities, and create
common benchmarks of assessment.
The way Valley High School built their Master schedule is a symbolic
statement of where the priorities lie in terms of providing the most support to the
“neediest” students. Master scheduling is now a delicate operation at Valley High
School in which the “neediest” students take priority when scheduling. Based on
data-driven decision making the administration builds the master schedule around
student needs and they have been constantly looking at ways to support students and
help the teachers to support those students too. Administration has built the master
schedule backwards at Valley High School, by first scheduling English Language
Learners, RSP/SDC, and gifted and talented students. Administration placed the
216
courses in the right periods to service the maximum amount of students and then
built the general master schedule around these classes.
Another structural change was the relocation of the math classrooms to a
central location. At Valley High School the mathematics classes are now centrally
located in the main building on the second floor. The site administration agreed that
the location and placement of classrooms will drastically improve collaboration,
student achievement and improved instructional practices. Teachers are now able to
visit other math classrooms more readily and also use common resources from
teachers to improve instruction.
Valley High School provided a structural change to implement class-size
reduction to the CAHSEE course and all of the Freshman math classes. Now all
Freshman math classes have a maximum of twenty students per class in order to
increase student achievement in mathematics.
There has been a significant human resource change process at Valley High
School that has affected the hiring practices of teachers and the evaluations of
teachers. For the past eight years the Principal has been highly involved with a
variety of faculty members in all of the hiring of teachers at Valley High School. The
Principal has personally hired over 40% of the teachers that are presently on the
faculty. There has been a strong unified voice that the hiring of high qualified math
teachers over the past eight years has been monumental to increase student
achievement in mathematics and improve math instruction on the campus.
217
The Political and Symbolic Frames are evident to a lesser degree as part of
the change process. As a political leader the Principal not only took the time to have
one hour interviews with all of the current math teachers to get their feedback on
where they see areas of growth for the math department. He also took time to
understand the current practices in the department and see where there is and is not
commonality in instruction, expectation and classroom policies. The Principal was
politically involved with the school district in order to increase allocation and gain
political support to improve the school
Valley’s school culture has been a visible and supportive administration that
emphasizes high expectations of students in mathematics. The student achievement
at the school has been attributed the hard working teachers. The teachers on the
campus have been described by administration as highly dedicated and extremely
professional. Teachers also felt there was a shared vision of inquiry on the campus in
the department meetings. The Principal’s vision focused on shared leadership on the
campus and he felt that the more involvement you have with others the better the
results and outcomes. He has been committed to taking Valley High from “good” to
“great.” He felt Valley High School can reach greatness through collaboration,
inquiry and self-betterment.
Research Question 4
The fourth research question asked, “To what extent was strong instructional
leadership important in improving A) the mathematic programs/strategies and B)
mathematics achievement among students?” To answer this question there was an
218
examination of what was the role of the instructional leader in the improvement of
math achievement and what were the strategies utilized. This question used The
Educational Testing Services (ETS), “A Framework for School Leaders: Linking the
ISLLC Standards to Practice” which defines essentials aspects of instructional
leadership: vision for learning; supervision and monitoring of instruction;
community and politics; culture of teaching and learning; and data driven decision-
making. The following instruments 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 fourth research question was organized and presented as
follows: information, perceptions, and opinions about who the key leaders are that
promoted improved student achievement in math, description of the roles leaders
played in the development of the professional learning community on the campus,
description of how professional growth was supported, description of how teacher
collaboration was fostered, and analyzed with respondents’ results to questionnaires.
The findings confirm the value the school leadership places on data as a tool
and is evidenced in the use of data by the administration to make teaching
assignments, designing the master schedule each trimester and the appropriate
placement of students into math classes.
The role of leadership at Valley High School has been the stimulus for many
structures and practices that have been implemented to support student learning. The
Principal has taken more of a facilitative leadership role and encourages shared
219
decision-making. The Principal does not assume the role of the instructional leader
but rather has delegated this to those in supportive leadership roles. The Mathematics
Department Chair is most frequently identified by the teachers as the instructional
leader in their department and the most consistent and influential person affecting the
curriculum and instructional strategies.
The administration are viewed as the leaders on a larger scale, as the ones
responsible for the school in it’s entirety and as a resource for support specifically as
it pertains to providing necessary resources. It is evident that the math teachers and
non-math teachers perception of the culture of teaching and learning at Valley High
School, which is embedded within Standards-Based Instruction (SBI), is the most
significant contributor to improved math achievement. The role of the leader both at
the administrative level and the department level have been essential to the progress
and improved achievement in math.
The Principal of Valley High School has been instrumental in improving the
Math Program and increasing student achievement. He has created many changes at
Valley High School that promoted math achievement and teacher collaboration. The
following aspects were highly effective practices by the Principal that ultimately
improve math achievement: instilling a strong vision for learning, improving
supervision and monitoring of instruction, promoting a culture of teaching and
learning, implementing data-driven decision making, and encouraging teacher
collaboration.
220
Command and control devices are evident in changes in structure and
changes in organizational routines (Hess, F. M., 2005). It was evident that the
Principal was a structural and instructional leader who established the policies,
routines and structures within the organization. He also guided the administrative
team to establish the guides of acceptable behavior, i.e., expectations within the
organization through the supervision and monitoring of instruction. The educational
leader was monumental in improving the hiring and evaluation procedures at Valley
High School. There was consistency in the faculty’s accounts that the Principal was
instrumental in the change process of the evaluation process by being more pro-
active in the classrooms and holding high expectations for new hires.
Valley High School Principal has used data-driven decision making to drive
the instruction of the mathematics department. The Principal explained how there
was a healthy internal competition amongst the faculty to improve student
achievement, which drives improved instruction. The Principal encouraged the
Leadership Team to figure out ways to create ownership of what is going on at
Valley High School. The element of this framework regarding Data Driven Decision
Making and Analysis relates to the extent to which the leadership utilizes data as a
tool to inform the instructional program, and to positively impact student learning
and influence the master schedule. This is an area that the leadership has given
consistent focus to.The school leaders have sought to infuse the use of data into
conversations between teachers and with administration as a means of making
instructional decisions and student placements.
221
Research Question 5
The fifth research question asked, “How did leaders in the school resolve the
dilemmas about instructional leadership?” To answer this question there was an
investigation of the impact that the Instructional Leaders expertise or lack of, had in
their ability to support the teachers and the instructional math program. This
framework was developed to address this question of expertise and was divided into
two distinct components predicated on the two different parts of the research
question. First, an assessment tool, flow chart, was created to allow the investigator
to ascertain the level of expertise in math of the instructional leader. Secondly, this
question will address how the key leader overcame obstacles that were faced to
improve student achievement in mathematics. The following instruments 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 fifth research question was
organized and presented as follows: information, perceptions, and opinions about
obstacles the school face in the implementation of changes related to improvement
achievement in mathematics, description of how site leadership worked to overcome
the obstacles, description of structural, human resource, political, and symbolic
changes implemented by site leadership, and analyzed with respondents’ results to
the questionnaires.
The administrative leadership, while they are not the math experts on the
Valley High School campus, is able to utilize their leadership expertise to access
222
strategies that have created an instructional program across the school that is
designed with the student and faculty needs in mind. The teachers identify the
administration as participating in a facilitator capacity. These key leaders
acknowledge the expertise of others to support and improve the math instructional
program.
The Principal emphasized quality Standards-Based Instruction (SBI), raised
expectations through the increase in graduation requirements for mathematics,
making strategic teaching assignments, increased collaboration with teacher inquiry
to design courses, and emphasized interventions for lower performing students by
implementing an Algebra Readiness course and tutoring for all students in
mathematics, as strategies they used to improve student achievement in mathematics.
There has been a team approach to solving problems at Valley High School.
The Principal has been highly reliant on other administrators, counselors, and
department chairs when making decisions and implementing change. He encouraged
inquiry and discussion to how to implement change on the campus. He has actively
listened to the ideas and points of view spoken and then expressed his view. The
Principal has emphasized a high degree of curriculum and course revision at Valley
High School. Much of the curriculum designed at Valley High School was from
data-driven decision-making and shared leadership. The Principal has been highly
involved in providing interventions for lower performing students at Valley High
School. The administration has offered math tutoring, which has been a priority
intervention offered to struggling students. The CAHSEE Support, Algebra
223
Readiness, and Algebra A/B courses are all intervention classes designed to support
lower performing students. Many teachers have found the math teacher tutoring the
most effective way to improve student achievement on the campus by providing one-
on-one time to re-teach specific skills to students.
There are specific strategies the Principal used to create human resource,
political, structural, and symbolic change at Valley High School. The following are
strategies used by the Principal to overcome obstacles that have a high degree of
success: delegate leadership to assistant with greater expertise, empower department
chair, emphasize inquiry and problem solving, emphasize quality instruction,
emphasize raised expectations, emphasize strategic teacher assignments, emphasize
revised course scope and sequence and/or curriculum, and emphasize interventions
for lower performing students. One of the most frequent response expressed by the
faculty and leadership team was the principal’s desire and fostering of shared
leadership. The administration has encouraged shared decision-making and increased
collaboration amongst the staff over the past eight years at Valley High School. This
ability and willingness to reach out and engage others is not only a reflection of
leadership but also an indication of confidence. The principal has encouraged experts
to share their knowledge with others and create a team-oriented approach to solving
critical challenges at Valley High School.
Conclusions
The findings in this case study of one urban high school in Southern
California, Valley High School provides confirmation for the importance of a
224
focused and deliberate approach to school reform within mathematics. Valley High
School has demonstrated consistent and significant sustained student achievement
within the area of math. The leadership team at Valley High School has made
deliberate and instrumental reforms within instruction, teacher collaboration,
curriculum and decision making that has significantly improved student
achievement. The research has found that both federal and state level policies
regarding monitoring the progress of all students have been influential in the school
reform efforts.
There were several themes that emerged from the analysis and triangulation of
the qualitative and quantitative data collected at Valley High School. The analysis of the
findings suggested that specific actions the Principal took at the school site played a
key role in the success of the school design by promoting change in the evaluation,
hiring, teacher collaboration, and curriculum reform. The Principal recognized when
change is needed can reform the evaluation and supervision procedures to improve the
quality of instruction and student achievement. Valley High School’s Principal
promoted standards-based instruction, curriculum mapping, common assessments
and pacing plans for all math teachers to stay in synch with one another and provide
more meaningful conversations about instruction in the department meetings. The
Principal also recognized when change was needed by making strategic hiring
practices and necessary placement of teachers.
A school that empowers others as instructional leaders reduces the barriers to
implementation and increases the probability of sustainability. According to Schmoker
(2001), “Change has a much better chance of going forward when Principals team up
225
with teachers who help to translate and negotiate new practices with the faculty”
(p.116). Lead teachers were empowered as instructional leaders and to become mentors
to the teachers in their department. The lead teachers distributed leadership and
increased the school’s capacity to assist teachers in improving instruction.
The role of the leadership has been critical to the progress of the school. This
is reflected in the ability of the Principal and his administrative leadership team to
empower others and utilize the strengths of teachers as valuable resources without
positional power interfering in decisions that support students. The Math Department
Chair has been identified as a constant and incredible resource to all math teachers as
a coach and leader of on-going mathematic reform. He has been a critical leader,
who has been highly involved in the creation of the master schedule, mathematics
pacing calendars, common assessments and curriculum design. The department chair
has also been integral in providing coaching to mathematics teachers and sustaining
a high level of collaboration and teacher inquiry. Both the Principal and Math
Department Chair have promoted data-driven decision making and allowed for
shared leadership when creating new math interventions and courses to meet the
diverse needs of the student body.
This research through surveys, interviews and student achievement
demonstrate how Valley High reformed school design, instructional practices and
leadership all influence the achievement of a school. These three elements are at the
foundation of Valley High School’s effort to reform their instructional program to
support student learning and provide additional intervention and instructional
226
strategies to improve student achievement in mathematics. As Valley continues in
their efforts the researcher hopes that the site will continue to “greatness” in their
journey and continue to increase student achievement and expectations. There is an
expectation that Valley will continue to perfect their academic programs that will be
evidenced by an increase in the number and diversity of students taking Advanced
Placement (AP) courses, the number of students meeting the A-G college entrance
requirements and an increase in the number of students entering a four year college
from Valley High School.
Several core themes emerged from the analysis and triangulation of the
qualitative and quantitative data collected. The analysis of the findings suggested that
some areas played a key role in the success of the school design. Also, some potential
areas needing improvement emerged that could hinder sustainability of the school
design if interventions were not taken. The following were “Best Practices” and areas
to improve.
Best Practices
The five “best practice” conclusions that emerged were:
1. A principal who recognizes when change is needed can reform the evaluation
and supervision procedures to improve the quality of instruction and student
achievement. There was a culture where the evaluation system was not
handled appropriately and in most cases non-existent for most teachers. The
new principal implemented high expectations of teachers and increased
classroom visitations to encourage dialogue between the administration and
faculty on standards-based classroom practices. Feedback on observations
227
and supervision was also shared with key leaders as hopes to get coaching for
a struggling teacher and also promote a discussion in department meetings
where teachers are sharing and collaborating in their instructional practices.
2. Principals who are instructionally focused and support district/state policy can
make curriculum reforms to improve the quality of instruction. Valley High
School’s principal made it a priority to reform the educational curriculum and
improved daily instruction with standards-based instruction. The curriculum
is closely tied to the state standards and is created around a student-centered
approach and outcomes. Key math teacher leaders designed curriculum
mapping, common assessments and pacing plans for all math teachers to stay
in synch with one another and provide more meaningful conversations about
instruction in the department meetings. Teachers use the results from the
common assessments to guide their instruction for the following year.
3. A principal who recognizes when change is needed can make strategic hiring
practices and necessary placement of teachers. There are more serious
practices in place with the hiring of teachers. The system of seniority that was
unconsciously in place crumbled with the new accountability system at
Valley High School. The most highly qualified teachers are strategically
placed in classrooms where students, such as ELL and Special Education,
need the most support.
4. A principal who recognizes when change is needed can take the necessary
intervention steps to protect its staff, students, and community. The high-stakes
228
accountability system made the principal aware that there was a school-side
need to focus on student learning and instructional improvement. The reform
was to ensure that all students master Algebra and pass the CAHSEE. The
change from one-year Algebra to two-year Algebra supplemented with Algebra
Readiness, was implemented in an attempt to improve instruction and narrow
the achievement gap among students.
5. A school that empowers others as instructional leaders reduces the barriers to
implementation and increases the probability of sustainability. According to
Schmoker (2001), “Change has a much better chance of going forward when
principals team up with teachers who help to translate and negotiate new
practices with the faculty” (p.116). Lead teachers were empowered as
instructional leaders and to become mentors to the teachers in their department.
The lead teachers distributed leadership and increased the school’s capacity to
assist teachers in improving instruction.
Areas to Improve
The five areas needing improvement with the mathematics reform at Valley
High School are:
1. Organizations going through change require constant feedback and open lines of
communication with all members of the organization. Schools that implement a
top-down approach need to specifically focus on ensuring that expectations are
clearly communicated throughout the entire organization especially to
individuals that will be expected to demonstrate results. Valley High School’s
standards-based instructional plan was communicated to the lead teachers, but it
was not communicated effectively to the classroom teachers. Due to a lack of
229
professional development the majority of classroom teachers were unaware of
what the expectations were for classroom instruction in the math class.
2. Organizations that are promoting a professional learning community fostered by
collaboration need time and resources to implement this approach. Teachers
need the time to collaborate and share their instructional practices with one
another. It also requires resources for teachers to watch one another teach and
have shared inquiry with the lesson design and instructional strategies.
Meaningful collaboration with teachers at feeder schools requires that teachers
have a chance to sit down with one another to have a thoughtful conversation
about instructional strategies and expectations.
3. School site administrators also need to attend math in-services, trainings and
conferences training to serve as effective instructional leaders. The principal has
not attended an in-services or conferences for math instruction. He allows a
small percentage of teachers to attend the conferences with hopes that they will
find a new program to implement at the school. Leadership needs to take a top-
down approach to research-proven instruction strategies that are successful with
increased and sustained mathematic achievement. The administrative team
members received limited or no training on effective mathematics instruction,
which truly hindered their ability to provide feedback to teachers on their use of
the instructional strategies.
4. Common assessments need to be more frequent to provide accountability data
that is meaningful to all stakeholders. The one common interim assessment for
math classes does not provide useful and ongoing information for teachers that
would assist them in modifying their current instruction. More attention needs
to be directed to monthly common standards-based assessments which can be
230
used to guide department meeting conversations to the quality of the
instructional strategies used.
5. “Professional development should be determined by an analysis of the skills
and knowledge the staff will need to carry out the school’s plan” (Tucker &
Codding, 1998, p.319). There is a lack of professional development in
mathematics at the school site. Time, money and resources need to be allocated
for the professional development of the entire math department and
administrative team. An expert in the field of mathematics is needed to come
into the school to consult and train the staff on increasing and sustaining math
achievement.

Implications and Recommendations
The findings and conclusions of this study have led to the following
implications for those implementing instructional reform:
Site Administrators
1. The site administrators need to have a clearly defined, well communicated,
and focused vision for the school’s mathematic program. The school’s
goals and priorities should revolve around current national and state
expectations for districts, schools, and students.
2. Acknowledgement and acceptance of the school’s strengths and identified
needs is crucial in making informative decisions that will have a positive
impact on the community at large. School administrators must assess the
needs of the district and schools with accurate data in order to implement
231
and sustain an effective systemic design that is supportive of its
instructional focus.
3. Site administrators must demonstrate confidence, enthusiasm, and
pedagogical knowledge to support the successful implementation of their
reform efforts. Additionally, they must recognize the fact that in order to
promote reform efforts, certificated, classified, student body, and
community at large must be empowered to assume responsibility and
ownership to affect positive and lasting results.
4. All site administrators need to be trained and develop the expertise in the
elements of the reform effort in order to effectively provide guidance and
support to the classroom level.
Teachers
1. Lead teachers must understand their vital role in ensuring the integrity of the
school design be implemented accordingly. They must be committed to
encouraging and modeling inquiry at all department meetings.
2. Teachers’ level of implementation determines the sustainability of the district
design. Additionally they are required to familiarize themselves with the
district design and establish an intrinsic desire to further their professional
growth and personal development.
Implications for Further Research
Based on the findings of this study, the following reflect recommendations
for additional research in this area:
232
1. To conduct similar research with other urban high schools with the
instruments improved and refined to better capture the information.
2. Further research on urban schools outside of the southern California region
would provide a broader perspective and insight on what is working in
schools across the country that have similar demographics and challenges.
3. A longitudinal study on the same topic of math achievement in our urban
high schools could provide and identify sustainable practices that have been
utilized by like schools.
4. The implementation of the “top-down approach” in implementing systemic
change is dependent upon different levels of support. It would be of value to
implement a qualitative analysis designed to investigate the intrinsic attributes of
the site administrator in their efforts to support this methodology and determine
how various dimensions of personality of the educational leader would facilitate
successful implementation of the “top–down approach.”
5. The value of such research cannot be underestimated when attempting to
ascertain an efficient design to implement systems change. In our continued
efforts at assuring a positive relationship between organizational change and
our constantly changing culture, it is of the utmost significance that we
continually monitor, analyze, re-evaluate and modify our efforts at
implementation of systems operations in order to obtain long range
sustainability and successful survival of the organization.
6. Research that seeks to identify a connection between different content area
instructional programs and student achievement in math.
7. It would be of interest to study a district that provided uniform training to all
233
school site administrators on their district design and determine how the
professional development affected the extent of implementation and reform
effectiveness at schools and the classroom levels.
8. Research that identifies consistent elements that are present in math programs
utilized by urban high schools that have demonstrated positive growth.
9. 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, as a concurrent class (co-enrollment
in Algebra), or another undiscovered configuration.
Recommendations for Future Research
Based on the findings of this study, the following recommendations are made
regarding future research in this area:
1. In order to ascertain the sustainability of this reform effort, it is recommended
that a follow-up research design be implemented to determine the degree to
which elements of the reform need be modified or reevaluated systemically.
2. Effective communication models may affect the accuracy and efficiency of
information transmitted within an organization. Future research of districts
implementing instructional improvement efforts can serve as models on how the
efficiency of its communication system within the infrastructure of the
organization influences its implementation and its impact in assuring successful
systemic change.
3. It would be advisable to determine the effectiveness of the implementation of a
district design and its relationship to funding. Districts should provide equitable
234
level of support so that all participants could acquire uniform professional
development training to implement the district design.
4. A district’s decision-making approach in adopting and implementing a district
design may effect the outcomes. It would be advisable to study a district that
used a “bottom-up approach” to ascertain the efficacy and long-term
effectiveness as a means for systemic change. It is recommended that further
research be conducted to focus on a comparative analysis of this design to
determine its overall reliability and validity as an effective and successful means
for systemic change in comparison to a “top-down approach.”
5. The implementation of the “top-down approach” in implementing systemic
change is dependent upon different levels of support. It would be of value to
implement a qualitative analysis designed to investigate the intrinsic attributes of
the site administrator in their efforts to support this methodology and determine
how various dimensions of personality of the educational leader would facilitate
successful implementation of the “top–down approach.”
6. It would be of interest to study a district that provided uniform training to all
school site administrators on their district design and determine how the
professional development affected the extent of implementation and reform
effectiveness at schools and the classroom levels.
7. The value of such research cannot be underestimated when attempting to
ascertain an efficient design to implement systems change. In our continued
efforts at assuring a positive relationship between organizational change and
our constantly changing culture, it is of the utmost significance that we
continually monitor, analyze, re-evaluate and modify our efforts at
235
implementation of systems operations in order to obtain long range
sustainability and successful survival of the organization.
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Abstract (if available)

Abstract Poor student mathematics achievement in American public schools, as determined by national and international rankings in math has resulted in 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 tremendous amount of school reforms have occurred effecting both students and stakeholders. However, despite dramatic, timeconsuming, and costly efforts, 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.

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Asset Metadata

Creator Erlandson, Staci Lynn (author)

Core Title Secondary math reform and the role of policy, practice, and instructional leadership on math achievement

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 05/12/2008

Defense Date 01/29/2008

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

Tag OAI-PMH Harvest,secondary math reform

Language English

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

Creator Email erlandso@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1238

Unique identifier UC1293847

Identifier etd-Erlandson-20080512 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-76670 (legacy record id),usctheses-m1238 (legacy record id)

Legacy Identifier etd-Erlandson-20080512.pdf

Dmrecord 76670

Document Type Dissertation

Rights Erlandson, Staci Lynn

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