University of Southern California Dissertations and Theses

Secondary school reform: student achievement in mathematics -- a case study: Hot Springs High School

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Secondary school reform: student achievement in mathematics -- a case study: Hot Springs High School

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SECONDARY SCHOOL REFORM: STUDENT ACHIEVEMENT IN
MATHEMATICS – A CASE STUDY: HOT SPRINGS HIGH SCHOOL

by

Melvin J. Surdin

____________

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

May 2007

Copyright 2007 Melvin J. Surdin

ii

TABLE OF CONTENTS

LIST OF TABLES iv

LIST OF FIGURES v

ABSTRACT vi

CHAPTER 1 – OVERVIEW OF THE STUDY 1
Introduction 1
Problem Statement 8
Purpose of the Study 11
Research Questions 11
Importance of the Study 12
Assumptions 14
Limitations 15
Delimitations 15
Definition of Terms 16
Organization of the Study 19

CHAPTER 2 – LITERATURE REVIEW 20
Introduction 20
Conclusion 48

CHAPTER 3 – RESEARCH METHODOLOGIES 50
Introduction 50
Sample and Population 52
Conceptual Frameworks 60
Data Collection Instruments 72
Data Collection 76
Data Analysis 78
Validity and Reliability 79
Conclusion 79

CHAPTER 4 – DATA FINDINGS, ANALYSIS, AND DISCUSSION 81
Introduction 81
Research Data 92
Analysis and Discussion 130
Summary 142

iii

CHAPTER 5 – SUMMARY, CONCLUSIONS, AND IMPLICATIONS 143
Background of the Study 143
Purpose of the Study 146
Methodology 147
Selected Findings 151
Conclusions 157
Implication for Practice 160
Recommendations for Future Research 163

REFERENCES 165

iv
LIST OF TABLES

Table 1 Bolman and Deal’s Four Frames 66

Table 2 Instructional Leadership Framework 69

Table 3 Assessment of Principal’s Expertise in Math 71

Table 4 California Basic Educational Data System (2004-2005) 85

Table 5 CST Algebra I (2003-2005) 86

Table 6 Upper and Lower Two Performance Bands in
Algebra I (2003-2005) 87

Table 7 CST Algebra I – All State of California Students
Between 2003-2005 88

Table 8 CST Algebra I – All State of California Students 89

Table 9 CST Algebra I –HSHS School District – All Students 90

v
LIST OF FIGURES

Figure 1 Research Question and Instrument Development 60

Figure 2 School Design 63

Figure 3 Effective Math Programs 64

vi

ABSTRACT

The purpose of this study was to examine those factors contributing to
significant and sustained gains in math performance by students at a large urban
public high school. In a case study of a Southern California high school
demonstrating significant improvement in math over a three year period as evidenced
by student performance on the California Standards Test in Algebra I, five research
questions focused on the patterns of math achievement for various students, policy
initiatives as well as curriculum, instruction and related issues, the change process
employed by the school, the role of instructional leadership and the manner in which
key leaders overcame a lack of expertise in math.
Following the local district mandated adoption of California math standards,
the principal and other key leaders embarked on the development and
implementation of a comprehensive set of reform strategies. These reforms included
using formative assessment to drive instruction and fostering a student centered
approach to instruction. Focusing on early intervention, the math faculty devised
strategies to assist students gain the skills necessary to access basic concepts and to
avoid falling behind. Working with the math department chair, the principal
provided a strong and clear vision for reform, closely monitored instruction and built
the capacity necessary for the math faculty to work in a collaborative manner. The
principal’s leadership fostered a change in the math faculty’s level of accountability
and new and creative approaches to instruction. The principal positively affected

vii
school culture by providing meaningful incentives for change, engaging in highly
symbolic activities reinforcing the importance of achievement in math and
developing strong relationships with students and their families. As teachers took
more responsibility for student outcomes, student performance improved. Teachers
proactively developed formative assessment instruments closely linked to
instructional goals and objectives. Recommendations for future research were
presented including examining a high school receiving strong local district support, a
more targeted implementation of reforms over a longer period of time, a similarly
situated school where the administration had greater expertise in math instruction
and comparative studies with other schools in the local district aimed at isolating
those reforms providing the greatest long term improvement in student achievement
in math.

1

CHAPTER 1

OVERVIEW OF THE STUDY
Introduction
The successful launch of Sputnik in 1957 challenged American notions of
cultural and educational superiority (Marzano, 2003). Fearing claims of soviet world
dominance as both a realistic possibility and powerful threat to our economic
prosperity and cultural values, American educational institutions, in particular, were
forced to revisit and reappraise the quality of our students’ academic achievement,
especially in the vital areas of mathematics and the physical sciences. Almost
overnight, a sudden urgency swept through American society demanding our
students acquire the skills necessary to compete more effectively with the obviously
successful soviet educational system. In the early 1960s, a new administration set
lofty goals of sending a man to the moon as, at least in part, a symbolic restatement
of American superiority requiring a reinvigorated commitment to rebuilding and
restructuring our educational institutions. Unfortunately, the United States’ space
program proved far more successful than the American education system,
particularly the latter’s lack of effect on the education of socially disadvantaged
students (Coleman et. al., 1966).
National studies (Gonzales, 2004) documented the poor academic
performance of American students, particularly those of high school age, when
compared with their peers not only in the Soviet Union, but also in Europe and Asia.

2
Moving into the 1980s, these concerns were further exacerbated with the economic
renaissance of the Japanese economy and the flood of high quality consumer
products entering American markets and the apparent loss of entire industries to
foreign competitors. An extended period of recession and retractions in the
American economy greatly affected formerly robust industrial regions while
changing technologies placed greater emphasis on highly skilled jobs. Oil
embargoes and energy dependence further contributed to a sense of America failing
to the meet the challenges of the second half of the twentieth century. Charged by
the Reagan-Bush administration with the responsibility of investigating the state of
public education in the United States, the findings of the National Commission on
Excellence in Education’s seminal study A Nation at Risk: The Imperative for
Educational Reform gained significant currency among the American public for its
description of America’s mediocre and profoundly dysfunctional educational
systems (Marzano, 2003).
A close reading of the prosperity of 1950s America reveals tremendous
disparities in the distribution of economic success and opportunity among and
between social classes and races. During the late 1950s and early 1960s, reactions to
the American civil rights movement highlighted deep divisions in American society
based primarily on racial, ethnic, regional and social differences. African American
students in particular, following generations of legal and social hostility, segregation
and neglect, understandably demonstrated poor academic achievement, higher drop
out rates and lower levels of literacy and math skills than their typical White peers

3
(Balfanz & Legters, 2004). This academic achievement gap persisted throughout the
1970s and 1980s growing to include significant numbers of newly arrived Latino
students similarly struggling to achieve academic success (Harris & Herrington,
2006). White students of lower socioeconomic status also demonstrated lower
academic performance levels when compare to their more financially fortunate peers.
Dedicated to the notion all students can and should learn, the achievement gap has
challenged American educators seeking to develop strategies and methods designed
to meet the educational needs of struggling students regardless of race, ethnicity or
class (Sirin, 2005).
The findings of studies such as Trends in International Mathematics and
Science Study (TIMMS) further underscore the generally perceived understanding
that American students were academically out-performed by students from other
highly developed countries, particularly Germany and Japan. In 1995, TIMMS
assessed students from over 23 countries in science and mathematics, at three grade
levels. At the fourth grade, students from the United States scored above average in
both math and science when compared to their international peers. By the twelfth
grade, the performance of American students was among the lowest in both math and
science. Pointing to the particular difficulties of minority and many immigrant
students, blame was often placed on ethnicity and socioeconomic status while other
critics looked to school reform as the most likely solution to poor student
performance.

4
The recent academic success of Asian American students in public schools
as well as institutions of higher education, further demonstrates social, ethnic and
cultural performance gaps among and between American students, with African
American and Latino students struggling to reach proficiency in core academic
subjects while Asian American and White students of higher socioeconomic status
continue to make significant progress (Thernstrom & Thernstrom, 2003).
Responding to the failings of the American educational system in general,
and to the achievement gap in particular, recent federal legislation demands greater
accountability of students and educators, assessment through high stakes testing,
while establishing ever-increasingly demanding benchmarks for all students without
exception. Research (Olson, 2006) indicates over the course of the past decade,
American students have responded well to the recent emphasis on standards and
accountability by achieving greater levels of success on high stakes assessments,
particularly in the area of mathematics. Unfortunately, these gains – although
substantial – have not closed the achievement gap; despite extensive reforms and
greater levels of accountability, the achievement gap persists (Harris & Herrington,
2006).
The majority of African American, Latino and students of lower
socioeconomic status in general, continue to score far below their White peers and
those from economically and culturally advantaged families on national and
statewide assessments in math (The Nation’s Report Card: Mathematics, 2005). Of
particular concern is the failure of students to achieve proficiency with

5
computational skills (Loveless & Coughlan, 2004). Deemed essential for success in
higher-level math courses such as algebra and geometry, middle and high school
students demonstrate a limited knowledge of basic math facts, particularly the ability
to manipulate fractions and other fundamental computational skills. This lack of
knowledge helps explain their high failing rates in secondary level math courses and
on the math sections of recent high school exit examinations (Olson, 2006).
Math achievement poses significant problems for urban youth. High school dropouts
typically struggle with math courses and find the challenges posed by graduation
requirements – successful completion of algebra and geometry classes – frustrate
their attempts to succeed in school (Teitelbaum, 2003). Faced with continuously
repeating courses they are convinced they will never pass, many students reasonably
conclude they will never graduate and see no compelling reason to continue in
school. Further, success in math classes is closely linked to success in related
science courses. Failure to grasp basic mathematical concepts alienates students
from the learning process and leads them to conclude school is irrelevant, further
contributing to expressions of failure and already weakened notions of personal
respect and self-esteem.
The ensuing Federal and state reforms designed to improve student
performance in math tend to focus on a more demanding curriculum and developing
highly trained educators (Taylor et al., 2005). These programs primarily target
younger students. Better educated teachers and curriculum design form the
foundation for reform. In addition to a high quality education and a curriculum more

6
responsive to student needs, secondary school reform requires a determined effort to
overcome a history of academic failure and often-entrenched forces committed to
maintaining comfortable pedagogical methods and traditions (Clewell et al., 2005).
Anchored by strict academic standards and increasing expectations for
student success, nationally school districts have implemented a wide range of
comprehensive mathematics programs typically focusing on elementary school
reform strategies including providing academically rich curricula, instituting research
based teaching methods and approaches, and developing well-trained instructors
encouraged to implement these new programs as intended (Weiss & Pasley, 2004).
Similar approaches for middle and high school students are encouraged. Focusing
specifically on meeting high school graduation requirements – core courses and
passage of high school exit examinations – secondary school reform (Clewell et al.,
2005) tends to concentrate on greater opportunities for students to learn essential
math skills, professional development aimed at increasing teacher knowledge,
progressive teaching strategies, and opportunities for remediation (including block
programming, after school tutoring, and Saturday schools).
Encouraged by, and responding to the continuing national debate about
student academic success, particularly for poor and minority students, new school
designs centered on student achievement have produced encouraging results.
Programs integrating mathematics and core subjects, for example, have proven
highly effective (Draper, 2002). Similarly, an approach connecting essential math
principles to high interest problem-solving situations stimulates student interest and

7
participation (Bottge, Heinrichs, Mehta & Hung, 2002). Drawing connections
between student concerns and the curriculum has proven highly effective. Research
indicates (Burnett & Wichman, 1997) contextualizing math problems tends to reduce
math phobia and generates a greater level of interest in the subject matter. Similarly,
presenting the study of math through a study of student centered, highly interesting
and realistic word problems, while simultaneously developing related language
skills, has proven effective. These teaching strategies apply a holistic approach
combining and interweaving core concepts and themes across the curriculum
(Draper, 2002). Math classes, in particular, benefit from an emphasis on high
interest and conceptually relevant concrete examples. Additionally, integrating
advanced computer based strategies further serves to stimulate student interest
making the learning process more attractive and accessible to students (Blume,
Garcia, Mullinix & Vogel, 2001).
These approaches and strategies require new policy initiatives and school
designs. School site administrators play an important role in the implementation and
successful follow through of curriculum reforms. Particularly when perceived as
personally engaged in the reform process, administrators significantly impact the
effective implementation of these new strategies (Chance & Anderson, 2003).
Commitment over time and dedication to the overall success of the school is
essential for school site administrators seeking to establish new priorities. Principals,
in particular, may dramatically affect and influence reform efforts. Developing

8
relationships built on trust and cooperation proves critical for the successful
implementation of necessary reforms (Bryk & Schneider, 2003).
Similarly, collaboration between teachers across the curriculum is essential
when building a cohesive work environment conducive to change. Working
partnerships between administrators, teachers, and support personnel foster
confidence and trust (Marks & Printy, 2003). Consistent reinforcement of core
values and revisiting the essential reasons behind the need for change stimulates and
motivates school personnel. The research indicates school site leadership must
engage in innovative and compelling programs as they are likely to encounter
resistance from established personnel (Marzano, 2003). Similarly, administrators
must establish control and effectively communicate the need for strong instructional
leadership as a key factor for shifting the emphasis on failing students to one of
academic success (Marzano, 2003). Given the vast number of challenges faced by
students, most beyond the control of school personnel, requires innovative changes
in instruction designed to specifically address student needs. Strategies and methods
addressing the root causes of the difficulties students face when attempting to master
mathematics must be considered an essential component of any new curriculum and
leadership reform effort. Present levels of student performance are a starting point
for success and should not be viewed as merely an expression of past failures.
Problem Statement
A great deal of attention is directed to the seemingly insurmountable
challenges facing public high schools and students, particularly those located in an

9
urban setting. Despite a substantial investment of economic and educational capital
in an era of increasingly limited resources, many urban high school students continue
to demonstrate poor academic success, particularly in the area of mathematics.
Increasing expectations and greater accountability focus attention on student
performance. Many school districts have expanded their graduation requirements to
include receiving a passing grade in Algebra I. California requires successful
passage of a high school exit exam (both math and language arts sections) as a
graduation requirement. Given the high rates of poor student performance in math,
providing a demanding curriculum and increasing graduation requirements may
initially seen counterintuitive however, research indicates increased expectations and
clearly communicated goals leads to improved student performance (Reynolds &
Teddlie, 2000).
Despite statistics documenting difficulties in math, high dropout and low
graduation rates, there are urban high schools whose students have consistently
experienced significant gains in math performance. These schools report a
significant number of students moving from low performance bands to proficiency
and above on the California Standards Test (CST) in Algebra 1. The statistics
include urban high schools without extraordinary resources, a large infusion of
capital, or instructional leaders particularly well versed or highly experienced in the
area of mathematics or math instruction. What is not known or properly understood
in these cases are those factors contributing to student achievement. Further
research, study, and analysis is required to determine the effects of district policy,

10
district and school site leadership, curricula, professional development, parent,
teacher, student involvement, and overall reform designs and initiatives on student
achievement.
This study examines each of these factors in a realistic setting and seeks to
determine which factors, or combinations thereof, contribute directly to student
success. The study examines the role of instructional leaders and their participation
in the development of the math program. The study collects and analyzes data
pertaining to their level of involvement regarding curriculum and instruction.
Similarly, this study looks at math teachers and their relationship with administrators
and key instructional leaders. Issues of cooperation between administration and
faculty will be examined and the manner of supervision will be described and
discussed. Of particular concern is the manner in which the math faculty was
provided opportunities for growth and development on either an individual or
departmental level. Given that most administrators are generally not math experts,
the study seeks to determine how these individuals were able to develop successful
programs.
The study also looks at the math curriculum seeking to determine its effect on
student performance. Specifically, the study will look at curriculum from the
perspective of content and manner of presentation, and the relationship between
textual materials, instructional strategies and teaching methods. The study also looks
at teacher preparation and training, and the role of professional development on
teacher quality and student outcomes. Each of these factors will be examined

11
through interviews, questionnaires and surveys in an attempt to determine their
relationship to student outcomes.
Purpose of the Study
This study explores an urban high school where students demonstrate
significant levels of high achievement in math as evidenced by classroom
performance, school wide assessments and high stakes test results. Issues of reform
design, curricula, pedagogical strategies, instructional leadership and other related
factors would be reviewed. Similarly situated high schools will benefit from
learning how these factors contribute to student success. Site level analysis will
provide a framework for creating an effective school environment conducive to
student achievement in mathematics. The study similarly investigates district level
policies, procedures and leadership decisions further establishing high levels of
student achievement.
Research Questions
This study will attempt to answer the following 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?

12
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?
Importance of the Study
Competency in math is particularly important for the economic health and
well being of our society. Proficiency in math serves as a gateway for further
educational and economic success in a highly competitive global economy. This
study will present, analyze and examine those contributing factors to the math
achievement of successful urban high school students. The study will consider a
number of relevant factors including curricula, program design, and manner of
implementation, leadership and school and community participation. It will also
investigate relationship between school leaders and faculty, teaching methods and
strategies, and the overall design of the math program. Particular attention will be
given to the role of professional development its effectiveness in developing strong
leadership teams and developing effective teaching techniques.
The findings will be valuable to educators working with urban high schools
students attempting to achieve math proficiency sufficient to meet graduation
requirements, while also providing students meaningful post-secondary educational
and/or vocational opportunities. Given the pervasive difficulties facing urban high
school students in math, the findings of this study will provide similarly situated
schools important information regarding program design, pedagogical techniques

13
and strategies, and professional development. The study also provides a foundation
for school reform and methods for the implementation of successful teaching
practices. This information is useful to both administrators and teachers seeking to
provide their students with the tools necessary to demonstrate math proficiency.
The study will illustrate the manner in which an urban high school was able
to overcome the odds and help students succeed in math. The relationship between
instructional leaders and the math faculty will prove instructive for administrators
seeking a model for collaboration, and strategies for motivation and team building.
The analysis of the math curriculum may influence other schools seeking to replicate
the results of the school examined in the case study, and textbook publishers
developing more effective materials assisting teachers attempting to communicate,
develop and explain complex ideas and abstract concepts while remaining interesting
and motivating for students struggling to gain fluency in an historically difficult
subject area. Teaching strategies and methods are also examined providing
information for instructional leaders, math coaches and department chairs seeking to
change embedded cultures and past practices. Issues such as directing faculty to
focus on student outcomes while implementing appropriate teaching strategies and
methods are discussed.
The study may also prove helpful to local districts attempting to support
struggling high schools. This study provides information regarding the necessary
elements for capacity building and resources required for success. The study
illustrates effective instructional leadership and the role local districts play in

14
providing school site administrators the support and guidance they need to
effectively implement curriculum reform and new school designs. The study may
also serve as a motivational piece inspiring leadership and commitment to change for
school leaders including administrators and teachers.
The study will also contribute to the large body of theoretical research and
writings available on a variety of subjects including instructional leadership, teacher
quality, professional development, curriculum, and instructional strategies. The
study will provide information regarding the application of many of these otherwise
theoretical considerations to a realistic and highly replicable setting. The findings of
this study provide data testing the applicability of widely discussed educational
theories and the basis for further studies looking at student performance in urban
settings.
Assumptions
The study assumes a relationship between strong instructional leadership,
research based instructional strategies, school reform and improved student learning.
It was assumed the conceptual frameworks and data collection instruction provided
valid information documenting the effects of leadership and school reform on
improved student performance. It also assumed the individuals interviewed and
surveyed provided credible and truthful responses to the researcher.

15

Limitations
This study will explore one urban high school demonstrating unexpected
student success in Algebra I. The school chosen was drawn from a pool of urban
high schools similarly demonstrating unexpectedly significant academic success in
the area in Algebra 1 for two consecutive years. The program design, curriculum,
academic strategies and techniques reflect the implementation of a specific approach
to student success in the area of math as evidenced by this particular urban high
school. The study will take place during one academic school year and assess the
practices in place during this period of time. The researcher has limited resources for
the study and will rely primarily on interviews, questionnaires and surveys.
Delimitations
In developing the study, the cohort agreed to restrict the study to urban high
schools reflecting a diverse student body. The schools from which this study was
drawn have a population in excess of 1,500 students and would generally be
considered representative of large, ethnically diverse urban high schools with a
significant number of poor and economically disadvantaged students. The schools
considered for the study are comprised of at least 50% Latino students and more than
50% of the students are considered of low socioeconomic status based on their
participation in free or reduced lunch programs. Additionally, the schools
considered for this study do not have unusual economic resources nor are they
engaged in math programs that could not be replicated in similarly situated schools.

16

Definition of Terms
For the purpose of this study, the following terms are defined as follows:
Accountability: a specific program or defined effort for holding school
districts, administrators, site supervisors and teachers responsible for the academic
performance of their students (Powers, 2004).
Achievement gap: the documented difference in achievement between
minority students, English language learners and students from families of lower
socio-economic status when compared to those from the dominant social class
(Mubenga, 2006).
Academic Performance Index (API): a statewide system of school
performance ranking setting growth targets and providing similar school
comparisons on an annual basis (California Department of Education, 2001).
Adequate Yearly Progress (AYP): a yearly measure of a state’s progress
towards targeted minimum levels demonstrating improvement of student academic
performance based on a range of performance indicators.
Assessment: the process of collecting data from a variety of sources for the
purpose of determining a student’s present level of performance.
Benchmark: an expectation of student performance at various levels
(California Department of Education, 2001).
Best practices: incorporating research based instruction in to daily teaching
methods and strategies.

17
California High School Exit Exam (CAHSEE): a presently contested high
school graduation requirement based on an assessment of student performance in the
areas of Language Arts and Mathematics (California Department of Education,
2001).
Capacity: The ability to flexibly respond to external demands in order to
translate high standards into effective instruction and strong student performance
comprised of qualitative and quantitative factors residing within structures, processes
and relationships (Massell, 1998).
Conceptual framework: a consistent and comprehensive integration of
research literature, theories and other relevant information forming the basis for the
analysis of research findings.
Constructivism: a theory of learning which describes the learning process
as one where new information builds on preexisting knowledge and beliefs. New
data may expand existing knowledge or modify previously held beliefs (Neal, 2004).
Content standards: statewide expectations of what students should not and
be able to do at each grade level in a range of content areas.
Design: a course of action intended to affect change at either the district or
school site level.
Data driven decision-making: a process of making decisions about
curriculum and instruction based on an analysis of classroom and standardized test
data (Massell, 2000).

18
Equity: the belief that all students receive fair and equal treatment and
access a high quality education.
Highly qualified teacher: a credentialed teacher with demonstrated
knowledge of the subject matter they are assigned to teach.
Implementation: the practical application of ideas intended to achieve a
specific goal.
Instructional leadership: an individual who influences, directs and motivates
activities designed to improve student learning (Marzano, 2003).
National Assessment of Educational Progress (NAEP): a national, ongoing
assessment of American students in various subject areas including mathematics,
science, reading and writing.
Performance Bands: levels of student achievement based on a demonstrated
mastery of specified content standards. California identifies five performance levels
for its statewide standards based assessments: advanced, proficient, basic, below
basic, and far below basic (California Department of Education, 2001).
Professional development: generally structured learning opportunities for
administrators, teachers and staff to develop knowledge and skills necessary to
improve teaching and student learning.
Sanctions: consequences imposed for not meeting expected performance
outcomes.
Standards-based design/reform: curriculum designs built on state content
standards.

19
Standards-based instruction: curriculum specifically designed to address and
incorporate the California content standards. The goal is to help students acquire
proficiency and then mastery by acquiring specific skills in each of the content areas.
Organization of the Study
Chapter 1 includes the introduction, the statement of the problem, the
background, purpose and significance of the study, research questions to be
answered, the theoretical framework and definitions of key terms. Chapter 2 reviews
relevant literature and addresses the following topics: the achievement gap in
mathematics, math curricula and programs specifically designed to meet the needs of
struggling students, instructional leadership and the factors contributing to student
success. Chapter 3 presents the methodology and relevant background, the
participants, the selection process and its rationale, and the overall design. Chapter 4
presents the findings of the study and their impact and effect on each of the research
questions. Chapter 5 describes the significance of the study, implications for
practice and conclusions and recommendations for further research.

20
CHAPTER 2
LITERATURE REVIEW
Introduction
American public high schools are the subject of increasing concern to
educators, researchers and policy makers due to wide spread reports of poor student
performance, high dropout rates and an achievement gap largely impacting poor and
minority students. The problem of low student performance is particularly acute in
the area of mathematics with many urban high schools reporting fewer than five
percent of their students achieving minimum levels of proficiency on high stakes
performance assessments. As a proposed model for reform at the school site and
district level, this study will review the procedures and practices of a successful
urban high school reporting improving math test scores and higher rates of student
proficiency. The study will also analyze teaching proficiency and teacher training,
curriculum design, school and district capacity for reform, instructional leadership
and district level involvement contributing to improving student performance.
The Academic Performance of American High School Students
Historical Trends
The successful launch of Sputnik in 1957 sent shock waves through a
relatively complacent and self-confident America of the 1950s (Marzano, 2003).
Fearful of Soviet ambitions for world domination, almost overnight Americans
seriously questioned their assumed position of technical and educational superiority,
particularly in the area of sophisticated weapons systems and space exploration.

21
Heretofore largely unchallenged, political leaders, educators and social critics began
a serious analysis and re-examination of American educational institutions, focusing
on the competitiveness of America’s public education system especially when
comparing American students to students from other industrialized nations
(Hanushek, 2003).
Almost simultaneously, questions about social inequality and the role of race
in American society began to focus on the American education system. Education
was viewed by many in positions of social and political influence in the early 1960s
as the single most important factor in moving large numbers of people from an
inescapable cycle of poverty to economically viable middle class status. As a
corollary to Lyndon Johnson’s ambitious economic program commonly known as
the War on Poverty, the Civil Rights Act of 1964 authorized a nationwide survey of
educational opportunities for minority children. The Equality of Educational
Opportunity Study – also known as the Coleman report (Coleman, Campbell,
Hobson, McPartland, Mood, Weinfeld, & York, 1966) – categorized the results of
achievement tests taken by more than 600,000 first, third, sixth, ninth and twelve
grade students into ethnic and cultural groupings. A large number of teachers were
also questioned regarding their educational background and training. Surprisingly,
the study revealed expected inequalities of classroom facilities and resources, teacher
training and curriculum designed had far less influence on student success than
family background, cultural environment and peer interaction. In effect, the
importance of schools on achieving social and economic equality was far less than

22
generally believed. The study revealed the most important factors contributing to
academic success were more a product of one’s social status and class ranking than
educational opportunity. The unintended and unexpected results of the study
ultimately changed the focus from concerns about educational disparities and
inequalities to greater attention on efforts to stimulate economic opportunities for
families of color.
The work of Christopher Jencks in the early 1970s (Jencks, Smith, Ackland,
Bane, Cohen, Grintlis, Heynes & Michelson, 1972) further substantiated the findings
and conclusions of the Coleman Report: inequality of educational resources did not,
as had been widely believed, play as important a role in student achievement as
socioeconomic status. Essentially, Jencks read the Coleman report data as placing
the greatest emphasis on wealth versus poverty as the key factor determining and
predicting educational success. The effect of the Coleman and Jencks studies was to
devastate educational reform efforts seeking to equalize economic resources for
minority students.
Perhaps first gaining momentum with Brown vs. Board of Education (1954)
and its emphasis on the disparities of economic resources between and among
students from different racial and ethnic backgrounds, Coleman and Jencks diverted
political and social capital from public school reform centered on equalizing
resources, to efforts to improve the economic condition of African Americans. The
1960s and 70s witnessed significant reform efforts including the so-called War on
Poverty, affirmative action legislation, anti-discrimination statutes in employment,

23
fair housing, job training, welfare assistance, head start and other government
programs designed to increase income levels and social capital among members of
the lower socioeconomic classes. Simply put, these studies led to the view that
differences in educational resources play a minimal role when predicting academic
achievement while stressing social and economic equality as determinative of
educational success.
The deepening national concern over the quality of American public
education was further exacerbated by the seminal 1983 publication: A Nation at
Risk: The Imperative for Educational Reform. The work product of the National
Commission on Education, the study reported a steady decline in the quality of
American public education beginning in the early 1950s. The commission focused
on four principal areas of concern: content, expectations, time on task and teaching.
Regarding content, the commission found a public high school curriculum far less
focused on college preparation or even vocational education than on providing a
scattering of electives and general education tracking classes. They deemed the high
school course of study pointless and without a central purpose. The commission was
particularly concerned with declining expectations evidenced by high grades but less
study and homework, lowering of college admission requirements, reduced standards
for minimum competency tests, reduced emphasis on mathematics, science and
foreign languages, and less challenging texts and course requirements. The
commission was also concerned about the use of time by American schools and
students compared to those of other nations. The commission discovered American

24
students spend less time in the classroom, less time doing class work and homework,
and are rarely instructed in time management and efficiency. According to the
findings of the commission, for a significant part of the school day, American
students are engaged in off task, non-essential activities. Finally, the commission
took issue with the quality of American educators, their preparation and teaching
abilities. They argued most teaching preparation courses emphasized methods
courses with far less time developing subject matter knowledge. Additionally,
teachers were paid relatively low salaries, often took second jobs and were seldom
involved in significant decision making regarding curriculum or textbook adoption.
They noted a severe shortage of qualified teachers in the areas of mathematics and
science with additional shortages in the areas of foreign language and special
education with an overwhelming number of non-qualified teachers working in the
core areas.
The findings of Nation at Risk were widely disseminated and credited with an
abrupt change in the American public’s perception of the quality of their educational
system (Guthrie & Springer, 2004). Particularly disturbing, the report found the
mediocre quality of our public schools affected all students regardless of race or
socioeconomic status. The problems with the American education system, the report
held, were rampant and widespread placing the economic and political future of this
country at great risk. The notion America was likely to lose its central position of
economic, political and military dominance frightened an American public wary of
Soviet military intentions, our reliance on foreign sources for non-renewable sources

25
of energy and the increasing flood of high quality, low priced imported products.
The 1980s saw the United States lose many smokestack industries to foreign
competitors and a decline in manufacturing jobs. The importation of electronics,
steel and automobiles produced in Asia – and the corresponding loss of
manufacturing jobs in the United States during the 1980s – was but one example of
the long term consequences of a struggling economic system beset by a sense of
complacency and mediocrity challenged by aggressive competitors who, not
surprisingly, boasted vibrant economies and highly successful academic institutions.
The message generated by Nation at Risk was only by improving public
education could the United States continue to maintain its formerly unchallenged
status as the world’s leading economic, cultural, and military power. The skills
necessary to compete in a global economy demanded a high quality education,
particularly one focusing on math and science. Simply producing unskilled workers
had little social relevance and is not in this country’s long term interests. The study
also served to rebut powerful conservative political forces determined to reduce
federal involvement in education. In effect, the study made education a national
concern demanding strong federal leadership and a massive infusion of research,
study and analysis. It also played an important role in shifting the emphasis from
school resources to student performance and outcomes. Spawning numerous studies
and commissions, Nation at Risk has had a lasting impact on the public’s perception
of the nature of a high quality education and a greater understanding of the demands
placed on our students if they are to succeed in a highly competitive job market.

26
Gone, for the most part, are the high paying, labor-intensive jobs prevalent during
the first half of the twentieth century. The innovations of the past quarter century
demand highly skilled workers forced to compete in an intensely technical and
rapidly changing global economy driven by innovation and the ability to rapidly
respond to change.
Criticism of public education continued throughout the 1990s buttressed by a
growing sense America was losing its competitive edge, particularly in the
international market place of goods and ideas. With the spread of globalization and
industrialization, researchers were once gaining concerned with the performance of
American students when compared to those from other nations. Generally
considered the most important study since Nation at Risk, the 1995 Third
International Mathematics and Science Study (TIMMS) further documented the
comparatively lackluster performance of American students. The study compared
the curricula, instructional practices, school capacity and assessments of fourth,
eighth and twelfth grade students with those from other countries in the areas of
science and math. The results of the study were devastating for American educators:
the data indicated our curriculum is not challenging, there is little emphasis on
developing problem-solving skills, most students do not take advanced math or
science classes, and are taught by less than fully qualified teachers. Focusing on
eighth graders, the study found they are ill prepared for the rigors of a high quality,
demanding high school education. Most vexing, American fourth graders perform
very well when compared to students from other countries. Eighth graders however,

27
tend to start falling behind and twelfth graders fell below the international average in
both math and science.
Studies since TIMMS reveal American students beginning in the late 1980s
have begun to demonstrate modest gains in the area of mathematics but still lag far
behind in comparative international studies. The more recent National Assessment
of Educational Progress similarly reports slightly improved math scores and little or
no improvement in reading levels.
The Achievement Gap
Brown v. Board of Education (1954) addressed the issue of racial segregation
in public schooling and the notion students provided services in a segregated system
could receive an equivalent education. The court struck down racial segregation in
public schools ruling segregated schools inherently unequal. Much of the evidence
presented to the court documented the poor performance of African American
students. Integration, it was argued, would not only remove the vestiges of
inequality from our school system, it would provide African American students the
opportunity to achieve similar levels of success as their White peers.
Unfortunately, despite national efforts to undo the effects of decades of
segregation and other reform efforts, the achievement gap persists (Johnson, 2002).
Generally, poor African American, Latino and Native American students
demonstrate limited academic success while significant numbers of middle and
upper income White and Asian students demonstrate higher levels of academic
proficiency. During the 1970s and 1980s the gap between racial, ethnic and

28
economic groups began to narrow, however beginning in the 1990s the gap, once
again, began to widen (Blank & Gruebel, 1995; Haycock, 1998).
In 1997 the College Board began a two-year study, the National Task Force
on Minority Achievement (1999), addressing the issue of the shortage of high
achieving African American, Latino and Native American students. The Task Force
found the achievement gap persistent and wide-reaching beginning in elementary
school and continuing through postsecondary education and including minority
students from all socioeconomic levels. The Task Force concluded the achievement
gap is a result of numerous factors including poverty, cultural differences, limited
educational opportunities, racism and prejudice, and the limited resources of
minority families, schools, and communities. Of particular importance for the
purpose of this study, the Task Force found only 1 in 10 African American, Latino,
and Native American high school seniors scored at the proficient level on the 1996
NAEP math and science tests.
A study of California high schools by Education Trust-West (2004), Are
California High Schools Ready for the 21st Century?, focused on graduation rates,
course completion and student achievement. The report answered its central
question in the negative, reporting low graduation rates, limited enrollment in and
availability of core courses, and overall poor performance on the standards-based
California Standards Achievement Test. The study noted particularly unfortunate
results for African American, Latino and low-income students. The study described
these students as doing far worse than their peers reporting, for example, graduation

29
rates of between 55% to 60% for African American and Latino students compared to
rates of 80% and 90% respectively for White and Asian American students. The
achievement gap was also apparent on the mathematics portion of the California
High School Exit Exam (CAHSEE) with approximately 78% Asian and 68% White
10th graders passing in 2003 compared to 35% Latino and 31% African American
10th graders.
The most obvious implications of the achievement gap pertain to the limited
ability of African American and Latino students to gain meaningful employment and
to move large numbers of individuals from poverty to middle and upper middle class
socioeconomic status. The authors of the Education Trust-West (2004) study,
discuss the importance of the high school diploma as the minimum credential
necessary to enter college, university or a job-training program, the military, or to
achieve gainful employment. They cite business leaders as requiring workers with
strong skills in the core academic subjects including algebra, geometry and statistics.
They describe a convergence between success in school (particularly college) and in
work, noting American high schools are not adequately preparing students for either
endeavor.
The implications of the achievement gap for the United States are
frightening. Long term prospects include increasing and deepening pockets of
poverty, dysfunctional largely minority urban centers, rampant unemployment, an
inability to sustaining basic social services, and an ever increasing drain on the
resources of an already declining middle class. A minority of highly educated

30
professionals will be asked to fund a largely unsupportable, and rapidly growing,
sector of our society. It is unclear if this forecast of a highly unbalanced economy
can sustain itself over time.
The Importance of Achievement in Mathematics
The relationship between education and income is well documented (Rose &
Betts, 2001). Higher levels of training are required to meet the demands of our
technical age operating in a global economy. The loss of high paying factory jobs to
foreign markets furthers the plight of American workers of limited educational
background and experience. The ready availability of immigrant workers apparently
willing to work for substandard wages in labor-intensive jobs adds further pressure
on the job market. Service sector jobs employing large numbers of workers with
limited education do not provide adequate wages to move from poverty to middle
class status. The authors of Ed-Trust-West (2004) note the tremendous increase in
the number of college educated office workers over the past thirty years. Similarly,
the manufacturing sector – historically a reliable source of employment for high
school dropouts – has seen a tremendous decrease in the employment of workers
who have not attained at least a high school diploma.
The relationship between the amount and quality of mathematics courses
taken in high school and future educational and economic success is the focus of a
Public Policy Institute of California study, Math Matters: The Links Between High
School Curriculum, College Graduation and Income (2001). The study concludes

31
that math courses have a decided effect on future academic and financial success,
and all students benefit from a rigorous math curriculum.
Drawing from data collected in a nationwide 1980 study of 10th grade high
school students including transcripts, postsecondary educational degrees and
earnings 10 years after their anticipated high school graduation date, the authors
compared the relationship between the level and quality of math courses taken and
future levels of education and income. The authors found approximately 25% of
10th grade students enrolled in the lowest level vocational math courses. They also
found African American and Latino students twice as likely as Whites and three
times as likely as Asians to complete their math studies at this lower level. These
students typically did not progress very far in school and had lower income levels
than peers who completed higher-level mathematics courses.
At the other end of the spectrum, the study indicates those students
successfully completing advanced math courses including calculus had a far greater
likelihood of earning a college diploma. For every level of rigor, students had an
increasingly greater chance of graduating from college. Again, the higher-level math
courses were generally populated by White and Asian students.
The finding of Math Matters were further supported in a 1997 report,
Mathematics Equals Opportunity, prepared for the then United States Secretary of
Education, Richard Riley. The report builds on the premise that students with a solid
foundation in mathematics are likely to have greater success in postsecondary
education and the job market. The report further focuses on the importance of

32
success in mathematics at the 8th grade level, considered the gateway to success in
high school math and science courses. The authors of the report found:
• Students who take rigorous mathematics and science courses are much more
likely to go to college than those who do not.
• Early success in Algebra is essential for later success in higher mathematics
and science courses.
• Low-income students successful in rigorous mathematics and science classes
were far more likely to attend college.
• Low-income students are less likely to take rigorous mathematics and science
classes than students from higher-income families.
The study also found students in public and private schools enrolled in a similarly
rigorous curriculum scored equally on high stakes achievement tests. Additionally,
students whose parents were determined to be involved in their children’s education
were more likely to take higher level mathematics classes in the 8th and 9th grades.
While success in algebra may be a key factor for future academic and
financial success, understanding algebraic principles and concepts requires a solid
foundation in basic computational skills (Loveless & Coughlin, 2004). Whereas
students’ scores on the math tests of the National Assessment of Educational
Progress (NAEP) over the period 1990 to 2003 have steadily increased, Loveless and
Coughlin (2004) contend these results mask a significant decrease in students’
acquisition of computational skills that helps to explain the widely reported
difficulties faced by high school algebra and geometry students. They further

33
contend these basic computational skills are not only essential for success in algebra
and geometry, as previously noted they are important predictors of future earnings
due to the close connection between completion of higher level math classes, college
graduation rates and meaningful employment.
An analysis of computation skills returns full circle to a re-examination of the
previously discussed achievement gap. Reviewing current NAEP trends, Loveless
and Coughlin (2004) find a significantly greater failure to achieve basic
computational skills at all age levels among African American students compared to
their White peers. Low levels of math computational skills appear to coincide with
similarly lower overall mathematics performance, high graduation and college
completion rates, and future earnings.
State and National Efforts to Improve High School Math Achievement
With increased emphasis on student and teacher accountability in the face of
discouraging reports documenting overall poor student performance – particularly in
the area of mathematics – the past several decades have witnessed numerous reform
efforts designed to reverse these downward trends. Among the most important of
these are establishing rigorous state content standards, improving curriculum and
instruction, better preparing teachers, and related reform efforts.
Standards-based Reform Movement
Responding to the numerous research articles and studies mentioned above
and the general perception that American public school students were not achieving
at expected levels, what is now generally referred to as the standards-based reform

34
movement began as the result of a 1989 agreement between President George H. W.
Bush and governors that students upon completion of grades 4, 8, and 12 will be able
to demonstrate competency in core subject areas including English, mathematics,
science, history, and geography (Klein, Braams, Parker, Quirk, Schmid, & Wilson,
2005). The general response to this agreement was the development, at the state
level, of academic standards designating specific levels of competency and skills
students needed to attain at the designated grade levels. The standards movement
received additional support in 1994 in the Goals 2000: Education America Act
(1994) and revisions of Title 1 of the federal Elementary and Secondary Education
Act (1994). In 1996, an education summit of business and political leaders lent
further support to the standards-based reform movement and by 1998, 47 states had
developed K-12 standards in mathematics (Superfine, 2005).
The No Child Left Behind Act of 2001 (NCLB) conditioned federal financial
assistance to the states on the development of standards in math and reading in
grades 3 through 8, in addition to requiring testing assessing student and school
performance based on the achievement of proficiency determined by mastering state
standards. Today we find schools defining themselves as standards-based, requiring
teachers in core areas to teach to the standards (Klein, Braams, Parker, Quirk,
Schmid, & Wilson, 2005). Textbooks, lesson plans, teacher training and
performance reviews, student achievement and school success are, to a large extent,
aligned to and judged by state standards. State standards form the basis for measures
of accountability as required by NCLB and accordingly, drive instruction. Teachers

35
are encouraged to display applicable standards in their classrooms (often in “student-
friendly” terms) and demonstrate the relationship between their lessons and the
requirements of the standards. Textbook manufacturers have been quick to respond,
aligning their publications to state standards (and often incorporating the standards in
the text).
The challenge of the standards-based reform movement is to develop math
standards that address the academic needs of students and to become part of a
process of teaching and learning resulting in higher levels of achievement. As noted,
mastery of computational skills in the early grades is essential for later success in
algebra and geometry. These skills must be included in math standards (Klein,
Braams, Parker, Quirk, Schmid, & Wilson, 2005). Additionally, individuals
thoroughly familiar with mathematics and math education should have a role in the
development of standards.
Curriculum and Instruction Reform
Marzano (2003) notes curriculum is an extremely difficult term to define and
may include virtually any activity occurring in the classroom involving the teacher
and/or the school. However, researchers (Hightower, 2002; Rose & Betts, 2001)
contend curriculum reform (understood as implementing best practices) is an
important factor in improving student achievement. There has been a significant
body of work on preferred curriculum design and instructional practices (Weiss &
Pasley, 2004) focusing primarily on student outcomes. The implementation of these
reforms varies from district to district and is largely determined by district and

36
school site leadership, resources and capacity for reform. Following an analysis of
350 math lessons over a period of 18 months, Weiss and Pasley (2004) reported on
the characteristics of highly effective curriculum and instruction. They defined a
highly effective math lesson as likely to provide students with important concepts,
improve their understanding of the subject matter and the ability to successfully
solve grade level math problems. Drawing from highly effective lessons they report:
• Content of the lesson is significant and important
• Content is appropriate for the developmental levels of the students
• Content information as presented by the teacher is accurate
• Students are intellectually engaged
• The pace and level of understanding was appropriate for the developmental
levels of the student
• The teacher was able to adjust the lesson to meet the students’ level of
understanding
• Teachers emphasized higher order questions
• Teachers created a climate likely to generate questions, ideas, and
conjectures.
• Teachers maintained intellectual rigor and presented challenging ideas.
Teacher Quality
Researchers agree the teacher is the most important factor affecting student
learning (Sanders & Horn, 1994; Wright, Horn and Sanders, 1997). Citing
Haycock’s (1998) analysis of Sanders’ study, Marzano (2003) reports over the

37
course of a school year, a highly effective teacher, on average, produced gains of
about 53% in student achievement as compared to the least effective teachers who
produced only about 14% student achievement gains. Marzano (2003) explains
these results noting students typically gain about 34 percentile points in achievement
during one academic year. Accordingly, highly effective teachers far exceed our
normal expectations whereas ineffective teachers fall far below. These disparities
increase over time. Accordingly, students who spend much of their academic career
in classrooms taught by ineffective teachers demonstrate enormous differences in
academic achievement from those students taught be highly effective teachers.
At a 2004 summit, the United State’s Department of Education developed
long-range goals to develop teachers with a strong background in mathematics and
student learning. The Department of Education expressed the desire to have the
teaching of mathematics considered a profession. The Department of Education is
concerned with encouraging a link between professional knowledge and research-
based teaching and strategies, particularly for those individuals entering the teaching
profession from a professional background in math or science.
The current accountability movement has had a significant impact on teacher
education and credentialing. Recognizing the importance of a highly effective
teacher, NCLB places increasingly rigorous demands on teacher qualifications and
training. The goal is to place highly qualified teachers (defined as an individual
educated in the subject matter for which she is assigned to teach and has completed a
rigorous teacher training/credential program) in all classrooms. Many school

38
districts (Darling-Hammond, Hightower, Husbands, LaFors, Young & Christopher,
2005) recognize teacher training must be an ongoing process and have developed
programs designed for beginning teachers, and continuing education for veteran
teachers, while struggling to place highly qualified teachers in appropriate
classrooms.
School-related Factors
In addition to the reforms mentioned above, research (Marzano, 2003) also
indicates certain school level factors (matters typically within the exclusive control
of the school, such as particular policy decisions or initiatives) can have a
considerable effect on student achievement. Marzano lists these factors as (1) a
guaranteed and viable curriculum, (2) challenging goals and effective feedback, (3)
parent and community involvement, (4) a safe and orderly environment, and (5)
collegiality and professionalism. Marzano (2003) illustrates the impact of a school
effectively addressing each of these factors on student achievement by noting:
Specifically, if a test on which you would normally expect half
the students to pass and half the students to fail were given to
students in effective schools, 72.4 percent of those students
would pass the test and the remainder would fail. In the
ineffective schools however, only 27.6 percent of the students
would pass the test. In the aggregate then, the research
indicates that schools, when run effectively, make a big
difference in student achievement.

Following a review of a large body of research on school level factors (Edmonds,
1979; Good & Brophy, 1986; Levine & Lazotte, 1990), Marzano (2000, 2003) found
he was able to group their finding into these five broad categories ranked in order of

39
importance. According to Marzano, each factor plays a critical role in its affect on
student achievement and forms the basis for the action steps each school must
consider and address as it formulates a plan for reform taking into account site and
district specific needs and circumstances.
New School Designs
In order to accommodate reforms necessary to address the low performance
and achievement levels of students, particularly in urban high schools, a variety of
new school designs have been proposed (High School Reform, National and State
Trends, 2005). These designs incorporate the above-mentioned reforms and build in
capacity to address the particular needs of inner city urban high schools. It is now
recognized contemporary high schools were built on a “factory model” serving large
numbers of students who moved from class to class throughout the school day and
were exposed to a wide range of courses. In the “factory model” setting, teachers
operated independently of one another in relative isolation. High school teachers
typically present curriculum – largely derived from textbooks – idiosyncratically
while designing their own pacing plans, teaching methods and strategies. Teachers
choose to cover those parts of the curriculum they felt most important, develop a
personal teaching style and emphasize content areas they feel are of particular
interest to their students (and/or themselves).
Current reform efforts have labeled the factory model as “archaic” and not
well suited for the varied needs of our current urban high school student population –
students typically from culturally diverse backgrounds, often with limited English

40
language skills and similarly limited background knowledge and academic
preparation.
Drawing largely from case studies of successful urban high schools, a
generally consistent set of findings evidence the following shared characteristics:
• High expectations and a rigorous curriculum
• A variety of instructional strategies that engage students and are
connected to realistic applications
• Collaboration between students and staff
• Leadership and a school culture focusing on student outcomes
• Professional learning communities of faculty and staff familiar with
research based strategies designed to meet the needs of their students
• Support mechanisms for struggling students.
The High School Reform study (2005) discusses the comprehensive reform
model (CSR) as an example of one of many new school reform designs. The
comprehensive reform model brings together numerous research based approaches
and strategies adapted to meet the needs of a particular school(s) and student
population. The CSR model appreciates the need to develop a comprehensive and
fully integrated set of strategies and approaches (Marzano, 2003). Over time, as
schools develop and refine successful models, they provide a research-based proven
starting point for other similarly situated schools looking to adopt a reform model.
The High School Reform study recognizes there are many different comprehensive

41
reform models. Accordingly, each school would have to adopt, modify and tailor a
reform model to meet their specific circumstances and needs.
In a publication of the Bill and Melinda Gates Foundation, High Schools for
the New Millennium (1998), describing a variety of reform models and strategies, the
authors strongly suggest students should be offered small, innovate public high
schools with a flexible structure and approach to teaching and learning. Again, their
call is for small, rigorous, highly demanding, personalized and deeply committed
public high schools focused on student outcomes. In order for small, highly effective
schools to succeed, the authors argue, policy makers must provide the necessary
resources to support a wide variety and range of approaches and school designs.
A great deal of emphasis is repeatedly placed on physically smaller schools
as the cornerstone of reform. The study argues smaller schools have a proven record
of increased graduation rates, reduced incidents of violence, and a greater capacity to
meet the needs of diverse students. The study also points out smaller schools
typically encourage greater collaboration between administrators, teachers, and staff,
and foster the sharing of ideas while promoting supportive relationships and
constructive criticism. An outgrowth of the smaller schools approach is the concept
of small learning communities, where traditional large high schools are structurally
(if not, physically) divided into a number of discrete programs housing typically no
more than 500 students. The organizing principle of small learning communities is
division along subject matter or areas of interest. The small learning community

42
approach is also influencing the construction of new, much smaller high schools
centered on a unifying theme or area of study.
Effective Instruction of Math
Beginning in the late 1980s, the single most influential force driving the
reform of math instruction is the National Council of Teachers of Mathematics
(NCTM), particularly their publications setting content and curriculum standards for
math (2000, 1989). Their publications coincided with the establishment of rigorous
standards in education during the administration of George H. W. Bush and
continuing throughout the Clinton administration (Goals 2000: Educate America
Act, 1994).
During the 1990s, research in mathematics has moved from teaching by
explaining concepts and processes to a constructivist model (Woodward, 2004), with
greater emphasis on problem-solving. Proponents of the constructivist model
(Thompson & Cobb, 1998; Noddings, 1993) of math education encourage teachers to
instruct students to think and act like a mathematician (Schifter, 1996). In this new
reform model, students work in cooperative learning groups on realistic, interesting
and meaningful problems over considerable periods of time. A suggested framework
for a constructivist math curriculum involves:
• Including problems from a variety of situations connected to students’ lives
• Develop strong content knowledge to be able to guide student learning and to
think like a mathematician

43
• Provide opportunities for students to express themselves speaking and
thinking like a mathematician
• Use traditional teaching methods to guide student learning where necessary
• Model the use and application of math ideas
• Assist students develop their math reasoning (Schifter, 1996).
The constructivist model relies on developing communication (sometimes
referred to as accountable talk) by and between students and also a committed
personal involvement on the part of students in the learning process. The
constructivist model avoids telling students how to arrive at a solution but rather
encourages independent thinking and group collaboration. In this model, the math
teacher acts as the facilitator assisting students through the process of discovery
(Draper, 2002). Constructivist models respond to students’ demand for relevancy
providing an opportunity for personal involvement in the problem and its solution.
Strong Leadership and High School Reform
Reforming an urban high school’s mathematics program requires strong
leadership and a deeply felt commitment to support and sustain change over time.
Marzano (2003) argues leadership may be the single most important factor for school
reform. As Marzano notes, virtually every aspect of change requires strong
leadership. Marzano cites a variety of sources linking strong leadership with:
• Developing a clear mission statement and set of goals and objectives
• The overall school climate and culture
• The attitude and participation of teachers

44
• The classroom practices of teachers
• The organization of curriculum and instruction
• Students’ opportunity to learn.
Each of these components is an essential factor for reform and each is associated
with, and benefits from, strong leadership.
Fullan, Bertani and Quinn (2004) cite the significant achievement in literacy
made by students in the Toronto District School Board, gains on the Iowa Test of
Basic skills by students in the Chicago school district and increases in the percentage
of students achieving proficiency on literacy and mathematics assessments in
England as a direct result of strong leadership linked to school reform. In a related
study, Fink and Resnick (2001) provide similar findings for the Community School
District 2 in New York City, also drawing a connection between strong leadership
and increased student achievement.
The Role of the High School Principal as Instructional Leader
The high school principal is often described (Fink & Resnick, 2001) as
occupying the most influential sight based administrative leadership role, particularly
when discussing the essential factors necessary for school effective reform and
sustainable change. Historically, the school principal has been viewed as a manager,
seldom in the classroom and generally removed from daily instructional issues and
concerns. There have also been notions of the principal as a supervisor of staff and
student affairs. This view is somewhat suspect (Blase & Blase, 2004) as it tends to
characterize the principal as all knowing, particularly in the area of teaching

45
strategies as well as the content knowledge expert in all of the core academic
subjects. Supervision also carries pejorative connotations undermining the values
embedded in notions of learning communities and shared leadership.
The research (Blase & Blase, 2004; Fink & Resnick, 2001) indicates the
extent to which the role of the principal is changing, especially in the present context
of the accountability movement and the demand for improved student achievement
and the closing of the achievement gap. No longer viewed as simply an
administrator, the principal is now considered an important instructional leader,
participating in and contributing to school reform and increased student performance.
High school principals are expected to play key roles in the development of
curriculum, collaborating with teachers and establishing mission statements. They
are also expected to set high standards and maintain high expectations from teachers,
students and staff. High school principals set the tone of the school and play an
important role establishing the culture and climate. Davis, Darling-Hammond,
LaPointe, and Meyerson (2005) describe the present role of principals:
Principals are expected to be educational visionaries,
instructional and curriculum leaders, assessment experts,
disciplinarians, community builders, public
relations/communications experts, budget analysts, facility
managers, special programs, administrators, as well as
guardians of various legal, contractual and policy mandates and
initiatives. In addition, principals are expected to serve the
often conflicting needs and interests of many stakeholders,
including students, parents, teachers, district office officials,
union, state and federal agencies (p. 4).

46
Fullan (2002) carries the generally expected duties of the principal even
further by taking a philosophical approach to the role of school principal. Beyond
the specific enumerated duties and responsibilities mentioned above, Fullan argues
successful school principals must also be high-minded, moral agents of reform and
change. Fullan describes effective principals as change leaders moving far beyond
the typically expected task of improving test scores (and other indices of student
achievement) and setting instructional goals and expectations, to one of the vastly
more complex responsibility for transforming school culture and the teaching
profession. Fullan is concerned with developing leaders who can build a system
with a sustainable capacity for change and a commitment to student learning and
teaching based upon research and dedicated to creating life-long learners. He sees
the effective principal as a leader who boosts teacher morale, strengthens
relationships between administration and staff, encourages the development of
problem solving thinking skills and develops highly engaged teachers.
Drawing on the work of Collins (2001), Fullan (2004) describes the effective
leader as not only a catalyst for change but a committed leader devoted to developing
future leaders. The effective principal is also an individual who has foresight to
build capacity for sustainable change and to motivate team members to buy into a
shared vision. Effective principals, according to Fullan, collaborate with all team
members, including parents and community leaders. Effective principals place
specialized instructional leaders in key positions of curriculum development and

47
implementation, effective administrators into prominent managerial positions as and
collaborators and students and their families into key decision-making roles.
Leadership Implications for High School Math Reform
The research indicates reform requires strong leadership, not necessarily a
math expert or an individual with a great deal of experience teaching mathematics.
An effective leader (Marzano, 2003) creates the culture and climate necessary for
reform by setting directions, developing the individuals necessary to implement
reform and leading organizational and cultural reform efforts.
A study of public elementary school principals for the Consortium on
Chicago School Research, School Leadership and the Bottom Line in Chicago
(Sebring & Bryk, 2000) – applicable to secondary principals – describes three key
areas in which successful principals excel:
• Leadership style
• Reform strategies
• The issues on which they focus
Addressing a limited number of highly visible problems, focusing on long-term
changes to the core curriculum, collaboration, and developing a set of consistent
expectations and incentives were found to be key strategies of effective principals.
Each of these factors is a necessary component of successful leadership and is clearly
applicable to mathematics’ reform efforts, even in those cases where the school
principal is not an expert in math or math instruction. Developing an effective
mission statement, building a climate conducive to change, collaborating with

48
individuals who have the appropriate content knowledge and teaching skills, and
building a school design with the necessary capacity for reform, are all essential
characteristics of an effective leader.
Conclusion
American high schools are failing a significant portion of our student
population. In particular, far too many African-American, Latino and Native
American students leave high school unprepared for the complexities or our modern
society. High dropout rates and limited educational achievement disproportionately
affects students from ethnic minorities. Without an adequate education, these
students are ill prepared to compete in our increasingly complex society. Of
particular concern, is low performance in mathematics. With increasingly
demanding high school graduation requirements, failure to succeed in math often
leads to dropping out of school early, poor performance in other core areas such as
science, reduced graduation rates, and limited financial or educational success
following high school.
This study examines an urban high school beating the odds. With its students
demonstrating increasing math scores over two consecutive years, this study
examines and analyzes those research-based practices and reforms contributing to
student success. The study looks at instructional leadership and the role key leaders
played in efforts to reform school practices. The math curriculum, its
implementation, professional development and teacher collaboration will be
examined against the backdrop of recent research indicating the importance of

49
professional learning communities, committed instructional leadership, new school
designs and curriculum reform. The study focuses on an urban high school without
extraordinary resources and will examine the instructional leadership of an
administration without a particular expertise in mathematics or math instruction.
The information developed in this study will prove beneficial to other similarly
situated schools looking to improve student achievement particularly in the area of
mathematics while serving as repository of information, research and data about a
high school exceeding expectations.

50
CHAPTER 3

RESEARCH METHODOLOGIES

Introduction

This chapter outlines the design, instrumentation, data collection, and data
analysis for this case study. The primary purpose of this study was to examine a
successful mathematics program at an urban high school. This study sought to
determine those factors contributing to student success in math including curriculum,
teacher preparation and training, school design, instructional leadership and related
school reforms. The study also examined professional development, implementation
of the curriculum reform in classrooms, and the relationship between strong
leadership and improved student achievement. The selection of the specific school
was based on specific selection criteria.
Five research questions provided the framework for the study:
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 are related to improved math achievement at 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
program/strategies and b) math achievement among students?

51
5. How did instructional leaders respond in academic areas in which they
were not experts?
In order to address the five research questions, the researcher conducted a
case study of an urban high school demonstrating significant improvement in math
achievement over a three-year period. A case study was selected as the most
appropriate and effective research method when addressing the complexity of issues
contributing to improved student achievement. A case study provides the
opportunity to develop a detailed, comprehensive, and context sensitive
understanding of the various factors contributing to student achievement at a
particular high school (Patton, 2002). A case study can account for, analyze, and
give meaning to the numerous individuals, activities, programs, policies, resources
and other related factors committed to, and participating in, the process of advancing
student achievement.
The research methods incorporated in this study include interviews of the
school principal and assistant principal responsible for curriculum, key individuals
participating in mathematics and school wide reform efforts including the math
department chair and math coach, math and other teachers. The interview questions
are designed to elicit responses identifying participants’ views regarding math
curriculum reform and its implementation, teaching methods, and instructional
strategies, in addition to issues pertaining to instructional leadership. A survey was
also administered to teachers requesting responses designed to elicit specific
information related to math reforms, curriculum, and instructional leadership.

52
Any information connected with this study or identifiable with the school
site, or any specific participant will remain completely confidential. Participants’
interviews or survey responses were not released to any other party for any reason.
All data was kept in a locked cabinet and destroyed immediately after the completion
of the study. During discussions with co-researchers, at no times were participants
identified by name. Interview participants were assured confidentiality and
anonymity. Study participants were informed their participation is completely
voluntary and they could withdraw from the study at any time without any
consequences.
Sample and Population
Purposeful sampling was employed in selecting the specific school site for
this case study. The researcher was interested in developing and analyzing
information, in depth, from an urban high school meeting specific selection criteria.
The case study approach is particularly useful when focusing on a relatively small
sample in order to gather a great deal of information about a particular subject
(Patton, 2002). The purpose of this study is to examine the particular practices at a
specific high school that led to improved academic achievement in math.
The school selected met the following requirements for this case study:
• Improvement in math achievement as evidenced by results on the California
Standards Test (CST) in Algebra I for three consecutive years.
• Student diversity as defined by a student population of at least 50% ethnic
minority.

53
• Public high school in the Southern California region of at least 1200 students.
• A state wide rank of 5 or higher.
• Diverse student population with at least 50% non-white students.
• Leadership stability defined as the same principal for at least three
consecutive years during the period of improved student achievement.
An 11-member cohort directed by Dr. David Marsh, Associate Dean of
Academic Programs, University of Southern California, worked together to develop
the sampling criteria and identifying schools meeting these requirements. Qualifying
schools were identified using the following process:
1. A data file was downloaded from the California Department of
Education’s web site using DataQuest service.
2. The data file was exported into Microsoft Excel to create a spreadsheet
that was used to analyze and filter the available data in an effort to identify
schools fitting the profile.
3. Knowing the group would need to research student improvement on the
California Standards Test 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 Southern California.
4. Preliminary efforts to use more stringent requirements did not yield a
sufficiently large enough sample; accordingly additional adjustments were
made. For example, when the student enrollment parameter was set to
1500, the percentage of minority students at 65%, and the statewide rank

54
at 6 or higher, there were only 28 schools meeting all of these
requirements.
5. The second attempt to establish an appropriate sample involved adjusting
the parameters to an enrollment of not less than 122, a minority population
of 50% or more, and a statewide rank of 5 or higher. The sample
population then rose to an acceptable level of 110 schools.
6. Members of the cohort were then assigned 10 of the 110 schools and
asked to record CST scores in Algebra 1 for the years 2003, 2004, and
2005, and to enter the data into a spreadsheet.
7. The cohort then assigned an absolute value to the improvement 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 the top two performance bands. These totals were added to
indicate an overall level of improvement. For example, if a school
decreased the number of students scoring in the bottom two performance
bands 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

55
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 scores as calculated in the
example detailed above.
9. Using the above-described process yielded 44 schools qualifying for the
study.
10. A geographic map locating the qualifying schools was developed to assist the
cohort members choose a school for their study.
11. Each of the cohort members selected a qualifying school for their study.
Selected School
Based on the foregoing criteria, the researcher selected Hot Springs High
School (HSHS), Hot Springs Unified School District, for this case study. Located
120 east of Los Angeles in the Coachella Valley, Hot Springs is a well-known
celebrity desert hideaway, resort, country club, and retirement community. Famous
for its golf courses and high profile neighboring cities of Rancho Mirage, Palm
Desert, and Indian Wells, Hot Springs boasts a truly diverse community of wealthy
elderly retirees and snowbirds, boasting second homes of the rich and famous
alongside a well-healed friend community. Most recently, Hot Springs has become a
popular destination for younger families seeking affordable housing in the immediate
and surrounding communities. With desert temperatures providing year round
sunshine, Hot Springs provides a unique lifestyle for its residents who choose to live

56
far removed from the traffic and congestion of nearby Los Angeles, Orange and San
Diego Counties.
To a large extent, HSHS students are drawn from more recently arrived
families drawn to the desert by the relatively low cost housing prices and a
community perceived to be less threatened by the challenges of large urban centers.
Construction, resort industry, service and agricultural jobs provide employment to
families with school age children. A vibrant and expanding housing market offers
competitive home prices and a source of employment in construction and related
trades.
Established in 1936, HSHS serves approximately 1,900 students in grades 9-
12. HSHS has a principal, 3 assistant principals, and 78 faculty members (including
14 full time math teachers). HSHS is comprised of a diverse student population
with an ethnic balance of 41% White, 45% Hispanic, 5% African-American and 9%
other (including Filipino-American, American Indian or Alaska Native, Asian-
American and Pacific Islander). Fourteen percent of the students are classified as
English Language Learners (ELL) and 43% participate in the free/reduced lunch
program.
HSHS received a three-year accreditation (2004) from the California State
Board of Education and the Western Association of School and Colleges (WASC).
The school offers honors classes in English, the sciences, mathematics and
corresponding advance placement courses. The school also offers vocational
training in the areas of automotive technology, graphic design, welding, police

57
science, computer technology and publishing. There is a Money, Marketing, and
Management Academy for students interested in pursuing a career in business.
Additionally, HSHS enjoys a close relationship with the Riverside County Office of
Education’s Regional Occupational Program offering classes designed to develop job
related skills for students. In 2005, HS Unified School District took back all of its
special education classes formerly served by the Riverside County Office of
Education and is in the process of forming a Special Education Local Plan Area
(SELPA) including Desert Sands and Coachella Valley Unified School Districts and
breaking away from the Riverside County SELPA.
Student Achievement
HSHS has posted improved Academic Performance Index (API) scores from
2001 (592) to present (696). The school is ranked 6 when compared to other
California high schools (statewide raking) and is the highest achieving
comprehensive high school in its district. The principal has been at HSHS for more
than 5 years and the school has demonstrated stability in both administration and
faculty during this period. The school has experienced a significant increase of
students over this period of time (1700 in 2001) to the present 1900 (2005) while
posting increasing test scores.
Study Participants
Participants included the school principal and the chair of the math
department. These two individuals have a great deal of information and shared
responsibility concerning overall teaching and learning objectives for the math

58
department. They play an instrumental role in developing instructional practices and
strategies, and serve as a liaison between teachers and district administrators. The
principal and math department chair were interviewed separately over a period of
several days. The interview questions were designed to elicit detailed information
regarding policy initiatives, the change process, instructional practices and
leadership, and the level and type of support provided to the school in general, and
the math department, in particular. The interview questions anticipated a range of
possible answers and were designed to allow the interviewee to provide expanded
answers and for the interviewer to ask follow-up questions.
Key instructional leaders also participated in this study including a lead math
teacher and an additional 5 members of the math faculty. The lead math teacher was
interviewed using the same instrument as the principal and the math department
chair. The 5 math teachers were interviewed using the Teacher Interview instrument.
The teacher interview also asked a series of open ended questions designed to elicit
full and complete responses for interviewees. These questions also provided the
interviewer the opportunity to answers follow-up questions or to seek clarification.
Finally, all teachers were surveyed (using separate instruments for math and non-
math teachers) to determine their views about the math curriculum, recent reforms,
instructional leadership, the change process, and the role played by key leaders in the
implementation of the math program. The researcher was interested in learning
about those factors participants considered important to the increased math
performance of HSHS students. The survey questions were also designed to gather

59
teachers’ views regarding those factors and individual(s) responsible for improved
student performance in math.
Instrumentation
The instrumentation in this study was developed by a cohort of doctoral
candidates working on a thematic dissertation under the direction of Dr. Marsh.
Each of the eleven-member group agreed to do a case study of a public high school
demonstrating increased performance of students in Algebra I for two successive
years. Based on a particular set of sampling criteria, each member of the cohort
chose a specific school for their study. Working together, the cohort agreed upon a
series of instruments for the purpose of eliciting data related to the factors
contributing to increased student achievement and designing instruments to gather
information responsive to each of the research questions. These instruments
included a school profile, teacher interviews, key leader interviews, and a survey.
Groups of students were assigned the task of developing each of these instruments.
Figure 1 illustrates the relationships between the research questions and the data
collection instruments.

60
Figure 1: Research Question and Instrument Development

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

Conceptual Frameworks
In order to guide the research necessary to answer the 5 research questions,
the cohort developed conceptual frameworks for each of the research questions. The
conceptual frameworks outline key factors related to each of the research questions.
The conceptual frameworks were developed by members of the cohort and were
drawn from recent studies and sound educational practices.
Conceptual Framework – Research Question 1
Research question 1 asked for a profile of student performance in math at
HSHS. The question requires the collection of data documenting student
performance over time and evidencing improved student performance. The cohort
agreed to use general reporting data most often found in the research evidencing
school performance and a matter of public record. Compiling regularly reported data
concerning student performance informed the conceptual framework for research

61
question 1. The cohort agreed to compile data pertaining to student performance on
the CSTs, analysis of performance bands, Algebra 1 passing rates, overall school
dropout and graduation rates, and overall student performance in math classes.
The cohort agreed CST scores in Algebra 1 would provide the primary data
necessary to support the study and were determinative in the original selection of the
schools studied by the cohort, including HSHS. Improved student success in
Algebra I was considered a significant indicator of a successful math program given
the importance of Algebra I as a part of the school curriculum, in most school
districts a graduation requirement, closely connected to later success in school, and
an important predictor of post-secondary achievement and increased earnings.
The school profile would supply data concerning student performance based on CST
scores and API scores over a three-year period and includes an analysis of changes in
the performance bands. Additionally, the school profile provides general
demographic information including student population, grade level student
distribution, class sizes, teachers training, years of experience and credentialing,
socio-economic status and language proficiency, dropout and graduation rates. The
profile provides a basis for comparison to other similarly situated schools and the
comparative ranking of HSHS to other California high schools in terms of
population, ethnic breakdown, socioeconomic status and teacher qualifications.
Conceptual Framework – Research Question 2
Research question 2 addresses the issues of a) school based policy initiatives
contributing to increased student performance and b) curriculum reform and its

62
implementation (and related teaching methods and strategies). Two conceptual
frameworks were developed in order to adequately and appropriately respond to the
distinct sections of research question number two. The cohort addressed the first
section of the question concerning school level policy initiatives by looking at school
design, including learning activities, student performance assessments, curriculum,
and school culture. The cohort developed a conceptual framework (Figure 2)
reflecting these four aspects of school design and the most pertinent subcategories.
Data concerning the nature of these four general factors and their influence on
student achievement responds to the issues of policy initiatives designed to increase
student performance and evidence supporting their relationship to increased student
success. The school design framework provides a multidimensional approach to data
gathering providing information closely related to school success and often
interdependent.
Research question 2 also addresses the issue of an effective math curriculum.
The Effective Math Programs conceptual framework (Figure 3) illustrates three
general areas of concern: classroom practices, standards based instruction, and
curriculum design. Drawing from the literature, it incorporates numerous subtopics
supporting each general category. The subtopics address issues of instruction,
assessment, and teaching approaches and methods, providing an opportunity to

63

Figure 2: 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

64

Figure 3: Effective Math Programs

Effective Math Programs
Curriculum Design
Student-Centered Curriculum.
Instruction Driven by Student Outcomes.
Emphasizes Conceptual Understanding.
Focuses On Problem Solving.
Incorporates Current Learning Theory
Scope and Sequence Supported by
Learning Theory.

Classroom Practices
Effective and Coherent lesson design.
Promote High Levels of Student Engagement.
Make Use of Prior Knowledge.
Culturally Relevant
Standards Based Instruction
Assessment Aligned to Standards.
Data Drives Instruction.
Common Performance Rubrics

65

closely examine actual practices, underlying teaching philosophies, teacher attitudes,
instructional reform, and the alignment of standards, instruction and assessment.
This conceptual framework guides the data collection process, the development of
appropriate instruments and the scope of the inquiry. It also provides an outline of
best practices against which actual programs and their implementation may be
evaluated.
Conceptual Framework – Research Question 3
Research question 3 addresses the change process used by HSHS to
implement a successful math program. The question assumes the HSHS math
program was developed over time by an individual(s) and/or organizational
commitment to improve student performance involving all, or in part, instructional
leadership, curriculum reform, professional development, instructional strategies and
new school designs. Efforts to effect substantial change in the complex setting of a
public high school is expectedly often met with resistance. Embedded organizational
structures and procedures, fear of losing power and control, and concerns about
accountability and responsibility may hinder reform efforts. In Reframing
Organizations: Artistry, Choice, and Leadership (2003), Bolman and Deal provide
four frames (or perspectives) from which to view an organization. These four frames
form the basis of the conceptual framework developed by the cohort to assist in the
development of instruments and the collection and analysis of data pertaining to the

66
change process. The frames provide the researcher with four different perspectives
from which to understand the effect of change on an organization. In order to
acquire a comprehensive understanding of the change process, the cohort developed
instruments while taking into account the four frames: structural, human resources,
political and symbolic (see Table 1).
Table 1: Bolman and Deal’s Four Frames
Frame Structural Human
Resources
Political Symbolic
Metaphor
for
organization
Factory or
Machine
Family Jungle Carnival,
Temple,
Theater
Central
Concepts
Rules,
Roles, goals,
Policies,
Technology,
Environment
Needs, Skills,
Relationships
Power,
Conflict,
Competition,
Organizational
politics
Culture,
Meaning,
metaphor,
ritual,
ceremony,
stories,
heroes
Image of
Leadership
Social
Architect
Empowerment Advocacy Inspiration
Basic
Leadership
Challenge
Attune
Structure to
task,
Technology,
environment
Align
Organizational
and human
needs
Develop
Agenda and
Power Base
Create Faith,
Beauty,
Meaning

Bolman and Deal’s four frames also serve as approaches to understanding the
effect of change on the school and respond directly to research question 3 seeking to
determine the change process employed by key leaders. Change agents
(administrators, key leaders or teachers) might attempt to reform the HSHS math

67
program by affecting, altering, changing or manipulating any one (or more) of these
frames. The change process, for example might have involved modifying the
organizational structure of the math department providing, for example, greater
autonomy to teachers or passing on responsibility to the department chair. It is also
possible that administrators or district level officials dictating policies and initiatives,
or imposing a highly scripted curriculum, may have directed the change process in a
top down manner without regard to the opinions of math department personnel.
Similarly, the change process may have involved political strategies involving a
change in the school’s power structure, or confrontation with deeply entrenched
individuals protecting their established areas of control or authority. In any event,
the four frames provide a range of perspectives for understanding the change process
employed at HSHS and a framework from which to view the organization
holistically. It against this backdrop the researcher is able to organize the collection
of data and interpret the results in a meaningful and cohesive fashion.
Conceptual Framework – Research Question 4
Research question 4 addresses the issue of instructional leadership and
provides a framework to assess and evaluate HSHS leadership and its role in
improving student performance in math. The cohort was particularly interested in
examining the role played both individually and collectively by school site leaders
including the principal, assistant principal in charge of curriculum, math coach,
department chair and lead teachers. Questions concerning their specific actions, how
they came to agreement, responsibility for implementation, interpersonal

68
relationships between and among school leaders and faculty, and their background,
knowledge, and experience in math, math instruction, and student achievement.

The cohort was also interested in exploring leadership style, philosophy and
responses to problems, people and issues. Of particular interest was the decision
making process of key leaders, particularly those without a strong background in
mathematics. The cohort explored capacity building and sustainability of reform
efforts and whether or not school leaders addressed these either in action plans or
when making individual decisions regarding the math program. The cohort is also
interested in key leaders roles in the development of the plan and the acquisition and
allocation of resources necessary to design and implement the math program.
Working as a group, the cohort developed a conceptual framework (Table 2)
addressing instructional leadership from the point of view of the knowledge an
effective leader would be expected to have in order to successfully initiate,
implement and sustain change over time, develop the capacity to build an appropriate
curriculum, use data to drive decision making, and the ability to respond in a timely
manner to unforeseen problems or unintended consequences of their programs and
decisions. The conceptual framework is drawn from Johnson (2003), Hessel and
Holloway (2002) and the Principal Standards developed by the California
Department of Education.

69
Given the importance attributed to school leadership (Marzano, 2003), this study
explores the manner in which leaders influence factors related to improved student
performance in math. These factors include delegation of authority, adoption of
curriculum, teacher hiring and retention, student motivation, and structural and
political organization of the school. Marzano (2003) notes leadership has a strong
relationship with school missions and goals, the overall school climate, teacher
attitudes and morale, classroom practices, organization of the curriculum and
students’ opportunities to learn. Each of these factors is examined and data collected
through the various instruments developed by the cohort.
Table 2: Instructional Leadership Framework
Instructional Leadership Framework
What an effective leader must have knowledge of . . .
Vision for Learning Supervision and
monitoring of
instruction
Community and
Political
Culture of
Teaching and
Learning
Data Driven Decision
Making and Analysis
Facilitates the
development,
articulation,
implementation and
stewardship of a
vision of learning that
is shared and
supported by the
school community.
Observes and monitors
instructional program.
Provides constructive
feedback in a timely
manner to all teachers.
Collaborates with
families and
community
members,
responds to
diverse
community
interests and
needs, and
mobilizes
community
resources.
Advocates,
nurtures, and
sustains a school
culture and
instructional
program.

Uses data as a tool for
informing instruction
and supporting student
learning.
Vision:
Develop
Communicate
Implement
Monitor
Evaluate
Address obstacles.
Classroom observations
on a daily/weekly
basis.
Allocates resources to
ensure successful
teaching and learning.
Supervision of
personnel.
Hiring of personnel that
supports the learning
goals and vision of the
school.
Understands the
values of diversity.
Understands
community needs.
Involves the
community in the
school.
Provides
opportunities for
community
involvement.

Valuing of students
and staff.
Developing and
sustaining school
culture.
Culture that is
inclusive and
respectful of
diversity.
Implements practice
for culturally
relevant teaching
and learning.
Celebrates students,
teachers and staff.
Utilize assessment to
place students
appropriately.
Formative assessment
Summative assessment
Disaggregate data by
students, classes, and
cohorts.
Use data to guide and
improve instructional
programs.
Use data to create
master schedule.
Use data when
developing pacing and
instructional plans.

70

Key components of the framework involve the effective leader’s vision, supervision
practices, relationship with the community and other political forces, involvement
with teaching and curriculum, and an ability to use data to drive and inform decision-
making.

Conceptual Framework – Research Question 5
Research question 5 addresses the issue of school site leadership not having a
particular expertise in math or math instruction in a school demonstrating marked
increases in student achievement in math. The conceptual framework developed by
the cohort follows the NCLB criteria for a highly qualified instructor (Table 3). The
benchmarks include a review of credentials held, post secondary course of study,
college major and minor courses of study, and classroom experience. The
conceptual framework provides a series of steps and a flow chart leading to one of
three possible conclusions: the principal has high, medium or low levels of expertise
in math.
In addition to the principal, the conceptual framework provides a rating basis
for other key instructional leaders’ expertise in math including the department chair,
math coaches, lead teachers and the math faculty. What follows and in need of
examination are the actions taken by individuals in a position to effect change and
whether or not their actions and decisions can be related to their levels of experience

71
and knowledge in math. Issues of delegation of authority, training, seeking outside
assistance, acquisition of targeted resources, reliance on scripted curriculum, areas of
emphasis, are all necessary areas of study and analysis.

Table 3: Assessment of Principal’s Expertise in Math

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Data Collection Instruments
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
Does the Principal
have a minor or
taught math?
Yes No
Medium
Expertise
Low
Expertise

73
Following the completion of the conceptual frameworks, the cohort
developed data collection instruments. The cohort developed a key leader interview
guide, a teacher interview guide, and a math and general teacher survey
questionnaire.
School Profile Instrument
Members of the cohort agreed comprehensive school data provides important
background information, illustrates important changes over time, student
performance patterns, and other factors associated with the school potentially
impacting student achievement in math. Recognizing the massive amount of school
profile data available, the cohort agreed to use widely reported data such as the
School Report Card including demographics, student performance, and general
information related to school reform and student achievement. Much of this
information is readily available to the public through numerous informational
sources including the California Department of Education.
Demographic information is readily used to determine ethnic makeup,
student socio-economic status, and data regarding teachers including credentialing
information and years of experience. This information also includes the number of
English Language Learners, students enrolled in the Free/Reduced lunch program,
classroom sizes, grade level populations and special education statistics.
Additionally, information pertaining to teachers includes NCLB compliance issues
including educational levels and subject matter competency. These issues provide a
contextual setting for HSHS and a point for comparison to other schools.

74
Student performance data is a central concern of this study as it reflects
achievement levels providing a threshold from which to evaluate curriculum, teacher
practices, reform strategies and instructional leadership. It also provides information
regarding performance trends. This information also forms a point of comparison
when viewing student populations at other schools. Looking at student outcomes
provides information regarding the efficacy of student programs and reforms.
Additionally, general background information regarding prior reform,
changes in curriculum, staffing changes, modifications in programming and
leadership all provide useful information when evaluation which factors were most
closely related to improved student performance. This information also provides a
base from which to determine the sustainability of reform programs and resources
necessary to maintain student performance over time.
Key Leader Interview Guide
Strong instructional leadership has been referred to (Marzano, 2003) as the
single most import component of school reform. The Key Leader Interview Guide
was developed by the dissertation cohort with the goal of determining key leaders
and ascertaining their contributions, opinions and concerns about HSHS’s math
program. Initially, HSHS’s principal was approached informally and fully informed
about the topic and data collection needs of the researcher. The principal approved
of and agreed to the case study expressing a strong desire to assist the researcher
obtain necessary information.

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The principal identified two leaders he felt most important to the math program and
who had made the greatest contributions to its success: the chair of the math
department and a lead math teacher. The principal, math department chair and math
lead teacher were interviewed by the researcher. Each of these individuals was
separately interviewed for approximately two hours over the course of several days.
The researcher tape recorded each of the interviews and transcribed them.
The interview guide is aligned to research questions 2 – 5. The interview guide
contains 16 questions. The questions are designed to elicit responses identifying
important policy initiatives, curriculum strategies and methods, structural changes
and the contributions of school personnel to improved student achievement. The key
leaders were also asked to describe any obstacles to reform. Of particular interest to
the cohort is the manner in which key leaders developed and implemented policy
initiatives, the change processes involved, and the manner in which they supported
school reform. Accordingly, interview questions were designed around the concerns.
Teacher Interview Guide
The cohort developed a series of 7 interview questions to be administered to
all math teachers. Five math teachers agreed to participate. The interview questions
were aligned with research questions 2 – 5. Each teacher was asked the same
questions and their responses were tape-recorded and later transcribed.
The introductory teacher interview questions asked for demographic
information including their teaching position, years of experience, credentials held
and training. The remaining five questions were open-ended and designed to obtain

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teachers’ opinions about a variety of factors including: the role of school leaders, the
math curriculum, school reforms, student performance, and other related factors.
The primary purpose was to collect data pertaining to teachers’ opinions and
observations regarding factors they thought contributed to improved student
performance. The questions asked teachers to develop their opinions, offer support
for and explain their answers. The questions were intentionally structured in a
manner providing an opportunity for follow-up questions by the researcher.
Math Teacher Questionnaire
The math teacher questionnaire consists of 50 questions. Teachers are asked
to respond to each question by choosing from one of five possible choices ranging
from strongly agreeing to strongly disagreeing to the statement contained in each
question. The questions are aligned to research questions 2 – 5. The questionnaire
was presented to each teacher assigned at least one Algebra 1 class.
The math teacher questionnaire was designed by the cohort to elicit specific
information to close ended questions. Math teachers were asked their opinions on
very specific information. The data collected provides detailed information about
specific practices and identifiable reforms. The purpose was to acquire targeted
information regarding matters identified in the research as having an important effect
on student math achievement.
General Teacher Questionnaire
The general teacher questionnaire consists of 30 questions. Teachers are
asked to rate their responses to each of the questions on a five-point scale ranging

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from strongly disagree to strongly agree. The questionnaire is designed to elicit
responses providing specific information in response to close-ended questions. The
questions were designed by the cohort and are aligned with research questions 2 – 5.
The questions asked for teachers’ opinions and evaluation of the role of school
leaders, school design, the reform process and change movement, curriculum and
student achievement. Each of the questions provides data supporting responses to
each of the research questions.
Data Collection
Following review and approval of the University of Southern California’s
Institutional Review Board (IRB), data collection began spanning a period of
approximately four months. The IRB required adherence to particular protocols
primarily concerned with maintaining participant confidentiality and voluntary
participation. The researcher followed all requirements of the IRB and obtained all
necessary documents before beginning the data collection process.
The first step in the data collection process was collecting and assembling
data pertaining to the school profile. Most of this information came from public
sources including the California Department of Education. Additionally, private
sources of information were used including Ed Data and Students First. This
information included demographics, student performance data and general
background information. The data collected provided information regarding
distribution of students in various classes, class size, courses offered, number of

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teachers, school’s structure and staffing. The data included information regarding
student ethnicity, language proficiency and socio-economic status.
The next step in the data collection process was an interview with the school
principal. This interview provided information about school structure, key leaders,
departmental and staffing concerns, overall issues concerning student performance
and the math program. The interview with the principal provided a wealth of
information regarding the operation and structure of the school. The researcher used
the key leader guide for the interview. The principal identified two key leaders he
believed responsible for improved student achievement in math: the chair of the
math department and a lead math teacher.
Following the interview with the school principal, the next step in the data
collection process was an interview of the math department chair and the lead math
teacher. Each was administered the key leader interview questions and their
responses recorded and transcribed. The key leader interviews provided a significant
amount of information regarding the reform process, the role of instructional
leadership, school design and student performance. The key leaders offered their
opinion regarding matters they felt important to the change process. Each identified
those factors they felt provided the greatest contribution to student success. The key
leaders were also asked to identify teachers they felt played a role in student success.
Five math teachers were then interviewed using the Teacher Interview instrument.
The 5 math teachers were asked to describe their current position, educational
background, credentials held, years of experience and any specialized training in

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math. Following these introductory questions, the 5 math teachers were asked 5
additional questions addressing policy initiatives, teaching strategies, the
implementation and support of the math program, the role of school leaders and
actions taken by school leaders they felt most directly affected student achievement.
Math teachers and the general faculty were then administered survey questionnaires.
As noted, a separate and distinct survey instrument was prepared for the math faculty
and the non-math faculty. The principal’s secretary graciously agreed to assist in the
distribution of the survey questionnaires. The questionnaires were placed in each
teacher’s faculty mailboxes on the school site. Participation was voluntary, however,
the principal and math department chair encouraged all faculty members to
participate in the study by including it in the daily school newsletter and in informal
conversations. The principal also addressed the math faculty and thanked them for
their participation. The math faculty consists of 14 teachers, and all 14 teachers
returned completed surveys. The non-math faculty consisted of 64 teachers, and 48
of the non-math faculty returned completed surveys.
Data Analysis
The data collected was analyzed in light of the five research questions. The
researcher looked for areas of agreement and trends common to all participants.
Particular attention was paid to areas of agreement regarding essential factors
contributing to student success. The data provided a picture of what most HSHS
administrators and faculty believed were the reasons for student success in math. It
offered insight into particular points of view and attitudes toward the school, its

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students and the math program. The researcher coded all data in order to group
opinions and points of view. The researcher also looked for differences in opinion
among various groups in order to find patterns or trends among the participants
based on their employment status or position.
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.
Conclusion
This chapter discusses the research methodology used in this study. Included
was a detailed discussion of the research questions, the instrumentation used to
collect data, the conceptual frameworks supporting the instrumentation, the data
collection process, the participants in the study, and the procedures for data analysis.
The data collection process began following approval by the University of Southern
California Institutional Review Board and the completion of the oral qualifying

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examinations. The researcher obtained approval of the study from the HSHS
principal and his permission to administer the data collection instruments.
The following chapter will outline the findings of the case study. The
findings will include those factors key leaders and faculty identified as essential
components of student success in math. The findings will provide administrator and
teacher evaluations of instructional leadership, the math curriculum, teaching
strategies and methods, and school reform. It will also provide information
regarding the change process and the degree to which school design reform
contributed to student achievement and the manner in which key leaders without a
particular expertise in math successfully contributed to improved student
achievement in math.

CHAPTER 4

DATA FINDINGS, ANALYSIS, AND DISCUSSION

Introduction

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The purpose of this study was to research and document how HSHS, a large
urban public high school with a high percentage of minority students from families
of low socio-economic background and limited formal education, without
extraordinary resources, achieved and sustained significant gains in the area of
mathematics as demonstrated by student performance on the California Standardized
Testing and Reporting assessments in math. The study identifies and examines those
factors research indicates most likely to contribute to student success including
district policy, district and school site leadership, curricula, professional
development, parent, teacher, student involvement, and overall reform designs and
initiatives. The study looks to the variety of methods and strategies HSHS
employed to successfully pull together these elements in a manner most likely to
contribute to student success and maintain their achievements in math performance,
over time.
In this chapter, the data collected for each of the five research questions will
be analyzed and discussed in detail. The data includes a presentation and discussion
of demographic and other statistical information describing HSHS including a
description of the student population, school leadership, faculty, facilities and
program development. The immediate historical background of HSHS will also be
discussed particularly as it relates to student achievement and the implementation of
reforms designed to increase student performance in mathematics. The data also
includes interviews of the school site principal, the math department chair, and five

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math teachers. Additionally, the results of two surveys (one designed specifically for
math teachers and the other for non-math teachers) are discussed and analyzed.
The interview and survey questions were designed to elicit responses directly
related to the five research questions presented in this study and to provide a greater
understanding of those factors administration and faculty felt played the greatest role
in improved student achievement. The interview questions were also designed to
encourage participants to expand on their particular explanations for, and critique of,
district and school policies, curriculum design, instruction, and other factors they felt
played an important role in advancing student achievement. The survey questions
covered a wide range of potential factors teachers, in particular, might be anticipated
to believe played an important role in student success. The interview and survey
questions also sought to seek guidance on, and support for, the potential applicability
of these factors to other similarly situated urban high schools looking to improve
student performance in math.
Data was collected as described in the guidelines outlined in Chapter 3. The
five research questions addressed student achievement, policy initiatives including
curriculum, instruction and other conditions related to improved math achievement,
the change process employed, the role of instructional leadership, and the strategies
and methods employed by instructional leaders without a particular expertise in
math.
The five research questions studied:
1. What was the pattern of math achievement for various students at the

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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?
Research Question 1: Pattern of Math Achievement
The first research question asked was, “What was the pattern of math
achievement for various students at the school?” For this question, Conceptual
Framework – Research Question 1 guided the data collection and analysis of student
performance in mathematics, over time. HSHS was chosen for this study because it
met the research cohorts’ purposeful sample and population requirements of:
• improvement in math achievement on the California Standards Test (CST) in
Algebra I for three consecutive years
• a diverse student population of at least 50% identified as ethnic minorities
• a student population with at least 50% non-white students
• a public institution with at least 1200 student
• a state wide rank of 5 or higher

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• leadership stability by retaining the same principal for at least 3 consecutive
years during the period of improved student achievement.
The cohort agreed to use CST scores in Algebra I as the primary data necessary
to support the study and to provide evidence of student gains in math performance.
Improved student success in Algebra I was considered a significant indicator of a
successful math program. It was further agreed general reporting sources such as
HSHS School Accountability Report Card and the California Department of
Education’s published performance data on statewide standardized assessments
would be used to establish the pattern of math achievement.
Student Enrollment, Racial and Ethnic Subgroups
HSHS reported (School Accountability Report Card, 2004-2005) a total
enrollment of 1,916 students for the school year 2004-2005, up from 1,707 students
in the 2001-2002 school year. The HSHS principal estimated an increase of
approximately 100 - 150 students for the school year 2005-2006 based on current
trends in the local housing market and a statewide shift in population growth from
the coastal to inland regions.
During the 2004 - 2005 reporting period, the ethnic and racial breakdown of
the student population at HSHS was 41% White, 45% Hispanic, 5% African-
American and 9% other (including Filipino-American, American Indian or Alaska
Native, Asian-American and Pacific Islander). HSHS has experienced an increase in
Hispanic students (41% to 45%) and a decrease in White students (46% to 41%) over
the past 4 years. During the 2004 – 2005 reporting period, 14% of HSHS students

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were classified as English Language Learners (ELL) and 43% participated in the
free/reduced lunch program. These latter figures are also anticipated to continue to
increase following population and demographic trends in the immediate and
surrounding neighborhoods. The availability of relatively low cost housing and the
over-heated job market fueled largely by the service sector, new construction and
related trades is generally considered responsible for attracting large number of
younger skilled and semi-skilled workers to the area served by HSHS.
As reported by the California Basic Educational data System (CBEDS), student
enrollment by grade level for the period 2004 – 2005 (see Table 4):
Table 4: California Basic Educational Data System (2004-2005)
Grade Level Enrollment
Grade 9 504
Grade 10 495
Grade 11 498
Grade 12 419
Total Enrollment 1916

California Standards Tests (CST)
Through the California Standardized Testing and Reporting (STAR) program,
students in grades 2 through 11 are tested annually in various subject areas, including
mathematics. As a component of the STAR program, the department of education
developed the California Standards Tests (CST) to assess student performance on the
California content standards. The CST results are reported using performance levels

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(bands): advanced (exceeds state standards) proficient (meets state standards), basic
(approaching state standards), below basic (below state standards) and far below
basic (well below state standards). The percent of students scoring at each
performance level is reported by grade and subject for all students, as well as
subgroups of students, and posted on the California Department of Education’s web
site. The reported state target is to have all students score at proficient or above.
HSHS was selected for study because it met the research cohort’s qualifying
criteria that, in part, requires a demonstrated improvement in math achievement as
evidenced by results on the CST in Algebra I for three consecutive years. The cohort
defined improvement as a significant decrease in the percentage of students
performing at the below and far below basic performance levels and a corresponding
increase of students performing at the proficient and advanced performance levels.
Student performance in Algebra I on the CST over a 3-year period is described as
follows (see Table 5):
Table 5: CST Algebra I (2003-2005)
CST Algebra I

Year Advanced Proficient Basic Below Basic Far Below Basic

2005 0% 14% 31% 42% 12%
2004 0% 8% 33% 46% 13%
2003 0% 5% 24% 46% 25%
These scores represent the combined results of all 9th, 10th and 11th grade students
tested in the subject area of Algebra I during the designated years (2003 – 2005).

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The test results indicate a sustained trend over three years moving students from
either below basic and far below basic to either basic or proficient. Whereas, only
5% of students tested in 2003 were designated proficient, 14% of the students tested
in 2005 achieved proficiency. Similarly, students identified as either below basic
and far below basic declined over the same period of time.
Combining the upper and lower two performance bands illustrates the
positive movement of students towards exceeding, meeting or approaching state
content standards in Algebra I from the period 2003 – 2005 (see Table 6):
Table 6: Upper and Lower Two Performance Bands In Algebra I (2003-2005)
CST Algebra I
Year Advanced and
Proficient
Basic Below Basic and Far Below
Basic
2005 14% 31% 54%
2004 8% 33% 59%
2003 5% 24% 71%

It is significant to note gains in student performance occurred during a period of
increased student enrollment and representation of students from ethnic minorities
and English language learners, while experiencing a corresponding decrease in white
students and those demonstrating English language proficiency.

State of California Comparison

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The considerable progress made by HSHS students becomes quite evident
when compared to the relatively static results of all State of California students tested
between 2003 and 2005 (see Table 7):
Table 7: CST Algebra I - All State of California Students Between 2003-2005
CST Algebra I – State of California – All Students
Year Advanced Proficient Basic Below Basic Far Below
Basic
2005 3% 16% 30% 37% 14%
2004 3% 15% 26% 42% 14%
2003 4% 17% 29% 34% 16%

Whereas, HSHS moved from 5% of all students tested on the CST Algebra I
examination scoring proficient in 2003 to 14% in 2005 (a gain of 9%) state results
remained essentially the same (a 1% decrease). Again, the marked progress of
HSHS is set against a background of increasing minority representation and students
from families of lower socioeconomic status and a long history of poor performance
on standardized tests particularly in core academic subjects.
Combining the upper and lower two performance bands further illustrates the
positive movement of students towards exceeding, meeting or approaching state
content standards in mathematics when compared to state results. The significant
progress of HSHS students compares favorably to results posted by all California

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students. Not only in the highest performance bands but also in the basic category,
HSHS students outperformed statewide scores (see Table 8).
Table 8: CST Algebra I - All State of California Students
CST Algebra I – State of California – All Students
CST Algebra I – State of California – All Students
Year Advanced & Proficient Basic Below Basic and Far Below Basic
2005 19% 30% 51%
2004 18% 26% 56%
2003 21% 29% 50%

HSHS and HSHS District Comparison
The HSHS Unified School District includes three comprehensive high schools of
similar student populations, historical rates of student performance, demographics,
ethnic and minority representation and socioeconomic status. When compared to the
combined scores of all students in the HSHS district, HSHS demonstrated much
greater levels of student achievement and progress moving students from below and
far below basic to basic and above. District wide scores reflect little or no
movement compared to the significant progress demonstrated by HSHS. HSHS
administrators and school leaders contend the advancements made by HSHS results
from specific HSHS polices, leadership and change processes as opposed to district
wide reforms. Their views are documented by the specific progress of the HSHS
District when compared to HSHS (see Table 9).

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Table 9: CST Algebra I - HSHS School District - All Students
CST Algebra I – HSHS School District – All Students
Year Advanced Proficient Basic Below Basic Far Below
Basic
2005 1% 9% 25% 47% 18%
2004 0% 9% 29% 48% 14%
2003 0% 7% 25% 46% 22%

The improved performance of HSHS when compared to the overall district
performance levels reflects on the specific approach taken by the HSHS
administration. Not relying on district mandates, many of the policy initiatives and
reforms mentioned below were developed by HSHS administration and staff without
relying on district support. District offers of support were often viewed as
insubstantial and ineffective. Reform generated from within and responsive to
specific schools needs proved far more effective. The leadership offered by the
school principal and math department chair proved critical in advancing student
achievement and improving the quality of math instruction at HSHS by tailoring
reforms to the results of collaborative efforts to adopt and implement state math
content standards and then develop instructional strategies necessary to achieve

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success. Free from the constraints of district mandates, the HSHS administration and
staff felt free to move quickly and with little or no opposition to develop a math
program responsive to their students and to which they could wholeheartedly lend
their support.
Research Question 2: Policy Initiatives, Curriculum Instruction, Related Conditions
The second research question asked, “What policy initiatives as well as
curriculum instruction and related conditions are related to improved math
achievement at HSHS?” Research question 2 addresses the issues of a) school based
policy initiatives contributing to increased student performance and b) curriculum
reform and its implementation. For this question, the School Design and Effective
Math Programs conceptual frameworks guided the data collection and analysis of the
school’s policies and reforms for improving student performance.
The interview questions of key school leaders were designed to elicit
responses directly related to specific research questions. In order to collect data
responsive to research question 2, the questions asked of key leaders directed the
interviewee to consider a range of policy initiatives including No Child Left Behind,
Annual Yearly Progress (AYP), highly qualified teacher requirements and to reflect
on these issues as they related to the math program at HSHS (the thrust of research
question 2).
In reference to research question 2, the math teachers were asked to describe
and discuss policy initiatives and/or mathematics curriculum they felt contributed to
improved math achievement. In the case of the five teachers interviewed, they were

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not provided with prompts or a prefatory statement that might influence their
answers.
Research Data
Improved Student Performance
Improved math achievement at HSHS is a result of a series of closely related
factors and policy initiatives including:
• adopting state content standards
• raising levels of accountability
• implementing standards in all classrooms
• aligning curriculum to the state standards
• research based teaching practices
• recruiting highly qualified teachers
• establishing a positive school culture
• benchmark assessments
• rewarding student success
• responding to the demands of standardized testing.
Adopting State Content Standards
Responding to his perceptions about how policy issues affected his efforts to
improve student achievement in math, the HSHS principal referred to the Board of
Education and a former superintendent’s cooperative efforts imposing a district wide
adoption of the California academic standards in the spring of 2001 as marking the

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beginning of a period of sustained and ongoing reform efforts designed to improve
student achievement. As described by the HSHS principal:
Faced with the demands of the recently passed No Child Left
Behind legislation in Washington and a well-documented
history of poor performance in English and math, particularly
among minority students – mostly Hispanics from poor families
– the former HSUSD superintendent with strong support from
the Board of Education, established a series of initiatives
designed to transform the district, and HSHS in particular, into a
standards based high school. There was a strong commitment to
turn things around particularly for our underperforming students
and content and teaching standards with a strong sense of
accountability was viewed as the most effective way to change
our past history of teaching and learning.

The math chair recalls, “We were all aware of the movement towards greater
accountability and a sense that we could no longer accept students failing as part of
the normal course of events.”
The former superintendents efforts began a sustained period of adopting state
content standards in all of the core academic subjects and their implementation in
classroom instruction. The math content standards provided a comprehensive and
cohesive basis to formulate curriculum goals and to guide student assessment. Often
mentioned was the notion that there was now a basis for instruction serving both as a
guidepost and a unifying factor. Whereas previously there had been only general
agreement on content, teachers were often the sole determiner of the nature and
design of classroom instruction. Teachers often taught a subject based on their
personal level of expertise and interest. The results were mixed and unpredictable.

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Adoption of content standards regularized instruction and formed a basis for
objectively guiding teacher evaluation and student assessment.
The district mandated adoption of state content standards was the only formal
reform imposed from outside of the school. Although math coaches and consultants
were offered, HSHS administration and staff developed the math program from
within built on the implementation of the standards. The standards supported
reforms in teaching, instructional methods and strategies, school culture and
accountability.
Raising Levels of Accountability
Raising demands of the school in general and teachers and students in
particular significantly altered the approach to teaching and learning at HSHS.
While state content standards established the possibility of a pedagogical and
assessment framework, the movement to adopt and implement standards was viewed
as closely related to the federal No Child Left Behind legislation and the
accountability movement. Most teachers interviewed felt there was a direct
correlation between No Child Left Behind and standards based instruction – in fact
several thought content standards were required by the No Child Left Behind
legislation. The emphasis on student achievement and the notion of holding teachers
accountable for student success were important policy initiatives contributing to
improved student achievement.

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Holding administrators and faculty accountable for student performance
played a significant role in improving the quality of instruction. As described by one
teacher:
Many teachers, particularly veteran teachers, were accustomed to
blaming students, and their families for students’ failures in
school. Even though many of us would not come out and say
these things in public or to school administrators, quietly we felt
most of the problems with our school were not the teachers’
responsibility. Television, lack of parental involvement, laziness,
society, student culture, and ethnic cultural differences were all
held responsible for student failure. Grading on a curve
encouraged and made acceptable a certain amount of student
failure and we generally believed students were responsible for
failing grades. Particularly with the objective nature of math
tests it was hard to do anything else but fail students who could
not pass their tests or did not turn in homework. With standards
based instruction and No Child Left Behind we were told at
professional development sessions we needed to have all of our
students succeed. At first, for many of us – particularly the
veteran teachers – this seemed ridiculous but, over time, it did
change our way of looking at our students and thinking about
how and what we were teaching.

This shift in responsibility is an important component of accountability and is closely
linked to the standards based movement. HSHS teachers felt a distinct need to
improve student performance and took responsibility for their performance. The
relationship between content standards, instructional reforms and accountability
formed the basis of the reforms resulting in improved student achievement.
Implementing Standards
Encouraging and effecting the implementation of standards in the classroom
was the product of the efforts of a team put together by the math department chair.

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Large type standards were printed and presented to each of the teachers for
prominent display in the classroom. Drafting standards in language accessible to
students was the subject of professional development meetings held as a series of
buyback days before the start of the school year. Teachers discussed the standards in
student language and were instructed to post the standard for each lesson on the
board throughout the lesson. Locating the standards in the classroom was considered
a significant component of classroom observations and included in teacher
evaluations. Students were assigned the task of writing standards in student friendly
language as part of their class and homework. Student led discussion about the
standards further helped to imbed the standard in the learning process. Every lesson
required linking the standard to the skill being taught and was considered essential to
the learning process.
Aligning Curriculum to the Standards
In addition to providing uniformity and structure, the school wide adoption of
content standards influenced the delivery of instruction. With an ongoing policy of
repeated assessment and the sharing of student work, teachers recognized – and were
encouraged – to share successful strategies, methods and techniques to improve
student achievement. In addition to raising levels of accountability, teachers strove
to maintain high personal standards of effective instruction and to learn from one
another. Recognizing data was readily available comparing a variety of factors
important to classroom instruction, grade level teachers were aware of their relative
effectiveness. It was clearly in their best interest to learn from one another and to

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share their strategies for implementing and teaching to the standards. Successful
strategies were circulated throughout the department and implemented with the
assistance of the math department chair and lead teachers.
The math department chair developed a program to train teachers in the
content standards and to familiarize teachers with their connection to the curriculum.
The math faculty developed sample lessons and assessments collaboratively for each
of the significant content areas. These sessions also served to promote discussion
among faculty about the standards and new teaching methods and approaches they
might implement for specific lessons and content areas. The collaboration also built
cohesion in the department and encouraged a collegial approach quite removed form
the past practice of isolated teaching and instruction. The opportunities to meet as a
department also helped develop personal and professional connections between
teachers dedicated to improving teaching and learning.
Purchasing Algebra I textbooks aligned to the state content standards was an
expensive but effective tool to align content standards to instruction. The newly
adopted texts included all of the applicable math standards and keyed lessons around
each of the standards. Supplemental consumables also assisted in teaching and
assessment. These supplemental materials provided students with an opportunity to
easily transport home vital information and to make continuing assessment practical
and useful. The supplemental material provided English language learners and
students with a learning disability differentiated materials designed to meet their
level of need and understanding. Each of these materials was part of an integrated

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teaching and learning system saving teachers valuable instructional time by
developing suggested lessons plans, examples, approaches, strategies and
assessments. The texts also served as a further unifying factor providing for
common assessments and subject-alike performance evaluations.
Research Based Teaching Practices
Developing research based teaching practices was an important factor in
improved student performance. Research studies established strategies and
approaches likely to improve math instruction. HSHS administration recognized
they did not need to set aside valuable instructional time to experiment with a variety
of untested approaches given the broad body of research available. A significant role
of school leaders was to bring appropriate research practices to the faculty and
effectively implement instructional strategies targeting the specific needs of HSHS
math students. Most of the information they acquired was through school based
professional development opportunities and publications provided to them through
the department chair. Several teachers reported wanting to engage in practices where
results have been proven and are likely to lead to student success. They often
mentioned the importance of results based practices grounded in the research
literature. All of the teachers interviewed were aware of several leading researchers
in the field of education and often referred to studies in their responses. One teacher
noted, “There is no longer a need to guess at effective teaching practices or methods
… the research it out there and we just need to have the resources and time to apply
them in our classrooms.”

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The principal noted: “We are made aware through our meetings with the
superintendent, ACSA (Association of California School Administrators), various
publications, math professional meetings and publications, and in numerous other
ways about ongoing research in the area of school reform.” The math department
chair and lead teacher were able to recite the names and works of numerous
educational researchers and could talk fluently about their work. They could readily
cite statistics pertaining to math performance at HSHS and at other high schools in
the district and immediate vicinity. The principal mentioned how he received copies
of current books and articles on leadership, school reform and teaching practices
from colleagues, professional organizations and seminars he attend, and was readily
aware of the importance of research-based methods. The principal noted one of the
key policy initiatives was to more closely adhere to research-based organizational
and teaching practices. He cited the work of Dr. Loren Resnick, in particular what
he referred to as the nine principles of learning, and Robert Marzano. The math
department chair also felt it important to engage in comprehensive professional
development strategies grounded in research and based on student outcomes.
Among the more successful teaching strategies was early identification of
students likely to struggle in Algebra I and designing strategies to address their
needs. The faculty developed a continuing assessment strategy where students were
held accountable for learning by explaining the content of each exercise. Until
students demonstrated proficiency a variety of responses were designed to meet the
needs of the student before they fell too far behind. Struggling students were paired

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with more successful students. Class and homework became a shared activity where
group members helped support one another. Team teaching was implemented for
difficult lessons and to provide different approaches and teaching styles for
struggling students. Student work was shared at weekly faculty meetings and served
to help develop a range of teaching strategies. Student progress was closely
monitored and every effort was made to not let identified students fall behind.
Struggling students were provided after school counseling by individuals familiar
with the student’s work samples. Saturday classes were also initiated and taught by
teachers working in conjunction with the math faculty.
The strategy for identifying and working with students having difficulty in
Algebra was a multi-tiered approach. Early identification, continuous assessment,
repetition, re-teaching, ability pairing, changing teaching styles, after school and
Saturday school assistance were all key components. The opportunity to meet as a
department to debrief and share experiences was also a key factor towards
developing effective teaching strategies. The opportunity to exchange thoughts and
ideas was a critical component in developing highly effective teaching strategies. In
addition, these meetings boosted staff morale and maintained teacher motivation.
Recruiting Highly Qualified Teachers
Recognizing the significant impact of highly qualified teachers on student
learning, HSHS modified recruitment procedures to attract teachers familiar with
current research based practices or those showing a sufficient capacity to work
within the current culture and climate of high expectations. The school

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administration broke away from the long established procedure of relying on the
district for teacher recruitment. A more aggressive policy was implemented
involving school staff recruiting candidates from their universities and colleges,
attendance at well-attended job fairs, designing brochures touting the benefits of the
district and region, creating an attractive and user friendly web site designed to
promote the school and individual departments and identifying highly qualified
teachers from surrounding school districts and offering incentives within the capacity
of the school to draw those teachers to HSHS. This aggressive policy was developed
by the site principal and refined in several meetings with school leaders and local
employment agencies.
A key factor was identifying the core source of prior recruitment problems:
attracting younger teachers to an area known largely as a retirement community and
then retaining them beyond their first year of teaching at HSHS. The recruitment
team sought to overcome this general perception and to tout the advantages the area
offered to younger individuals looking to eventually purchase homes and establish
families. The recruitment team took advantage of local realtors and adapted their
promotional incentives to draw interested parties to the desert area. The relatively
low cost of housing, financial incentives for first home purchases, mentoring
programs and social opportunities were heavily pitched at interviews. Additionally,
younger teachers developed a program where they “adopted” new teachers and
helped them integrate into the culture of the community and explore social activities
helping them connect to the community. Encouraging friendships and helping to

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overcome homesickness played a key role in recruiting potentially highly qualified
younger teachers and increasing rates of retention.
Establishing a Positive School Culture
The adoption and implementation of math content standards had a significant
effect on creating a school culture largely held responsible for improving student
achievement. This standards based school culture involved changing the role played
by teachers moving from individual and isolated instruction to one of shared
responsibility and participation in a collective effort to improve student achievement.
The HSHS principal described this change of culture as “opening the classroom door
and letting the sun shine in.” He particularly appreciated having knowledge of, and a
say in, instruction (content and strategies). He had often felt “closed out” of the
classroom and never sure about the quality or content of teaching. “Frankly, I really
had little idea of what was going on in many classrooms and could only suspect there
was very little teaching taking place based on student grades and things you hear
through the grapevine.” He reported he was concerned with the quality of teaching
in several instances but felt powerless to effect personnel changes except in
extraordinary circumstances.
Teaching to the content standards regulated classroom instruction and gave
school administrators an opportunity to direct the content and nature of instruction
and provide them with an objective measure by which they could evaluate teachers.
The principal in particular felt he now had an opportunity to review teacher
performance against an established standard and had some ability to determine

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teacher effectiveness. Similarly, teachers had a clearer understanding of what was
expected of them. The culture shift was reported as palpable and important to
addressing the needs of the students. Most importantly, as with curriculum, teaching
was held against objective standards and open to scrutiny. This served as a
motivational factor for many and opportunity for improvement where needed.
Benchmark Assessments
The implementation of benchmark assessments on a regular basis proved to
be an extremely important policy initiative widely credited with improving student
performance. Implemented in the 2002 – 2003 school year and further refined in
subsequent offerings, the common assessments were developed by math department
teachers in collaboration with the department chair. The assessments tracked a
pacing plan developed by teachers. The goal was to test emerging skills at critical
junctures. This scheme provided an opportunity to re-teach and reinforce before
getting out too far ahead of the students.
A math teacher interviewed explained the importance of common
assessments:
Once a pacing plan was developed so that all math teachers
would be at approximately the same place at the same time, the
common assessments let us know as a group how all of us were
doing. Realizing that most of us had the same results helped
resolve our concerns about being compared unfavorably to one
another. I am sure it motivated a few teachers who we felt
needed to work a little harder. It also let us know where our
students were and go back and work with them before we got too
far past them or they lost total interest in the subject. Also, it
stimulated interesting and creative teaching methods to help
struggling students. It also formed the basis for Saturday school

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and after-school tutoring. The more we tested, especially
because we were all of us using the same tests, the more helpful
the results and the more it influenced our teaching in a positive
way.

Math teachers repeatedly referred to common assessments as among the most
important of all of the new policy initiatives leading to improved student
performance for a variety of reasons including instant feedback, a means of
determining the effectiveness of their teaching, a way to compare their results to
those of other math faculty, providing the opportunity to recognize areas of difficulty
before students fell too far behind or lost interest in the subject matter and helping
teachers develop more innovative strategies to meet the needs of struggling students.
Illustrating the importance of constant assessment, one teacher
noted. When I first came started at HSHS, we would talk about
what we are teaching and would ask the same thing of other
teachers. Now we ask each other, “Did the students understand
this lesson?” So now we focus on student learning instead of
focusing on the teacher.

Another teacher observed, “…assessments are given nearly every day on different
standards students are expected to known on state exams.”
The common benchmark assessments connected the content standards to
student performance and were a central unifying factor linking teachers together to
provide uniform instruction. They provided essential feedback guiding instruction
and teaching methods and strategies. They gave teachers information regarding
student progress and provided important information regarding areas of need. This
information formed the basis for the development of teaching approaches designed to

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specifically target problematic content and to assist all students develop their
Algebra skills. The benchmarks also provided the math department chair
information regarding the performance of teachers. The results suggested areas of
strength and where there was need for improvement. Teachers also viewed the
results as both informational and a source to motivate their performance. Given they
recognized their performance was tied to student outcomes they were most interested
in finding ways to improve teaching quality.
Rewarding Student Success
With the approval of the Board of Education, the principal instituted a policy
of rewarding student success on the CST in Algebra I. The policy initiative provided
any student scoring basic or above would receive at least the grade of C in Algebra I
regardless of prior grades in the class. For many failing or barely passing students,
success on the CST meant receiving a passing grade or better in a class (Algebra I)
necessary for graduation. Although detailed records were not kept, the math
department chair reported several dozen failing students received a passing grade in
Algebra I because of their success on the CST.
Responding to the Demands of Standardized Testing
Standardized testing had a significant effect on improving student math
achievement by improving the quality of teaching and instruction, influencing school
culture in a positive direction emphasizing student performance and raising the level
of accountability for administrators, teachers and students. The principal recognized
the importance of standardized tests in terms of the school’s standing with the

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California Department of Education and the United States Department of Education,
the impact on school morale, the widespread media coverage and the fear of negative
publicity and finally, the possibility it may affect his own job security and reflect on
his job performance. All of these factors, in his view, positively affected student
achievement in math.
Standardized testing brought into focus the notion quality of instruction was
open to public scrutiny, well publicized and capable of improvement. The HSHS
administration recognized they were charged with improving student performance
not simply managing the affairs of the school. The connection between testing and
student improvement is subtle and difficult to define. None of the HSHS staff felt
teaching to the tests necessarily meant students were gaining greater knowledge or
facility in math. The emphasis on standardized testing however changed the
perspective and attitude of administration and faculty towards finding ways to
improve student performance and not simply report student efforts independent of
the quality of instruction. The standardized tests served as much as a benchmark of
teaching quality as student performance. Accordingly, the overall effect of
standardized testing engaged faculty in the process improving student performance.
Summary
Improved student achievement was attributed to a number of interconnected
factors starting with the implementation of standards based instruction,
improvements in teacher performance, higher levels of accountability for staff and
student, benchmark assessments and significant and important changes in school

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culture. Built largely from within, the reforms mentioned established clear
expectations and measures to gauge improvement and areas of needed development.
Uniform standards lent themselves to developing consistent teaching and greater
levels of accountability. Of marked importance was implementing change and
establishing a climate of success in the face of a long history of poor performance,
particularly in the area of math. The change process and strategies to improve
student performance is the subject of research question three.
Research Question 3: Change Processes/Strategies To Improve Student Performance
The third research questions was, “What change process did the school use
to enhance its math program and strategies to assist students in math?” Research
question 3 addresses the changes necessary to successfully implement the various
policy initiatives discussed in response to research question 2. Data collection for
this question was organized in reference to a conceptual framework reflecting the
work of Bolman and Deal’s Four Frames. Bolman and Deal contend an organization
can be viewed through four distinctive frames: structural, human resources, political,
and symbolic; each frame serves as an approach to understanding those changes key
leaders felt necessary to implement the policy initiatives described in response to
research question 2 and their effect on the institution.
Interviews with individuals identified by the researcher as key leaders – the
principal, math department chair and a lead teacher – provided the primary data
describing structural changes, personnel changes, political issues and symbolic
methods employed to implement policy initiatives. Attention was directed to

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Bolman and Deal’s Four Frames. A copy of the framework was provided for their
reference and clarification, and each interviewee was informed about them and told
they would be referred to prior to commencing the interview.
Research Data
The data revealed numerous structural, personnel, political and symbolic
methods and changes were necessary to implement key policy initiatives and to
change the school culture. Indeed, the school principal felt his greatest contribution
– and the area of greatest resistance – to improved student success was his role in
convincing personnel to make the changes necessary for a standards-based high
school with greater levels of accountability. Although there was general agreement
change was necessary, implementation threatened establish patterns of practice and
power throughout the school. The following discussion addresses the change
process organized by the Bolman and Deal’s four frames starting with structural
changes followed by a discussion of human resource, political and symbolic changes
necessary to implement agreed upon policy and reform initiatives.
Structural Changes
Establishing a standards-based high school with greater levels of autonomy
and reforms in instruction required changes in school structure. The school principal
stated he felt it most important to provide each department greater autonomy to
establish policy initiatives department members felt would have the greatest chance
to influence student performance. Accordingly, the principal established regular
meetings with department chairs to discuss any and all matters they felt important to

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effectuate and implement change. He saw himself as a facilitator and as a tool to
develop and obtain resources department chairs felt they needed. He did establish a
set of priorities he felt important: standards based instruction, common assessments,
pacing plans, job-alike professional development, benchmark assessments, data
driven curriculum and assessments, faculty buy-in and participation, and continuous
review and reassessment of department progress based primarily on student
outcomes. The principal stated he felt his job was to set the tone and the agenda but
it was his department chairs working with lead teachers and influential members of
the faculty to implement changes.
The department chair recognized the district was organized in a top down
manner and the principal was following directives from the superintendent and the
assistant superintendent responsible for educational services. The principal, to a
great degree, agreed the district operated in a top down manner, and that he was
largely a conduit of information from the district to the school site while charged by
the Assistant Superintendent of Educational Services to initiate policy developed at
the district level. The principal felt he had a certain amount of autonomy and
latitude but was still quite aware of, and concerned about, district oversight.
Regularly scheduled ninety minutes per week job-alike meetings held
throughout the school year served as an important contributing factor to improved
student success. During these meetings, teachers reportedly talk about what is and is
not working in their classrooms and what to do next to improve student performance.

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The math chair noted the alignment of teaching curriculum and common pacing
plans make these conversations much easier and more effective.
The principal stated he did not feel the new policy initiative required any
serious structural changes other than those already mentioned. He felt the greatest
emphasis involved a change in the school culture supporting the implementation of
policy initiatives and developing a highly qualified faculty. Regarding structure, he
was most concerned about maintaining his former role as administrative and
instructional leader.
Teachers surveyed largely reported their participation developing common
assessments and rubrics was a significant change in the organization of the school.
Teachers surveyed also reported they helped to develop strategies used to improve
instructional practice. The math department chair helped to explain these responses
by noting the recent involvement of teachers in development of the pacing plans,
common assessment instruments and rubrics for these assessments. Department
chairs actively sought the participation of teachers and teachers were recognized for
their development of instructional strategies. The math department chair noted this
was an important factor because it drew a direct connection between teacher
participation and student success.
Human Resources
Following the adoption of standards-based instruction, the district offered the
services of a math coach and math consultants. Drawn largely from individuals with
close connections to the superintendent’s office, this offer was viewed with suspicion

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by administrators and faculty. Not well received by the math department and lacking
specific knowledge of the school in its key leaders, HSHS administrators rejected
this proposal by offering the services of the math department chair and a key teacher.
Ultimately, this decision served to boost school morale and demonstrate the site
principal’s loyalty to existing staff. The principal garnered respect from established
veteran teachers by responding positively to their fears of reassignment and found
greater credibility when attempting to implement the standards-based reforms
described in response to research question 2.
The principal’s concern regarding staffing as noted in the response to
research question 2 involved increasing the number of highly qualified teachers. The
principal was concerned with filling faculty openings with teachers who would and
could commit to the desert area and demonstrate sufficient flexibility to adapt to the
changes necessary to implement the reforms designed to improve student
achievement. “Any talk about looking for less experienced teachers because of
lower salaries is no longer even a consideration,” reported the principal. The
department chair stated, “More than at any time I can remember, we are looking to
hire the most qualified teachers available, which means a combination of experience
and training.” The principal recalled a music teacher taught two periods of Algebra
and a physical education teacher taught a section of geometry when qualified staff
were not available. “For a long time, we filled positions with the teachers we had,”
stated the principal. He continued, our need to improve student achievement and the
federal “No Child Left Behind” legislation changed all that and brought out to the

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school and public the hiring and staffing problems we had, especially with math
teachers.”
Based on information provided by the principal and the math department
chair, they did not report significant human resources changes however, both
mentioned the district’s extensive recruiting policies and resources and the efforts of
site staff as well. The principal also described the seemingly endless travel of the
human resources hiring staff, the number of job fairs, the aggressive advertising and
the substantial increase in salaries and other benefits offered to applicants. The
math department reportedly has historically had difficulty finding qualified teachers
and the present demands for highly qualified individuals places even greater pressure
on the human resources hiring staff.
All of the Math teachers interviewed as of the date of this study are deemed
“highly qualified” although several recently completed credential programs
(including coursework) and qualifying examinations required by current legislation
and district demands. Many discussed their concerns about remaining appropriately
credentialed and the increasing demands placed on them to continue their education.
One teacher discussed the issue content knowledge: “Whereas once we received our
credential we could feel secure in our position, today we often discuss among
ourselves the need to stay current and to increase our knowledge of math and
pedagogy.” Another math teacher mentioned how, when he graduated from college,
a bachelor degree in math was more than sufficient whereas today many younger

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teachers entering the profession have a master degree, or beyond, and are also more
familiar with a wide variety of teaching methods and styles.
Several teachers mentioned they operated under a great deal of stress brought
about by the demand for greater student success. One teacher noted, “I guess you
could say I did feel superior to many of my students because I had always done well
in math and always thought it was a somewhat innate ability. Now I felt the burden
was on me to teach them math not just rely on their native abilities, or inabilities.”
The same teacher went on to say. “I liked being considered a tough teacher and a
hard grader. Now I must pay more attention to their learning and make sure they
understand the material.”
Based on teacher surveys, the HSHS has not made any significant personnel
changes regarding experts or math coaches. The staff has remained stable from the
period 2001 – 2006. The emphasis on personnel has been to complete credential
requirements and maintain a highly qualified staff.
Political Issues
When asked about political issues, the principal stated the superintendents
largely determined policy initiatives. He felt it was his task to help facilitate and
implement district directives. The principal stated he was not consulted on many
curriculum driven issues but rather counseled. He said he understood his role was to
create the atmosphere necessary to successfully effect change. He said he felt that he
was a conduit through which district leaders would learn about the school and get
feedback regarding district-based decisions.

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The math department chair reported there was what he called a “healthy”
political climate at the school site. He described the principal as “hands off” but
supportive regarding the math department. The principal would defer to the math
department because of their expertise. The principal confirmed that he felt the math
department personnel were better equipped to deal with issues directly related to
their students. Although the principal insisted on being kept informed, he left
specific curriculum design issues to department leaders.
The specific issues the principal felt might be considered political were more
about outlook rather than power. He felt it necessary to change the school culture
and climate from what he described as teacher-centered to student-centered. He felt
the symbolic changes mentioned below were important to effecting and
implementing these changes while maintaining faculty support.
Symbolic Methods
As noted in the answer to research question 2, changing school culture was
considered essential to both administration and staff. The principal stated it was
absolutely necessary to change school culture as prerequisite to changing student
performance. He argued all of the proposals to improve student performance
required administrators and faculty to turn HSHS into a student centered institution
driven by results. He also talked about the existing climate that held low
expectations, particularly for students of color, and a lack of drive to turn things
around:

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Most of the faculty in the late 90s felt we could not change
student performance. They had low expectations based on
what the perceived student limitations. They were not doing
well largely because they came from poor families, had
limited language skills and little ambition or desire to succeed,
defined school culture. My job was to turn that around.

The starting point, according to the principal, was to establish HSHS as a
standards-based high school:
This became out motto as well as our goal. We are going to
become a standards based high school. This defined our goal
while establishing a new framework from which to judge the
school. We created banners and hung them in the hallways
and all of the classes. Each teacher was asked to display the
standards they were teaching in their classroom and refer to
them throughout the lesson. Classroom observation centered
on the display and reference of standards.

The principal also observed he had to get teachers to “buy into” the changes.
I used the phrase standards based high school, at every
opportunity. When we met for faculty meetings or at professional
development sessions I continuously referenced that HSHS is now
a standards based high school. I felt like I could not say it often
enough. Keep the message simple but repeat it over and over
again.

From these changes, the principal reasoned, would come a change in school culture.
He proposed having teachers participate in re-writing the standards in “kid
language.” He scheduled teachers to meet in job-alike professional development
sessions where they could work out the ways in which they would present the
standards and also propose lesson plans to teach the standards. The teachers also

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developed the benchmark assessments used on a regular basis to check for
understanding:
If the teachers developed the assessments they would have
greater faith in their relevancy and usefulness. I needed
them to be the actors in the culture change … it had to
come from them for effectiveness and sustainability. We
developed job-alike professional development,
collaborative development of standards in student
language, a shared approach to displaying and teaching the
standards and common assessments driven by the teachers
and their input. We kept sending out the message that
things have changed and we all needed to become part of
the solution. I had to help teachers move away from
complacency to action. They needed to take responsibility
for their students’ education.

The principal stated most of these changes could be viewed as symbolic, but they
made a difference by changing the attitudes of teachers and the culture of the school.
The math chair also noted the importance of the symbolic changes following
the decision to adopt state content standards. “We not only wanted to change the
culture as it affected teachers, we also wanted to change students’ ideas about the
school,” he related. The need to change the culture was also a theme supported in
the interviews of several teachers.
Recognition of teacher accomplishments was also a significant symbolic
practice also initiated by the principal:
I discussed this at length with the superintendent. I wanted to
find ways to motivate teachers through symbolic efforts like
awards for specific accomplishments. We gave out gift cards
to local coffee shops, restaurants, bookstores and
teacher/office supply stores. We would award anything we
could that would help teacher morale and build in some

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healthy competition. Highest attendance, scores on
benchmark assessments, improvement at any
level…whatever we could think of. And it worked. The
teachers loved award dinners, gift cards, any form of
recognition of the accomplishments. All so this helped to
build a climate of teaching and learning and got us away
from accepting the status quo.

The teachers supported the principal’s view about awards, recognition and changing
school culture. One teacher noted, “For the first time in a long time, I felt that I was
an important part of the school, and we could make a difference in our students’
lives.” The teacher continued, “It is all about the climate and culture of the school.
We want our students to view this as a place of learning, not just a social
experience.” This teacher stated symbolic changes were essential components in
transforming the climate and culture of the school to one of a high quality, learning
institution.
The math department chair discussed the importance of having teachers
consider themselves experts and professionals. Much has change, he observed, from
the view of teachers as less capable than working professionals. “The view, teachers
are some how less qualified than those employed in the private sector is eroding with
the emphasis on highly qualified teachers and research based practices,” according
the math department chair. He suggested the entire teaching profession has “been
elevated” by increasing expectations for students and educators. “Although these
things are symbolic, perhaps, and a matter of personal interpretation, they do make a

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difference,” he said. “It is all about how we perceive ourselves and value job we are
doing,” he concluded.
Summary
The change process posed a significant challenge to HSHS administration.
The successful transformation of the school’s culture to that of an effective,
standards-based learning community played an important role in improved student
achievement requiring primarily motivational and symbolic change. School
leadership considered the change process the most difficult obstacle – and most
important factor – necessary to improving student achievement. Working with
existing staff and research-based practices, the change process was largely directed
by the principal and effected with great determination and understanding of pre-
existing conditions and the natural fears and concerns of a veteran faculty.
Supported by key leaders, the principal brought teachers and students together with
enthusiasm and great energy. Staying on message, focusing on preferred outcomes
and celebrating each successful accomplishment paved their path to success.
Research Question 4: Instructional Leadership
Research question 4 asked, “How was instructional leadership important in
improving a) the math program/strategies and b) math achievement among
students?” Research question 4 addresses the role of instructional leaders and the
perceived importance of instructional leadership. Data collection for this question
was organized in reference to the instructional leader conceptual framework and

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explores the manner in which leaders influence factors related to improved student
performance in math.
The Instructional Leadership Framework is constructed around those factors
an effective leader must have knowledge of, and participate in, including a vision for
learning, supervision and monitoring of instruction, community and political
concerns, the culture of teaching and learning, and data driven decision making and
analysis. Data was collected in response to each of these factors and framed by each
of the above-mentioned categories.
School Leadership
The HSHS principal is the primary instructional leader based on interviews
with administrative staff and math department faculty and in response to a survey of
the general faculty. The math department chair, for example, described the school
principal as the force behind the transformation of school culture, improving
instruction, implementing standards based instruction and motivating teachers and
staff. The principal orchestrated all substantive changes, brought together key school
leaders, monitored instructional programs, played an active role in developing
curricula and was the motivational force behind changes in school culture. Key
leaders largely viewed the documented improvement in math achievement as the
outgrowth of the efforts of the principal when first challenged by the superintendent
in the face of a long history of poor performance. Accordingly, data collection
focused on the actions of the principal as the key instructional leader and was
organized by the five central factors of the instructional leadership framework.

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Vision for Learning
The principal’s vision permeated the HSHS campus and was often referred to
as the most important motivational aspect responsible for improved student
achievement. The principal repeatedly promoted the notion HSHS was going to
become a successful educational learning community built on a standards-based
instructional curriculum. He often spoke of HSHS as committed to creating life-long
learners and as a standards-based high school. His vision of a learning community
and a standards-based high school addressed the historically widely held view of the
school as little more than a social gathering place prior to moving on and out in the
work world. Low graduation rates, for example, once taken for granted, were now
no longer acceptable. The principal at every opportunity challenged formerly
accepted views. Regarded for many years as a low performing school, the
principal’s vision argued against entrenched attitudes largely accepting mediocrity as
the norm. The principal spoke of his vision at every opportunity and worked hard to
bring key leaders on board. The concepts of excellence, personal responsibility and
opportunity were repeatedly mentioned at every opportunity.
The principal used symbolic acts to promote his vision. Banners were
erected in highly visible locations promoting and honoring success. T-shirts with
positive and motivating phrases were distributed freely to students. The number of
days before critical academic testing events were posted on the central bell tower and
every school member participated in the count down. The principal delivered
motivational speeches in each classroom on a routine basis as well as at larger

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gatherings including before well-attended athletic events. Faculty meetings were
often described as being similar to big game pep rallies. At every opportunity, the
principal strove to bring staff on board and to keep them on message. The principal
successfully motivated staff and communicated his message to all members of the
school community.
Supervision and Monitoring of Instruction
Whereas, the principal was clearly the key visionary leader he did not see
himself as an instructional leader but rather as an administrator, facilitator and
manager. The principal was largely responsible for the professional growth of math
teachers by providing strong support and encouragement to collaboration between
teachers, comprehensive professional development, and bringing resources to the
math department. He discussed his support for a comprehensive professional
development plan that would start with introducing standards based instruction.
Professional development would include teacher collaboration on the issues of
developing a plan for presenting standards to students, develop pacing plans and
lesson plans based on the standards, prepare assessments and other benchmarks to
assess students understanding of the standards. His efforts included providing
research based information and speakers, textbooks based on the standards,
curriculum reform built on the standards and lessons clearly incorporating standards
based instruction and engaging students in accountable talk concerning the standards.
The math department chair echoed the views of most of the HSHS
administration and staff that felt the principal was indeed a strong instructional

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leader to the extent he exercised a powerful leadership role by formulating a clear
vision, supporting the professional development efforts of the math department, and
his constant support of the movement to develop a standards-based curriculum. “All
of us felt that developing standards, constant relevant benchmark assessments,
research based curriculum reform and a change in school culture where student
outcomes and data drive instruction, were necessary to improve student achievement
and turn the school around,” related the math chair. He felt the principal provided
the support necessary to implement these changes through both words and deeds.
The math department chair specified important curriculum reforms attributed
to the efforts of the principal and his efforts to incorporate them into daily lesson
plans:
In order to help students we needed to improve their basic
computational skills and help them with abstract
reasoning. With the former, review and re-teaching were
crucial, even if not a part of grade level curriculum.
Students simply did not have fluency particularly with
multiplication and division. With abstract reasoning it is
more difficult. Sometimes the problems involved
language comprehension also a basic understanding of
the process of abstract reasoning. We needed to check
for understanding each step of the way and be sensitive to
the needs of individual students. We could not gloss over
new material and we needed to find a way to explain
concepts many students had difficulty grasping. It meant
our teachers needed to be committed to student
understanding and less concerned about what or how they
were teaching material. ‘Whatever it takes’ became a
sort of unstated motto of our department. Then at job-
alike meetings, we would share what we had discovered
and the results of our efforts. The principal understood
our concerns and provided us with a great deal of his
personal support and always assisted in facilitating our

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requests for materials, supplies and time. Where the
principal was most helpful was in giving us his support
for our ideas and demands. He made time available for
us, he was willing to help us with scheduling, he listened
to our ideas, and he helped us when we needed resources
(textbooks, software and data).

The principal developed weekly department meetings fostering teacher
collaboration in response to his discussions with department chairs and lead teachers.
Time was set aside each week where teachers could share information and ideas
while reflecting on and expressing their concerns to one another. The math
department chair credited the principal with following through on ideas presented to
him by the math department and committing himself and the school’s limited
resources to policies and programs, such as the weekly department meetings, which
he believe contributed to increased student performance.
Community and Political
The principal effectively communicated on a regular basis with community
activists, parent organizations and the business community. His primary concern
was the perceived lack of parent involvement particularly at the high school level.
Initially, when discussing the low performance of many students, he reported parents
felt their child’s education was the responsibility of the school and they were ill-
equipped to help when they refused to cooperate, complete assignments or needed
help with their homework. Develop of school/home partnership was a critical
response and a necessary factor for improving student achievement.

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Working with the math department chair, the principal developed a program
where each teacher routinely provided parents with general information regarding
student performance, curriculum, goals and objectives, and specific information
regarding their child’s performance. He also instituted a policy of weekly telephone
calls where students were excessively absent and/or not completing assignments.
Parent conferences were routinely held when a teacher felt a student was at risk of
failing.
Community activists were also consulted to develop better outreach programs
to families and to involve them in their student’s education. Articles were published
in the local newspapers and flyers in Spanish and English were widely distributed
throughout the community describing the school program and important news
regarding testing, textbooks and curriculum. Meetings were held in the evening and
on Saturdays to better accommodate parent needs and Spanish-speaking individuals
were always present to translate and interpret.
Culture of Teaching and Learning
Creating life-long learners, planning a vision for the school, its staff and
students, reaching out to the community and including the concerns of parents as an
important factor in developing a successful school environment was essential to
providing the groundwork necessary to develop a school culture dedicated to
teaching and learning. The principal emphasized, and passed on to key leaders, the
fundamental purpose of HSHS was to develop life-long learners and critical thinkers.
He expressed a concern that classes should be taught from the perspective of

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engaging students in the learning process and involves the development of critical
thinking skills rather than the mere recitation of wrote information. Connections to
life experiences, particularly for high school students, were a critical factor that must
be embedded in the curriculum. In this regard the principal promoted the concepts of
accountable talk where students critically engage with one another as they acquire
needed information and develop the ability to analyze as a function of the learning
process.
Data Driven Decision-Making and Analysis
Benchmark assessments drive instruction at HSHS and this program was
largely the results of the principal’s efforts working with the math department chair.
Tracking student progress in order to provide early intervention has been widely
cited as an important factor contributing to improved student achievement in math.
Teachers receive continuous feedback on teaching effectiveness and student
progress.
Uniformity of data collection extends to the application of common
assessments and pacing plans. The result of the collaborative efforts of the math
department under the tutelage and direction of the principal, the data collected
informs instruction while providing opportunities to gauge whether or not students
understand new material and are acquiring necessary skills. Linked, once again, to
the standards, the assessments and pacing plans provided a feedback loop ensuring
mastery of the standards. Progress is monitored by the principal and assists him to
develop appropriate and targeted professional development, evaluate teachers and

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staff and guide instructional programs. It also assists the principal in teaching
assignments and staffing.
Summary
The HSHS principal demonstrates strong and effective instructional
leadership. He provides a powerful and compelling vision for learning, supervises
and monitors instruction, works well with community leaders and parents, has
developed a culture of teaching and learning and grounds his decisions regarding
instructional programs, professional development, on data. The principal is well
respected by faculty and staff and engages on an ongoing basis with instruction and
student performance. He has instilled the concept of life long learning and
standards-based instruction in both teachers and students.
Research Question 5: Instructional Leaders Not Math Experts
Research question 5 asked, “How did instructional leaders respond in
academic areas in which they are not experts?” Research question 5 addresses the
role played by an instructional leader who does not have expertise math. Data
collection for this question was organized in reference to a conceptual framework
assessing the principal’s expertise in math. Based on this conceptual framework the
researcher deemed the principal as having low expertise in math.
Math Expertise
The principal does not have a math degree or credential and has not taught
math. Accordingly, the principal deferred to the math department chair and lead
teacher for specific information regarding math curriculum and pedagogy. Largely

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responsible for overall reform of the school, the principal spearheaded the
development of a standards-based high school and successful learning community.
Working with the math department chair, the principal organized and promoted
several programs integrating state content standards in all classrooms, aligned the
curriculum to the standards, changed school culture, motivated faculty and students,
and formulated an overall design for improved student achievement.
Despite limited expertise in math, the principal focused largely on
implementing standards and changing school culture. In order to promote content
standards he formulated policies requiring the posting of standards in each classroom
and working with students to re-write the standards in student language. He attended
professional developments and monitored the development of these programs and
reviewed the data assessing the effectiveness of the standards-based learning. He
was well aware of general pedagogical principles and argued for their
implementation. The principal explained the development of standards, their
applicability, lessons plans derived from and based on the content standards,
benchmark assessments to determine levels of student understanding, and a student
centered approach to teaching and learning, was not subject/content dependent.
Where and when he needed specific information he would look to research and/or
consult with district math experts.
Collaborative Leadership
The principal relied heavily on the input of the math department chair to
assist tin the implementation of his program. He attended all professional

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development meetings and challenged the math faculty to explain to him the manner
in which they intended to improve student achievement. By attending staff
discussions, the principal learned about the challenges faced by the faculty while
participating in building approaches to address their students’ needs. Working with
the faculty the principal not only lent support to the development of curriculum and
teaching practices, he demonstrated his commitment and understanding of their
investment in the system and dedication towards their students. He also served as a
facilitator bringing together disparate interests, styles and approaches to develop
collegiality among individuals of strong opinions and varying views.
Capacity Building
The principal recognized the math faculty needed more time to work together
to develop a collaborative response to their over arching charge: the need to improve
student performance and achievement in math. The principal took responsibility for
beginning the dialogue but recognized he would have to rely on the individual and
collective expertise of the math department. Additional opportunities to brainstorm
teaching strategies, methods and approaches were best served during the school day
and on a regular basis. Relying on research indicating comprehensive strategies
were more effective, the principal also served to fashion the debate by convincing
members of the math department the need to think long range and to develop ideas
that would be sustainable over time.
Providing additional time was a serious challenge given the mandate to
maintain specific instructional hours and teacher union concerns regarding the length

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of the school day and unpaid extra duty time. The principal strenuously argued for
district funding of additional overtime for the math department to meet regularly and
consistently. Once established, the principal helped to formulate the agenda as a
means of keeping the department focused and on track.
Data Driven Decision-Making
Regardless of his specific expertise, the principal established the notion all
decisions regarding the math program would be drawn from research-based
principles supported by data. Relying on formative assessments as a reliable
indicator of student achievement, he constantly argued the data collected should be
the primary factor driving instruction. Accordingly, he strongly supported the
introduction and continued use of benchmark assessments as an important policy
initiative. The principle strenuously pursued the idea students must be able to
demonstrate knowledge of the standards, regardless of content, and assessments must
clearly test students on the specific skills required by content standards.
Summary
The success of the math department and improved student achievement
supported the principal’s view that content knowledge was not necessary to reform
the curriculum and change school culture. The principal recognized implementing
content standards and developing accurate benchmark assessment would form the
foundation for improved student achievement. He also appreciated the importance
of relying on research-based practices as a basis for motivating a complacent faculty
and a school culture willing to accept mediocrity. Each of these reforms were

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eventually well received and widely considered largely responsible for turning
around years of lackluster student performance and a disaffected faculty in the
process of creating a standards-based high school and successful learning
community.
Analysis and Discussion
Five conceptual frameworks facilitated the analysis of data. General public
reporting data including the School Report Card and Department of Education
standardized testing results was used as the basis of the conceptual framework
organizing the response to research question 1 and documenting improved student
achievement in Algebra I over time. The school design framework served to
organize and aid in the collection of data providing information regarding those
policy initiatives and reforms contributing to improved student performance and the
effective math programs framework similarly served to assist in the data collection
directly related to program reforms. Bolman and Deal’s four frames formed the
basis for understanding the change process employed by HSHS school leadership
faced with implementing the policy initiatives and reforms described in response to
research question 2. The instructional leadership framework addresses the issue of
instructional leadership and provides a framework to assess and evaluate HSHS
leadership and its role in improving student performance in math responsive to
research question 4. Research question number 5 addresses the issue of school site
leadership not having a particular expertise in math or math instruction. A
conceptual framework was developed by the cohort to determine the leadership’s

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level of expertise. Examining improved student performance from the point of view
of each of these research questions provides a greater understanding of the manner
and method by which HSHS improved student achievement in math.
Research Question 1: Patterns of Math Achievement
Following many years of disappointing CST scores in Algebra I, starting in
2001 and continuing through 2005, HSHS students demonstrated a sustained
significant improvement moving a considerable number of students from basic and
below basic to proficient. The results are all the more remarkable considering the
minority student population – students generally struggling on standardized tests –
increased at the same time test scores increased. Given the general lackluster
performance of similarly situated large urban public high schools, HSHS certainly
beat the odds.
The principal and math department chair were well acquainted with school
culture, student performance patterns, curriculum, resources and other factors closely
related to student performance. The math department chair in particular having
already worked at the high school for more than ten years, and the principal for five,
played heavily in the development, planning and implementation of a variety of
reforms and policy initiatives described in this study. Given their background and
experience at the school site, they were thoroughly familiar with prior patterns of
student performance and school culture, quick to recognize the need to identify
struggling students early in the process and the importance of providing strong
leadership. Whereas, the high school had an embedded policy of attempting to

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remediate once a student demonstrated failure, the principal implemented a variety
of assessments designed to respond pro-actively before the student failed. His
repeated emphasis on early intervention was key to the success of reform movement
in the math department and provided an opportunity to work with students early in
the semester before they fell behind.
Early intervention raised additional problems involving teaching strategies
and methods. Having developed a strong, working relationship with faculty
members, this helped him address their concerns about formative assessment and
early intervention. His meetings with faculty focused on changing their perspective
to focus on the development of skills rather than relying on summative assessments.
This, of course, required teachers to move beyond presenting, explaining and
repeating information but also involved addressing the needs of students not grasping
key concepts. This posed a unique challenge to teachers who, at first, clearly did not
know how to respond to struggling students. The general view held by many
teachers reflected their belief the learning process was the work of the student and
not a responsibility of the teachers. The principal, through personal contacts and
group meetings, shifted the focus to a student centered learning environment. This
proved to be a key piece of the puzzle and perhaps the most important component in
his reform efforts. Reframing each discussion by starting from a student-oriented
perspective, the principal provided a positive learning environment better suited for
the needs of HSHS math students. Shifting their orientation and focusing on the
learning process was held largely responsible for improved student performance.

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Also highly effective was the reinforcement provided by professional
learning opportunities demonstrating and articulating the importance of
understanding the specific challenges faced by HSHS students. Rather than talking
(and often complaining) about student effort, the focus shifted to outcomes and
results. Coupled then with the notion assessment results are as much a reflection on
the quality of teaching and learning, the faculty moved in the direction of working
with students (targeting specific needs) rather than simply delivering instruction.
Research Question 2: Policy Initiatives, Curriculum and Related Conditions
Faced with a history of low performance, the initial reform efforts were
initiated by a former superintendent’s directive to adopt and implement state content
standards in all core academic classes. The district did not develop a program for the
implementation of content standards but left this task to each of the district’s three
high school principals. The HSHS principal was largely responsible for the effective
adoption and implementation of the state content standards in the math department
that proved to be the central policy initiative responsible for improved student
achievement. The principal developed a program whereby he would work with each
department to implement standards as the basis for all lesson plans supported by
continuous formative assessment.
The district demand to implement a standards based curriculum provided key
leaders an opportunity to address issues of low student performance and a culture of
low expectations. The principal maximized this opportunity by addressing
entrenched practices and attitudes, refocusing teachers on student outcomes,

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demanding accountability and imposing a regimen of formative assessments.
Having the ability to place responsibility on the district and the widely publicized
national accountability movement as evidenced, for example, by NCLB, the
principal deflected criticism and opposition from veteran teachers while developing
his reform program.
A highly effective component involved building collaborative relationships
with individuals he identified as key leaders (most important, the math department
chair). Working in close cooperation with these individuals, the principal
demonstrated his high level of personal investment in the reform of HSHS thereby
serving as an example of the commitment he felt necessary to improve student
performance. Similarly, the principal’s efforts to get buy-in from the math
department eased the transition and adoption of a standards-based curriculum and set
the stage for even more significant reforms.
A key component to the implementation of curriculum standards was
including the faculty on decisions affecting their classrooms and teaching strategies.
An important example was the posting of standards in each classroom written in
language accessible to students. Being a part of the collaborative process and fully
engaged in the implementation of this policy was considered empowering and was
an effective tool bringing the faculty in step with the administration’s efforts to
reform classroom teaching strategies and methods. The development of student-
friendly standards further assisted in producing a connection between faculty and
their students.

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Perhaps, more importantly, providing information from the perspective of the
student served as a driving force behind many of the reforms implemented at the
high school. Recognizing education is most successful when it is a student-centered
activity, many of the reforms started from the perspective of understanding the
educational experience from the student’s point of view. Particularly when working
with older students, their experience and interests often serve as the key to drawing
students into the educational process and having them engage with classroom
activities and assignments. This is particularly difficult with an abstract, conceptual
subject such as Algebra. Even this recognition serves as a better starting point than
working from the textbook out to the student. Constant feedback and support served
as the best response by keeping students and their instructor working through the
learning process together as a team.
Formative assessment proved to be the successful companion policy initiative
supporting the move to a standards-based high school. The principal recognized the
importance of gauging student success both as a teaching tool and a guide for
instruction. The formative assessments quickly provided teachers with necessary
feedback as to the effectiveness of their teaching style and whether or not they were
reaching their students. Early identification of struggling students was considered a
critical product of continuous formative assessments. Responding at the earliest
stages to students struggling to acquire necessary skills aided in instruction,
classroom design and organization, and the delivery of curriculum. Direct
instruction targeting the actual needs of students proved far more effective than

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general instruction designed for the hypothetical average student. Formative
assessment also gave rise to the need to differentiate instruction based on the
learning styles and capacity of students.
Providing faculty with increased opportunities for collaboration was often
cited as having a significant effect on teacher effectiveness. Working as a group
under the direction and guidance of the principal, the faculty was able to draw from
their individual and collective experiences. Most instructive was sharing student
work and developing common pacing plans. Student work provided teachers the
opportunity to learn and develop teaching methods responsive to students while
common pacing plans regularized instruction and provided the opportunity for an
objective discussion of curriculum, teaching strategies, methods and approaches.
The principal’s attendance at faculty meetings provided him with the opportunity to
learn first hand the needs of the department, develop trust and appreciate the needs of
the faculty.
Research Question 3: The Change Process
The principal used the district demands to implement curriculum standards as
the starting point for reforming HSHS. He effectively set the stage for the change by
building off of this starting point and then addressing key areas of concern:
curriculum, teaching strategies and methods, assessment and instruction. A
significant component was ability to change the manner in which teachers came to
understand their role in the educational process. Rather than simply presenting
“work” and then grading student efforts, the faculty came to recognize they needed

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to focus on learning rather than instruction. This change of perspective had an effect
on aspects instruction. The principal’s efforts to reframe the discussion by asking
teachers to put themselves in the place of struggling students and grasping how
difficult it was for many of them to understand abstract concepts turned many
teachers away from traditional instructional methods to designed to engage the
student and address areas of need. This starting point drove many faculty members
to develop far different approaches to individual lessons than they might otherwise
have considered and created a needed dialogue between them to find more effective
teaching strategies.
The core component of the change process was changing school culture on
several levels including the perception, participation and attitude of faculty, students
and their families. Described as generally moribund with little student interest or
participation, limited parent involvement and a complacent faculty, the principal
invested significant energy into reframing perceptions of the school and its role as a
learning community. Employing numerous approaches and relying heavily on
symbolism, the principal generated enthusiasm for student success. The principal
used a pep rally approach for drumming up support and conveying his enthusiasm.
Incentives were built in to the daily regime, recognition of success and making
success acceptable were key components of his approach. Distributing T-shirts with
inspirational slogans, organizing assemblies and dances around accomplishments,
focusing on the need to prepare for standardized testing, posting results in a
competitive spirit, engaging students in the learning process and maintaining high

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levels of visibility contributed to a highly charged atmosphere fueled by a sense of
accomplishment. Many features common to athletics become commonplace and
transformed to create the sense of academic competition where group success
benefited the individual. The competitive spirit turned students into achievers
whereas they might not have any interest in academic success. The process was
important because it engaged students and made them voluntary partners in the
process of their own education.
Research Question 4: The Role of Instructional Leadership
Strong instructional leadership was a critical factor leading to improved
performance on math assessments. The principal was the key ingredient motivating
change, designing the reform process, stimulating collaboration, finding and
empowering key leaders and monitoring progress. The principal established himself
as a strong instructional leader by creating a strong vision of the school as a
successful learning community and providing the leadership and capacity to achieve
his goals. Relying largely on building instruction on a standards-based model,
supported, directed and guided by formative assessment, the principal established a
goal, a process and the means to gauge teacher and student achievement. The
principal communicated his message to faculty and students by staying on message,
summarizing his views with clarity and simplicity, and restating his goals at every
opportunity. He voiced where he wanted the school to go and was able to use his
position to communicate in any number of forums.

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The principal also provided needed oversight to instructional programs by
facilitating and monitoring the implementation of research based practices and
methods. His personal involvement helped to insure the development of programs
responsive to the needs of students and helped maintain his vision of a standards-
based high school. The principal was able to respond when his assistance or ability
to bring additional resources was required. The weight of his office and personal
prestige often aided the implementation of programs and cut through bureaucratic
impediments. He was able to resolve differences and maintain continuity and avoid
factional disputes or personality conflicts.
The principal’s connection to the community developed over a considerable
period of time proved a great asset influencing student achievement and parent
cooperation and involvement in school affairs and the educational demands of the
school and the math program. The healthy school/parent partnership developed by
the principal assisted in monitoring student behavior and helping teachers with
students who might otherwise not complete assignments, attend school on a regular
basis or engage in disruptive behaviors. The united front of school and family
proved effective in keeping students on task and providing an opportunity to respond
to difficulties or challenges faced by the student and/or his family. Families were
also persuaded to share issues outside of the school setting that might directly
influence student performance. This information guided teachers who developed a
better understanding of student’s personal needs and family situation.

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The principal’s knowledge of community values and their attitude and
culturally driven beliefs about education and the role of the school allowed him to
bring together groups that otherwise shifted blame and/or responsibility for problem
students. His credibility was useful when addressing serious issues and bringing
together individuals from very different backgrounds. The partnership he developed
with parents was made apparent to students who behaved quite differently once they
realized the close connection between school and family, and parents and teachers.
The principal’s involvement with families greatly influenced classroom behavior and
student performance by providing a sense of individualization to the educational
process.
The principal expended greater energy in promoting his vision of the school
as a learning community and the need to change the school culture. His efforts
through various policy initiatives stemmed from his strong leadership role and his
recognition of the need to redirect and reframe the school in a positive manner. In
this area his experience and knowledge of the school and community was
extraordinary helpful. His efforts to change school culture were most often held
responsible for the overall improvement of test scores and other indices of student
achievement.
Research Question 5: Leader Who Does Not Have Expertise in Math
The principal does not have a math degree nor has he taught math. In his role
as an effective and highly visible instructional leader, the principal compensated by
promoting research based educational strategies, working closely with key leaders

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well-versed in math pedagogy, applied generally well-accepted educational methods
and approaches and used assessment results to drive instruction. By placing his trust
in the expertise of the math department chair, the principal provided the opportunity
for motivated and dedicated individuals to take the lead and bring expertise to the
fore.
The principal recognized the teacher-centered model of instruction was not
working. Although he may not have had specific solutions to the problems at hand,
he recognized the need to help struggling students early in the process was essential.
To some extent, his lack of expertise was an advantage. By asking math faculty to
demonstrate their suggestions and participating in their planning sessions, he saw the
instructional process as a student. This sense of viewing the learning process
through the eyes of the student permeated all of his reform concepts and was an
important part of his vision. Bringing the focus back to the student and away from
the faculty changed the tenor and tone of instruction. Reminding faculty that
traditional methods of instruction did not work for many math students at HSHS, he
challenged them to rethink their lessons, goals and methods.
The effectiveness of the principal as an instructional leader proved
instrumental when working in an area where he had little expertise. By bringing
basic pedagogical and research-based practices to the math department, he was able
to allow other to implement his vision tailored to the specific needs of the math
students. The principal participated in faculty meetings where he gained an
understanding of the issues facing the math faculty, engaged in discussions with

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faculty and staff regarding teaching challenges, familiarized himself with students
and their issues, and worked with parents and community leaders to change school
culture. His involvement and level of understanding of the needs of faculty and
students empowered the math department and boosted morale. Each of these actions
directly influenced the quality of teaching and learning leading to higher test scores.
Summary
This chapter serves as a review of the findings, analysis and interpretation of
data for this study. The five research questions were answered through the use of
data and an analysis of various documents, interviews and surveys. The discussion
included a description of the school profile, policy initiatives and strategies, the
change process, and the role of instructional leaders to improve student achievement
in math. Chapter 5 will include a summary, conclusions, and implications of the
study.

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CHAPTER 5

SUMMARY, CONCLUSIONS, AND IMPLICATIONS

Background of the Study

The educational performance and achievement of American public school
students has been an issue of considerable concern and debate since, at least, the late
1950s. Beginning with the launch of Sputnik in 1957, the presumed superiority of
American scientists, physicists and engineers was seriously challenged by the
startling and unexpected success of the Soviet space program. This singular event
was soon followed by an ongoing and intensive examination of our educational
institutions. Focusing particularly on mathematics as the cornerstone of success in
the sciences and related fields, studies comparing American students with those of
other industrial nations lead to the conclusion our public schools were not providing
many of our students with a quality education and the preparation they need to
compete in an increasingly competitive environment. Similarly, studies focusing on
basic benchmarks of success concluded large numbers of American students were
not mastering core skills in the areas of reading, writing and mathematics. Our
national sense of well-being was challenged by the bitter reality of underperforming
students, poorly prepared and often unqualified teachers, and eroding public
resources and institutions.
These national studies also revealed a growing achievement gap between
students of color, recently arrived immigrants and the poor, when compared to white
students, typically from families of greater wealth and social status. This

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unacceptable achievement gap marked a cultural divide among American students
determined largely by race, class, status, wealth, and education. All too often, a
chronic failure to achieve was located among those individuals most in need of the
opportunities offered by a quality education. Recurring cycles of poverty among
minority groups in particular featured a lack of education and a failure to acquire
necessary skills to compete in the labor market.
With the expansion of globalization and a marked decline in the number of
high paying manufacturing jobs available to low and unskilled workers, the
American workforce is now torn between low paying service sector jobs largely in
the fast food restaurant and retail sector, on the one hand, and well paid skills-
intensive positions in the business, computer, medical, engineering, sciences and
pharmaceutical fields, on the other. Success in the modern work place demands
greater skills and more education than in past eras when workers could rely on
readily available manufacturing jobs guaranteeing relatively high wages and job
security. Even lower paying, labor-intensive entry-level factory jobs, particularly in
the garment industry, are moving overseas.
The high school diploma today serves more as a minimum benchmark of a
successful education rather than the culmination of one’s educational career. The
high school diploma is often viewed as a prerequisite for a college or university
education – the first step toward acquiring those skills necessary for meaningful
employment. The increasing number of high school drop outs, especially from the
urban core and among minority youth, coupled with an immigrant workforce willing

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to accept sub par wages, breeds the possibility of rampant unemployment and
underemployment, and the consequences of a poorly paid, unskilled work force: a
lack of adequate health care, sub standard housing, gang infested neighborhoods and
a life lived in constant fear of crime and violence with little hope for improvement.
Increasing pressures on the health care system, urban decay, violent crime and unmet
demands for essential social services tears at the fabric of an unbalanced society.
The pressure placed on young people to succeed in school is coupled with the
realities of a demanding job market and poor prospects for economic security
without the skills needed to enter into the relative stability offered by middle class
social and economic status.
Of particular concern is the poor performance of American high school
students in math. The Nation’s Report Card: Mathematics 2005 reports the majority
of African-American, Latino and students of lower socioeconomic status, continue to
score far below their White peers and students from economically and culturally
advantaged families. Failure to achieve proficiency with computation (Loveless &
Coughlin, 2004) is of particular concern as it has a dramatic negative effect on
students’ later ability to acquire skills necessary for success in Algebra and
Geometry. Additionally, failure to acquire essential math skills is largely responsible
for high failing rates in core academic subjects and on exit examinations (Olson,
2006) contributing to high school drop out rates.

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Purpose of the Study
The purpose of this study was to examine the reforms, strategies and methods
employed by an urban public high school that overcame the challenges of poor
student achievement in math. Despite the declining performance of many American
urban public high schools, HSHS is one of a number of well-documented examples
of a successful school beating the odds. Typically, these schools have responded to
the various challenges mentioned above by fostering and implementing a whole host
of reforms driven by research based strategies and studies designed to meet student
needs while simultaneously increasing the performance of both teachers and
students. These reforms include strong instructional leadership, standards based
instruction, highly qualified teachers, student-centered strategies and methods,
greater accountability, high expectations, formative assessment, data driven
instruction, creative approaches to curriculum design and significant changes in
school culture.
Five research questions defined the areas of investigation and parameters for
this study. These 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 are related to improved math achievement at the school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?

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4. How was the instructional leadership important in improving a) the math
program/strategies and b) math achievement among students?
5. How did instructional leaders respond in academic areas in which they
were not experts?
Methodology
This case study used primarily qualitative methods to investigate HSHS, an
urban comprehensive high school, achievement in math on the CST scores over a
three-year period. Triangulation of data collected from interviews, district
documents, observations, collaborative exchanges with other members of the
research team, and quantitative reports published by the State of California and the
School Accountability Report Card, strengthened the validity of the findings. In
addition to publicly reported data, five conceptual frameworks formed the basis of
the interview and survey questions used to collect data designed to answer each of
the five research questions. The research-based conceptual frameworks and
instrumentation were developed during the summer of 2006 by a team of doctoral
students at the University of Southern California under the direction of Dr. David
Marsh, Associate Dean of Academic Programs.
Sample
One urban high school was purposively selected as the unit of analysis to
study as a means to develop a deeper understanding of the reforms employed to beat
the odds and improve student achievement in math. The school chosen, HSHS, is
representative of many struggling urban high schools with a majority ethnic minority

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student population from families of low socioeconomic status, a history of poor
performance and limited capacity and resources. HSHS over a three-year period
made substantial and significant gains in academic performance on the STAR test in
Algebra I following the implementation of an intentional effort to improve teaching
and learning.
Data for the study was collected from November 2006 through February
2007. A school profile instrument provided data regarding general background
information illustrating changes over time in student performance. Five conceptual
frameworks provided the foundation for the instrumentation used to provide
responses to research questions 2 - 5. The School Design Framework reflects four
research-based categories influencing effective school design. These categories
include student performance assessments, learning activities, school culture and
curriculum. These areas also address and organize data collection surrounding
targeted policy initiatives influencing the design of a highly effective school. The
School Design Framework provides a multidimensional approach to data gathering
providing information supporting improved school success in teaching and learning
and improved student achievement on formative and summative assessments. The
Effective Math Programs Framework incorporates three general areas of concern:
classroom practices, standards-based instruction, and curriculum design. It also
incorporates numerous subtopics drawn from the research literature. The subtopics
address instruction, assessment, and teaching approaches and methods, and provided
the researcher the opportunity to explore actual practices employed by the math

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department on an ongoing basis. The Bolman and Deal’s Four Frames Framework
guided and organized data collection responding to questions concerning the change
process necessary to implement needed reforms and policy initiatives. This
conceptual framework provided the researcher with four different perspectives from
which to understand the effect of change on HSHS and the manner in which key
leaders were able to implement those changes they felt necessary for improved
student achievement. The Instructional Leadership Framework addresses the issues
of instructional leadership and provides a framework to assess and evaluate HSHS
leadership and its role in improved student achievement in math. The framework
assists in the organization and collection of data related to the roles played by key
leaders, their actions including how they came to agreement on specific initiatives
and reforms, the manner for assigning and delegating duties and awarding
responsibility for the implementation of policy initiatives, and information regarding
their individual backgrounds and experience. Given the high level of importance
placed on instructional leadership in the literature, the researcher was particularly
interested in the manner in which key leaders assumed and defined their role in the
process and how they formulated and supported policies they felt would lead to
improved student achievement. The Assessment of Principal’s Expertise in Math
Framework rated the HSHS principal’s level of math expertise. This information
formed the basis for data collection concerning how a leader with limited experience
in math was able to effectively determine and implement substantial policy
initiatives related to improved student achievement in math. The manner in which

151
the principal was able to assert his authority and control in a content area in which he
has limited knowledge and background was important to the study as it illustrated
how a strong instructional leader compensates for limited content area information
and yet is able to define, determine and implement general research-based principles
that led to improved student achievement.
Four instruments provided the foundation for the collection and analysis of
data:
1. The Key Leader Interview Guide was developed by the cohort to ascertain
the contributions, opinions and concerns of those individuals identified as
playing important leadership roles.
2. The Teacher Interview Guide consists of 7 interview questions
administered to all HSHS math teachers. The questions elicited responses
concerning the background, experience, education and expertise of the math
faculty in addition to specific teaching practices and approaches they believe
contributed to improved student achievement in math.
3. The Math Teacher Questionnaire is a written survey consisting of 50
questions posed to the math faculty asking teachers to respond to each
question by choosing from one of five possible choices ranging from strongly
agreeing to strongly disagreeing. Teachers were asked a series of close ended
questions targeting information related items identified in the research as
having a significant impact on student performance.

152
4. The General Teacher Questionnaire is a written survey consisting of 30
questions asking teachers to rate their responses to each of the questions
based on a five-point rating system ranging from strongly agreeing to
strongly disagreeing. The instrument was designed to elicit teacher responses
and evaluations of the role of school leaders, school design, the reform
process and the change movement, curriculum and student achievement.
The instrumentation, conceptual frameworks, and focal areas of inquiry were
presented by research question in the next section preceding selected findings for
each research question.
Selected Findings
A summary of key findings based upon the five research questions emerged
through an analysis of the data collected in this study. Included in this section are
the primary sources of data collected, instrumentation, and the selected findings for
each research questions.
Research Question 1: Pattern of Math Achievement
The first research question asked, “What was the pattern of math
achievement for various students at the school?” Data was collected from the School
Accountability Report Card and published information regarding demographics,
school capacity and resources, and student achievement in Algebra I on the CST
over a three-year period. Data was organized, charted and compared to student
performance statewide and across the local school district.

153
HSHS is representative of many large urban high schools with a majority
population of ethnic minority students drawn from families of relatively low
socioeconomic status. The school had a long history of poor performance and
underachievement particularly in the core academic areas. Only 60% of entering
freshman graduated and few HSHS graduates went on to college or university.
Teacher retention was a continuing source of concern and the math faculty had
difficulty attracting highly qualified, fully credentialed teachers. Curriculum
typically followed the design of the math textbooks and teachers developed their
own strategies for instruction without much guidance from administrators or
department personnel.
Beginning in 2001, the district wide adoption and implementation of
standards-based instruction led to a series of reforms designed to improve teaching
and learning. These policy initiatives and reforms were widely deemed responsible
for a significant change in the climate and culture of the school reflected in improved
test scores in Algebra I from 2003 through 2005. The sustained growth in
achievement occurred during a time of increased minority enrollment and sustained
financial pressures. HSHS achievement in CST scores far outpaced California
statewide results and those of the other local district public comprehensive high
schools.
Research Question 2: Policy Initiatives, Curriculum Instructions, Related Conditions
The second research question asked, “What policy initiatives as well as
curriculum instruction and related conditions are related to improved math

154
achievement at HSHS?” In exploring this question, data was collected through
interviews and surveys on the influence of specific policy initiatives and reforms,
curriculum and other related conditions, approaches, methods and strategies. The
researcher examined various research-based practices including standards-based
instruction, student-centered teaching and instruction, the role of assessment and
improvements in teacher quality.
The implementation of standard-based instruction was mandated by the
district but implemented at the site level through the collaborative efforts of the
principal and math department chair. This key policy initiative dramatically affected
the school on many levels including the organization of instruction, the role of
faculty in developing pacing plans and instructional strategies, the uniformity of
instruction, the reliance on data driven decision making, formative assessments
shaping interventions and responses to struggling students, the early identification of
students in need, and a concerted effort to recruit and retain highly qualified math
instructors.
Each set of reforms generated complimentary ideas building on research-
based practices. As students progressed, their shared work product formed the basis
for additional modification and suggestions for improving instruction. Similarly, the
uniformity of pacing plans and instructional goals served to bring teachers and
administrators together in a shared objective of improving student learning.
Whereas, one might have at first thought teachers would feel they were losing their
independence, they appreciated the collective approach to school improvement

155
building upon each other’s strengths and supporting one another through the change
process.
Most effective was the regular employment of benchmark assessments to
drive instruction. The early identification of struggling students avoided the typical
pitfall of students falling too far behind to catch up. Particularly important in math
where lessons build on prior knowledge and information, immediate interventions
resulted in higher rates of success and far fewer failing students. Coupled with team
teaching, differentiated instruction and creative approaches to instruction including
grounding math concepts in realistic problem-solving situations, led to greater
student involvement in the learning process and a more flexible approach to
instruction.
Research Question 3: The Change Process
The third research question asked, “What change process did the school use
to enhance its math program and strategies to assist students in math? Collecting
data and viewing responses to this question from a variety of perspectives allowed
for a multivalent approach to the dynamics of change and to address the need for
change against the backdrop of a well-established school with a veteran
administration and core faculty.
The most significant change factor involved transforming school culture.
Historically, viewed as a low performing comprehensive high school, the principal
and key school leaders set about to change staff and students’ perceptions and
redefine the high school as a community of learners engaged in accountable talk

156
demanding excellence in the classroom. In largely symbolic acts, the school
principal described the school as a standards-based learning community. Meeting
with students on a regular basis, the principal repeatedly delivered his message about
high expectations and improved student performance. Working with parents and
community leaders, he reinforced his message by introducing benchmark
assessments, demanding close collaboration among teachers, sharing student work
and holding teachers accountable for student success. Demanding improved student
performance and linking their success to the quality of instruction had a profound
effect on teacher’s attitudes.
Realignment of the instructional day including greater opportunities for
teacher collaboration changed the dynamic of the math department by demanding all
teachers participate in key decisions regarding pacing plans, curriculum, teaching
strategies and student performance. Chairing faculty meetings held on a consistent
and routine basis, the principal reinforced the notion that the administration was
committed to a change in school culture and student performance. Bringing their
students’ work into these meetings in the presence of the principal and department
chair and open to group discussion raised levels of accountability but, over time,
developed a sense of trust in one another. When convinced the goal was to improve
instruction and assist one another, the faculty operated in a cohesive and unified
manner.

157
Research Question 4: Instructional Leadership
The fourth research question asked, “How was instructional leadership
important in improving a) the math program/strategies and b) math achievement
among students?” Data collection for this question was organized in reference to key
factors important to effective school leadership and explores the manner in which
instructional leaders influence factors related to improved student performance in
math.
The HSHS principal demonstrates strong and effective instructional
leadership by formulating and clearly articulating a powerful vision that includes all
members of the school community, closely supervises and monitors instruction,
works to build community and parent involvement, developed a climate and culture
of learning and is well versed in research based practices and strategies. The school
principal worked closely with key faculty members developing instructional reforms
and data driven assessment practices.
Perhaps most importantly, the principal effected a comprehensive program
beginning with standards-based instruction but continuing through the process with
his involvement in developing a curriculum reflecting the shared needs and concerns
of HSHS Algebra I students, introducing data driven decision-making practices,
developing cohesion among faculty members and effectively communicating his
programs to students and their parents.

158
Research Question 5: Instructional Leader is not a Math Expert
Research question 5 asked, “How did instructional leaders respond in
academic areas in which they are not experts?” Particularly applicable because the
HSHS principal does not have expertise in math instruction, his efforts to develop a
strong math program involved an appreciation of general pedagogical principles, the
application of research-based strategies, collaboration with knowledgeable math
experts, building in structural changes to provide the math department with greater
planning time, and an understanding of the importance of the development of
effective interventions for struggling students. The principal built the capacity
necessary for change by closely monitoring and observing instructional practices
both at the planning stages and as implemented in the classroom.
Conclusions
During the analysis of data, several themes emerged for the findings with
respect to developing a standards-based high school and community of life-long
learners. Some of these thematic areas could be considered as “best practices” based
on the literature reviewed. There are also areas of concern that could impede efforts
to maintain high levels of student achievement and, if not appropriately addressed,
lead to regression.
Best Practices
Three areas of best practice that emerged in this study were:
1. Building a standards-based curriculum where both the teacher and students
have clear expectations for success. The district’s decision to implement

159
standards-based instruction began a reform movement linking instruction to
clearly defined goals and high expectations. Adopting the district mandate,
HSHS administration implemented standards-based instruction throughout
the school. The close link between clearly defined expectations, teacher
accountability and student centered learning followed the adoption of
standards- based instruction and improved the quality of teaching and
learning.
2. Close collaboration between administration and faculty to improve curriculum
proved important to rebuilding instructional programs based on student
outcomes. The participation of the principal strengthened his role as an
instructional leader gaining the respect and cooperation of faculty members.
3. The progressive use of benchmark assessment to allow for the early
identification of struggling students and building upon the data to provide
targeted instruction, methods and strategies. The interconnected relationship
between benchmark assessment and curriculum design is a significantly
important practice that could be adopted in all core academic areas. A
constant concern with Algebra I is losing students as the level of difficulty
increases over the course of the semester. By constantly assessing student
understanding and using creative instructional approaches as interventions,
greater student success was achieved resulting in reduced failure rates and
marked improvement on the CST.

160
Attention Areas
During the course of this study several areas in need of attention were
identified:
1. The transition to a standards-based high school was driven largely by the
energy and efforts of the site principal. The level of commitment and his
ability to work with his colleagues may not be easily duplicated or
generalized. The HSHS principal has a peculiar understanding of the
needs of his staff and students and ably communicates his vision as well
as his concerns. There is concern much of the reform efforts might be
abandoned without his input. The efforts of the principal, in particular,
need to be embedded in the daily operations of the high school. The
training of additional staff is essential to maintain continue and to reduce
the burden placed on this one individual.
2. There is a concern students may have reached their maximum levels of
improved achievement. The significant increase in student test scores
may be a result of the initial response to comprehensive reforms and
intervention strategies. This surge may tend to stabilize or even regress
without further analysis of student performance and the reasons for the
marked increase in performance.
3. Although early identification has proven successful, responses to
intervention may have to be refined given that a substantial number of
students are still scoring below basic on the CST. Despite the positive

161
results of the reform efforts, too many students are still not succeeding
and large numbers of students are not proficient in Algebra I. Greater
research in the specific causes for their failure must occur to maintain the
improvement in the number of students demonstrating proficiency in
math. Structural and symbolic changes need to be better supported by a
stronger curriculum design and strategies for those poorly performing
students.
Implications for Practice
As noted from the outset of this study, many urban high schools are seeking to
improve student achievement in math especially in the required core academic
subject areas. Student (and school) success is largely tied to publicly reported
performance data on high stakes examinations including the CSTs. The pressure to
succeed on state mandated tests (including math) is felt throughout the education
community and often drives school practices, hiring decisions, the organization and
design of curriculum, master schedules and planning. The findings and conclusions
from this study can provide insight and guidance to those concerned with improving
student achievement in math including:
1. A district-wide commitment to standards-based instruction. Although
generally well accepted, the HS Unified School District’s decision to
mandate the adoption of standards based instruction generated key

162
reforms including school culture, instructional programs and capacity
building.
2. Sufficient time must be made available on a regular and routine basis for
departments to work together collaboratively to address goal and
objectives, align teaching to the standards, and develop appropriate
teaching strategies and methods.
3. Standards-based instruction must be embedded in all facets of teaching
and instruction from the use of appropriate textbooks and materials, the
symbolic and effective display of standards-based instruction guidelines
in the classroom, as part of the teacher evaluation process included in all
lesson and pacing plans.
4. Students should be assessed at each step in the learning process and the
data derived from such assessments must drive instruction. Student
outcomes frame the quality of teaching and learning.
5. The early identification of struggling students – and the means to address
their needs – is an important component of any curriculum design.
Responding at the earliest stages to students falling behind leads to
greater success in the classroom and reduces the likelihood of failure.
6. Creative strategies must be employed to reach out to struggling students.
Team teaching, collaborative teaching efforts, using student work as the
basis for lesson planning and constant feedback is essential to improve
the quality of classroom instruction.

163
7. Strong instructional leadership must include a clear and concise vision
defining expectations and the role of faculty, students, parents and the
community. Effective leadership also involves participation in the
development of teaching programs, working closely with faculty and
supporting their efforts to reform curriculum and teaching strategies.
8. Developing and promoting uniformity of instruction, pacing plans, and
assessment instruments in order to develop a community of instructors
willing to work with one another and to share strengths and challenge
areas of need. An effective working environment encourages
cooperative efforts between and among teachers, which must be
developed, by the efforts of administrators and key instructional leaders.
9. Effective motivational strategies encouraging student success creates a
positive school culture and provides incentives for students who may not
understand the importance of success in math. Realistic inducements,
including rewards for success, are an effective motivational strategy.
Linking grades to results on standardized tests should be considered as
an important strategy.
10. Promoting family involvement in their students’ success is an essential
component of improved student achievement at HSHS. Family
participation must include an understanding of school expectations for
their student and the underlying reasons for school-based decisions.
Participation should be outlined by the school and clearly defined by the

164
administration. Parents cannot be expected to anticipate school
concerns – they should be clearly explained on a regular basis with
examples and suggestions for parents faced with realistic concerns.
Parent skill levels need to be addressed and they must be given
appropriate tools to monitor and observe their student’s behaviors.
Recommendations for Future Research
Throughout the data collection and analysis, future research was indicated in
several areas:
1. HSHS implemented reforms with little support or direction from the
local district. Further examination of, and comparison with, a similarly
successful school that received significant levels of support would
provide additional information about the effect of district involvement
and its impact on school site based decisions. It would be helpful and
instructive to examine how such involvement may have altered HSHS
reforms and the manner of implementation.
2. Further examination of data that would locate the most effective areas of
reform. Given the broad brush approach applied by the HSHS
administration and faculty wherein a whole series of reforms were
implemented simultaneously, data on specific strategies and reforms
might streamline the reform process and focus on those most likely to
produce preferred results.
3. The HSHS principal did not bring in to the school consultants or coaches

165
with a particular expertise in school reform and/or the math program. A
comparative study of a school relying on the efforts and expertise of
outside consultants would provide data on what might have been the
preferred approach. Issues of efficiency should be researched in addition
to the overall effectiveness of outside experts on student achievement.
4. HSHS is one of three comprehensive high schools in relatively close
geographic proximity however HSHS demonstrated much greater
improvement overall on standardized test scores. Comparative studies
between the math programs at the three high schools might isolate those
reforms that proved most successful and provide further ideas for
improvement at all three high schools.
5. HSHS’s success occurred over a short period of time and after a
significant and highly focused reform effort. Replicating the study in a
high school maintaining high levels of student achievement for a
considerable period of time would provide additional information about
the nature of the reforms, methods and strategies supporting student
improvement over time. The additional data may provide information
important to a school not wanting to regress after a short period of
improved levels of student achievement.

166
REFERENCES

Balfanz, R. & Legters, N. (2004). Locating the dropout crisis. Which high schools
produce the nation’s dropouts? Where are they located? Who attends them?
Report 70. Baltimore, MD: Publications Department, Center for Research on
the Education of Students Placed at Risk, Johns Hopkins University.

Bill and Melinda Gates Foundation. (1998). High schools for the new millennium.
Imagine the possibilities. Seattle, WA: Bill & Melinda Gates Foundation.

Blank, R. K., & Gruebel, D. (1995). State indicators of science and mathematics
education, 1995: State-by-state trends and new indicators from the 1993-94
school year. Washington, DC: Council of Chief State School Officers.

Blase, J., & Blase, J. (2004). Handbook of instructional leadership: How successful
principals promote teaching and learning. Thousand Oaks, CA: Sage
Publications.

Blume, J., Garcia, K., Mullinax, K., & Vogel, K. (2001). Integrating math and
science technology. Dissertation: Saint Xavier University.

Bottge, B. A., Heinrichs, M., Mehta, Z. D., & Hung, Y. H. (2002). Weighing the
benefits of anchored math instructions for students with disabilities in general
education classes. Journal of Special Education, 35(4), 186-200.

Bryk, A. S., & Schneider, B. (2003). Trust in schools: A core resource for school
reform. Educational Leadership, (60)6, 40-44.

Burnett, S. J., & Wichman, A. M. (1997). Mathematics and literature: An approach
to success. Dissertation: St Xavier University.

Chance, P. L., & Anderson, R. B., (2003). The principal’s role in standards-based
reform: Linking accountability to instructional improvement. Chicago: Annual
Meeting of the American Educational Research Association.

Clewell, B. C., Cosentino de Cohen, C., Deterding, N., Manes, S., Tsui, L.,
Campbell, P. B., Perlman, L., Rao, S., Branting, B., Hoey, L., & Carson, R.
(2005). What do we know? Seeking effective math and science instruction.
Washington, DC: The Urban Institute.

Coleman, J. S., Campbell, E. Q., Hobson, C. J., McPartland, J., Mood, A. M.,
Weinfield, F. D., & York, R. L. (1966). Equality of Educational Opportunity.
Washington, DC: U.S. Government Printing Office.

167
College Board. (1999). Reaching the top: A report of the National Task Force on
minority high achievement. New York, NY: College Board Publications.

Collins, J. (2001). Good to great: Why some companies make the leap … and others
don’t. New York: Harper Collins.

Darling-Hammond, L., Hightower, A. M., Husbands, J. L., LaFors, J. R., Young,
V. M., & Christopher, C. (2005). Instructional leadership for systemic
change: The story of San Diego’s reform. Leading systemic school
improvement #4. Lanham, MD: Rowman & Littlefield Publishing Group.

Davis, S., Darling-Hammond, L., LaPointe, M., & Meyerson, D. (2005). Review of
research. School leadership study. Developing successful principals. Palo
Alto: Stanford Educational Leadership Institute.

Draper, R. J. (2002). School mathematics reform, constructivism, and literacy: A
case for literacy instruction in the reform-oriented math classroom. Journal of
Adolescent & Adult Literacy, 45(6), 520-529.

Edmonds, R. R. (1979). A discussion of the literature and issues related to effective
schooling. Cambridge: MA: Center for Urban Studies, Harvard Graduate
School of Education.

Education Trust-West. (2004). Are California high schools ready for the 21
st

Century? Oakland, CA: Ed Trust-West Publications.

Fink, E., & Resnick, L. B. (2001). Developing principals as instructional leaders. Phi
Delta Kappan, 82(8), 598-606.

Fullan, M. (2002). The change leader. Educational Leadership, 59(8), 16-20.

Fullan, M., Bertani, A., & Quinn, J. (2004). New lessons for districtwide reform.
Educational Leadership, 61(7), 42-47.

Goals 2000: Educate America Act. (1994) P.L. 103-277. Retrieved November 12,
2006 from http://www.ed.gov/legislation/GOALS2000/TheAct/index.html

Gonzales, P., Guzman, J. C., Partelow, L., Pahlke, E., Jocelyn, L., Kastberg, D., &
Williams, T. (2003). Highlights from the Trends in International Mathematics
and Science Study (TIMMS). Jessup, MD: ED Publications.

168
Good, T. L., & Brophy, J. E. (1986). School effects. In M. C. Wittrock (Ed.),
Handbook of research on teaching (3
rd
ed., pp. 570-602). New York:
McMillan.

Guthrie, J. W., & Springer, M.G. (2004). A nation at risk revisited: Did “wrong”
reasoning result in “right” results? At what cost? Peabody Journal of
Education, 79(1), 7-35.

Hanushek, E. A. (2003). The lost opportunity. Education Next, 3(2). 84-87.

Harris, D. N., & Herrington, C.D. (2006). Accountability, standards and the growing
achievement gap: Lessons from the past half-century. American Journal of
Education, 112, 209-238.

Haycock, K. (1998). Good teaching matters: How well-qualified teachers can close
the gap. Education Trust, 3(2), 1-19.

Jencks, C., Smith, M. S., Ackland, H., Bane, M. J., Cohen, D., Grintlis, H., Heynes,
B., & Michelson, S. (1972). Inequality: A reassessment of the effects of
family and schooling in America. New York: Basic Books.

Johnson, R. S. (2002). Using data to close the achievement gap: How to measure
equity in our schools. Thousand Oaks, CA: Sage Publications.

Klein, D., Braams, B. J., Parker, T., Quirk, W., Schmid, W., & Wilson, W. S. (2005).
The state of state math standards, 2005. Washington, DC: Thomas B.
Fordham Foundation.

Levine, D. U., & Lezotte, L. W. (1990). Unusually effective schools: A review and
analysis of research and practice. Madison, WI: National Center for
Effective Schools Research and Development.

Loveless, T., & Coughlin, J. (2004). The arithmetic gap. Educational Leadership
61(5), 55-60.

Marks, H. M., & Printy, S. M. (2003). Principal leadership and school performance:
An integration of transformational and instructional leadership. Educational
Administration Quarterly, 39(3), 370-397.

Marzano, R. J. (2003). What works in schools: Translating research into action.
Association for Supervision and Curriculum Development. Alexandria: VA.

169
Massell, D. (1998). State strategies for building capacity in education: Progress and
continuing challenges. Philadelphia: Consortium for Policy Research in
Education.

Mubenga, P. T. (2006). Closing the achievement gap between African American
children and their Caucasians counterparts using collaboration learning
setting. Retrieved at:
http://www.eric.ed.gov/ERICDocs/data/ericdocs2/content_storage_01/00000
00b/80/31/ba/27.pdf

National Center for Educational Statistics. (2005). The nation’s report card:
Mathematics 2005. Retrieved July 3, 2006, from
http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2006453

National Commission on Educational Excellence. (1983). A nation at risk: The
imperative for educational reform [Electronic Version]. Retrieved March 5,
2006, from http://www.ed.gov/pubs/NatAtRisk/

National Council of Teachers of Mathematics. (2000, 1989). Principles and
standards for school mathematics. Reston, VA.

NCES (1999). Highlights from TIMMS: Overview and key findings across grade
levels [Electronic Version]. Report NCES 1999-081 from the Office of
Educational Research and Improvement, U.S. Department of Education.
Retrieved February 11, 2006, from http://nces.ed.gov/pubs99/1999081.pdf

Neal, K. L. (2004). Improving high school mathematics instruction: Using
constructivist pedagogy. Dissertation.

No Child Left Behind Act of 2001, Pub. L. No. 107–110, 115 Stat. 1425 (2002).
Retrieved April 16, 2006, from
www.ed.gov/policy/elsec/leg/esea02/index.html

Noddings, N. (1993). For all its children. Educational Theory, 43(1), 15-22.

Olson, L. (2006). States acting to raise bar on high school skills: Push to boost
readiness taking hold, survey finds. Education Week, 25, 20-21.

Perie, M., Moran, R., & Lutkus, A. D. (2005). The nation’s report card. NAEP 2004
Trends in Academic Progress: Three Decades of Student Performance in
Reading, 1971 – 2004 and Mathematics, 1973 – 2004. Jessup, MD: ED Pubs.

170

Powers, J. M. (2004). High-stakes accountability and equity: Using evidence from
California’s public schools accountability act to address the issues in
Williams vs. State of California. American Educational Research Journal,
41(4), 763-795.

Rampey, B. D., Lutkus, A. D., & Dion, G. (2005). The nation’s report card: Trial
urban district assessment. Mathematics 2005. Jessup: MD: ED Pubs.

Reynolds, D., & Teddlie, C. (2000). The process of school effectiveness. In C.
Teddlie and D. Reynolds (Eds.), The international handbook of school
effectiveness research (pp. 134-159). New York: The Falmer Press.

Rose, H., & Betts, J. R. (2001). Math matters: The link between high school
curriculum, college graduation, and earnings. San Francisco: Public Policy
Institute.

Sanders, W. L., & Horn, S. P. (1994). The Tennessee value-added assessment system
(TVAAS): Mixed-model methodology in educational assessment. Journal of
Personnel Evaluation in Education, 8(3), 299-311.

Schifter, D. (1996). A constructivist perspective on teaching and learning
mathematics. Phi Delta Kappan, 77(7), 492-99.

Sebring, P. B., & Bryk, A. S. (2000). School leadership and the bottom line in
Chicago. Phi Delta Kappan, 81(6), 440-443.

Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-
analytic review of research. Review of Educational Research, 75(3), 417-453.

Superfine, B. M. (2005). The politics of accountability: The rise and fall of goals
2000. American Journal of Education, 112(1), 10-43.

Taylor, C. S., Smith, P. R., Taylor, V. A., von Eye, A., Lerner, R. M., Anderson, P.
M., Banik, R. & Almerigi, J. B. (2005). Individual and ecological assets and
thriving among African American adolescent male gang and community-
based organization members: A report from wave 3 of the "Overcoming the
Odds" Study. Journal of Early Adolescence, 25(1), 72-93.

Teitelbaum, P. (2003). The influence of high school graduation requirement policy in
mathematics and science on student course-taking patterns and achievement.
Educational Evaluation and Policy Analysis, 25(1), 31-57.

171
Thernstrom, A., & Thernstrom, S. (2003). No Excuses: Closing the Racial Gap in
Learning. New York: Simon & Schuster.

Thompson, P., & Cobb, P. (1998). On relationships between psychological and
sociocultural perspectives. Raleigh, NC: Proceedings of the Annual Meeting
of the North American Chapter of the International Group for the
Psychology of Mathematics Education.

United States Department of Education. (1997). Mathematics equals opportunity.
Washington. DC: U.S. Government Printing Office.

Weiss, I.R., & Pasley, J. D. (2004). What is high-quality instruction? Educational
Leadership, 61(5), 24-29.

Woodward, J. (2004). Mathematics education in the United States: Past to present.
Journal of Learning Disabilities, 37(1), 16-31.

Wright, S. P., Horn, S. P., & Sanders, W. L. (1997). Teacher and classroom context
effects on student achievement. Implications for teacher evaluation. Journal
of Personnel Evaluation in Education, 11, 57-67.

Abstract (if available)

Abstract The purpose of this study was to examine those factors contributing to significant and sustained gains in math performance by students at a large urban public high school. In a case study of a Southern California high school demonstrating significant improvement in math over a three year period as evidenced by student performance on the California Standards Test in Algebra I, five research questions focused on the patterns of math achievement for various students, policy initiatives as well as curriculum, instruction and related issues, the change process employed by the school, the role of instructional leadership and the manner in which key leaders overcame a lack of expertise in math.

Linked assets

University of Southern California Dissertations and Theses

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Asset Metadata

Creator Surdin, Melvin J. (author)

Core Title Secondary school reform: student achievement in mathematics -- a case study: Hot Springs High School

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 04/19/2007

Defense Date 03/29/2007

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

Tag achievement,High School,math,OAI-PMH Harvest

Place Name educational facilities: Hot Springs High School (geographic subject)

Language English

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

Creator Email surdin@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m415

Unique identifier UC1485024

Identifier etd-Surdin-20070419 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-478040 (legacy record id),usctheses-m415 (legacy record id)

Legacy Identifier etd-Surdin-20070419.pdf

Dmrecord 478040

Document Type Dissertation

Rights Surdin, Melvin J.

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