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Secondary school reform and improved math achievement: a case study of site efforts at Mission Valley High School

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Secondary school reform and improved math achievement: a case study of site efforts at Mission Valley High School

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Content SECONDARY SCHOOL REFORM AND IMPROVED MATH ACHIEVEMENT:

A CASE STUDY OF SITE EFFORTS AT MISSION VALLEY HIGH SCHOOL

by

Roger Roy Rice

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

May 2007

Copyright 2007 Roger R. Rice
ii
ACKNOWLEDGEMENTS

I would like to express my gratitude to all those who have supported me throughout
the Doctoral program. I am especially grateful for the guidance and support
provided by my chair, Dr. David Marsh. I am also thankful for the input and support
provided by the other two committee members Dr. Carlye Olsen and Dr. Sylvia
Rousseau.
Thanks also go out to the administration and staff at Mission Valley High
School for all their help with this study. To the Trustees and Superintendent of the
OUHSD who recognize the value of continued professional growth. I appreciate all
your support.
A special thanks goes out to the L.A. weekend cohort members for their
constant feedback and support and for their passion and energy as we went through
our coursework. To my friends and colleagues Kyunghae and Kimberly, who
spurred me on to meet deadlines, caused me to reflect deeply on the work, and
livened up each day with their humor. I will miss our dissertation discourse, but I
know that we will continue to work together in the best interests of our students.
And most importantly, a special thanks goes to my family for putting up with
my absences and distractions. To my wife, Grace who encouraged me, but never let
me forget where my real priorities were – family first! To Matt and Katie for dealing
with Kimmy while I worked and to Kimmy for demanding the attention she so richly
deserves. Thank you all.
iii
TABLE OF CONTENTS

ACKNOWLEDGEMENTS .........................................................................................ii
LIST OF TABLES .....................................................................................................vii
LIST OF FIGURES ..................................................................................................viii
ABSTRACT.................................................................................................................x
CHAPTER ONE: INTRODUCTION TO THE STUDY ............................................1
Student Achievement in America ............................................................................1
The Achievement Gap..............................................................................................3
Student Achievement in Math..................................................................................3
Mathematics and Urban Youth ................................................................................4
Implications..............................................................................................................5
Reform......................................................................................................................6
New School Designs ............................................................................................8
Policy ...................................................................................................................9
Leadership..........................................................................................................10
Statement of the Problem…………………………………………………………12
Purpose of the Study ..............................................................................................13
Research Questions ................................................................................................14
Importance of the Study.........................................................................................15
Assumptions...........................................................................................................17
Limitations .............................................................................................................17
Delimitations..........................................................................................................18
Definition of Terms................................................................................................19
Organization of the Study………………………………………………………....21

CHAPTER TWO: REVIEW OF THE LITERATURE .............................................23
Student Achievement from an International Perspective.......................................24
Student Performance in America ...........................................................................27
Student Achievement in California........................................................................29
The Achievement Gap............................................................................................31
Opportunity to Learn..............................................................................................36
The Dropout Crisis………………………………………………………………..37
The Importance of Achievement in Mathematics..................................................39
Implications for the Future.....................................................................................44
State and National Reform Efforts.........................................................................46
Curriculum and Instruction ................................................................................47
Increased Accountability....................................................................................48
New School Designs ..............................................................................................51
School Cultures - Professional Learning Communities.................................54
School Size - Smaller Learning Communities...............................................54
Learning Activities.........................................................................................57
Student Performance Assessments.................................................................58
iv
Curriculum Foundations ................................................................................59
The Elements of Effective Math Instruction..........................................................60
Rigorous Content Standards...............................................................................61
Effective Instructional Practice..........................................................................65
Model Math Programs ...........................................................................................69
Building the Capacity for Growth………………………………………………...72
The Importance of Leadership ...............................................................................76
Visionary Leadership .........................................................................................78
Instructional Leadership.....................................................................................80
Leading Change .................................................................................................81
Instructional Leadership and Math.........................................................................83
Conclusion .............................................................................................................85
CHAPTER THREE: RESEARCH METHODOLOGY ............................................88
Sampling Criteria and Process ...............................................................................91
Selected School Profile ..........................................................................................94
Participants in the Study ........................................................................................97
Instrumentation ......................................................................................................99
Intellectual Frameworks.......................................................................................100
Framework for Research Question 1: School Profile of Student
Achievement Data............................................................................................100
Frameworks for Research Question 2: Effective Math Programs
and School Design ...........................................................................................100
Framework for Research Question 3: The Change Process.............................103
Framework for Research Question 4: Instructional Leadership .....................106
Framework for Research Question 5: Strategies to Overcome Lack of
Subject Matter Expertise...................................................................................108
Data Collection Instruments.................................................................................110
Instrument 1 - School Profile ...........................................................................110
Instrument 2 – Key Leader Interview Guide....................................................112
Instrument 3 – Teacher Interview Guide .........................................................113
Instrument 4 – Teacher Questionnaire .............................................................113
Data Collection.....................................................................................................114
Data Analysis .......................................................................................................117
Validity and Reliability........................................................................................119
Conclusion ...........................................................................................................120
CHAPTER FOUR: FINDINGS, ANALYSIS AND DISCUSSION .......................121
Data Findings .......................................................................................................122
Research Question 1: Pattern of Achievement in Math...................................122
Standardized Testing……………………………………………………….124
Course Enrollment Patterns in Math………………………………………128
Other Indicators……………………………………………………………130
Research Question 2: Policy and Practice........................................................131
v
Policies Related to Improved Student Achievement....................................132
Effective School Design...............................................................................137
School Cultures…………………………………………………………….138
Learning Activities………………………....………………………………140
Effective Math Program Design...................................................................141
Research Question 3: The Change Process......................................................149
The Structural Frame....................................................................................149
The Human Resources Frame. .....................................................................152
The Political Frame......................................................................................154
The Symbolic Frame. .................................................................................158
Research Question 4: Instructional Leadership ...............................................159
Vision for Learning. ...................................................................................160
A Culture of Teaching and Learning. . .......................................................163
Data-Driven Decision Making……………………………………………..166
Research Question 5: Strategies Re: Lack of Subject Matter Expertise .........168
Analysis and Discussion ......................................................................................177
Best Practices ...................................................................................................177
The Importance of Human Resources..........................................................177
Embracing the Era of Accountability...........................................................178
Standards-Based Instruction ........................................................................179
Strong Instructional Leadership ...................................................................180
Campus Climate and Culture .......................................................................183
Raising Expectations....................................................................................183
Overcoming Obstacles .................................................................................183
Items for Future Consideration……………..………………………………...185
Unanswered Questions…………………………………………………….185
Conceptual Knowledge vs. Procedural Knowledge……………………..185
Sustained Improvement………………………………………………….186
Human Resources…………………………………………….………….186
Professional Development…………………………………….…………187
Equity……………………………………………………………………187
Summary ..........................................................................................................…187
CHAPTER FIVE: SUMMARY, CONCLUSIONS AND IMPLICATIONS ……..189
Purpose of the Study ............................................................................................189
Methodology ........................................................................................................190
Sampling ..........................................................................................................190
Data Collection and Analysis...........................................................................191
Selected Findings .................................................................................................193
Research Question 1: Pattern of Achievement in Math...............................194
Research Question 2: Policy, Curriculum and Instruction...........................196
Research Question 3: Change Process .........................................................198
Research Question 4: Instructional Leadership ...........................................203
vi
Research Question 5: Leader’s Response to Lack of Subject Matter
Expertise.......................................................................................................205
Conclusions......................................................................................................208
Implications for Practice ..................................................................................211
Recommended Future Research.......................................................................219
REFERENCES.........................................................................................................221
APPENDICES .........................................................................................................230
Appendix A: Algebra I Objectives.......................................................................231
Appendix B : CST Gains and Losses for Identified Districts ..............................234
Appendix C: Key Leader Interview Guide ..........................................................237
Appendix D: Teacher Interview Guide ................................................................241
Appendix E: School Profile .................................................................................242
Appendix F: Math Teacher Questionnaire...........................................................245
Appendix G: Non-Math Teacher Questionnaire..................................................253
Appendix H: Math Teacher Questionnaire Results .............................................258
Appendix I : Data Collection Grid.......................................................................261

vii
LIST OF TABLES

1. MVHS Multiple Measures System – English/Language Arts 136
2. MVHS Multiple Measures System – Math 137
3. Teacher Responses to Standards-Based Instruction Items 142
4.Cumulative Quiz Process 146

viii
LIST OF FIGURES

1. SES and Math Achievement in Grade 8 33
2. SES and Math Achievement in Grade 4 34
3. Classes Taught by Under Qualified Teachers 40
4. United States Census Data: 1986-2000 45
5. Content Standards in Math – CDE vs. NCTM 64
6. Performance Expectations During Seat Time 66
7. Teachers’ Goals for their Lessons 67
8. Leadership and Improved Student Achievement 77
9.MVHS API Progress 96
10 Relationship of Data Collection Instruments to Research Questions 99
11.Effective School Design Framework 101
12.Effective Math Programs Framework 102
13.Bolman and Deal’s Four Frames 104
14.Instructional Leadership Framework 107
15. Assessment of Principal’s Expertise in Math 109
16. Strategies used to overcome lack of subject matter expertise 110
17. Growth on Algebra I CST Mean Scale Scores 127
18. Growth on Algebra I CST Proficient and Above 127
19. Enrollment in All Upper Level Math Classes 128
20. Distribution of Students Enrolled in Algebra I and Below 129
21. Average Class Size in All Math Classes 130
ix
22. Average Class Size for Algebra I and Below 148
23. Average Teaching Experience by Course – Math 148
24. 2002-03 Math Department Master Schedule 174
x
ABSTRACT

The purpose of this study was to learn more about how urban high schools
successfully bring together policy initiatives and local best practice to improve math
performance in their schools. In a case study of an urban high school in the Los
Angeles area of Southern California, five research questions focused on the pattern
of student achievement in math, policies and practices related to improved
achievement in math, the change process used at the school, the leadership practices
and the strategies used by the principal who was not an expert in math. Results
indicated that leadership from a variety of sources all worked to focus efforts on
standards-based instructional practices to move the school forward.
School leaders had the unique opportunity to build their school from the
ground up and focused on building a positive school culture, human resources issues
and the implementation of standards-based instruction. School pride and an
emphasis on academics was established using symbolism, ceremonies and rituals.
Hiring the best teachers possible and assigning teachers strategically ensured that the
neediest students were taught by strong, veteran teachers. Leadership was
effectively distributed in the delegation of important academic duties to the assistant
principal and math department chair.
As urban high schools seek to improve student achievement in math, the
findings and conclusions from this study can provide useful insight into instructional
and leadership practices that may prove effective for teachers and site and district
administrators working to improve student achievement in math. Future research is
xi
warranted in light of the need to learn more about how similar efforts may prove
effective in other core areas such as English and Science, with specific sub-groups of
students and how isolated areas of excellence thrive in otherwise stagnant
educational environments.
1
CHAPTER ONE
INTRODUCTION TO THE STUDY

For much of the past 50 years, improving the quality of public education has
been at the forefront of America’s political and social agendas. In perhaps the most
dramatic example of this focus, the National Commission on Excellence published A
Nation at Risk (1983) which warned that America could lose its competitive
advantage as a result of poor educational performance. Then, in 1990, the California
High School Task Force published Second to None: A Vision of the New California
High School which recommended sweeping changes in the structure and curriculum
of high schools in California. A decade later, Aiming High: High Schools for the
Twenty-First Century (CDE, 2002), echoed the urgent need to reform America’s
public high schools. State Superintendent of Public Instruction Jack O’Connell
introduced the report stating, “Now the challenges facing our young people are
greater than ever before. We cannot back away from our quest to improve schools;
we must continue to aim high. Otherwise, we will have failed our students”
(O’Connell, 2002).
Student Achievement in America
Recently, Microsoft Chairman Bill Gates (2005) renewed the call for high
school reform by publicly proclaiming, “America’s high schools are obsolete.” Gates
actively supported this effort by contributing more than $1.2 billion dollars to a
major high school reform effort further proclaiming, “This failure to prepare the next
generation for tomorrow’s challenges threatens our nation’s economic and civic
2
health.” Indeed, a new generation of research began to focus on the stagnating
achievement in the nation’s secondary schools. Such studies included The Education
Trust’s report, Stalled in Secondary: A Look at Student Achievement Since the No
Child Left Behind Act (2005) which concluded that student achievement in the core
areas at the high school level had not kept pace with gains at the elementary school
level. The report also noted the poor progress made in narrowing the achievement
gap at the high-school level. “In reading and math, for instance, both the Latino-
White gap and the gap between poor and non-poor students grew or stayed the same
in more states than they narrowed” (EdTrust, 2005).
In yet another report that voiced concerns about how America serves its high
school-aged students, Hall (2003) emphasized the inconsistency in how states
reported graduation and dropout rates. In Education Trust West’s report Getting
Honest About Graduation Rates: How States Play the Numbers and Students Lose,
Hall concluded that the true depth of the dropout problem was obscured since many
states either failed to report accurate numbers, or worse, failed to report their rates
altogether. Hall’s research indicated that even in the face of strict requirements laid
out in the No Child Left Behind Act (NCLB), 31 of the nation’s 50 states required
that only “some” improvement be made in these rates and that 2 others had no
requirement to improve at all. Further, only six states reported graduation rates at or
above 90% for the 2002-03 school year. Thus, despite decades of national attention
and the allocation of countless millions of dollars, the academic performance of
3
American high school students remained low for many types of students when
viewed by national objective standards and by international comparative studies.
The Achievement Gap
Much of the research that has contributed to this sense of urgency to reform
America’s high schools emphasized the gap in achievement between students of
color and their Anglo counterparts. This gap persisted despite widespread awareness
that socio-economic status (SES) remained the most reliable predictor of academic
achievement in America. Data collected by the National Center for Educational
Statistics (NAEP, 2004) indicated that gains made in the 1980’s in this area were
short lived as the achievement gap between Anglo students and their African-
American and Latino counterparts widened once again in the 1990’s. One example
of this was cited by Hall (2005), who used the Cumulative Promotion Index (CPI) as
a measure of predicting the probability that a student entering the ninth grade would
complete high school on time with a regular diploma. Hall’s analysis showed a huge
disparity along racial lines. Almost half of schools with a majority of ethnic
minority students had a CPI of less than 60%. For White dominated schools, only
9% exhibited the same low rate.
Student Achievement in Math
Another disturbing trend was the performance gap that existed in
mathematics, which represented an especially important problem in many respects.
Concerns about disparities in student achievement were validated in the Third
International Math and Science Study of 1995 (TIMSS). TIMSS assessed and
4
detailed student achievement in mathematics and science for students from more
than 23 countries in three different grades. Disturbingly, TIMMS revealed that
despite American students being above the international average in grade four, by
grade twelve American students scored among the lowest nations in both math and
science. These findings were troubling in light of another report, Math Matters: The
Link Between High School Curriculum, College Graduation and Earnings (2001)
which detailed the important relationship between successful completion of rigorous
coursework in mathematics and later success in life. Authors Rose and Betts found
that taking and passing rigorous math courses such as algebra and geometry helped
students of all types. These benefits included increased earnings over time and a
stronger likelihood of graduating from college. These findings were important in a
world which increasingly demanded technical proficiency and greater skill levels of
its workers.
Mathematics and Urban Youth
Mathematics proficiency was especially important for urban youth in light of
the numerous formidable challenges they faced as compared with their higher SES
and White counterparts. Some of these challenges were detailed by Klopfenstein,
(2006) who noted that lower teacher expectations had a detrimental impact on
student performance and that low income students were expected to be less likely
than other students to pursue a rigorous math curriculum. Furthermore, students
from lower SES families were often expected to carry the additional responsibility of
helping to support their families financially. In addition, King (1993) found that
5
teachers of color, teachers of math and science and teachers in urban schools (which
tend to have a higher proportion of Black students) left the teaching profession at the
highest rates (Klopfenstein, 2006).
In light of the importance of mastering rigorous mathematical coursework,
these findings were particularly troublesome and pointed to the urgency of
identifying and implementing effective math programs. Such programs have been
developed and were responsive to the findings of TIMMS that call for a greater focus
on conceptual understanding and more time spent in class on problem solving and
thinking critically about math. In addition, effective math programs were those with
clear and challenging goals, and whose content was aligned to those goals. Effective
math programs also engaged students in culturally relevant instruction and utilize
assessments that informed student learning and guided instruction. Effective math
programs were grounded in the national curriculum standards, were adaptable to a
variety of settings and addressed important individual and societal needs and finally,
made a measurable difference in student achievement (PL 103-227, 1994).
Implications
In his book As the Future Catches You, Juan Enriquez (2001) of the Harvard
School of Business warned of the dangerous combination emerging in America of
(a) the shifting of the world’s economy to one that is knowledge-based, (b) the strong
link between creating wealth and creating new knowledge in the fields of
mathematics and science, and (c) the rapidly changing demographics in America that
included a burgeoning Hispanic/Latino population that has not historically studied in
6
these fields. Enriquez pointed to ominous economic and societal consequences for
the United States if these trends continued. Friedman (2006) supported this point of
view and emphasized the rapidly changing economic and business climate in the
world and noted how much of the work that used to be done in America had now
been “outsourced” to other countries such as India.
Reform
In response to these concerns, state and national efforts to increase math
achievement in high schools focused on state standards, improved curriculum and
instruction, better prepared teachers and related reform efforts. Perhaps none of
these initiatives was more comprehensive than the reauthorization of the Elementary
and Secondary Education Act (ESEA) more commonly referred to as the No Child
Left Behind Act of 2001 (NCLB). NCLB operated under the premise that higher
expectations and increased accountability for districts, schools and teachers would
lead to increased student achievement and a corresponding reduction in the
inequitable conditions that existed in America’s public education system. NCLB
enacted an accountability system requiring schools to meet Adequate Yearly
Progress (AYP) towards established goals of student performance. The AYP
provision of NCLB required schools to ensure that all students were proficient in
core academic areas by the year 2014 and that in order to do so, schools must meet
intermediate benchmarks along the way (USDE, 2003).
In related efforts, states implemented comprehensive accountability systems
such as California’s Public Schools Accountability Act of 1999 (PSAA) which
7
included three basic elements. The Academic Performance Index (API) was designed
to measure student achievement and represents a value-added model of
accountability where schools receive an index score based on standardized
achievement tests and other factors and are judged on growth over time. The
Immediate Intervention Underperforming Schools Program (IIUSP) provided a
structured intervention plan and resources for schools not meeting their growth
targets. Finally, the Governor’s Performance Awards represented an effort to reward
schools and teachers for making academic progress. This part of the PSAA was
ultimately phased out due to a lack of funds. A study of the effectiveness of the
PSAA reported that California’s accountability system worked to focus schools’
attention on historically underperforming students who are often overlooked (AIR,
2003).
California’s accountability system, like many other states, relied heavily on
standardized test score results. As a result, most states had also codified a set of state
instructional standards in core academic areas including mathematics and language
arts. These standards were designed in part to level the playing field by ensuring that
consistent instructional opportunities are afforded all students. State standards also
appeared to be intended to align curriculum to the standardized tests upon which a
school’s success is so heavily weighted. A major difference between these recent
efforts and earlier reform movements was an emphasis on student outcomes as
opposed to teacher behaviors (DuFour, DuFour Eaker & Karhanek, 2004). Schools
that are not able to demonstrate increased student achievement on quantifiable
8
measures of student success now faced consequences. NCLB designated such
schools as “Program Improvement” schools and mandated an escalating series of
interventions to address academic shortcomings at the school. Such interventions
ranged from changing curriculum to releasing personnel deemed to “inhibit the
progress” of the school (USDE, 2003).
New School Designs
Out of an effort to support success in these new accountability systems came
new school designs that focused on student achievement and related school features.
One recent and significant movement in this area was the effort to form professional
learning communities (PLCs) at the school site level. DuFour (2004) argued that
PLCs could help add to a student’s existing set of developmental assets and had the
potential to increase student achievement as much or more than any other reform
strategy yet developed. Building PLCs involved creating cultures of rigor where
adults made it harder for students to fail and everyone in the community was
responsible for intervening when children fell behind. PLCs attempted to increase
rigor and strengthen relationships by breaking down the isolation typical in large
American high schools. In support of this effort, Lambert (2003) emphasized the
need for learning communities to increase leadership capacity by fostering leadership
in students, teachers and parents as well as administrators.
Large urban districts such as Los Angeles Unified School District (LAUSD)
turned to a related strategy as a major piece of their efforts to improve student
achievement at the high school level. LAUSD mandated that beginning with the
9
class of 2008, all of its students were to complete the admissions requirements to the
University of California system (A-G) and moved to restructure many of its
comprehensive high schools into smaller learning communities (SLC’s) (Gates
Foundation, 2005). SLC’s were primarily designed to address the impersonal nature
of large urban schools by breaking them down into smaller groups of students and
teachers, many times organized around a central theme, subject matter, or grade
level. Such efforts garnered wide spread support and prompted substantial funding
efforts by groups such as The Gates Foundation.
Policy
If America’s schools are to sustain increased student achievement, however,
building local capacity for improvement must be joined with new policy initiatives
and designs. Individual school sites cannot change the face of America’s public
education systems by themselves and “islands of excellence” will not be sufficient to
satisfy the public’s demands for increased student achievement. As schools seek to
meet the challenges associated with this accountability, state and local officials must
work to foster an environment conducive to the change process. California, for
example, has lobbied hard to revise provisions of the federal NCLB AYP program in
an effort to change it to a value-added model where growth is rewarded and serves as
the primary measure of a school’s success (CDE, 2006a). School districts have
worked to implement policies consistent with reforming its large comprehensive
high schools and local school sites have restructured in similar attempts to better
serve their communities and increase student achievement. At the same time, 236
10
high schools were labeled as Program Improvement schools during the 2004-05
school year (CDE, 2006b). Worse, more than 30 high schools progressed into the
fifth year of the Program Improvement process and therefore towards the possibility
of takeover or closure. This inconsistency called for further inquiry into best
practices related to instructional leadership.
Leadership
Strong instructional leadership was a necessary and key component in
fostering lasting change that positively impacted student achievement. Fortunately, a
considerable amount of quality research has been done to identify the essential
components of instructional leadership in this new context. The notion that schools
cannot implement lasting change without such leadership was supported by such
researchers as Marzano (2003) who emphasized the importance of effective
leadership in the schools by noting that, “Leadership is a necessary condition for
effective reform…,” (Marzano, p.172). Blasé and Blasé (2004) echoed this
sentiment and detailed the research on strong instructional leadership. One of the
primary components of such leadership was the importance of framing and
communicating clear learning goals for the school and supervising and evaluating
instruction in the pursuit of these goals. Instructional leadership also involved
coordinating curriculum and monitoring student progress to ensure that instruction
was closely aligned to the learning goals articulated by the instructional leaders at the
school. Maintaining high visibility and protecting instructional time were also seen
as critical components of instructional leadership. Finally, Blasé and Blasé noted the
11
importance of promoting staff development for teachers and providing incentives for
teachers and students as important aspects of instructional leadership.
The use of student achievement data to drive the instructional program was
also an essential component of instructional leadership. Johnson (2002) noted the
effectiveness of using student achievement data to break down historic and cultural
biases as well as creating dissatisfaction by highlighting shortcomings and areas of
weakness in the student achievement of students across instructional and
demographic lines. Using student achievement data also implied the development of
distributed leadership as an effective practice as data teams began to work together to
analyze student achievement patterns and developed strategies for addressing areas
of weakness in the instructional program. Ultimately, strong instructional leadership
was seen as essential to creating the environment necessary to implement and
maintain lasting change initiatives in the public schools (Marzano, 2003).
Making effective use of the strategies noted above for instructional leadership
was especially important for high school principals since the job of running large
urban high schools was recognized as immensely complex. High schools in
Southern California often exceeded 2000 students and offered a wide array of
curricular programs and extra-curricular activities. No one person can be an expert
in all content areas making it especially important for school leaders to practice
effective instructional leadership as they respond to the challenge of improving
student achievement. Making use of the strategies noted above as well as using
effective delegation, hiring curricular experts, and focusing on effective pedagogy
12
are a few of the ways school leaders can overcome a lack of in depth subject matter
knowledge. In addition, developing a culture of inquiry where teacher leadership
can thrive is an effective means of demonstrating sound instructional leadership
(Marzano, 2003).
Statement of the Problem
America’s competitiveness in the global economy depends on producing
workers who are well educated and highly skilled. At the same time, evidence is
mounting that student achievement at the high school level is progressing only
marginally and lags behind the gains made at earlier levels of schooling. These facts
make it evident that schools and districts need to act in ways that ensure that all
students succeed at high levels. In order for this to occur, however, it is imperative
that schools use consistent, proven methods that are readily adaptable to diverse
educational settings. For this to happen, school leaders must continue to learn more
about how urban high schools bring together policy initiatives and local best practice
to improve student achievement in math.
While much research has been done on effective leadership practice in
general, little is known about how to effectively improve mathematics achievement
school-wide. More specifically, discovering a school’s pattern of math achievement
and learning more about how that pattern is related to the school’s curriculum and
instruction represents an important challenge for site leaders as they work to sustain
growth in math achievement over time. Likewise, sound policy decisions and an
13
awareness of how change takes place in the context of large urban high schools are
both critical to this effort.
Furthermore, instructional leaders charged with the responsibility of
improving student achievement must rely on a solid base of research to make data-
driven decisions. Therefore, it is important to study how instructional leadership is
effectively carried out in high schools, especially those demonstrating improved
student achievement in math. Several issues seem especially relevant to instructional
leadership in this setting including the reality that school principals often do not have
strong pedagogical knowledge in mathematics instruction yet are held accountable
for improving student achievement in this area. In consideration of the importance
of leadership under these circumstances, it is troublesome that so little is known
about how leaders work in this context.
Learning about how successful site administrators behave in the context of
leading curriculum and instruction, especially in the critical area of math is an
especially important first step in finding effective strategies that work to improve
student achievement. Without this knowledge, urban schools with large numbers of
at-risk students are likely to continue practices that have historically resulted in
disproportionate drop out rates for students of color and will ultimately fail to meet
the NCLB mandate that all students be proficient by 2014.
Purpose of the Study
The purpose of this study was to learn more about how urban high schools
successfully brought together policy initiatives and local best practice to improve
14
math performance in their schools. In addition, school leaders often have limited
expertise in mathematics yet are tasked with carrying out functions related to fiscal,
personnel, organizational leadership, data analysis and review, in order to improve
student achievement. And because so little is known about how leaders worked in
this context - the study also focused on how instructional leadership was effectively
carried out in high schools, especially in the effort to improve student achievement in
math.
Research Questions
The research questions that guided this study were:
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seemed 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?
15
Importance of the Study
Meeting the call for improved student achievement, especially in math, is
imperative for the future of America’s public educational system and for the
economic well-being of the nation. State and federal accountability systems have
been built around the need to ensure the success of all students. State standards have
been designed and implemented to ensure that the achievement gap is closed and that
all students have access to the same rigorous curriculum and succeed at high levels.
Despite these sweeping efforts, practical sources of information to guide
instructional leaders in this area are not as readily available as they ought to be. By
examining how urban high schools successfully bring together policy initiatives and
local best practice to improve the math performance of their students and how
instructional leadership is effectively carried out in high schools, this study provides
an additional resource for educators at all levels, including researchers and policy-
makers.
Teachers work daily to bring about the improved achievement so eagerly
sought, but are often removed from the research involved in discovering what sound
practice and policy look like. In addition, much attention has been given to the
importance of distributed leadership in public schools and of the power of teacher
leadership. Without a thorough understanding of what constitutes these critical
facets of instructional improvement, teachers are unlikely to benefit from the
research in this area. This study highlights the importance of the role of the teacher
in the change process and of effective teacher leadership in general.
16
Site instructional leaders are in a unique position to create the environment
necessary to foster instructional improvement and to implement changes dictated by
research and policy initiatives. In addition, site administrators striving to improve
student achievement in math can benefit from this study by reviewing how others in
similar circumstances brought together policy and instructional practices to achieve
their goals.
Likewise, district level administrators and school board members are tasked
with setting policies that often have profound effects on teaching and learning.
These leaders can use the information in this study to better inform the types of
support their principals need to meet the challenges they face. As they seek to
support the school’s efforts to effect sustained improvement in math achievement,
these policy makers need access to as much practical knowledge as possible since
many times, their roles are not based in practice, but in politics. The value of this
study is similar for those in state and federal policy making roles since while they are
removed from the classroom, they are still responsible for setting policies that can
profoundly affect educational outcomes on a large scale.
For educational researchers seeking to explore related issues, this study will
serve to inform and enlighten their inquiry. In a broader sense, this study adds to the
field of knowledge associated with increased student achievement in general and
math more specifically. Finally, this study may also serve to add to that field of
research associated with instructional leadership within the context of secondary
school reform.
17
Assumptions
This study assumed that student achievement in math was in part a product of
a sound instructional program and effective pedagogy. It also assumed that
instructional leadership was necessary to create an environment conducive to
improving student achievement in math. And while the research questions and data
collection instruments were influenced in the direction of the site principal providing
such leadership, the study methodology was flexible enough to find that leadership
where it existed. The assumption that leadership was important to improving student
achievement did not, therefore exclude the possibility that such leadership may have
come from other sources such as department chairs, other site administrators, or
teacher leaders. This study attempted to discover the essential elements and
accurately tell the story of the school’s success regardless of the sources of
leadership that most influenced the improvement in student achievement at the site.
The data collection instruments used in this study were based on sound
conceptual frameworks and considered valid instruments for the collection of data.
Respondents were expected to be truthful and information obtained from them is
assumed to be reliable.
Limitations
Due to limitations on the length of time allowed for this study, and the
absence of a formal budget, the data collected was limited to an investigation of one
public high school and is specifically concerned with one content area – math. Data
collection occurred over a two month period in the Fall of 2006. These constraints
18
and the corresponding approach limit the ability to generalize specific results to other
schools and/or content areas. While efforts were made to prevent undue bias, the
researcher did not have control over any bias already present in the participants.
Participation was voluntary and therefore results are limited to those participants
who agreed to be interviewed and/or return one of the questionnaires used in the
study. The analysis of the data was subject to researcher interpretation, but was
based on how the data collected interacted with and fit within the specific concepts
delineated in the conceptual frameworks.
Delimitations
Given the limitations noted above, the field of inquiry was limited to allow
for a more in depth analysis of the critical factors associated with improved student
achievement in math. With this in mind, a descriptive, analytical case-study
approach was used to gather data from one public high school in Southern
California. The qualitative approach and sample size used in the study limit the
ability to generalize the results to other situations. The school studied was
purposefully selected based on the following criterion:
1. Improvement in math achievement as evidenced by improvement on the
California Standards Test (CST) in Algebra I.
2. Urban and diverse as evidenced by a student population of at least 1200
students with more than 50% from ethnic minority groups.
3. Public high school in the Southern California region
19
4. Leadership stability as defined by a principal being at the school for at
least three years.
Definition of Terms
For the purpose of this study, the following terms were operationally defined
as follows:
Academic Performance Index (API): The Academic Performance Index
(API) is a numeric index (or scale) ranging from a low of 200 to a high of 1000 that
reflects a school’s or local educational agency’s (LEA’s) performance level based on
the results of statewide testing (CDE, 2002).
Adequate Yearly Progress (AYP): NCLB requires that each child and each
"sub-group" of children have their progress measured and reported annually. Ensures
that schools are held accountable for the achievement of all students (USDE, 2002).
Accountability: A system that includes academic achievement scores,
specific information about curriculum, teaching practices, and leadership practices
ultimately aimed at directing the focus to individual student progress (Reeves, 2004).
Assessment: A measurement of a student’s particular skill or knowledge that
may be written, oral, or performance in nature. Standardized assessments were
administered and scored in exactly the same way for all students to measure specific
skills and knowledge (Olsen, 2005).
Benchmark: An articulated expectation of student performance at specific
grades, ages, or developmental levels (Olsen, 2005).
20
Leadership Capacity: Broad-Based, Skillful participation in the work of
leadership (Lambert, 2003).
Conceptual framework: A consistent and comprehensive integration of
research literature, theories, and other pertinent information that was the basis for the
collection of data and analysis of findings within the study (Olsen, 2005).
Content standards: Content standards were designed to encourage the highest
achievement of every student, by defining the knowledge, concepts, and skills that
students should acquire at each grade level (CDE, 2006).
Data-driven decision making: The process of making decisions about
curriculum and instruction based on the analysis of classroom data and standardized
test data. Data-driven decision making used data on operational functions, the
quantity and quality of inputs, and how students learn to suggest educational
solutions (Olsen, 2005).
Equity: An operational principle for shaping policies and practices which
provide high expectations and appropriate resources so that all students achieve at
the same rigorous standard- with minimal variance due to race, income, language or
gender (Hart & Germaine-Watts, as cited in Johnson, 2002).
Implementation: The translating of an idea into action in order to accomplish
the specified goal (Olsen, 2005).
Instructional improvement: A change in the structures or opportunities that
enabled quality teaching, thus resulting in improved learning (Olsen, 2005).
21
Instructional leadership: What good principals do that leads to such impacts
as improved teacher morale and motivation, enhanced self-esteem and confidence,
and reflectively oriented instructional behavior (Blasé and Blasé, 2004).
Professional development: Opportunities for staff to develop new knowledge
and skills that improved their teaching ability. Also termed “staff development” in
some literature (Olsen, 2005).
Reform: A change effort that was undertaken to improve the educational
system (Olsen, 2005).
Standards-based reform: The change to an educational system that utilized
subject-matter benchmarks to monitor student achievement, assessments aligned
with standards to measure student performance, and accountability systems that
provided rewards or sanctions to district, schools, and students based on student
performance. Implementation of all three components—standards, assessment, and
accountability—was termed standards-based accountability (Olsen, 2005).
Teaching and learning: Based on the premise that effective instruction
resulted in strong student performance, improving teaching and learning referred to
the demonstration of improved instruction, even in the absence of precise student
outcome measurements (Olsen, 2005).
Organization of the Study
This dissertation begins with Chapter 1 which contains an overview of the
study, the statement of the problem, the purpose of the study, the significance of the
study, the research questions to be answered, and the definitions of terms. Chapter 2
22
reviews the literature relevant to the study beginning with a broad overview of
student performance and moving to more specific issues affecting student
achievement. These factors include accountability models, leadership, reform
strategies and instructional strategies in mathematics. Chapter 3 presents the
methodology used in the study, including the sampling and selection process of
participating schools and individuals; the research design; and the methodology used
to conduct the study. The findings of the study, with analysis and discussion of the
data are detailed in Chapter 4. Chapter 5 summarizes the study and proposes
possible implications for practice. References and appendices follow this section.
23
CHAPTER TWO
REVIEW OF THE LITERATURE

The call for increased student achievement was not a new phenomenon in
America, but in recent years, outcries about the quality of public education reached a
fever pitch. Beginning with A Nation at Risk in 1983, a steady stream of studies and
reports emphasized that the academic performance of American high school students
was low for many types of students when viewed by national standards and by
international comparative studies. Opening with the ominous phrase, “Our nation is
at risk,” (USDE, 1983, p.1) the report noted that “International comparisons of
student achievement, completed a decade ago, reveal that on 19 academic tests
American students were never first or second and, in comparison with other
industrialized nations, and were last seven times” (USDE, 1983, p. 3). The
consensus was that little had changed in the last two decades to mitigate the findings
in A Nation at Risk, yet there was now an overwhelming depth of research fueling a
reform movement that was driven by practical, relevant research.
A review of the literature pertinent to this study necessitated that several
distinct areas of concern were detailed. First, it was important to note the general
status of student achievement in America’s public schools today. Using this
perspective as an overview allowed for a more comprehensive understanding of
where American schools and its students were falling short of expected outcomes
and provided a solid foundation for understanding the many secondary school reform
strategies aimed at increasing student achievement. State and national perspectives
24
lent context to this review as did an analysis of American students’ collective
performance compared to their peers internationally. In addition, because student
achievement in math was especially important to the country’s future in a globally
competitive, technological, and knowledge-based economy, a review of how
American students fared in this critical area was central to this study. Moreover, no
review of student achievement in America would be complete without an
examination of the ongoing challenge represented by the achievement gap between
Anglo students and students of color. This gap needed to be addressed if America’s
schools were to realize true equity and success for all students. Finally, as schools
and districts seek to address these concerns, they must turn to effective research and
understand how excellence in instructional leadership supports successful reform
efforts. Without data-driven and research-based solutions, practitioners are likely to
continue the struggles of their predecessors.
Student Achievement from an International Perspective
Numerous studies over the past few decades have documented the stagnating
achievement of American students in comparison to their counterparts in other
countries. Perhaps the most effective of these efforts was a series of studies
conducted by the International Association for the Evaluation of Educational
Achievement dealing with student achievement in math and science. The initial
studies in this series began on a modest scale involving 13 countries in the 1960’s
with the First International Math Study and the First International Science Study and
were followed up twenty years later with the Second International Math Study and
25
the Second International Science Study. In 1988, the two studies were combined
into the First International Assessment of Educational progress, which was given to
13 year-old students in six countries. The findings in these studies were not
favorable for American students despite some of the research being questioned on
technical grounds.
Then, in 1995, the Third International Mathematics and Science Study
(TIMSS) found that American students in grades four and eight were being
outperformed in math and science by their counterparts in several foreign countries.
TIMSS made a more thorough effort to ensure that the sample populations were
comparable across nations, and the findings mirrored those in the earlier studies –
American students were not at the top of the list. Follow up studies in 1999 (TIMSS
1999) and 2003 (TIMMS 2003) confirmed that little progress was made overall,
despite gains in isolated areas. In mathematics for example, TIMSS 1999 found that
American eighth graders scored below 18 other nations participating in the study.
Among the nations that outperformed American students on this measure were
Hungary, Slovenia, Australia, The Republic of Korea and Japan. Singapore scored
highest on this measure with a scale score of 604, more than 100 points higher than
the American score of 502.
TIMMS 1999 also demonstrated that American students in the eighth grade
were not showing significant academic growth in math or science, except amongst
isolated populations. For example, between 1995 and 1999, there was no change in
the achievement levels of eighth grade students in math or science. This lack of
26
progress was noted across gender and ethnic lines with the exception of Black
students in the eighth grade who showed an increase in their achievement in math
between 1995 and 1999.
Following TIMSS 2003, Gonzales (2004) noted a continued lack of progress
made by American eighth graders, who were bettered by students in 12 other
countries on the same measure. American students in grade 8 did, however,
significantly improve their performance in solving problems related to Algebra and
Data, but failed to show any measurable growth in the concepts associated with
Geometry, Measurement and Numbers between 1999 and 2003. These isolated areas
of growth contributed to an improvement in the relative ranking amongst comparison
nations between 1999 and 2003, yet as noted earlier, American students ranked no
higher than 12
th
internationally in this comparison. It was this type of inconsistent
progress that fueled calls for the systemic reform of American public high schools.
The relatively weak showing of American students in math revealed in the
TIMSS studies was confirmed in the findings of the Program for International
Student Assessment (PISA) 2003. PISA presents a profile of student achievement for
each participant country detailing the percentage of students who were able to
perform at varying degrees of proficiency, the average math scale score relative to
other nations, and the spread in the performance between the highest and lowest
performers was measured for each country. On the first measure, American students
performed near the bottom with a relatively low percentage of students performing
higher level math compared with their international peers. The American
27
distribution on this measure scored lower than 27 of the 40 participating nations, just
behind Latvia and Hungary. On the second measure, America’s average scale score
for fifteen year-olds in math was only higher than 12 nations. Finally, American
students showed a much wider variance in achievement than the schools with
comparable average mean scores suggesting that there is much work to be done to
close the achievement gap (NCES, 2004).
Student Performance in America
The National Assessment Governing Board (NAGB) was established in 1988
and charged with overseeing the operations of the National Center for Educational
Statistics (NCES) (Vinovskis, 1998). Responding to the direction set by the NAGB,
the NCES worked to regularly assess the state of affairs in American education and
regularly published the National Assessment of Educational Progress (NAEP) also
called The Nations Report Card. A major component of the NAEP was comprised
of annual reports entitled The Condition of Education. These reports assessed 40
indicators which in turn were broken down into mini-reports detailing the status of
American education in areas such as academic achievement in reading and math as
well as other curricular areas. In the most recent such report, The Condition of
Education 2005, findings showed that 15-year-old students in America scored below
the average for 29 industrialized nations. In addition, earlier progress seemed to
have stalled since 1998. One example of this is that while the dropout rate declined
overall since 1972, it remained fairly stable over the past decade (NCES, 2005).
28
Another major component of the Nation’s Report Card was the Trends in
Academic Progress Report. The NAEP 2004: Trends in Academic Progress detailed
progress over three decades in reading and mathematics. The assessments were
given to students at ages 9, 13 and 17 and results were reported as average scale
scores, percentiles, and performance levels on a 500 point scale. The findings in this
report generally mirrored those of other similar reports where moderate growth was
shown over time for students in the primary grades, but little or no growth was
evidenced at the secondary level. An example of this cited by the NAEP 2004 was
that since 1972 the percentage of students scoring in the advanced level (scale score
of 350 and above) in reading grew from 16% to 20% for 9-year-olds. For 13-year-
old students, 10% scoring at that same level in 1972 grew to 13% in 2003.
Contrastingly, for 17-year- old students, the percentage fell from 7% to 6% (NCES,
2005).
In January of 2005, Ed Trust published Stalled in Secondary, A Look at
Student Achievement Since the No Child Left Behind Act. The report reviewed
findings in the 23 states who reported at least three years of student achievement data
and noted “…encouraging news at the early grades and disappointing progress at the
secondary level.” One of these findings was the relatively slow progress made in
high school math, for example, where only 14 states demonstrated improvement
while six states actually declined. The report also detailed how high school progress
in closing the achievement gap has been much slower than at the elementary level.
This failure is especially apparent in math where only six states narrowed the gap in
29
math achievement between White and Latino students while in eleven states, the gap
actually widened.
Student Achievement in California
Responding to the call for increased student achievement, the California
Department of Education published Second to None: A Vision of the New California
High School (1992). This report envisioned a school system with world-class
standards and world class curriculum. Ten years later, Aiming High: High Schools
for the 21
st
Century built on this theme by outlining specific strategies for
implementing a rigorous standards-based instructional program designed to increase
student achievement (CDE, 2002). These high profile reports were also concerned
with the challenge of engaging all students and promoting increased equity as an
approach to closing the achievement gap. EdSource (2002) also noted that the
highest degree of growth has occurred at the elementary level, with high school
growth being minimal. One indicator associated with this lack of progress was that
only 64% of ninth graders passed the English/Language Arts portion of the
California High School Exit Exam. Recently, it was widely publicized that in the
class of 2006, the first class required to pass the test in order to earn a diploma, more
than 47,000 seniors had yet to pass the exam (EdSource, 2006).
Ed Trust West (2004a) reported that despite huge investments made in public
education, there have been disappointing results for high schools on meeting both the
federal and state accountability targets. In their report Achievement in California –
Where are we Now?, it was noted that only 51% of California’s high schools met
30
their AYP objectives as compared with more than 75% of elementary schools. This,
despite setting modest benchmark levels for how many students must perform at
proficient levels. For the 2003-04 school year, only 11.2% in English and 9.2% in
math had to perform at that level. This disappointing showing mirrored the findings
reported earlier which noted that student achievement at the high school level
consistently lagged behind progress made in earlier grades.
Such indicators reflecting modest progress in academic achievement were
bolstered by concerns in related areas as well. For example, the Education Trust
West (2004b) published a report entitled Are California High Schools Ready for the
21
st
Century?. Among the concerns noted in the report was the failure of California
to adequately address the number of students not graduating. As of the class of
2003, fully one third of students had not earned diplomas. This situation was even
more problematic in that the graduation rate in California varied significantly by
ethnicity. The report notes a high rate of 89% for Asian students compared with
59% for African-American and 57% for Latino students. The report’s conclusions
were that (a) too few schools made sure students graduate, (b) too few high schools
made sure students took and succeeded in the right courses, and (c) too few high
schools made sure students actually learned the key skills. These findings led to
three recommendations: Schools needed to (a) make sure that all students had the
benefit of highly qualified and effective teachers, (b) make high level courses the
recommended, or “default” curriculum for all students, and (c) provide materials –
curriculum, textbooks and benchmark assessments aligned to California Standards –
31
and the instructional supports that ensure students succeed in these courses (EdTrust
West, 2004b).
The Achievement Gap
It has been well documented that American students failed to achieve at
levels comparable to their international peers, but it was also true that similar
disparities existed within this country as well. These disparities were commonly
referred to as the achievement gap and had deep roots that were very closely tied to
socio-economic status and ethnicity (Lane, 2004). While these gaps were most
prevalent in the Midwest and Northeast, they often existed even within the same
school, where middle class Black students tended to score lower on achievement
tests than middle class White students. Some of the reasons cited for this gap were
differences in:
1. Parental Involvement
2. Teacher Expectations
3. Teacher Race
4. TV
5. Test Bias
6. Curriculum
7. Opportunity to Learn
8. Stereotype threat
9. Number of Books in the home
32
Lane (2004) noted that African-American and Latino 17-year-olds do math
and read at the same levels as White 13-year-olds. In addition, these differences
played out in different graduation and college completion rates for these groups.
In addition to showing how American students fared against their
counterparts in other nations; TIMSS also provided a rich source of data supporting
the existence of an achievement gap in America, which despite some areas of
progress, has persisted and has represented a serious challenge for the country. A
review of TIMMS data detailed an obvious relationship between ethnicity and
student achievement in core academic areas. In math achievement for example, the
average scale score for fourth grade Anglo students in 2003 was 542 compared to
472 for African-American students and 492 for Hispanic or Latino students. This
same disparity was observed in eighth grade students as well where the average scale
scores for Anglo students is 525 versus 448 and 465 for African-American and
Hispanic or Latino students respectively. And while the gap has narrowed between
1995 and 2003 for Anglos and African-Americans – from 84 points to 70 – the same
cannot be said for the gap between Anglos and their Latino counterparts where the
gap remained near 50 points.
One significant area of improvement seems to be the growth made by
African-American students in mathematics achievement. TIMMS found an increase
in the average scale score for African-American eighth grade students to be on the
order of 15 points between 1995 and 2003. In addition, African-American fourth
33
graders grew 29 points from 419 to 448 during the same time period. TIMMS has
determined both of these growth figures to be statistically significant.
Socio-Economic status (SES) also appeared to be related to student
achievement in math as detailed in TIMMS. Figure 1 illustrates the steadily
decreasing achievement in math for 8th graders as the rate of free or reduced priced
lunch participation goes up. Figure 2 shows the same pattern for American students
in grade four.
Figure 1 – SES and Math Achievement in Grade 8
547
531
505
480
444
0
100
200
300
400
500
600
Average Score
Less Than 10% 10-24.9% 25-49.9% 50-74.9% >75%
Percentage of Students in Public Schools Eligible for Free or Reduced Priced Lunch

34
Figure 2 – SES and Math Achievement in Grade 4
567
543
533
500
471
0
100
200
300
400
500
600
Average Score
Less Than 10% 10-24.9% 25-49.9% 50-74.9% >75%
Percentage of Students Eligible for Free or Reduced Priced Lunch

Ed Trust West (2004) reported similar findings noting that of those schools in
California that did not meet their Annual Measurable Objectives (AMO) targets
under NCLB; the struggle was with Latino, African-American and special education
students in math. In those same schools, 97.7% of White student sub-groups met
their AMO as compared to 50.9% of Latinos and 44.3% of African-American sub-
groups. Likewise, this gap extends to lower SES student sub-groups where only
75.7% of these sub-groups met their target. Such gaps in achievement were
obscured in the design of the API system where it was common for schools to meet
their school-wide API target and not make AYP under NCLB. In fact, during the
2003-04 school year, 64% of all schools in California grew in their API enough to
35
meet their target, yet 2339 schools met API and failed to make AYP. This seemingly
contradictory circumstance was made possible by the presence of a large gap in
achievement between those achieving at high levels, and thereby driving the API
upward, and those lagging behind.
This sentiment is supported in Reaching the Top: A Report of the National
Task Force on Minority High Achievement (The College Board, 1999). The report
asserted that eliminating the achievement gap was the most important challenge in
education today and summarized factors contributing to the gap in achievement.
First, past academic success appeared to be the best predictor of future academic
success. In addition, such influences as SES status and parental education levels also
were highly correlated to academic achievement. These factors were complicated by
issues related to cultural differences and peer influences which were often
disempowering in a traditionally Eurocentric model. Correspondingly, the report
emphasized the need to reform schools in order to better meet the needs of all
students. State standards and high stakes assessments have put tremendous pressure
on schools to pay attention to the achievement of all student sub-groups and to
implement progressive strategies to ensure success for all students. While some
isolated progress has been made as noted in TIMSS, such efforts must be much more
widespread and intensive if the achievement gap is to be eliminated permanently
(The College Board, 1999).
36
Opportunity to Learn
Many have argued that the achievement gap was more accurately described
as a failure of the American educational system to provide all students with the same
opportunity to learn (OTL). This concept was identified by Marzano (2003) as the
single most important factor related to student achievement. As early as the 1960s,
OTL was described by Carroll (1963) as being characterized by differences in three
distinct areas (Tate, 2005). First, content exposure and coverage variables dealt with
the degree to which teachers covered the curriculum. As Stevenson and Stigler
(1992) noted, teachers were faced with the daunting task of covering an
overwhelmingly broad curriculum. As such, teachers regularly omitted curriculum
at their own discretion, and when different teachers omitted different topics, the
result was inevitably a learning gap. Second, content emphasis dealt with
differences in how topics were chosen within the curriculum and with how students
were selected for a curriculum based on higher level thinking skills or basic skills
instruction.
Tate (2005) noted that tracking students through ability grouping resulted in
huge disparities along racial lines. African-American and Hispanic students were
less likely to be enrolled in higher level math classes than middle class White
students. The third distinction outlined by Carroll was quality of instruction delivery
variables, which dealt with how differences in how classroom pedagogical strategies
affected student learning. This last item was supported by the widely documented
fact that in inner city schools that were disproportionately populated with
37
traditionally minority youngsters, students were taught by less experienced, under
credentialed teachers when compared with their counterparts in higher SES schools
populated with a majority of Anglo students (Klopfenstein, 2006).
And while some schools espoused approaches emphasizing a one-size fits all
approach to raising the bar, Tate’s report, Access and Opportunity to Learn are not
Accidents: Engineering Mathematical Progress in Your School (2005) details the
dangers of a “color blind” approach to education that put up barriers to math
achievement for all students. These obstacles include:
1. Persistent Tracking
2. Fewer opportunities for African-American and Hispanic students to learn
from the best qualified teachers.
3. Less access to technology,
4. Cultural discontinuity between school mathematics and the family life of
diverse student groups.

The report concluded that being open to new designs and a variety of strategies
to address the diverse needs of students was fundamental to providing equity in math
instruction and an equal opportunity for all to learn at high levels.
The Dropout Crisis
Closely related to the concept of OTL was the more widely publicized
problem of high school dropouts. It was self-evident that students couldn’t learn the
standards if they were not in school. Balfanz and Legters (2004) conducted a study
for the Center for Research on the Education of Students Placed at Risk and detailed
38
what has become common knowledge. American high schools were not working for
a large percentage of students, especially those from poor and minority families.
Almost half of all African-American students and 40% of Latino students attend high
schools where graduating was not the norm. This compares to only 11% for White
students and the problem was not getting better. Between 1993 and 2002, there was
a 75% increase in the number of schools categorized at the lowest levels of success
in promoting students from grade 9 to grade 12 on time, a high correlate of high
dropout rates. Furthermore, a majority minority school was five times as likely to
have weak promoting power as a majority White school.
The Education Trust (Hall, 2005) also recently published a document critical
of the states’ failure to acknowledge the true extent of the problem. The report noted
that, “Most states significantly understated the problems that students are facing in
finishing high school. Some states used questionable graduation-rate definitions,
while others provided no information at all about the graduation rates of the students
who are facing the biggest challenges in high schools—low-income students,
students of color, students with disabilities, and students with limited English
proficiency.” In reaction to the widely perceived and chronic under-reporting in this
area, organizations such as the Education Trust and the Harvard Civil Rights
Alliance developed a Cumulative Promotion Index (CPI), a statistical measure of
how likely it is that a ninth grader at a given school will graduate in good standing on
time in four years. The disparity between the state reported graduation rates and the
CPI was alarming. For example, for African-American students in California during
39
2002-03, the state reported graduation rate was 77% compared to the CPI rate of
55%. The results were similar for Latino students whose rates were respectively
81% and 57%. These large differences represented a huge discrepancy between
what was being reported by the states and what was most likely to happen to actual
students in the public school system. Further, when Ed Trust compared state
reported graduation rates to CPI rates across the nation, they found that in almost
every case the disparity was bigger for students of color than it was for Whites.
The Importance of Achievement in Mathematics
As early as 1973, the literature was beginning to focus on the critical nature
of mathematics as a precursor to future success. Sells (1973) called math “The
critical filter” and noted that achievement in math was linked to access to higher
paying prestigious occupations. TIMSS and other studies have subsequently
demonstrated how the performance gap in math achievement represents an especially
important problem in many respects. As Figures 1 and 2 above illustrate, there
appeared to be a significant relationship between SES and math achievement.
Ethnicity also appears to be related to math achievement. Figure 3 below
demonstrates large disparities in the quality of teaching being provided to low-
income schools and points out a growing area of concern.
40
Figure 3 – Classes Taught by Under-Qualified Teachers
25
40
14
20
19
31
16
18
0
5
10
15
20
25
30
35
40
45
50
Percentage
Math Science English Social Science
Subject Matter
Less Than 20% Free Lunch Greater than 49% Free Lunch

These facts are troublesome in consideration of a study done by Rose and
Betts entitled Math Matters: The Link Between High School Curriculum, College
Graduation and Earnings. Like Sells, the authors noted a strong correlation between
the highest level of math taken by students and indicators of future success such as
annual earnings and degrees earned. For example, 73% of students studied who had
taken calculus had earned a bachelor’s degree as opposed to only 6% of students
whose highest level of math was pre-algebra. The rate of those earning bachelors
degrees increases as the rigor associated with their highest math class taken
increases. For those whose highest math class was algebra or geometry, 13% earned
their bachelors degree, and for those taking intermediate algebra, the rate increased
41
to 34%. Those taking advanced algebra demonstrated even more success, with 55%
earning a bachelors degree.
Rose and Betts also showed that students whose highest math class taken was
pre-algebra earned $10,000 less per year in 1999 dollars than their counterparts who
had taken Calculus. Like the data collected on degrees earned noted above, the rate
of earnings increased steadily with the rigor of the highest math class taken. In the
example cited, this translated into an annual income difference of more than 40%
between the two groups. Because of this strong relationship, the authors studied how
well math curriculum explained the difference in earnings relative to ethnicity and
SES. For the group studied, the gap in earnings between Anglos and their Black or
Latino counterparts was almost entirely explained by demographic features such as
parental income and education levels. It was important to note however, that this
study revealed that math curriculum explained about one fourth of the difference in
earnings between the lowest socio-economic group and those in the middle class.
More importantly, it explained almost entirely the gap between those in the next to
the lowest SES group and those in the middle class.
The findings noted above demonstrated that math achievement was especially
important for urban youth. This point was further emphasized in a 1997 White paper
published by the United States Department of Education entitled Math Equals
Opportunity. Then Secretary of Education Richard Riley detailed the importance of
taking rigorous math, especially for lower income students saying, “In fact, the
42
benefit of taking rigorous courses is greatest for students of low-income families.”
Among the USDE’s (1997) most important findings were:
1. Students who take rigorous mathematics and science courses are much more
likely to go to college than those who do not. Data from the National
Educational Longitudinal Study (NELS) reveal that 83% of students who
took Algebra I and geometry went on to college within two years of their
scheduled high school graduation. Only 36% of students who did not take
Algebra I and geometry courses went to college. While nearly 89% of
students who took chemistry in high school went to college, only 43% of
students who did not take chemistry went to college. (p.5)
2. Algebra is the “gateway” to advanced mathematics and science in high
school, yet most students do not take it in middle school. Students who study
algebra in middle school and who plan to take advanced mathematics and
science courses in high school have an advantage: approximately 60% of the
students who took calculus in high school had taken algebra in the 8
th
grade.
However, 1996 NAEP data reveal that only 25% of U.S. 8th graders enrolled
in algebra, and that low-income and minority students were even less likely
to take algebra in the 8th grade. (p. 5)
3. Taking rigorous mathematics and science courses in high school appears to
be especially important for low income students. Low-income students who
took Algebra I and geometry were almost three times as likely to attend
college as those who did not. While 71% of those who took Algebra I and
43
geometry went to college, only 27% who did not take those courses went on
to college. By way of comparison, 94% of students from high-income
families, and 84% of students from middle-income families who took
Algebra I and geometry in high school went on to college. Sixty percent of
students from high-income families and 44% of students from middle-income
families who did not take Algebra I and geometry went to college (pp. 5-6).
4. Despite the importance of low-income students taking rigorous mathematics
and science courses, these students are less likely to take them. Students from
higher-income families are almost twice as likely as lower-income students to
take algebra in middle school and geometry in high school. They are more
than twice as likely to take chemistry (p. 6).
5. Mathematics achievement depends on the courses a student takes, not the
type of school the student attends. Students in public and private schools who
took the same rigorous mathematics courses were equally likely to score at
the highest level on the NELS 12th grade mathematics achievement test.
Students whose parents are involved in their school work are more likely to
take challenging mathematics courses early. Students whose parents were
involved in their education were more likely to take courses like algebra and
geometry in the 8th and 9th grade than students whose parents were not
involved (p .6).
44
Implications for the Future
Juan Enriquez of the Harvard School of Business recently emphasized the
implications of failing to educate America’s students adequately in math and science
in a speech delivered to the general assembly of the California School Boards
Association (CSBA, 2005). Enriquez spoke passionately and eloquently about the
importance of increasing the quality of math and science education and attracting
minority youngsters into these fields before they entered college. His sense of
urgency was stoked by his research into the critical importance math and science
skills had in a knowledge-based economy. In earlier works, Enriquez (2001)
detailed the strong link between a nation’s wealth and the ability it has to generate
new patents in high tech fields such as biotechnology and engineering. He described
potentially disastrous effects for the nation if it shrinks from the challenge of
adequately educating the fastest growing minority group in the country – Hispanics.
This challenge was made especially difficult since that same group has
historically been disinterested in math or science-related fields in college. As Figure
4 demonstrates, Hispanics represented the fastest growing portion of the U.S.
population moving from just under ten percent to over sixteen percent in 2000.
Enriquez noted that unless the U.S. found a way to encourage more students of color,
especially Hispanics, to enter math and science-related fields, America faced a future
where its competitive advantage would be threatened by a failure to produce
sufficient numbers of engineers and other high tech professionals capable of
45
producing the knowledge and patents necessary to fuel the economy and move the
nation forward.
Figure 4 – United States Census Data: Ethnic Distribution 1986 to 2000
70.4
61.2
16.1
17.2
9.9
16.3
2.8
4.1
0.9 1.2
0
25
50
75
100
Percent of Population
White Black Hispanic Asian/Pacific
Islander
Native
American
Ethnicity
1986 2000

In his book As the Future Catches You, Enriquez (2001) illustrated this
danger by contrasting the developing economies of Malaysia and Singapore.
Malaysia’s leader was warned in the mid 1970’s that many of its most highly
educated residents, many of whom were Indian and Chinese, were leaving the
country. The Malaysian government’s reaction was indifferent at best.
Contrastingly, Singapore made a conscious choice to focus its educational challenge
on developing world class engineers by focusing on making the implementation of a
rigorous mathematics curriculum a national priority. Whereas Malaysia had once
46
been a far wealthier nation, it now ranked a dismal 82
nd
in the world in wealth per
person compared to Singapore’s rank of 9
th
in the world (Enriquez, 2001).
State and National Reform Efforts

In response to concerns about the quality of public education in California
and in the nation, numerous organizations have studied how best to address the
deficiencies noted above. These studies resulted in a strong body of research upon
which practitioners were able to draw. Among these reports was West Ed’s High
School Reform, National and State Trends (2005) which synthesized research in the
field and identified key strategies most likely to yield positive results. Among the
agencies whose research was included in the report were: Achieve Inc., Education
Trust, Gates Foundation, National Association of Secondary School Principals
(NASSP), California Department of Education, and the Legislative Analysts Office.
West Ed identified three major themes that arose from the vast compilation of
recommendations. They were:
1. Strengthen systemic incentives to raise student performance
2. Increase faculty and student supports for learning
3. Redesigning school programs and structures.

It was not surprising then, that State and national efforts to improve student
achievement in high schools focused on improving curriculum and instruction,
increasing accountability through standards and assessments, and redesigning
America’s schools to better serve students.

47
Curriculum and Instruction

Improving curriculum and instruction was a complicated matter made more
challenging by the vast diversity of America’s schools. Efforts to do so however,
included requiring more rigorous coursework, implementing state-wide content
standards and aligning standards and assessments with post secondary expectations.
The California Department of Education (CDE) reported that students with test
scores in the lowest quartile learned more in academically rigorous courses than they
did in “either lower level vocational courses or non-college prep courses in which
they are traditionally enrolled.” Coupled with the finding that students were more
likely to pass rigorous courses than lower level courses, CDE reported that for
schools which sought to improve student achievement, it was prudent to enroll as
many students as possible in more challenging coursework. Finally, CDE reported
that students who were expected to master more rigorous content were more
persistent, achieved at higher levels and were better prepared to enter the world of
work (CDE, 2005).
The implementation of content standards represented one of the primary
strategies states have used to respond to the call for increasing the rigor of their
curriculum. In 1994, the federal government added emphasis to this movement
through the Goals 2000 Act and through a revision of the Title I program (Klein,
2005). In 1996, educators and business leaders convened a summit designed to
respond to the public demands for increased student achievement and called for
“New World-Class standards.” By 1998, 47 states had developed content standards
48
in mathematics. The Fordham Foundation contributed to the movement by
publishing studies in 1998 and 2000 in which they reviewed and reported on the state
of state content matter standards in math. States continued to revise their standards,
and in 2001 the NCLB Act mandated what had previously been encouraged – states
must have content standards in math. NCLB also raised the bar by making 100%
proficiency the goal and by making federal funding contingent upon making progress
towards that lofty aim. The Fordham Foundation (Klein, 2005) once again published
a report on The State of State Math Standards and found that while many states had
generally weak standards, California was not one of them. California’s standards in
math earned high marks and were called, “Worthy of emulation.” Reeves (in
DuFour, 2005) supported rigorous standards, despite the existence of flaws and noted
that while many standards in their present form required substantial revision, content
standards were an important way to address fundamental issues of equity. In the
absence of objective standards, schools were likely to return to the bell curve and the
“destructive process of evaluating student performance based upon who beat whom.”
Increased Accountability

The effort to increase accountability in American public education was
perhaps best exemplified in the requirements associated with NCLB as noted earlier.
NCLB had two dominant components that effectively raised the bar for school
systems across the nation. First, public schools were required to verify that every
student was performing at a proficient level in core academic areas by the year 2014.
As a part of this mandate, schools were required to demonstrate Adequate Yearly
49
Progress (AYP) towards 100% proficiency in order to remain in good standing with
the federal government. Schools and districts that failed to make their AYP
benchmarks were labeled as Program Improvement schools and were subject to
increasingly intrusive interventions ranging from mandated staff changes such as the
removal of the school’s principal to curricular program changes and eventual
takeover by the state (USDE, 2002).
The second major accountability provision under NCLB was the Highly
Qualified Teacher (HQT) provision which was designed to ensure that every student
in America was taught by a Highly Qualified Teacher. Teachers in core academic
areas were required to be HQT compliant by the end of the school year in 2007.
Teachers earned HQT compliance primarily by demonstrating subject matter
competency. This was done via a university major, earning 32 units in a given
subject area, passing the appropriate subject matter exam or through a Highly
Objective Uniform State Subject Evaluation (HOUSSE). The HOUSSE process
involved documenting a combination of units earned, staff development taken,
experience teaching the subject, leadership roles, teacher lesson observation and
portfolio development. Districts not complying with the HQT provisions of NCLB
may ultimately face sanctions including a loss of part or all of their federal funds
including Title I (CDE, 2004).
In California, accountability measures were also in place to support NCLB.
As a part of California’s Public Schools Accountability Act of 1999, the Academic
Performance Index (API) was developed as a measure of a school’s progress in
50
improving student achievement. It was a value-added system with an ultimate goal
that required a minimum score of 800 for all schools. Schools received their API
score based on a formula comprised mainly of standardized test results and were
required to improve 5% annually relative to the difference between their current API
score and 800. Schools already scoring 800 or above are required to improve by at
least 1 API point per year. The API system places enormous pressure on school and
district leadership since there are little or no consequences built into the system for
those most responsible for teaching and learning – teachers and students (CDE,
2005a).
California addressed this glaring flaw by introducing a strong element of
accountability for students when it implemented the California High School Exit
Exam (CAHSEE). The CAHSEE faced numerous delays and challenges, most
recently in the Valenzuela v. O’Connell case. Students challenged the validity of the
CAHSEE on the grounds that students of color and low socio-economic status are
being taught by under qualified teachers and that California was “ill equipped to
adequately prepare its students to take the exam” (Wright, 2006). These challenges
were decided, however, in favor of accountability for students in the May 2006
California Supreme Court decision upholding the enforceability of the CAHSEE in
the Valenzuela case.
Another layer of accountability in California was the provision that each
public school in California was required to publish an annual accountability report
card that detailed for the public key facets of the school’s operations. The School
51
Accountability Report Card (SARC) requirement began as a mandate under
Proposition 98 in 1988 and required schools to report on such things as their AYP
status under NCLB, graduation rates using a federally mandated formula, and HQT
compliance rates.
In addition, a more recent requirement focusing on the equitable allocation of
resources forced school districts to break out financial data on teacher salaries by
site. This new requirement was aimed at addressing the concern that schools in
lower SES areas generally received fewer resources than their counterparts in more
affluent areas, including the investment represented by teacher salaries. Since most
teacher salary schedules in California grant higher pay to those with more experience
and advanced degrees, it stood to reason that disparities in experience and
presumably knowledge would be exposed in the amount of money expended on
teacher salaries at each site. These new requirements represented a trend in
accountability that was not likely to cease any time soon and represented attempts to
ensure equity in public education. It was likely that accountability for districts,
schools, staff and students would continue to play an important role in the efforts to
improve student achievement (CDE, 2006c).
New School Designs

Responding to the need for comprehensive high school reform, efforts were
made to develop new school designs that focused on student achievement and related
school features. Marsh and Codding (1998) identified five basic elements for such
designs including (a) school cultures, (b) smaller school size, (c) quality learning
52
activities, (d) student performance assessments, and (e) strong curriculum
foundation. These five elements were based on a strong foundation of research,
much of which began in the late 1970’s with Ron Edmonds, who along with other
researchers of the decade identified (a) strong administrative leadership, (b) an
emphasis on basic skill acquisition, (c) high expectations for student achievement,
(d) a safe and orderly environment, and (e) frequent monitoring of student progress
as the most important school level factors affecting student achievement (Marzano,
2003).
New school designs were strongly influenced and supported by this research
and later findings such as those of Levine and Lezotte (1990) who used an analysis
of case study data from the top 25% of schools to produce their own list of school
level factors affecting student achievement. These factors included: (a) climate and
culture, (b) focus on central learning skills, (c) appropriate monitoring of skills, (d)
practice-oriented staff development, (e) strong leadership, (f) parental involvement,
(g) high expectations, and (h) effective instructional arrangement and
implementation.
A decade later, Sammons, Hillman and Mortimore (1995) used more
quantitative methods to arrive at a similar list of indicators that included (a)
professional leadership, (b) a focus on teaching and learning, (c) shared vision and
goals, (d) a learning environment, (e) high expectations, (f) positive reinforcement,
(g) monitoring progress, (h) pupil rights and expectations, (i) home-school
partnerships, and (j) being a learning organization. While these studies were well
53
received and provided a solid basis for future literature and studies, Scheerens and
Bosker (1997) relied on an even more rigorous process and arrived at a rank order
list of school level factors in terms of their degree of impact on student achievement.
Scheerens and Bosker found that the following factors were most effective, in order:
1. Time to cover the material
2. Monitoring the progress of students
3. Pressure to Achieve
4. Parental Involvement
5. School Climate
6. Content Coverage
7. School Leadership
8. Cooperation.
In 2000, Marzano worked to reanalyze the data and refine the work of
Scheerens and Bosker and published the following rank order list:
1. Opportunity to Learn
2. Time
3. Monitoring
4. Pressure to Achieve
5. Parental Involvement
6. School Climate
7. Leadership
8. Cooperation
54
School Cultures - Professional Learning Communities
Identifying the school level factors that effected student achievement
represented only part of the answer to school improvement, however. Fortunately,
many educational reformers have begun the process of designing and implementing
new school designs that incorporated the elements of effective schools identified by
Marsh and Codding in ways that positively impacted student learning. One of the
most promising of these approaches involved the transformation of traditional high
schools into Professional Learning Communities (PLCs). PLCs were designed to
attack the challenges inherent in large high schools by increasing rigor, raising
expectations, and providing strong support networks that would prevent students
from “falling through the cracks.”
PLCs focused on how adults behaved when students failed (DuFour, 2004).
Consistent with raising expectations for students by increasing academic rigor, PLCs
made it more difficult for students to fail by increasing interventions and support in a
myriad of ways detailed in further sections of this chapter.
School Size - Smaller Learning Communities
Another way school leaders worked to address the need to reform high
schools involved the implementation of SLC’s. The Bill and Melinda Gates
Foundation led the way in advocating for the need to redesign today’s large
impersonal high schools. “Today’s large impersonal high schools were designed for
a different era and a different economy, and they are leaving far too many young
people behind.” So began the Gates Foundation Report High Schools for the New
55
Millennium (n.d.). The report highlighted that America’s high schools (a) allowed
one quarter of students to read below proficient levels, (b) failed to graduate 30
percent of their students and (c) prepared far fewer low income than high income
students for college. In response, they advocated for increased academic rigor,
personalization, and relevance for students. SLC’s took many forms but generally
were designed to accommodate fewer students than traditional settings thereby
helping teachers and administrators make more meaningful connections with
students.
Breaking schools down into smaller units was not a new endeavor, however,
and Oxley’s analysis (2005) of the research associated with SLC’s noted a long
history of such efforts. In the 1960’s the effort was referred to most commonly as
creating houses and schools within schools. In the 1970’s magnet schools and mini-
schools were the terms of the decade and in the 1980’s and 1990’s they were known
as charter schools and now, smaller learning communities. While each movement
had nuances distinct form the rest, at their core, they attempted to produce more
personalized and relevant learning experiences for students. Most recently, the
emphasis turned to the collaborative nature of the work of students and teachers,
hence the use of the term communities.
Gregory (2000) also summarized the research in the field which has noted
several areas where smaller schools appear to be beneficial. These included:
1. The likelihood that large schools experience more violence.
(Kaufman, Choy, Chen, et. al., 2000)
56
2. Schools between 600 and 900 produced the highest achievement (Lee
and Smith, 1996).
3. Those students who had the most trouble with school, including poor
and African-American students, benefited most from small high
schools (Friedkin and Necochea, 1988).
4. In New York City, smaller high schools cost slightly less per graduate
than larger schools with much higher dropout rates. (Robertson 1995).
5. In Chicago, student achievement, persistence, and performance were
stronger in small schools. Students in these schools had better
attendance rates, significantly lower dropout rates, and higher grade
point averages than did students in larger schools (Wasley, et. al.,
2000).
Oxley (2005) emphasized how small structure and curriculum and instruction
were mutually supportive elements of the practice (Cuban 1986; Eisner, 1988).
Implementation was critical to the success of SLC’s and was often left incomplete
(Oxley, 2001). Oxley (2005) also reported that Cotton (2001) identified five key
elements to gauge the successful implementation of an SLC. First, SLC’s must have
a level of self-determination. SLC’s also benefited from developing a self-identity
characterizing their vision and unique characteristics. Third, SLC’s had an increased
level of personalization that allowed teachers to respond to students’ particular
strengths and needs. Teachers in SLC’s were leaders. They took responsibility for
57
the education of their students and hade the authority necessary to do so. Finally,
assessment data was used for accountability of both students and the SLC in general.
Learning Activities
Marsh and Codding’s (1999) concept of learning activities referred to those
school-wide efforts associated with challenging students to think by implementing a
rigorous and relevant curriculum. It involved posing real world problems and
working to develop a culture of inquiry and collaboration. Blasé and Blasé (2004)
reported finding five common attributes of successful PLCs that addressed these
critical aspects:
1. Supportive and shared leadership where principals and teachers
shared leadership roles and decision making.
2. Shared values and vision. Principals and teachers worked together to
identify a powerful, yet practical view of a school vision based on
common values and beliefs.
3. Collective learning and application of what has been learned.
Teachers and Administrators worked to respond to what they learn
when student achievement data is analyzed.
4. Supportive conditions that foster collaboration and problem solving.
5. Sharing of professional practice where peer review of instructional
practices was commonplace.

58
Student Performance Assessments
Student performance assessments were an essential part of the Marsh and
Codding (1999) model of newly designed schools for several reasons. First
assessments linked to standards worked to improve student performance by
providing them with opportunities to demonstrate their level of understanding.
Teachers were likewise encouraged to provide assessments that measured not
whether a student performed at the national average, but whether they had mastered
the standard. Second, using standards-based assessments to gauge student
performance was seen by teachers as an invaluable professional development
opportunity. Such assessments also provided a sense of equity to educators and
parents alike, who were now assured that expectations for students at one school
were the same for students across the town.
Standards-based assessments were also supported by a second major
characteristic of successful PLCs as described by DuFour (2004) - a culture of
collaboration. Breaking down the isolation that was so often the norm for high
school teachers was essential for PLCs. One way PLCs did this was by forming
teams of teacher leaders who worked to develop common assessments and rubrics
for evaluating levels of student achievement; review student work and establish
common goals. These teams differed from common committees present on high
school campuses today in that they focused on improving classroom practice above
all else. Key to this effort was making public what was traditionally private.
59
Curriculum Foundations
Effective school designs changed the curriculum to one that was more
student-centered in different ways. First, relevance was key and could be achieved
through career and technical education and high interest academies. In addition,
student learning outcomes became the essential focus of these newly designed
schools. DuFour (2005) affirmed these findings in his book On Common Ground;
The Power of Professional Learning Communities in which he identifies “Big Ideas”
associated with PLCs. First, PLCs were formulated with the idea that the primary
mission was not that every student was taught, but that every student would learn.
This was an important distinction and represented a departure from commonly held
belief systems and entrenched cultures where teaching was the constant and learning
was the variable. DuFour emphasized the role of PLCs in reversing this trend by
establishing a new culture where high levels of learning become the given and
teaching had to be adjusted to ensure such an outcome. PLCs relied on intervention
as opposed to remediation. They acted quickly to identify students at risk of failing
and did not leave it up to students to seek help, but mandated that the student
participate in the most appropriate intervention likely to help the student succeed.
The primary difference was in the timeliness of the response and on the willingness
of adults to accept the responsibility for student learning.
Successful PLCs fostered a more effective curriculum by building teams of
teacher leaders who worked collaboratively to develop common assessments and
rubrics. Marzano (2003) also pointed out the need to pay attention to the gaps
60
between the intended curriculum (formal curriculum), the implemented curriculum
(what the teacher actually teaches) and the attained curriculum (what the students
learn) (Marzano, 2003). This was consistent with DuFour’s emphasis on student
outcomes as opposed to teacher behaviors. PLCs responded to student need by
focusing on results. Teachers worked in teams to assess student achievement data in
light of comparative norms school-wide and state-wide. They reflected on areas of
concern and developed ways of improving individual instruction and collective
capacity. They avoided making excuses for poor student performance and embraced
unfavorable data as a way to grow professionally and improve the quality of
education they provide. PLCs worked at refocusing their attention away from
school-wide issues like discipline and morale and instead, paid attention to goals that
affected student learning. Effective PLCs focused on results by assessing their own
success, not based on what interventions they had implemented, but by how much
student learning had improved as evidenced by the data. The key, again, was to
focus on what students learned, not what adults taught (Dufour, 2004).
The Elements of Effective Math Instruction
As schools sought to redesign themselves in ways that facilitated increased
rigor and greater personalization, they also had to recognize the need to strengthen
teaching and learning in mathematics more specifically. This required a greater
understanding of the elements of effective mathematics instruction including
rigorous content standards, effective pedagogy, and meaningful professional
development.
61
Rigorous Content Standards
Effective mathematics instruction began with a strong curriculum aligned to
content standards. Former state Superintendent of Public Instruction Delaine Easton
displayed her understanding and support for this concept in her introduction to the
California Content Standards publication (CDE, 1997). Easton noted that the era of
reform began in response to A Nation at Risk proclaiming the dangers of “A rising
tide of mediocrity.” Further, she described three relevant characteristics that make
standards such a powerful tool in the effort to improve math instruction. First, she
proclaimed, “Standards are a bold initiative.” Implementing content matter
standards in math helped California move beyond reform and into competition with
the best educational systems in the world by adding an element of rigor that was seen
as “rigorous,” and “firm, but not unyielding.” In addition, standards set a benchmark
for student achievement at high levels by allowing for local control and classroom
creativity. “Standards describe what to teach, not how to teach it.” Finally,
standards were important to improving math instruction because they represent an
enduring commitment, not a passing fancy. They should be seen not as a new layer,
but as the foundation. (Easton, 1997).
The goal of California’s mathematics educational program, as communicated
in the standards had six basic parts:
1. Develop fluency in basic computational skills
2. Develop an understanding of mathematical concepts
62
3. Become mathematical problem solvers who can recognize and solve
routine problems readily and find ways to reach a solution or goal
when no routine path is present.
4. Communicate precisely about quantities, logical relationships, and
unknown values through the use of signs, symbols, models, graphs
and mathematical terms.
5. Reason mathematically by gathering data, analyzing evidence, and
building arguments to support or refute hypotheses
6. Make connections among mathematical ideas and between
mathematics and other disciplines.

These goals represented an important point of reference in today’s
confrontational climate where educators and researchers feuded openly about the
nature and emphasis of mathematics instruction. These feuds were referred to in the
literature as the Math Wars and pitted those who favored a strong emphasis on
building foundational level skills as a necessary part of mathematics fluency and
those who espoused a more conceptual approach to math. The goals cited above
represented a combination of these factors. Those responsible for crafting the
introductory part of the California standards publication apparently recognized the
nature of this dispute and attempted to incorporate strong elements of basic skills and
procedures with an emphasis on higher level thinking and mathematical concepts.
This balanced approach is evidenced in the following statement made in the
introduction to the standards, “The standards emphasize computational and
63
procedural skills, conceptual understanding, and problem solving. These three
components of mathematics instruction and learning are not separate from each
other; instead, they are intertwined and mutually reinforcing.” Further, the standards
indicated that students should practice basic skills sufficiently to commit them to
memory and know how and when to apply them. This is not to mean that
commitment to memory of procedures is an end unto itself. The standards also
emphasized that students must be able to apply their skills to real world problems. In
part, the standards indicate, “Schools that utilize these standards “enroll” students in
a mathematical apprenticeship in which they practice skills, solve problems, apply
mathematics to the real world, develop a capacity for abstract thinking and ask and
answer questions involving numbers and equations” (CDE, 1997).
In high school the math standards for Algebra I served an important function.
First, Algebra I was a primary gatekeeper course for access to the higher level math
classes linked to future success as noted earlier in this review. In addition, Algebra I
content standards formed an important part of the mathematics portion of the
CAHSEE which many students had difficulty passing. The Algebra standards
communicated the following goal:
Symbolic reasoning and calculations with symbols are central in Algebra.
Through the study of Algebra, a student develops an understanding of the
symbolic language of mathematics and the sciences. In addition, algebraic
skills and concepts are developed and used in a wide variety of problem
solving situations (CDE, 1997).
64
This goal was supported by a comprehensive set of 25 objectives (see
Appendix A) that focused on procedures and manipulation of formulas despite the
balanced approach outlined in the introduction. They reflected a clear bias towards
procedural knowledge as opposed to conceptual understanding. In reaction to this
bias, the National Council of Teachers of Mathematics (NCTM) developed its own
Algebra Standards for grades 9-12. These standards were almost entirely conceptual
in nature. Figure 5 details standards in Algebra developed by the state versus those
developed by NCTM.
Figure 5 – A Comparison of Algebra Standards and their Emphases
California Standards (Procedural) NCTM Standards (Conceptual)
3.0 Students solve equations and
inequalities involving absolute
values
Understand the meaning of equivalent
forms of expressions, equations,
inequalities, and relations.
4.0 Students simplify expressions
before solving linear equations and
inequalities in one variable such as
3(2x-5)+4(x-2)=12
Use symbolic algebra to represent and
explain mathematical relationships.
9.0 Students solve a system of two
linear equations in two variables
algebraically and are able to
interpret the answer graphically.
Students are able to solve a system
of two linear inequalities in two
variables and to sketch the solution
sets.
Judge the meaning, utility, and
reasonableness of the results of symbol
manipulations, including those carried
out by technology.

10.0 Students add, subtract, multiply
and divide mononomials and
polynomials. Students solve mutli-
step problems including word
problems by using these techniques
Identify essential quantitative
relationships in a situation and determine
the class or classes of functions that
might model the relationships
14.0 Students solve a quadratic equation
by factoring or completing the
square
Draw reasonable conclusions about a
situation being modeled
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Effective Instructional Practice

Understanding what constituted effective instructional practice began with a
discussion of the prevailing culture of math instruction in America. Kinard (2006)
noted that this culture was best exemplified by three basic characteristics. First,
there was an overwhelming effort to cover expansive amounts of content. This
dynamic had serious side effects including anxiety on the parts of teachers who felt
pressured to cover each of the content standards in their course. Such efforts were
made even more difficult in the face of district-wide benchmark assessments that
required material to be covered by pre-determined deadlines.
A second characteristic of American mathematics instruction was a focus on
product rather than process. Kinard’s theory in this regard was supported by the
earlier review of California’s content standards and TIMMS findings detailing how
much time was spent in American math classrooms on various activities. The
TIMMS Videotape Classroom Study (Stigler, 1999) examined classroom teaching
strategies and time on task and found that American students were likely to spend
about 37% of a given lesson sharing homework assignments and another 25% of the
lesson actually working on homework. With a total of 62% of lesson time used in
this way, little time was left to develop deeper understanding of the concepts being
taught.
Kinard’s third premise was that mathematics instruction in America focused
too much on mechanics and algorithm as opposed to developing concepts. This idea
was also supported by TIMMS where it was demonstrated that higher performing
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countries spent considerably more time developing concepts than did their American
counterparts. Figure 6 illustrates how little time American classrooms spent on
developing concepts. This finding was not surprising given the stated goals of
teachers for their respective lessons. Figure 7 shows that American teachers
emphasized critical thinking in mathematics far less than their counterparts in
Germany and Japan, where the emphasis was more on thinking than on skills.
Figure 6 – Performance Expectations During Seat Work
89.2
6.3
4.5
42.5
13.8
43.8
94.9
4.9
0.2
0
10
20
30
40
50
60
70
80
90
100
Mean %
Germany Japan U.S.
Practice Procedure Apply Concept Invent/Think

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Figure 7 – Teachers’ Goals for Their Lessons
55
31
25
73
61
22
0
10
20
30
40
50
60
70
80
% of the Lesson
Germany Japan U.S.
Skills Thinking

Dieckman and Montemayor (2004) reviewed research into effective math
instruction, and noted that the predominant practice in math instruction contributed
to student failure in math since it involved “rote learning of patterns rather than
seeking reasons and explanations; requiring students to “just follow along” with
procedures that seemed arbitrary and did not engage their critical thinking; ignoring
student attempts to make connections across ideas; and prescribing to the theory of
“no pain, no math gain.” This point of view was also supported by the research of
Kinard noted above. The elements found by Dieckman and Montemayor to be
“ingredients for success” in math instruction were:
1. Students’ natural curiosity was a powerful hook for experimentation
and discovery.
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2. Establishing mathematics as fundamentally relevant reduced students’
perception of math as arbitrary and ultimately, unknowable.
3. Students created and explained various chains of mathematical
reasoning.
4. Interactive and dynamic lessons entailed the serious consideration of
all student responses and explanations.
5. Students found learning rewarding and energizing and were self-
motivated to continue exploring.
Specific to English Language Learners, the following elements were
identified as helpful in deepening their mathematical understanding:
1. Content, language, and meta cognition were integral to instruction
(Echeverria, Short, and Voght, 2003)
2. Clearly understood visuals and universal shapes were used to explore
concepts, irrespective of language ability.
3. Group conversations exploring math concepts developed both basic
informal communications skills and cognitive academic language
proficiency (Cummins, 1986).
Achieving these goals required carrying out the curriculum creatively and
using multiple approaches and methodologies. Teachers in effective math classes
involved all students in higher order thinking skills and conversations. They
acknowledged contributions made by the students and encouraged students to make
connections that were meaningful to them and their lives. These strategies
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presupposed the essential element of equity as outlined by NCTM which includes
three critical aspects; (a) high expectations and worthwhile opportunities, (b)
accommodating differences to help everyone learn math, and (c) resources and
support for all classrooms and all students (NCTM, 2000).
Model Math Programs
Identifying model math programs in light of the animated and sometimes
rancorous debate described above was somewhat problematic. In March 1994,
President Clinton signed Public Law 103-227, which included Title IX, the
“Educational Research, Development, Dissemination, and Improvement Act of
1994.” This legislation restructured the Office if Educational Research and
Improvement and empowered it to conduct a wide range of activities and research
with the goal of improving education in America. It also established two pilot expert
panels including one on math and science education. This panel was composed of 15
experts in math or science from around the nation and their primary task is to help
identify model programs in math and science. Towards that end, the panel
established criteria and procedures to be used in the submission and review of
programs wishing to be considered for this distinction. The criteria were as follows:
1. The program’s learning goals were challenging, clear, and appropriate
for the intended student population.
2. The program’s content was aligned with its learning goals, and was
accurate and appropriate for the intended student population.
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3. The program’s instructional design was appropriate, engaging and
motivating for the intended population.
4. The program’s system of assessment was appropriate and designed to
inform student learning and to guide teachers’ instructional decisions.
5. The program could be successfully implemented, adopted, or adapted
in multiple educational settings.
6. The program’s learning goals reflected the vision promoted in
national standards in mathematics education.
7. The program addressed important individual and societal needs.
8. The program made a measurable difference in student learning.
Programs could be identified as promising for no more than five years, at
which point they must meet a more rigorous set of criteria in order to be identified as
exemplary, or be removed from the promising list. Being identified as exemplary
meant providing convincing evidence of effectiveness in multiple sites with multiple
populations in relation to two of the following indicators:
1. The program had evidence of gains in students’ understanding of
mathematics.
2. The program had evidence of gains in inquiry, reasoning, and
problem solving skills.
3. The program had evidence of improvement in course enrollments,
graduation rates, and post secondary school attendance.
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4. The program had evidence of narrowing the gap in achievement or
accomplishment between disaggregated groups.
5. The program had other evidence of effectiveness or success.
In 1999, the USDE released a list of 10 promising and exemplary math
programs that met the criteria outlined above. The "exemplary" programs announced
by the Department of Education were:
1. Cognitive Tutor Algebra
2. College Preparatory Mathematics (CPM)
3. Connected Mathematics Program (CMP)
4. Core-Plus Mathematics Project
5. Interactive Mathematics Program (IMP)
The "promising" programs were:

1. Everyday Mathematics
2. MathLand
3. Middle-school Mathematics through Applications Project (MMAP)
4. Number Power
5. The University of Chicago School Mathematics Project (UCSMP)
The process of identifying promising math programs continued and in 2000,
the USDE identified two more promising math programs. One of these two was
most relevant to this study in that it applied directly to the issue of high school level
algebra. The I CAN Learn program was a computerized algebra curriculum that is
designed to be responsive to help ethnically diverse inner city youth in grades 7-10.
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Student proficiency in problem solving was a primary goal. The program was seen
as especially valuable in its ability to encourage women and students of color to
become more interested in mathematics and in its balanced approach to teaching
mathematical procedures early and accurately. The program made use of discussion
and collaboration as well as allowing multiple approaches to solving the problems
posed. Reviewers of the program found statistically significant pre-post test gain
scores for participating students and that they performed better than the control
group on standardized tests by a statistically significant margin.
Building the Capacity for Growth
If schools are to effectively address the immense challenges they face in
ways that result in sustained improvement of student achievement, they must work to
build local capacity for improvement, and be supported by new policies, initiatives
and designs. The elements of effective school design discussed earlier relied on the
solid support provided by policies that empowered schools to undertake reform
initiatives. The National Association of Secondary School Principals (NASSP)
recently issued a set of eight federal legislative recommendations for supporting high
school reform. Published in their report entitled Advancing High School Reform in
the States: Policies and Programs (2005), NASSP advocated for legislative support
in the following areas:
1. Increased academic rigor that reflects the integration of curriculum
instruction and design.
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2. Personalized instruction that is based on the academic needs of the
individual student
3. Targeted strategies to raise achievement scores of low performing
students to grade-level proficiency.
4. School-wide initiatives to improve reading and writing literacy
5. Multiple assessments that are aligned with state standards and include
performance-based measures to provide schools with individual
student data to improve teaching.
6. Collaborative, inclusive leadership and strategic use of data
7. Improved subject area competency and content pedagogy of current
and incoming faculty members.
8. Technical assistance for high schools identified as in need of
improvement.
It was not surprising that the concepts supported by NASSP were
predominately concerned with site level functions given the constitution of the
group’s membership. It was worth noting however, how consistent these
recommendations were with concepts associated with new school designs, especially
PLCs.
The Education Trust and the Heritage Foundation reported on high poverty
and high performing schools and while critical of the liberal definition of success
used in the studies that initially identified schools as successful, Harris (2006)
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confirmed the usefulness and importance of policy and accountability. Among the
recommended policy implications were that:
1. Policy makers continue the recent focus on measurable student
outcomes, such as test scores, but redesign policies to hold educators
accountable only for those factors within their control.
2. Policy makers take a comprehensive approach to school improvement
that starts in schools but extends into homes and communities, and
addresses basic disadvantages caused by poverty.
3. All educational stakeholders acknowledge that educational inequity is
caused by problems in both schools and communities—and avoid
trying to blame the problem on schools alone.
These concepts were equally consistent with PLC development and new
school designs and if implemented would make it much easier for schools to
implement the appropriate changes at their sites.
California’s non-partisan Legislative Analysts Office (LAO) weighed in on
the issue of high school reform in May of 2005 publishing its report entitled
Improving High Schools: A Strategic Approach (Hill, 2005). LAO identified five
major policy areas that significantly affect high schools. First, in mandating the
coursework taken by California’s high school students, the state determined what its
students were taught. Another way that the state affected students was in it support
for Regional Occupation Programs (ROP). ROP programs offered options for
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students to gain valuable hands-on career and technical education while still in high
school and as the state moves to advocate for more relevance in education, ROP
program support was vital according to the LAO. In addition, the California High
School Exit Exam represented the establishment of a minimum threshold for student
achievement for those expecting to earn a high school diploma. State content
standards and the content standards tests represent two more strategies the state
employed in an effort to increase academic rigor. In recognition of the state’s
significant role in these areas, the LAO recommended five major policy initiatives to
support improved high schools in California:
1. Increase accountability by strengthening incentives, resetting the
state’s standard for proficiency under the NLCB and increasing the
importance of using graduation and dropout rate data in the state’s
accountability system.
2. Create a mandatory intensive career planning process that increases
parental involvement.
3. Improve the reliability of student achievement data provided to state
and local decision makers, especially dropout and graduation rate
data.
4. Allow for greater flexibility to districts in the use of categorical
money.
5. Allow students more choices in their education beyond a four-year
college degree.
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In sum, the recommendations in these three comprehensive reports represented
a strong and consistent direction for providing schools the freedom and resources
necessary to reform themselves into more effective learning organizations.
The Importance of Leadership
Recognizing that leadership significantly impacted so many of the dynamics
listed above, it was fortunate that a great deal of recent research has focused on how
effective leadership has contributed to a school-wide effort to increase student
performance. While the literature on leadership was voluminous, this study was
focused specifically on how leadership was brought to bear on improving student
achievement, specifically in math, in the high school setting. As such, this study
limited its review of leadership to this area of practice.
Waters, Marzano and McNulty (2005) demonstrated the importance of
leadership ability and its potential impact on student achievement in their meta-
analysis of the research into how effective leaders behaved in relation to student
achievement. What they found was that one could predict strong growth in student
performance as leadership ability increased. The average correlation between these
two characteristics in their review of the data was approximately .25. Figure 8 below
shows how significant growth in a leader’s ability can have significant effects on
improved student achievement.

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Figure 8 – Leadership Ability and Student Achievement: Predicted Increase in
Student Achievement When Leadership Ability Improves from 50
th

Percentile to 84
th
and 99
th
Percentile.
From 50th
Percentile
34
From 50th
Percentile
10
From 50th
Percentile
49
From 50th
Percentile
22
0
10
20
30
40
50
60
70
80
90
100
Percentile
Increase in
Leadership Ability
Increase in Student
Achievement
Increase in
Leadership Ability
Increase in Student
Achievement
To 84th
Percentile
To 60th
Percentile
To 99th Percentile
To 72nd
Percentile

These findings were important and emphasize the need to learn more about
those specific leadership practices found to be strongly related to student
achievement. Among the practices most highly correlated with student achievement
were:
1. Monitoring and evaluating the effectiveness of school practices and
their impact on learning (.27 average correlation).
2. Knowledge of Curriculum, Instruction and Assessment (.25 average
correlation).
3. The leader is a change agent who is willing to and actively challenges
the status quo (.25 average correlation).
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4. The leader seeks input by involving teachers in the design and
implementation of important decisions and policies (.25 average
correlation).
5. Manages the culture of the school by fostering shared beliefs and a
sense of community and cooperation (.25 average correlation).
The authors noted the powerful nature of effective leadership and its impact
on student achievement, emphasizing that in one study a correlation of .50 was
noted. This translated in to an achievement differential of as much as one standard
deviation or as much as 19 percentile points. They also emphasized two major
factors that influenced a leader’s ability to bring about such positive impacts. First,
leaders had to properly focus on practices most likely to have a positive impact and
properly understand the magnitude of the change they were making (Waters,
McNulty & Marzano, 2005).
Visionary Leadership
Building a shared vision based on student achievement was critical to the
success of high school reform. Togneri and Anderson (2003) studied three
successful reform efforts and found common characteristics of visionary leadership
that started with a vision statement clearly focused on student learning and
instructional improvement. They also identified common processes that helped
instructional leaders get beyond good intentions to actual implementation of the
effective leadership practices known to positively impact student achievement. First,
it was important to build a vision for which others in the organization take
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ownership. Successful leaders in the districts studied by Togneri and Anderson
sought input from educators and community members as well. Community forums
and focus groups were held to learn more about stakeholder goals for their children.
Taking the time to involve as many as possible was seen as a way to ensure broad
ownership of the vision that will translate into positive action rather than mere
compliance.
Once the vision is established, it was important that it be more than a piece of
paper. The vision should be used to guide decisions and create momentum towards
lasting change. Doing this requires making the vision visible to everyone. Chula
Vista Elementary School District for example, created a chart to publicly display
entitled, “Strategic Goals and Shared Values.” This chart displayed an itemized list
of core values including such items as Literacy, Equity and Collaboration. The
approach used by another of the districts studied was similar. Minneapolis School
District posted a twelve point plan for improving academic performance and
graduation rates for students of color. This plan included commitments made by the
schools, the students, and joint efforts between school and home (Togneri &
Anderson, 2003).
Marzano’s (2003) review and summary of the research into the importance of
such goal setting practices supports the findings noted above. For example, Wise
and Oakey (1983) found strong academic gains in schools where such leadership
practices were strong. Such progress was evidenced by average percentile gains
ranging from 18 to 41 points. These findings were further supported by Lipey &
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Wilson (1993) and Wallberg (1999) who found academic gains in schools with
strong goal setting practices ranging from 18 to 21 percentile points. These studies
suggested that establishing common visions and measurable goals could be powerful
in increasing student achievement.
Instructional Leadership
In their work Handbook of Instructional Leadership, Blasé and Blasé (2004)
detailed the characteristics of effective instructional leadership and included many of
the same concepts noted above. First, an effective instructional leader was one who
made instruction the subject of candid and frequent conversations with teachers.
Effective leaders recognized teaching as a complex art and were able to analyze it as
such. They worked to develop non-threatening relationships with teachers that were
characterized by risk taking and eliminating the fear of making mistakes. Effective
leaders also provided time for teacher collaboration by building in structures that
supported such interaction among the staff. Waters, Marzano and McNulty (2003)
identified components of effective leadership indicative of these types of
communications and that supported Blasé and Blasé. Examples included a .19
correlation between relationship building and student achievement, and a .23
correlation between effective communications and student achievement.
Blase and Blasé (2001) also advocated that leaders balance support and
guidance with building leadership capacity by creating opportunities for others to
serve in leadership roles. This perspective necessitated that leaders recognized
teachers as intellectuals, not merely as technicians and as such, were due a great deal
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of respect in the process of guiding them through their own professional growth.
This also implied that effective instructional leadership involved empowering
teachers to develop self-efficacy by involving them in decision-making on the
campus. Once again, this finding was supported by Waters, Marzano and McNulty
(2003) who noted a .3 correlation between the extent to which a leader involves
teachers in the design and implementation of important decisions and policies with
increased student achievement.
Leading Change
Marzano (2003) identified key principles of effective leadership in the
change process. One of these principles was that “Effective leadership for change is
characterized by specific behaviors that enhance interpersonal relationships.” This
idea emphasizes the human side of implementing change. Marzano outlined three
sets of behaviors that supported this effort which were characterized by (a) optimism,
(b) honesty, and (c) consideration. While no one distinct personality type was
identified, Marzano emphasized that leaders in the school were bound to face
obstacles and that effective leaders thought and communicated in ways that did not
“catastrophize” the challenges they face (Seligman, 1991).
Marzano (2003) advanced these concepts further by emphasizing the
importance of leading change through relationship building and collaboration, noting
that effective leadership is a critical component for successful school reform.
Marzano details three critical aspects of leadership that contribute to improved
student achievement. The first principle is that “Leadership for change is most
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effective when carried out by a small group of educators with the principal
functioning as a strong cohesive force.” This was true because although strong
leadership from the principal was vital to the change effort, the evidence in the field
supported the idea that lasting change initiatives could only be realized when
supported by teachers and administrators. Further, Marzano noted as a part of this
principle, that because teachers were key to successful implementation of change
initiatives, they must be involved in the decision making process. Therefore,
successful change was ideally led by a strong leadership team.
Marzano’s second principle was that, “The leadership team must operate in
such a way as to provide strong guidance while demonstrating respect for those not
on the team.” Participation by those teachers not on the leadership team was to be
encouraged in order to assure that dissenting points of view were considered when
decisions are made. This level of involvement was meant also to ensure that the
principal and leadership team did not fall into the trap of micromanagement. In fact,
Friedkin and Slater (1994) did a study of 17 elementary schools using student
achievement as an indicator of leadership effectiveness and found that those
characteristics associated with effective leadership included availability to discuss
ideas, seeking teacher input for key decisions, and portraying confidence in teachers.
Behaviors not linked to effective leadership included those associated with
micromanagement such as frequent staff meetings, reviewing teachers’ lesson plans,
and providing feedback on specific instructional problems or individual lessons
(Friedkin and Slater, 1994).
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Instructional Leadership and Math
It was true that the literature in the field of instructional leadership was
extensive and that much was beginning to be known about the importance of
mathematics and what makes a strong mathematics program. What was not known
so well was how those with little expertise in math went about facilitating increased
student achievement when they were not experts themselves. Jennings and Likis
(2005) reported strategies used at an urban school seeking to overcome the
challenges they faced in math achievement. The school developed three goals
including (a) to become proficient in math by mastering grade level standards, (b) to
improve reading and writing in math word problems and strengthen comprehension
of math word problems, and (c) have students demonstrate a positive attitude
towards math. While this last objective may be difficult to quantify, positive results
at the site were achieved using the following leadership strategies:
1. They ensured that math extended beyond the classroom by holding
math contests outside the classroom, sending math challenges home
to be completed with parents.
2. They hosted math family nights where parents and children did math
together.
3. They created new staff roles, including parent academic liaisons to
solicit parent support for math improvement and to partner with
parents on math activities.
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4. They organized math tutoring to improve math skills in identified
students
5. They created support for teachers through math coaches and math
focused professional development
6. They created changes by increasing math instructional time,
organized flexible grouping for math skills proficiency development,
integrated math across the curriculum, and created internal math
assessment strategies to monitor math progress more pro-actively
(Jennings and Likis, 2005).
What was known a little better, was how successful principals have behaved
in high performing, high poverty schools to support student achievement in general.
Research into how the critical element of leadership affected student achievement in
schools with high poverty has yielded some consistent findings. The Chicago
Schools Academic Accountability Council studied such schools and their leaders and
published a report entitled Leave No Child Behind (1999). It noted, “The data
demonstrate that students can flourish academically regardless of their background
and that race, poverty and other urban challenges are not reasons for academic
failure.” The report found that principals in high performing, high poverty schools
believed that all student could succeed at high levels and were characterized as being
“…passionate, hands-on responsive leaders who are visionary, set goals and are good
at both politics and management.”

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Conclusion
For the last 25 years, much attention has been paid to the quality of education
provided to America’s children in its public school system. Despite constant public
pressure and numerous legislative mandates aimed at increasing student
achievement, academic growth was marginal at the high school level. As a result,
state and federal legislation ushered in a new era of accountability characterized by
high stakes testing. The federal NCLB mandated adequate yearly progress for
students and required that students be taught by highly qualified teachers. Schools
were now expected to produce results or face increasing interventions.
In response to the increasing demands imposed on them, schools and school
districts began to remodel themselves into more efficient and accountable entities.
States such as California made massive investments in education including the
implementation of content standards and the upgraded instructional materials that
accompany them. In addition, many states implemented high stakes exams such as
the CAHSEE in California.
Despite these new systems of accountability and investments in the public
school system, progress at the high school level continued to compare unfavorably
with gains made at the elementary level. International comparisons and the
staggering dropout rate demonstrated the necessity of improving the way America’s
schools served their students. The achievement gap between White students and
students of color persists and was evidenced in disparities in opportunity to learn.
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Differences in the quality of facilities, teachers, and persistent ability grouping all
pointed to a failure of America’s schools to provide equal opportunity to all students.
In addressing these disparities, research has shown the importance of math as
an indicator of future success. Students taking and passing rigorous coursework in
math were more likely to graduate from college and earned more money during their
careers. And because students in urban schools were taught more often by under-
qualified teachers and were less likely to enroll in rigorous math courses, this
problem was especially onerous on urban youth.
New school designs that reduced isolation, increased rigor, and made
curriculum meaningful and relevant for students represented the best chance for
realizing sustained growth over time. Professional learning communities acted in
ways that made it harder for students to fail, while at the same time challenged
students to take more rigorous coursework. They also worked collaboratively to
develop common assessments and provide meaningful interventions for students who
fell behind. It was not enough any more to focus on teaching strategies. Schools
were now required to focus on student outcomes and work to ensure that all students
learn at high levels.
Effective instructional leadership was the most important element for lasting
school change. Yet those charged with creating the school culture described above
often did not have strong backgrounds in core curricular areas, especially math.
These leaders were now required to make data-driven decisions and rely on research-
based practices to help them overcome the daunting challenges they face. This
87
chapter has reviewed the literature around these critical aspects of educational
practice and which impact this case study directly.
88
CHAPTER THREE
RESEARCH METHODOLOGY
This chapter outlined the methodology used in this study and included a
detailed description of the research design, sampling criterion and process, and
methodology used for data collection and analysis. The purpose of this study was to
learn more about how urban high school leaders successfully bring together policy
initiatives and local best practice to improve math performance in their schools. And
because school leaders often did not have strong pedagogical content knowledge in
mathematics, this study examined how they marshaled resources and carried out
functions related to fiscal management, personnel, organizational leadership, and
data analysis to successfully bring about the growth they sought in math
achievement. This case study examined the following research questions:
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seemed 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?
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5. How did instructional leaders respond in academic areas in which they
were not experts?
Learning more about how school leaders pull together policies and practices
to improve student achievement was a complex matter. And precisely because the
challenge of this study was to describe the complexities of how one urban high
school went about improving its student achievement in math, a case study approach
provided the best opportunity to develop a rich description of the local context being
studied. As Stake (1995) has noted, “A case study is expected to catch the
complexity of a single case,” and, “We study a case when it itself is of special
interest. We look for the detail of interaction within its context.” (Stake 1995 in
Patton, 2002 p. 297)
Specifically, determining which factors contributed most to improved student
achievement represented an exceedingly difficult task. Were changes in staffing
most responsible? Was a new curricular program implemented? Did the students
and staff support these changes and was staff development provided as a part of this
effort? Such questions underscored how difficult it is to determine how the school
achieved the results it did. The case study approach allowed the researcher the
flexibility to follow the data where it led and to delve into areas of influence as they
revealed themselves. Stake (1995) has noted that these types of case studies are
especially appropriate when the study seeks to explore “in depth a program, an event,
an activity, a process, or one or more individuals.” Case studies are, “bounded by
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time and activity and researchers collect detailed information over a sustained period
of time”
In addition, because growth in student achievement in math was central to the
study, quantitative methods were also used to gather and report data in support of
this case study. Such efforts included gathering student achievement data, and other
statistical data used to support the descriptions presented in the study. Examples
included noting trends in achievement, enrollment and teacher hiring and assignment
patterns.
The unit of analysis for this case study was one public high school. All of the
instruments used in this study were based on current educational research and were
intended to elicit responses relevant to the research questions being examined.
Conceptual frameworks were used to support the analytical approach used in this
study and to provide a context for the reader. Every effort was made to verify and
support findings through a process of triangulation. Information and perceptions
detailed in participant interviews were cross referenced with source documents,
student achievement data, and other sources of reliable information whenever
possible. This process was intended to add to the reliability of the findings made in
the study. All information about the school and participants is factual, but
pseudonyms were used in all cases to protect anonymity and maintain
confidentiality.
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Sampling Criteria and Process
A purposeful sampling process was used in order to provide an opportunity to
conduct a thorough investigation and to explore more deeply the processes related to
the research questions of this study. Patton (2002) noted the appropriateness of this
approach by noting that such an approach “…permits inquiry into and understanding
of phenomenon in depth.” He further noted, “What would be bias in statistical
sampling, and therefore a weakness, becomes intended focus in qualitative sampling,
and therefore, a strength” (Patton, 2002 p. 230). Finally, the use of this approach
was supported by Patton’s assertion that using information rich cases allowed the
researcher to learn a great deal about issues of central importance to the purpose of
the inquiry. The school selected for the study was chosen consistent with this
approach to qualitative inquiry using the following criteria:
1. Improvement in math achievement as evidenced by results on the
California Standards Test (CST) in Algebra I.
2. Student diversity as defined by a student population of at least 50% from
traditionally ethnic minority groups.
3. Public high school in the Southern California region of at least 1200
students.
4. An Academic Performance Index score of at least 600
5. A State-wide rank of 5 or higher
6. Leadership stability as defined by a principal being at the school for at
least three years during the time the improvement was made.
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The eleven members in the cohort group worked together to develop the
sampling criteria, and then to identify schools in Southern California that met those
criteria. Qualifying high schools were identified using the following process:
1. A data file was downloaded from the California Department of
Education’s web site using the Data Quest 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 (see Appendix B).
3. Knowing that the group would need to research improvement in CST in
Algebra in a later step and that many schools would not have
demonstrated improvement, the group set a goal of a sample size of no
less than 100 schools in the southern California region.
4. Preliminary efforts to use more stringent requirements did not yield a
sufficient sample so adjustments had to be made. For example, when the
student enrollment parameter was set to 1500; the percentage of minority
students was set at 65%; the statewide rank set at 6 or higher, the sample
was limited to only 28 schools in southern California.
5. The second iteration included adjusting the parameters to an enrollment
of no less than 1200; a minority population of 50% or more and a
statewide rank of 5 or higher. The sample population then rose to a
satisfactory level of 110 schools in the southern California region.
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6. Students in the group were then assigned to research 10 schools each by
looking up and recording CST scores in Algebra I for the years 2003,
2004 and 2005 onto a common spreadsheet which one person in the
group compiled.
7. The group then assigned an absolute value to the 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 in the top two performance ands. These totals were added to
indicate an overall level of improvement. For example, if a school
decreased the numbers of students scoring in the bottom two performance
bands by 3% and increased the number of students scoring in the top two
performance bands by 5%, the school would have an overall
improvement score of 8%.
8. The group then reviewed the scores of all schools in the sample and
eliminated any school that:
a. Evidenced a decrease in the number of students scoring in the top
two performance bands from 2003 - 2005.
b. Evidenced an increase in the number of students who scored in the
bottom two performance bands.
c. Failed to evidence an overall improvement score as calculated in
the example detailed in number 7 above.
9. Using this process resulted in 44 schools qualifying for the study.
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10. A geographic map was then developed of the qualifying schools to help
cohort members select a school for their study based on proximity and
other relevant factors.
The group also worked to identify the population who would participate in
the study and included site administrators, key teacher leaders, and classroom
teachers. Site administrators and key teacher leaders were scheduled to be
interviewed using the Key Leader Interview Guide attached as Appendix C. All
math teachers at the site were asked to complete the 50 item Math Teacher
Questionnaire (Appendix F) whose results would provide the researcher with data
about teacher perceptions related to the research questions being studied. All
teachers at the site who were not math teachers were slated to complete a shorter
questionnaire designed to get their impressions about school-wide factors that might
be linked to the research questions. Participation was voluntary and all participants
were assured that all due efforts would be made to ensure confidentiality and
anonymity. Those interviewed were scheduled for at least one discussion with some
key leaders being interviewed more than once. All interviews were held on campus
and in an environment that ensured confidentiality.
Selected School Profile
The school selected for this study was Mission Valley High School in the Los
Padres Unified School District. The school was located approximately ten miles east
of Los Angeles in an area considered one of the original centers of Los Angeles life.
The historical area emerged with the establishment of the one of the early California
95
Missions in 1771. The community was extremely diverse and home to large Asian
and Hispanic populations. The signs on the front of most of the businesses in the
immediate area were printed in both English and either Chinese or Spanish. MVHS
was located along the bustling main street in the area bearing the community’s name.
The working class neighborhood where the school was located appeared more as a
business district than a residential area with the exception of a few run down houses
located across the street from the school.
The school district, established in 1887 and unified in 1992, educated
students in grades kindergarten through 12. The stated mission of the district was,
“It is the mission of the Los Padres Unified School District, founded in 1887, rich in
history, culture and diversity, to work in partnership with families, staff and the
community to meet the unique academic and social needs of each student. Through
extraordinary community collaborations and rigorous educational strategies, we
strive to produce graduates who excel academically, act responsibly and are
supportive citizens of the community and the world.” The district was comprised of
five elementary schools, one middle school and one comprehensive high school and
one continuation high school. The total district enrollment during the 2005-06
school year was 6130.
At 1820 students, Mission Valley High School was the largest school in the
district and reflects rich cultural diversity of the community. The two largest ethnic
groups in the school were Asian and Hispanic at 51.4% and 36% respectively. The
remainder of the school is comprised of 8.1% White, 3.2% Filipino and 1.0%
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African-American. More than 28 percent of the school’s students were English
Language Learners (ELL). Native Spanish speakers represent 8.8% of the school’s
population, Cantonese 7.8%, Mandarin 6.6%, 2.6% Vietnamese, and 2.7% other
languages. Approximately 40% of the students at Mission Valley High School
qualified for the free or reduced price lunch program.
The Student Handbook for 2004-05 notes the school’s “Commitment to
Constant and Never-Ending Improvement.” This commitment appeared to be
evidenced in the increasing scores on the API scores of the school where the school
has grown every year since 2001 from 681 to 769. During this same period of time
the school’s corresponding statewide rank has grown from a 7 to a 9. In addition, the
school has met its AMO targets each year since the inception of the program,
including all sub groups. Figure 9 illustrates the progress made in the school’s API.
Figure 9 – MVHS Academic Performance Index
681
724
747
769
620
640
660
680
700
720
740
760
780
2001-02 2002-03 2003-04 2004-05
API SCORE
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The administrative team at Mission Valley High School was comprised of a
principal and three assistant principals. The principal has served in that capacity for
the last eight years and has been at the school since its inception, serving the first few
years as assistant principal. The assistant principals have been at the school for 11,
13 and 5 years, respectively. Less than a year before this study began, the District
hired a new Superintendent following the tenure of a strong superintendent who had
served as an assistant superintendent before ascending to the superintendency.
MVHS was staffed with approximately 75 teachers and 5 pupil services
support staff. During the 2004-05 school year, 65 of the teachers were fully
credentialed representing 86.7% of the teaching staff. Three teachers were
University Interns and 7 were teaching on an emergency credential. This compared
with 93% state wide teaching with full credentials. The diversity of the teaching
staff was also evident in the following breakdown: 49% White, 26.7% Hispanic, 14.7
% Asian, and the remainder a mix of African-American, Filipino and “other.”
During the 204-05 school year, teachers at MVHS averaged 8.6 years of teaching
experience. There were nine first year teachers and 8 second year teachers during
the same period. The school was supported by 8 paraprofessionals, 9 clerical staff
and 22 other miscellaneous support staff.
Participants in the Study
The study was conducted in a manner that allowed for triangulation of data
from multiple sources. This was especially important for qualitative case studies
where individual or cultural bias can present challenges to validity and reliability.
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Document analysis proved to be a particularly important tool in this effort. The
school’s master schedule, for example, provided a wealth of data around class size
and teacher assignment patterns used to validate perceptions revealed in the
interviews and questionnaire results. The school site plan and budgets also proved
especially helpful in validating otherwise subjective data.
The following people participated in the study and proved to be rich sources
of information relative to the research questions being examined in this study.
Site Administrators. The school principal served as the primary instructional
leader on a high school campus and in this study; the principal was interviewed on
several occasions in an effort to collect detailed information and perceptions about
how the school achieved improvement in mathematics. Principals, however, have
often relied on their assistant principals to implement the elements of the
instructional program. As such, the assistant principal in charge of curriculum and
instruction was interviewed to help gauge factors affecting the effectiveness of the
instructional program.
Teacher Leaders. Teacher leadership was a key component in the study and
several teacher leaders participated in the study including the current and former
math department chairs
Classroom Teachers. Classroom teachers were the keys to successful
implementation of educational policy and were in the best position to have a feel for
how well practice is meeting expectations. Classroom teachers were interviewed in
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order to learn about their practice and perceptions related to the instructional
program at the school.
Instrumentation
The instrumentation used in this study was developed collaboratively by
eleven members of a dissertation cohort at the University of Southern California.
These Doctoral students met regularly during the Spring and Summer of 2006 in a
research seminar designed to facilitate this process. The collaboration included
open-ended discussions of the topics to be covered in the study and how best to gain
the data necessary to address the research questions noted above. The collaboration
also included working to identify the relationship between the research questions and
the data collection instruments to ensure maximum efficiency in the data collection
process. Figure 10 depicts the relationships between the various data collection
instruments used in the study and the research questions examined.
Figure 10: Relationship of Data Collection Instruments to Research Questions

Research Question
Instrument 1 2 3 4 5
School Profile X X
Key Leader
Interview X X X X
Teacher Interview X X X X
Teacher
Questionnaire
X X X X
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Intellectual Frameworks
Following the development of the chart depicted in Table 2, the members of
the cohort developed the actual instruments through a process grounded in
conceptual frameworks that identified key components of the major themes
associated with the research questions. Five such frameworks were developed and
guided the process of developing data collection instruments, including appropriate
questions associated with each instrument. In addition, the frameworks assisted in
paring down the instruments, again, to maximize efficiency in the data collection and
analysis process.
Framework for Research Question 1: School Profile of Student Achievement Data
Research Question 1 asked about the pattern of math achievement for various
students at the school. The school profile detailed above served as the framework for
research question one in that it provided a template for identifying areas of student
achievement in math where quantifiable data was available for analysis. Appendix E
included the relevant achievement data that was used in the researcher’s efforts to
identify the pattern of student achievement in math at the site.
Frameworks for Research Question 2: Effective Math Programs and School Design
Research Question 2 asked about the policy initiatives, curriculum and
instruction and related conditions that seemed to be related to improved math
achievement in the school. Two separate frameworks were developed to help in the
examination and analysis of this research question. The first was a framework
describing effective school design. The elements of this framework consisted of
101
Marsh and Codding’s model of school design discussed in some detail in Chapter 2.
The basic elements were reflected in Figure 11. First, the framework emphasized
curriculum foundations built on student-centered approaches and outcomes. School
cultures that enhanced effective school design were those that had meaningful
interactions between students and staff, ongoing professional development and
enhanced learning opportunities. Small school size was another essential feature of
Marsh and Codding’s design, but for the purposes of this study were reviewed as a
possible element contributing to school culture and was therefore included in that
aspect of this framework under meaningful interactions between students and staff.
Learning activities that challenge students to use higher order thinking skills, solve
problems and collaborate were also integral components of the framework. Finally,
the framework included student performance assessments rooted in effective
communications, problem solving and which emphasized conceptual understanding.
Figure 11 – Framework for Effective School Design
School
Design
Curriculum Learning
Activities
Challenge
Students to
Think
Students
Solve
Problems
School
Culture
Based on
Enhanced
Learning
Meaningful
Staff-Student
Interactions
Ongoing
Professional
Development
Collaborative
School-to-Career
Applications
Constructivist
Knowledge
Based on
Student
Outcomes
Student Performance
Assessments
Capture
Conceptual
Understanding
Capture
Problem
Solving
Capture
Communication
Skills
102
The second framework designed for this research question dealt with the elements of
effective math programs and was depicted below in Figure 12. The essential
elements included in the framework begin with a student-centered curriculum that
emphasized high degrees of conceptual understanding that ultimately led to an in-
depth mastery of computations and manipulations of mathematical symbols and
procedures as tools in the problem solving process. Next, the framework
incorporated rigorous, standards-based practices that relied on content standards and
assessments being closely aligned
Figure 12 – Effective Math Programs

Effective
Math
Programs
Classroom Practices

Effective and coherent
lesson design
Promotes high levels of
student engagement
Makes use of prior
knowledge
Cultural relevance
Curriculum Design
o Student-centered
curriculum
o Driven by learner
outcomes
o Emphasizes Conceptual
understanding
o Focuses on problem-
solving
o Incorporates current
learning theory
o Scope & Sequence is
supported by learning
theory
Standards Based
Instruction
Assessments aligned to
standards
Student achievement data
drives instruction and
decision
Common performance
rubrics through
collaboration
103
and on data-driven decision making. Finally, strong math programs relied on
effective and coherent classroom pedagogy that included sound lesson design, made
use of prior knowledge, was culturally relevant, and thereby promoted high levels of
student engagement.
Framework for Research Question 3: The Change Process
Research Question 3 asked about the change process used by the school to
enhance its math program and about strategies used to assist students in math. Blasé
and Blasé (2004) emphasized that a primary characteristic of an effective
instructional leader was the ability to understand and embrace the challenges of
change. For instructional leaders to effectively manage the change process, it was
important for them to posses an intimate knowledge of how the change process
worked from varying points of view. Bolman and Deal’s Reframing Organizations
(2003) provided leaders with a useful framework for addressing the diverse aspects
of complex organizations as they managed the change process and was detailed in
Figure 13. The authors did this by detailing four distinct frames from which to view
the operation of their organization: (a) structural, (b) human resources, (c) political,
and (d) symbolic. These four frames were used to better understand and categorize
the site’s efforts to bring about increased student achievement in math. Such efforts
were described in terms of these distinct areas of practice.
The structural frame emphasized rules, roles, goals and policies. The
effective leader aligned such elements to the goals of the organization and the
104
objectives of the change initiative. Bolman and Deal noted that many problems
traditionally attributed to individual failings were often more accurately
Figure 13 – 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
attributed to ill fitting structures, noting that, “Conscious attention to structure and
roles can make an enormous difference in a group’s performance.” Failing in this
effort led to a misalignment of people and structures resulting in stalled efforts and
inefficiency. Common obstacles to effective change in this frame included a loss of
clarity about one’s role, confusion and chaos. Good communications and realigning
policies to support and clarify roles was an effective means that leaders could use to
overcome these challenges to successful change.
The human resources frame involved creating a fit between people and
organizations. When these two elements were effectively aligned, organizations
105
thrived as their employees worked with energy and enthusiasm. Organizations
effective in this area gained a competitive advantage created by talented and
motivated employees. The human resources frame also emphasized individual needs
and relationship building. When these elements were ignored, employees tended to
withdraw, become indifferent, passive and apathetic. They also may restrict output,
resist change and otherwise sabotage the organization (Argyris, 1957). Within this
context, barriers to change included anxiety, uncertainty, feelings of incompetence
and neediness. The effective leader attacked these obstacles using training for new
skills, encouraging participation and providing psychological support
According to Bolman and Deal, every significant organizational process was
inherently political. This was true since organizations were comprised of disparate
interests competing in an “arena” for control over power and resources. Thus, the
political frame emphasized power, conflict and competition. Effective leaders in
today’s public schools must be able to deal with such diverse constituencies as labor
unions, school boards, parent organizations, community groups and classroom
teachers. These groups often had different points of view on issues of importance to
education. Successfully negotiating these differences and forming alliances may
prove critical to a leader’s ability to implement change effectively. Common barriers
to successfully implementing change included disempowerment and conflict
between winners and losers in the struggle associated with the change. Leaders
needed to recognize this danger and work to create “new arenas where issues can be
renegotiated and new coalitions formed.” (Bolman and Deal, 2003)
106
The symbolic frame emphasized the need for cultural competency. Effective
leaders were those who dealt well with rituals, ceremonies, and other ways of
building meaning within the school setting. Effective use of metaphors and stories
represented a powerful way for leaders to address objections and create buy-in and
ownership. Challenges in this regard appeared in the form of a loss of meaning and
purpose as well as a tendency to cling to the past. Creating rituals to transition to
new ways of doing things while working to celebrate the past may prove effective in
overcoming the inertia frequently associated with today’s public high schools.
Framework for Research Question 4: Instructional Leadership
Research Question 4 asked about how instructional leadership helped bring
about improved math strategies and programs as well as student achievement in
math. Figure 14 depicts the intellectual framework used in this study in support of
concepts associated with instructional leadership. The framework included five
distinct components beginning with Vision for Learning which involved the leader
facilitating the development of the vision being supported by the school community.
The framework also included a component for the supervision of instruction, or how
the leader observed and monitored instructional program and provided constructive
feedback in a timely manner to all teachers. The third construct in the framework
involved working effectively with the community and political aspects of leadership.

107
Figure 14 – Instructional Leadership Framework
Instructional Leadership Framework
What an effective leader must have knowledge of…
Vision for
Learning
Supervision
and
monitoring of
instruction
Community and
Political
Culture of
Teaching
and
Learning
Data Driven
Decision
Making
Analysis
1.0—Facilitates
the
development,
articulation,
implementation,
and
stewardship of a
vision of
learning that is
shared and
supported by
the school
community.

A- Developing
vision
B-
Communicati
ng the vision
C- Implement
the vision
D- Monitor and
evaluate the
vision
E- Addresses
obstacles to
vision
implementati
on and
realization

Observes and
monitors
instructional
program.
Provides
constructive
feedback in a
timely manner to
all teachers.

A-Classroom
observations on
a daily/weekly
basis.
B-Allocates
resources
ensure
successful
teaching and
learning.
*time
*peer support
*materials
*professional
development
C- Supervision of
personnel
D- Hiring
personnel that
supports the
learning goals
and vision of
the school

4.0--Collaborates
with families and
community
responds to diverse
interests and needs,
and mobilizes
community
resources.

A -Understands the
value of diversity
B- Understands
communities
needs
C -Involves
community in the
school
D - Provides
opportunity for
community
involvement

2.0 Advocates,
nurtures, and
sustains a
school culture
and
instructional
program

A- Valuing
students/staf
f
B- Developing
&
sustaining
the culture
C-Culture that
is inclusive,
respectful of
diversity
D- Implements
practices for
culturally
relevant
teaching and
learning
E-Celebrates
students,
teachers and
staff

Uses data as a tool
for informing
instruction and
supporting student
learning

A- Utilizes
assessment data to
place students
appropriately
B- Formative
benchmark school
site assessments
C- Summative
standardized
assessment
D- Disaggregate
data by students,
classes and
cohorts
E- Use data to guide
and improve
teachers
instructional
program
F- Use data to create
master schedule
G- Using data to
inform/improve
pacing
instructional plans
References
Johnson, Ruth S. (2002). Using data to close the Achievement Gap: How to measure equity in our schools. Thousand Oaks,
Corwin Press.

Hessel, Karen; Holloway, John. (2002). A Framework for School Leaders: Linking the ISLLC Standards to Practice. New
Jersey, Educational Testing Service.

www. cde.ca.gov- Principal Standards
108
This aspect of leadership involved collaborating with families and
community, responding to diverse interests and needs, and mobilizing community
resources. Working effectively to support a positive school culture where teaching
and learning are of primary importance constituted the fourth element of the
framework. This involves advocating, nurturing, and sustaining a school culture
centered on the instructional program. The final element of the framework involved
using student achievement data to make important decisions such as student
placement and curricular offerings.
Framework for Research Question 5: Strategies to Overcome a Lack of Expertise
Research Question 5 asked about how instructional leaders responded in
academic areas in which they were not experts. The framework developed for this
research question was divided into two distinct components based on the two parts of
the research question. First, an assessment was developed to help determine the
level of expertise the principal had in math. The process was based on the state of
California’s definition of a highly qualified teacher (HQT) under NCLB. This
definition was chosen precisely because the intent of the HQT provisions were aimed
at judging a teacher’s qualification primarily based on subject matter competency.
The assessment involved is detailed in Figure 15 and results in one of three levels of
expertise being assigned to the leader – high, medium, or low. Second, Figure 16
details a range of strategies the school’s leadership might use to improve student
achievement in math.

109
Figure 15 - Assessment of Individual Leader’s Expertise in Math

Source: NCLB Teacher Resource Guide [electronic version] located at
http://www.cde.ca.gov/nclb/sr/tq/documents/nclbresourceguide.pdf
Assessment of Principal’s Expertise in Math
Step 1
Is the Principal
HQT Compliant?
Yes No
High
Expertise
Step 2
Does the
Principal have a
credential or
major in math?
Yes No
Medium
Expertise
Has Principal
minored in or
taught math?
Yes No
Medium
Expertise
Low
Expertise
Step
3
110
Figure 16 – Strategies Used to Overcome a Lack of Subject Matter Competency

Item Strategy Approach/Source
1
Delegate Leadership to Assistant
with Greater Expertise
Delegation Approach
(Northouse, 2001 p. 58)
2 Empower Department Chair Teacher Leadership (Gabriel, 2005)
3 Bring in Outside Expertise
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
4
Emphasize Inquiry and Problem
Solving
Action Research
(Stringer 1999)
5 Emphasize Quality Instruction
Instructional Strategies
(Marzano, 2003 pp. 78-87)
6
Emphasize Strategies to Engage
Students in the Learning Process
Student Engagement
(Marzano, 2003 pp. 149-150)
7
Emphasize Articulation with Feeder
Schools
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
8 Emphasize Raised Expectations
Challenging Goals and Effective
Feedback (Marzano, 2003 pp. 35-46)
9
Emphasize Strategic Teacher
Assignments
HR Frame
(Bolman & Deal, 2003)
10
Emphasize Revised Course Scope
and Sequence and/ or Curriculum
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
11
Emphasize Interventions for Lower
Performing Students
Supplemental Services
(NCLB, 2001)
12
Emphasize Professional
Development
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
Data Collection Instruments
Instrument 1 - School Profile
The School Profile instrument was designed to provide a framework for
better understanding the myriad of characteristics that made up the school
community. The secondary school reform cohort worked to identify those elements
most likely to provide a comprehensive picture of the school being studied.
Characteristics were also chosen based on practical availability of the data. Data to
111
be collected was organized into three main areas of concern: Demographics, student
performance, and general school information. Most of the data collected for this
purpose was available on the California Department of Education’s web site.
Demographic data comprised a large part of the school profile and included
both student and teacher demographic traits. Teacher demographics included total
numbers of teachers; credential and NCLB Highly Qualified status; and years of
experience. Teacher data can yield a wealth of information about the instructional
program at the school and help shed light on potential strengths and weaknesses in
that area. Data collected for students included ethnicity, English Language Learner
(ELL) status; Free and reduced lunch status; and student enrollment patterns.
Likewise, student demographic data has the unique potential for illuminating the
potential challenges facing the school as it works to improve student achievement.
Student performance data was also an important component in the school
profile. Such data is directly responsive to one of the research questions being
examined in that it can help reveal the academic achievement pattern in the school.
Among the items compiled were the Academic Performance Index scores at the site
for the three years studied, CAHSEE pass rates; standardized test score data; and
other assessment data such as benchmark assessment data. By examining student
performance data, one can more readily identify areas of curricular strength and
areas that might merit further investigation. The data described above was collected
for the School Profile compiled into Appendix E and was presented in a table broken
down into the three areas identified above.
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Instrument 2 – Key Leader Interview Guide
The Key Leader Interview Guide was developed collectively by the cohort to
facilitate the collection of data relevant to research questions numbers 2 through 5.
In particular, key leaders were interviewed to help determine their perceptions of the
factors they believe were responsible for the observed improvement in student
achievement in math. The four page document was divided into one page per
research question and included a script for the interviewer to introduce each section.
The questions themselves were aligned to the elements of the particular conceptual
framework for each research question. The first section of the guide was for
Research Question one and included four open-ended questions aimed specifically at
policies related to high stakes testing and accountability.
The second section of the interview guide focused on Research Question 3
and had one question each related to the four frames of reference of Bolman and
Deal. The third section of the Key Leader Interview Guide focused on Instructional
leadership and had five open-ended questions. The guide concluded with a section
on Research Question 5 and asked about obstacles and strategies related to how the
leader responded to their own lack of expertise in math. The Key Leader Interview
Guide assumed an interview of no more than 40 minutes and included a set of open-
ended questions designed to allow the interviewer the freedom to explore emergent
themes and issues. This semi-structured interview process is based on Creswell’s
(1998) protocol. The Key Leader Interview guide is incorporated in this study as
Appendix C.
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Instrument 3 – Teacher Interview Guide
The Teacher Interview Guide was developed to facilitate the collection of
data relevant to research questions numbers 2 through 5. As with key leaders,
teachers were interviewed to help determine their perceptions of the factors they
believed were responsible for the observed improvement in student achievement in
math. The teacher interview guide was developed collectively by the cohort group
by ensuring alignment between proposed questions and conceptual frameworks and
specific research questions. The single-page interview guide assumed an interview
of no more than 30 minutes and 7 open-ended questions to allow the interviewer the
freedom to explore emergent themes and issues. The seven questions included
queries on the teacher’s background, their beliefs about educational policies affecting
their practice, changes at the school, leadership, and teaching strategies in use at the
school. This semi-structured interview process is based on Creswell’s (1998)
protocol. The teacher interview guide was incorporated in this study as Appendix D.
Instrument 4 – Teacher Questionnaire
The Teacher Questionnaire was developed to facilitate the collection of data
relevant to research questions numbers 2 through 5. Because there was a strong
interest in obtaining in-depth information from teachers of math as well as an interest
in learning about overall school-wide issues, two separate versions of the
questionnaire were developed. As with the interviews, teachers were asked to
complete the questionnaire in order to help the researcher develop an understanding
of how the staff felt at large about which factors were most responsible for the
114
observed improvement in student achievement in math. The teacher questionnaire
was developed collectively by the cohort group by ensuring alignment between
proposed questions and conceptual frameworks and specific research questions. The
teacher questionnaire used a 5 point Likert scale ranging from Strongly Agree to
Strongly Disagree. It was also assumed that it would take no more than 30 minutes
to complete and that the researcher would have to return more than once to collect as
many questionnaires as possible. The Math Teacher questionnaire included 50 items
and was incorporated in this study as Appendix F. The non-math teacher
questionnaire was developed to include 30 items providing teachers in subjects other
than math with an opportunity to share their perceptions around school-wide issues.
This instrument was attached as Appendix G.
Data Collection
This study collected data over a two month period from October 2006
through November 2006. The initial stage of data collection involved extensive
gathering of statistical data from the CDE web site that related to the school profile
and research question one. Data collected on site occurred in four distinct rounds to
allow multiple opportunities for gathering relevant data. After each round, interview
notes were analyzed and follow up questions identified for the next visit. This
multiple rounds strategy allowed for the follow up investigation in later rounds of
emergent themes and issues that arose in earlier rounds. In cases where such themes
emerged, data from multiple sources was gathered in subsequent rounds in every
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case possible. The reliability of the data using this triangulation method was thereby
increased.
A key step in the process of data collection was obtaining the approval of the
Institutional Review Board (IRB) prior to the collection of any data. IRB
committees are ethics committees charged with reviewing and overseeing human
subjects’ research done under the auspices of a given institution. The process was
guided by the principles of respect for persons, beneficence and justice and was
intended to ensure an ethical approach to research is guiding the study. As such the
process sought to ensure that the safety and privacy interests of study participants
were protected and that the study was one that sought results that would benefit
society.
The voluntary and informed consent of the participants was a primary tenet
of ethical research. The IRB review process sought to accomplish these and related
goals by requiring the submission of detailed documentation of the scope and
methodology involved in the study. The researcher’s proposal for the study included
such items as the Request of Claim of Exemption for Non-Medical Research, in
which, the researcher described the purpose of the study, the population to be
studied, and the methodology used in the study. For this particular study, the cohort
submitted one IRB proposal for the series of related studies being done by members
of the cohort described earlier. This process limited flexibility in some respects, yet
increased consistency among the researchers by requiring the same data collection
instruments and methodologies.
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Once the IRB gave final approval for the study to begin, the cohort group
returned to their list of qualified schools and approached the schools selected for
study. Site principals were contacted and informed about the details of the study and
once the site gave approval, data collection started soon thereafter. Participants were
informed of the need to give voluntary consent and informed that they could end
their participation at any time. The questionnaire was voluntary as well and the
researcher made more than one effort to collect those that were submitted.
During the first round of data collection at the site, the goal was to gain a
broad overview of the school. As such, the first interview was of the site principal.
The principal interview provided an opportunity to learn more about key leaders on
campus, instructional programs in general, the math program specifically, and
school-wide cultural factors affecting the school’s academic progress. Following
this interview, the School’s assistant principal in charge of curriculum and
instruction was interviewed with the goal of learning early in the process as much as
possible about the school’s instructional program. Key documents such as the
school’s master schedule, school curriculum guide, and most recent WASC report
were also gathered during this first round visit. The Math Teacher Questionnaires
were also distributed during this first visit to allow teachers more time to complete
the lengthy questionnaire before the due date.
The second round of data collection served as an opportunity to follow up on
aspects of the school’s culture and instructional program learned after analyzing the
data collected during the first round. The researcher spent time in math classrooms
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observing instruction and toured the campus to get a feel for life at the school. Key
leaders such as the current and former department chairs as well as math teachers
were interviewed during the second round of data collection. In addition, completed
math teacher questionnaires were collected and the data from these questionnaires
was compiled into a database of information (see attached Appendix H). Finally, a
second interview was held with the principal to follow-up on items gleaned from
both rounds of data collection to that point.
During the third round of data collection non-math teacher questionnaires
were distributed at a faculty meeting and teachers were given time to complete them.
The current department chair was interviewed again as was the principal. Follow up
questions based on issues arising from data collected in earlier visits formed the basis
and necessitated these interviews. In addition, more classroom observations were
made.
During the fourth round of data collection at the site, all teacher surveys were
collected and brief interviews were held with the assistant principal of curriculum
and instruction and the current department chair of the math department in order to
clarify issues of concern that had not yet been addressed. This process of “filling in
the gaps” allowed the researcher to effectively eliminate guesswork and tie up loose
ends.
Data Analysis
The purpose of this study was to produce a better understanding of how
effective instructional leadership works to improve student achievement in
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mathematics. Specifically, the study explored the various facets of instructional
leadership, the components of instructional effectiveness and the design of the
mathematics curriculum at the site in order to arrive at a reasonable explanation for
the success achieved by the school. Five research questions were developed to assist
in completing this study and data collection instruments were developed that were
aligned to the research questions in an effort to ensure efficiency within the study
and reliability of findings to be made following a review of the data collected.
Analyzing the data collected in the study involved several distinct
components. First, interviews were recorded and transcribed in a way that allowed
review by the participants. Following this verification, efforts were made by the
researcher to link relevant points made in the interview to aspects of the appropriate
conceptual framework. Copies of interview note transcripts were made as needed to
allow for cross filing onto thematic files indexed by the salient points of the
framework. This effort assisted with retrieval of data and in identifying themes that
emerged as more than one person noted a particular dynamic on campus.
A key strategy used in the analysis of the data collected in this study involved
the development of a spreadsheet using Microsoft Excel in which rows and columns
were designed to allow for the recording of relevant information according to which
framework, collection instrument, and research question the data was related. This
spreadsheet allowed the data to be compiled in a way that allowed the data to be
sorted and grouped to help in the identification of patterns in the data and in
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establishing the relative frequency of a given response. The spreadsheet design was
included as Appendix I.
Teacher questionnaire results were handled in a similar fashion. Scores for
each question were summarized and results entered into the spreadsheet noted above.
The entries identified to which research question each item was linked and which
framework component(s) was most relevant for data analysis purposes. Following
the entry of the data from the interviews and teacher questionnaires, the data in the
spreadsheet was sorted in such a manner as to reveal patterns of responses and
leading to reasonable conclusions related to the research questions.
Finally, source documents were analyzed and entered into the spreadsheet in
the same way that the data collected from the interviews and questionnaires were.
Such documents included but were not limited to the school profile, school site plan,
most recent WASC report, master schedules and budgets. Documents such as these
provided a rich source of information that served to confirm emerging themes that
became evident through analysis of the interviews and questionnaire results.
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
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notes to validate their contents. External validity was beyond the scope of the study
which used a single, case study methodology. While the findings in this study were
reasonable given the data collected, via a careful analysis, they were not
generalizable to other settings beyond the comfort level of the reader.
Conclusion
The purpose of this chapter was to describe the methodologies used in this
study. This description included a detailed description of the sampling criteria, the
data collection instruments, data collection process and data analysis methods. The
procedures used for this study were collectively developed by the students in the
cohort and were approved by the IRB of the University of Southern California. The
concepts and methodologies were reviewed by and gained the approval of the school
principal at Mission Valley High School. Data collection was mainly comprised of
teacher and key leader interviews and a teacher questionnaire. Document analysis
was performed and direct observations were made to triangulate data whenever
possible. The findings presented in the next chapter are based on a thorough analysis
of the data collected and will be expressed in terms of the research questions that
have guided this study.
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CHAPTER FOUR
FINDINGS, ANALYSIS AND DISCUSSION

Chapter Four presented the findings from a case study of one school’s efforts
to improve student achievement in mathematics. In order to learn more about how
high schools successfully brought together policy initiatives and local best practices
to improve math performance in their schools, one comprehensive, ethnically diverse
high school was selected to serve as the subject of this case study. With these goals
in mind the site’s efforts that led to improved student achievement in math were
examined. A case study approach was used to collect data related to how this
particular school worked to improve its student achievement in math over three years
from 2002-03 through the 2004-05 school year.
The findings presented were directly related to the following five research
questions:
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seemed 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?
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5. How did instructional leaders respond in academic areas in which they
were not experts?
This study examined Mission Valley High School’s efforts to improve
student achievement in math through avenues such as effective leadership practices,
sound curriculum and instruction and supportive educational policy. Four data
collection instruments were developed for this study and were used to collect data
relevant to the research questions above. These instruments included: (1) A Key
Leader Interview Guide (Appendix C); (2) A Teacher Interview Guide (Appendix
D); (3) A School Profile (Appendix E); and, (4) A Teacher Questionnaire with two
versions (Appendices F and G). The data collected for this study consisted of
information from interviews with key leaders and teachers, results from teacher
questionnaires, data gathered from source documents, classroom observations, and
quantitative data from the CDE Data Quest web site. Data was interpreted and
analyzed using triangulation where multiple sources of information were used to
support each other whenever possible. This methodology served to increase the
reliability and validity of the findings. The findings presented in this chapter were
presented in direct relation to the five research questions for the study and were
followed by a detailed analysis and discussion.
Data Findings
Research Question 1: Pattern of Achievement in Math
The first research question asked, “What was the pattern of Math
achievement for various students at the school?” Analyzing the pattern of
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achievement in math for the students of Mission Valley High School was facilitated
by the wide variety of data sets readily available through the California Department
of Education. The pattern of student achievement in math began to reveal itself
during a review of the Algebra I CST results used to as the sampling criteria for the
study. This pattern continued to emerge as data was collected on items such as
course enrollment patterns and Advanced Placement testing results. An analysis of
this data led to the following major findings for research Question 1:
1. Students at Mission Valley High School demonstrated more growth
on the Algebra I section of the CST than did their peers statewide.
2. Asian students out gained their peers statewide by a wide margin
during the time period researched.
3. Hispanic students out gained their peers statewide by a wide margin
during the time period researched.
4. White students out gained their peers statewide by a wide margin
during the time period researched.
5. ELL students out gained their peers statewide by a wide margin
during the time period researched.
6. Enrollment in upper level math classes increased during the years
studied.
7. Fewer students were enrolled in classes below Algebra I.
8. A high percentage of students taking the Advancement Placement test
passed in the final year of the study.
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9. The school dramatically improved the percentage of students passing
the CAHSEE in math.
Standardized Testing. The findings based on CST data began in the baseline
year of 2002-03, when MVHS students assessed in Algebra I demonstrated a mean
scale score of 305.1. When disaggregated by ethnic sub groups, the scores ranged
from a high of 329.4 (Asian) to a low of 289.7 (Hispanic). These scores can be
viewed in the context of statewide results, where the mean scale score for that year
was a bit higher than for MVHS at 309.5. The statewide gap in achievement was
similar to that exhibited at MVHS with Asian students demonstrating a mean scale
score of 354.3 and Hispanics scoring at 291.6. These scores revealed that for the
2002-03 school year, MVHS scored below the state average collectively as did the
ethnic sub groups. On a positive note, the ELL students and those considered SES
disadvantaged both outscored their peers statewide. For ELL students at MVHS the
mean scale score was 301.7 compared to a statewide average of 286.1. For SES
disadvantaged students, MVHS had a mean scale score of 306.8 compared with
294.5 statewide.
This same pattern of achievement was equally evident when the percentage
of students scoring proficient and above was used as the measure. Twenty-one
percent of students statewide scored proficient or above compared with 19% at
MVHS. Both statewide and at MVHS Asian students had the highest percentage of
students scoring proficient or above with 48% and 34% respectively. Hispanics had
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the smallest percentage of students scoring proficient or above with only 8% doing
so at MVHS and 11% statewide performing at this level.
In the second year examined (2003-04), the pattern of student achievement at
MVHS began to depart from the statewide trends. First, whereas the mean scale
score statewide actually dropped from 309.5 to 304.9, the mean scale score at MVHS
increased from 305.1 to 310.2. Similarly, the mean scale scores for Whites and
Hispanics dropped statewide, while those same student groups at MVHS
demonstrated strong gains. Hispanics at MVHS increased 7.1 points and White
students grew by just under 18 points. In addition a higher percentage of White and
Hispanic students scored proficient or above at MVHS while fewer did so statewide.
Also of note is the fact that the overall growth seen at MVHS occurred despite
having a larger percentage of students taking the Algebra I CST being composed of
ELL students. In the baseline year, just over 40% of students taking this exam at
MVHS were ELL while a year later, that percentage grew by more than 7%. The
ELL sub group at MVHS saw an increase in their mean scale score of almost four
points that year as well.
The following year, 2004-05, represented the third and final year of data
analysis and data continued to support the trends noted during the prior year. MVHS
students evidenced increased achievement in all significant sub-groups with
particularly strong gains being made by the ELL students. This was evidenced by an
increased percentage of ELL students scoring at proficient or above - from 14% to
25% and an increased mean scale score among the same students - from 305.5 to
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322. Almost as impressive was the school wide improvement made at MVHS where
the mean scale score jumped from 310.2 to 318.9. After only marginal growth the
year before, Asian students saw their mean scale score grow by more than 10 points.
White students at MVHS improved by 6.7 points as well. Statewide, there were
improvements in each group and as well, but the improvement was much less, with
Asian students statewide posting the largest gain of just over 5 points, less than most
gains earned by MVHS students.
Also worthy of note was the difference in achievement evidenced between
Asian and White students and their Hispanic peers. These gaps closed significantly
in the 2003-04 testing results, but seemed to increase slightly during the ensuing
year. Statewide, these gaps declined very slightly during the years studied. At
MVHS, the Asian - Hispanic gap closed by almost 4 points while the gap between
Whites and Hispanics widened by more than 10 points, fueled mostly by a large
increase in White students’ scores at MVHS. Hispanic scores increased, but not at
the same rate.
Figures 17 and 18 below demonstrate the increased student achievement in
math based on the Algebra CST and compare MVHS students to their statewide
peers using (a) mean scale scores and (b) percentage of students scoring proficient
and above.

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Figure 17 – Growth on CST Algebra I Mean Scale Scores
13.8
10.3
14.2
24.4
6.4
20.3
0.7
1.3
1.1
-0.1
-3.4
-1.7
-5
0
5
10
15
20
25
30
All Asian Hispanic White SES ELL
Sub Group
Net Growth
MVHS Scale Score Growth State Wide Scale Score Growth

Figure 18 - Growth in Algebra I Students Scoring Proficient and Above
6
4
8
35
0
9
-3
-2
-1
-1
-2
-1
-5
0
5
10
15
20
25
30
35
40
All Asian Hispanic White SES ELL
Sub Group
Net Growth
MVHS Proficient & Above Growth State Wide Proficient & Above

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White and ELL students demonstrated the most growth on the number of
students scoring proficient and above. Statewide, however, there was marginal
growth demonstrated by White, Hispanic and Asian students.
Course Enrollment Patterns in Math. Such success at MVHS may be attributable to
the numerous factors discussed later in this chapter, but one which warrants attention
at this point is the pattern of enrollment in math classes at MVHS. The pattern
outlined in Figure 19 represents an indication of the school’s efforts to raise
expectations for all students at the school. School-wide and for all significant sub-
groups, MVHS increased enrollment in all upper level math with the exception of
Hispanic students whose decreased enrollment overall at MVHS accounted for a
corresponding drop in enrollment in higher level math.
Figure 19 – Enrollment in All Upper Level Math Classes at MVHS
34.53%
36.37%
37.87%
32.00%
33.00%
34.00%
35.00%
36.00%
37.00%
38.00%
39.00%
2002-03 2003-04 2004-05
% Enrolled in Upper Level Math
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This pattern of enrollment was also evidenced at the lower levels of math
where the numbers of students enrolled in Algebra and below remained constant at
slightly above 560 students, but the proportionate share of students enrolled in
courses below algebra decreased by a large amount. Figure 20 below demonstrates
that the make-up of students enrolled in Algebra I and below changed to one that was
comprised of many more students being enrolled in Algebra than courses below
Algebra. Specifically, enrollment in Algebra increased from 290 students in 2002-03
to 335 students in 2004-05. At the same time, enrollment in Pre-Algebra dropped
from 122 students to 71. Combined with the findings noted above at the upper levels
of math, this pattern would appear to demonstrate a school-wide pattern wherein
students were challenged by being enrolled in higher level math classes than in past
years.
Figure 20 – Distribution of Students Enrolled in Algebra and Below
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
Percentage Below Algebra Percentage Algebra
Percentage Algebra 51.69% 47.59% 59.61%
Percentage Below Algebra 48.31% 52.41% 40.39%
2002-03 2003-04 2004-05

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Other Indicators: CAHSEE and Advanced Placement. In addition to improvement in
the CST scores in math, students at the school demonstrated increased achievement
in math as evidenced by a dramatic increase in the percentage of students passing the
CAHSEE in math. During the baseline year of 2002, only 37% of students at MVHS
passed the CAHSEE in math. While this passing rate surpassed that of students state
wide, it did so by only 5 percentage points. As demonstrated in Figure 21 below,
students at MVHS dramatically improved that passing rate to 83% by the year 2005.
And while students statewide also demonstrated solid growth- from 32% to 63%, the
gap between MVHS students and their counterparts state wide grew from 5 points to
20 points during that time.
Figure 21 – Growth in CAHSEE Pass Rates: MVHS and California
37
32
57
43
87
74
83
63
0
10
20
30
40
50
60
70
80
90
100
% Passing CAHSEE
2002 2003 2004 2005
MVHS California

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At the same time that the school was working to improve achievement in
math via the CAHSEE, it was also working to challenge students at the upper end of
the curriculum. School wide data showed that the growth I enrollment in Advanced
Placement (AP) classes grew from 292 students in 2001-02 to 415 students in 2004-
05. Encouragingly, students enrolled in AP math in the last year of this study
numbered 86. Of the 57 students enrolled in AP Calculus AB, 70.5% passed the AP
exam with a score of 3 or better. Even more encouraging was the performance of
students in AP Calculus BC where 25 of 29 students enrolled passed the AP exam
with a score of 3 or higher. Combined, this means that 61 of 86 students passed their
AP exam in math for a passing rate of almost 71%. The school wide pass rate for all
AP exams was 71.3%.
In summary, findings related to Research Question 1 demonstrated a strong
pattern of achievement in math at MVHS in comparison to state wide trends. School
wide and all significant sub-groups out performed their peers statewide in terms of
growth on the Algebra I CST. In addition, students at MVHS evidenced a dramatic
increase in the percentage passing the CAHSEE and students fared well on
Advancement Placement exams. Finally, the enrollment pattern in the math
department evidenced increased achievement in that more students were enrolled in
Algebra and fewer in pre-algebra and below.
Research Question 2: Policy and Practice
The second research question asked, “What policy initiatives as well as
curriculum, instruction and related conditions seem to be related to improved math
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achievement in the school?” Policies related to improved student achievement have
been outlined in this section. In addition, the framework used to analyze findings for
this research questions includes two distinct elements: effective school design and
effective math program design. Therefore, findings for this research question have
been presented in the areas of policy, school design and math program design.
Policies Related to Improved Student Achievement. MVHS teachers and
administrators repeatedly expressed during interviews that they appreciated the
opportunity to work in an environment of high stakes assessment and accountability.
MVHS Principal Dan O’Conner felt that in combination, these policies were a major
source of what he called the “Pressure Cooker” to succeed. In particular, Principal
O’Conner felt that the way that the public has focused on standardized testing results
has forced schools to work harder and focus on academics. This was true for him
since he felt that often-times results from standardized tests formed the basis for how
schools were judged by the public. O’Conner concluded his remarks on this topic by
commenting that these policies “Are influencing us very much.”
This influence is important in that teachers and leaders at MVHS readily
accepted the increased accountability for students and for the school as a whole.
Rather than being internalized as a burden, political pressure emanating from state
and federal policies demanding accountability were accepted by the teachers and
leaders at MVHS as a positive influence. The general feeling was that policies such
as NCLB, AYP, API, CAHSEE and HQT served the school well in two distinct
ways. First, such policies were seen as increasing accountability for students, since
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presumably they would no longer be able to graduate without demonstrated
proficiency. Second, teachers and school leaders saw the increased accountability
facing the school as a whole as a means to motivate teachers to refine their craft and
collaborate on best practices.
While it may have been true in the past that graduation was measured in seat
time, teachers and leaders at MVHS saw the CAHSEE as a way to motivate students
to focus on learning. Such focus seemed inevitable since prior to the CAHSEE,
students could graduate without having to demonstrate that they had learned math to
any significant degree. Now, seat time was not enough. Current Math Department
Chair Gerardo Sanchez agreed and said that the CAHSEE “Has really helped us
motivate many of the lower functioning students who were seemingly unmotivated
in the past.” Sanchez cited the data noted above on increasing CAHSEE pass rates
as evidence that students have begun to focus on learning the concepts as opposed to
doing the minimum amount of work possible to pass the class. He also pointed to
the fact that students were now attending tutorials and asking for help during lunch
in large numbers.
Beyond motivating students, however, the policies associated with school-
wide accountability helped motivate teachers to rethink how they did business.
Former Math Department Chair Miguel Gutierrez built on this theme by stating that
he felt the CAHSEE was the number one policy motivating the practice in math at
MVHS. When asked how teachers felt about the requirement that students pass the
CAHSEE, he indicated that they welcomed the accountability. According to
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Gutierrez, “We liked the threat. It gave us some teeth and made us focus.” Math
teachers at MVHS supported this point of view in their responses to the following
item on the Math Teacher Questionnaire: The requirement that students pass the
CAHSEE to earn a high school diploma has contributed to the school’s effort to
improve student achievement. Math teachers responded to this item with a mean
response of 4.5 on the 5-point Likert scale. This would lend credence to the idea that
during the years studied, the math teachers at MVHS used policies such as the
CAHSEE requirement to their advantage and believe it contributed to their success.
The implementation of the CAHSEE also helped shape instructional practice
and was illustrated in how the school initially accepted the challenge. During his
interview, former Math Department Chair Gutierrez recounted his early efforts to
learn as much as possible about the CAHSEE by attending conferences and reading
everything he could get his hands on in order to prepare his students. When early
results showed students at MVHS had a much higher pass rate in English than in
math, he said, “I was crushed.” He reported that this experience motivated him to try
to find ways to lead the department to achieve better results in the future. Gutierrez
made these efforts despite his concern that the poor results might also have been
partially attributable to the design of the test. Rather than blame the test, however,
he reportedly accepted the challenge and researched ways to lead the department and
the students to increased success.
Another example of how such policies shaped practice was shared by current
Math Department Chair Gerardo Sanchez who enthusiastically supported the policies
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requiring school-wide accountability. He indicated in his interview that policies
requiring increased accountability for the school translated into increased
accountability for teachers as they accepted the responsibility of increasing scores.
Specifically, Sanchez said that standardized testing provided the impetus the site
needed to really begin using student achievement data in a strategic way. He also
indicated how useful these requirements were in dealing with teachers who may have
been resistant to changing to a data driven and standards-based approach.
Overcoming such reluctance was key to garnering unified action in support of their
vision. To those who initially resisted change, he reportedly told them, “You can
disagree all you want, but it’s the law, it’s here, and we need to deal with it.”
These policies changed the practice in math at MVHS and were emphasized
by Assistant Principal of Curriculum and Instruction Dan Frisch, who indicated that
the need to demonstrate growth on standardized testing results “forced us to develop
common finals and pacing calendars in all core areas.” Developing common
assessments and rubrics ensured that all students had an opportunity to succeed by
ensuring that all students were expected to learn the same material. Pacing calendars
helped teachers define their work weeks and plan their lessons. Frisch felt that this
consistency was extremely important in increasing student learning in math. Frisch
also felt that in developing these common finals, MVHS and its students had
benefited from using formats that mirrored the CST and CAHSEE exams.
In addition to state and federal policies maximizing accountability, the Los
Padres Unified School District developed a multiple measures system of
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accountability that judges the success of MVHS based on three indicators each in the
core areas of English and Math. These indicators were based on academic
achievement in grades 9-11. Basically, the school collected data on how students
performed on each of these indicators and reported aggregate scores to the District.
In essence, the school was judged by how many students performed well on each of
these indicators. In this regard, it was a similar system to the multiple measures
system in place in California for a brief period of time before the API.
For the first indicator in English, MVHS developed its own 5-point scoring
rubric to rate student performance on the final exam. The remaining two indicators
in English were the students’ final grade in the course and their CST score in English
/ Language Arts. Table 1 shows the three components used in language arts.
Table 1 – MVHS Multiple Measures System – English/Language Arts
Subject Matter
Indicator
Final Exam
MVHS Rubric
Score Final Grade CST - ELA
Weight 1/3 1/3 1/3
MVHS SCORE
5 - Exceeds Standards 5 A Advanced
4 - Meets Standards 4 B-C Proficient
3 - Approaching Standard 3 D Basic
2 - Below Standard 2 F Below Basic
1 - Far Below Standard 1 Far Below Basic
Language Arts
In math, the first indicator was a student’s performance on the CST in their
respective course. The remaining two indicators were their final letter grade in the
course and the percentage correct on their final exam. Table 2 shows how these
components in math worked within the system.
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According to Department Chair Sanchez, the multiple measures system
contributed to the overall climate of accountability and helped to clarify
expectations. Teachers knew that students, and ultimately the school, would be
judged by how well they did in earning good grades, scoring well on final exams and
doing their best on the CST.
Table 2 – MVHS Multiple Measures System – Math
Subject Matter
Indicator
Final Exam
Score % Final Grade CST - Math
Weight 1/3 1/3 1/3
MVHS SCORE
5 - Exceeds Standards 90-100 A Advanced
4 - Meets Standards 70-89 B-C Proficient
3 - Approaching Standard 60-69 D Basic
2 - Below Standard 50-59 F Below Basic
1 - Far Below Standard 0-49 Far Below Basic
Math
Assistant Principal Frisch said that although he did not feel the system was directly
responsible for improving student achievement, he felt it “definitely” supported the
focus on student achievement in general and added to the culture of school-wide
accountability. Students were not individually affected by this measure of success
since the primary use of the aggregate score was for school-wide judgments.
Effective School Design
Effective school design was operationalized in this study through a framework that
emphasized:
o Student Assessments
o Curriculum
o School Culture
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o Learning Activities.
While the curriculum and assessments noted above were rather traditional,
this study noted distinct findings for this research question in the areas of school
culture and learning activities.
School Cultures. Research in this case study indicated that the school
maintained and promoted a positive school culture that emphasized and supported
student achievement. The framework used in this study emphasized three basic
elements of effective school culture including enhanced student learning, meaningful
staff-student interactions, and ongoing professional development. While this last
item was identified by the WASC Visiting Committee as an area for future growth,
data collected in this study supported the finding that MVHS promoted a positive
school culture in the first two areas. MVHS leaders emphasized academic success in
numerous ways.
The most recent WASC report recognized the positive staff-student
interactions present at MVHS noting, “The dedicated staff often volunteers beyond
their classroom commitments…” And perhaps most importantly, “The staff
members serve as strong role models for students and are extensively involved in the
cultural life of the school…” In addition, the visiting committee also mentioned in
its report that “Many staff members serve as school club advisors, tutors for students
after school and attend the various school activities.” Teacher Rachel Suarez was
asked in her interview about why she thought more negativity and resistance to
standards-based instruction was not present at MVHS. Her answer emphasized her
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belief that teachers at MVHS were dedicated to seeing their students succeed. She
gave numerous examples of how teachers at MVHS support their students and
emphasized that for her, student needs come before her own convenience. She ended
this line of questioning by declaring emphatically, “Anything I can do for the kids, I
will do!”
Examples of this dedication were replete in the math department of MVHS.
During the years studied, no fewer than 9 MVHS math teachers had participated in a
special program emphasizing math achievement called the Jaime Escalante Project
which had as its mission, the goal of ensuring that underrepresented minority
students were able to matriculate successfully through upper level math programs.
The Escalante project offered rigorous math instruction at a local college in intensive
six week courses offered during the summer months. Current Department Chair
Sanchez reported that four of the department’s current teachers were recruited
directly from the Escalante program. In addition, four math teachers, including the
current and former department chairs sponsored the school’s chapter of the Math,
Engineering and Science Achievement (MESA) which also sought to promote
increased levels of achievement in math and science for underrepresented students.
In addition, former Department Chair Gutierrez indicated that teachers at MVHS felt
they were a part of something special. He indicated that in the past, he would never
be at his school after hours and on the weekends, but now, “I am here all the time.”
Direct observations noted that site administrators were visible and out on
campus at lunch and during passing periods. They engaged students in conversation
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and appeared genuinely concerned about their well-being. Teachers greeted students
as they entered their classrooms and students responded frequently with animated
and sometimes personal conversation. Students appeared to feel welcomed to stay in
classrooms during lunch as evidenced by the number of students in the classrooms
and not out in the quad area during lunch time. Classroom observations noted
positive interactions between students and teachers. Finally, the WASC report also
noted that guidance counselors meet individually with all students to develop
personal learning plans as a means of helping students focus on long range planning
and future success.
Learning Activities. Another important finding linked to the framework for
this research question was that learning activities at MVHS were based on student
need and emphasized critical thinking and problem solving. Evidence of this
practice included several observations made by the WASC Visiting Committee
(V.C.) who noted in part that “The V.C. observed the careful and precise
differentiation of instruction to foster critical thinking…” In addition, the V.C. also
noted that the “Mathematics Department teachers teach effective problem solving.”
Finally, the report noted that at MVHS, “Higher order thinking skills are promoted
throughout the curriculum. Activities are varied, exploratory and student-centered.
Emphasis is placed on problem solving, application and meta-cognition.” Direct
classroom observations supported this finding as teachers frequently required
students to articulate their thought process and explain their answers in ways that
demonstrated deeper levels of understanding.
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Department Chair Sanchez mentioned in his interview that focusing on
critical thinking and conceptual skills has been a conscious effort, but has not been
without dissent. He maintained that while there are still a few teachers in the
department who stick to “traditional approaches” most in the department work hard
to make learning activities challenging and relevant to students. Sanchez used his
interview as an opportunity to demonstrate a program on the graphing calculator that
allowed students to draw a triangle and then manipulate the object in such ways that
they were able to “discover” the properties of a triangle.
Learning activities that focus on building deeper conceptual knowledge are
not limited to in-class lessons or with homework. Outside activities at MVHS also
included rigorous mathematical problem solving opportunities as well. Sanchez,
Gutierrez and two other teachers co-sponsored the school’s MESA program. As a
part of their involvement in this program, students experienced college visits, various
math-related contests, problems of the week in Scholastic Aptitude Test format, and
MESA Day in which student’s compete in math related projects such as designing
bridges to see which one can withstand the most pound per square inch before being
crushed. In addition, one teacher on campus sponsored project-based competitions
tying math and drafting together. Past projects included designing solar powered
boats and in another the school sponsored a Physics Day at Knott’s Berry Farm
where students used mathematical skills to analyze roller coaster design.
Effective Math Program Design. Among the most important findings in this
case study is the finding that MVHS has worked hard to implement the elements of
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standards-based instruction. This effort was evidenced in two main areas. First,
assessments were linked to standards and second, student achievement data was used
to drive instruction. Teachers surveyed identified this one factor more than any other
as positively impacting student achievement at MVHS. Table 3 below lists those
questions related to standards-based practices that averaged a rating of at least 4.5 on
the 5- point Likert scale where a rating of 4 would indicate “Agree” and a rating of 5
would indicate “Strongly Agree.”
Table 3 – Teacher Responses to Standards-Based Instruction Items
Questionnaire Question Mean
Math Tchr Teachers at our school teach standards-based lessons. 4.83
Non-Math Teachers at our school teach standards-based lessons. 4.65
Math Tchr Our school has successfully implemented common
assessments that support increased student achievement 4.58
Math Tchr
Periodic benchmark assessments provide useful data
that our teachers use to drive instruction 4.50
Results from the questionnaires evidenced that both math teachers and non-
math teachers at the school felt strongly about the degree to which they were
teaching standards-based lessons. In addition, math teachers overwhelmingly
perceived that common final exams and period benchmark assessments played a
major part in the improved student achievement in math at MVHS.
The effort to ensure standards-based instruction was being implemented at
MVHS approximately three years before the first year of the study. According to the
former department chair, the principal and the assistant principal, the District had a
strong assistant superintendent, Sandra Alturas, who actively supported standards-
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based instruction and who was later became superintendent in part due to her
academic expertise. During the years immediately preceding the study, Dr. Alturas
pushed for the implementation of standards-based instruction and held school sites
accountable for implementing such practices. The former department chair gave a
strong example of this effort. Gutierrez said that Alturas required him to make a
presentation to the School Board detailing the degree to which the math standards
were being taught at MVHS. Gutierrez responded by creating a simple grid where he
identified the standards along with a “yes” or “no” to indicate whether a given
standard was being taught at MVHS. As he recounted the story, Gutierrez designed
a simple chart to present that included relatively few “no's". This was apparently not
good enough for the Board who reportedly queried him for an explanation of each
“no” and asked for justification as to why it was not being taught.
Since that time, the effort to implement standards-based instruction has
progressed and was evidenced in the study in several ways. First, MVHS has
developed common final exams for each math course taught at the school. During
the development process, Gutierrez was asked to list the standard(s) measured by
each item on the exam and submit the draft exams for review. Teachers were only
allowed to administer the exams after the district had determined that all items were
aligned to appropriate standards. In addition, math teachers at MVHS collaborated
to develop common review guides for these common final exams which were used
by most teachers in the math department.
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Standards-based instruction was also evidenced the math department’s focus
on mastery learning. While none of the teachers interviewed used this terminology
during their interviews, they all emphasized the importance of re-teaching and
reviewing as often as necessary for their students to master the standards. Teacher
Rachel Suarez said in her interview that it was regular practice to spend more than a
few days reviewing for unit exams as a means of ensuring mastery. When Suarez
was asked how she and her peers felt about spending so much time on these reviews,
she replied that math teachers at MVHS generally agreed that these efforts were
worth the investment of time since student achievement results demonstrated
increased performance.
This standards-based approach focused on learning for all students where
lessons across the department were delivered according to pacing plans that ensured
that all students had access to the same rigorous curriculum. Direct observations of
Algebra I classes during the same week demonstrated that all classes observed were
working on graphing linear equations. Demanding the same access to rigorous
curriculum for all students was also included in visual reminders to students and staff
in the form of posters with the symbol used in London subways, “Mind the Gap.”
While this phrase had a completely different meaning in the context of the London
subways, at MVHS it served as a constant cue to teachers at MVHS. Department
Chair Sanchez was asked in his interview to explain what he felt was meant by the
slogan and he replied that everyone at MVHS knew that it was intended to remind
teachers that the achievement gap must be closed.
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Of the many standards-based practices implemented at MVHS, teachers and
administrators at MVHS singled out one practice in particular for much of the credit
for the improved performance in Algebra. The site developed cumulative quizzes
which were administered after each unit exam as a means of ensuring that students
had retained the knowledge and skills necessary to continue to master standards long
after their initial assessment. MVHS math teachers used the cumulative quizzes as
part of a three day assessment process after each unit. First, a given unit exam was
administered on day 1, and as the students finished the exam, they were given a
review sheet with between 50 and 100 items meant to prepare them for the
cumulative quiz. Students were then asked to complete the review guide in the time
remaining in the class or as homework if more time was needed. The problems on
the review guide were aligned to the standards covered in earlier units. On the day
following the unit exam, day 2, the teacher would typically work with students on
the answers to the problems on the review guide. On the third day, students would
take a cumulative quiz covering concepts from all units studied to that point except
for the most recent unit. Table 4 illustrates this process.
Table 4 – Cumulative Quiz Process
Day 1 Day 2 Day 3
Unit Studied
Unit Exam
Covers Units:
Review Guide
Covers Units:
Cumulative Quiz
Covers units:
1 1 N/A N/A
22 1 1
33 1,2 1,2
4 4 1,2,3 1,2,3
5 5 1,2,3,4 1,2,3,4
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Another critical component of standards-based instruction was that classroom
practices exhibited effective lesson design and promoted a high degree of student
engagement. Such practices were evidenced at MVHS in several key ways.
Classroom observations confirmed high student engagement. In one class, students
were asked to come to the board and work problems while explaining the thought
process they used to solve the problem to their peers. In another class, the teacher
used a random name generator that projects the selected student’s name on the
television monitor. The teacher then asked that student to work a problem and
explain the solution to his or her peers. Observations made during these classes
supported the finding that there was a high degree of student engagement during
these lessons.
Another way teachers made sure that students were engaged in their own
learning was through the use of appropriate instructional technology. One main way
teachers at MVHS worked to achieve this was through the widespread use of
graphing calculators. All teachers interviewed and both the former and current
department chairs mentioned this as a useful technique. One particular program
allowed students to enter algebraic equations into the device and then work the
problem step by step. If at any time the student’s answer was incorrect, the program
provided immediate feedback to the student. Teachers credited this immediate
feedback, combined with most students’ inherent interest in technology with
increasing student engagement in the math department. Gutierrez emphasized his
desire to hire teachers who were able to work with the technology adding that it was
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one of the first questions he asked of new teacher candidates. If the candidate
responded that he or she did not know how to use the technology, Gutierrez indicated
his response was always, “Are you willing to learn?”
Student engagement was also facilitated by the school’s commitment to
keeping class size lower in the lower level math classes. This commitment was
evidenced in the school’s participation in the state’s class size reduction program for
Algebra and Pre-Algebra. The most recent WASC report noted this commitment
(p.42) and Figures 22 and 23 depict the average class sizes of all math classes in
2004-05 and the average class sizes for Algebra and below during the three years
studied. Worthy of note was the significant reduction in the average class sizes of
Algebra Fundamental and Pre-Algebra.
Figure 22 – Average Class Size for all Math Classes in 2004-05
15.4
26.5
29.6
28.8
36
34
25.5
29
26
17.8
22.3
32.3 33
0
5
10
15
20
25
30
35
40
Pre Algebra
Algebra I
Algebra Fundamentals
Algebra II
Algebra II H
Geometry
Geometry H
Pre Calculus
Pre Calculus H
Calculus
AP Calculus AB
AP Calculus BC
AP Stats
Students Enrolled
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Figure 23 – Average Class Sizes for Algebra and Below for 2002-03 – 2004-05
20.3
22.3
23.3
16.3
22.5
18.3
17.8
22.3
15.4
0
5
10
15
20
25
Pre Algebra Algebra I Algebra Fundamentals
A vgC lassS ize
2002-03 2003-04 2004-05

The curriculum at MVHS was influenced strongly by student need and was
demonstrated by student assessment data. Examples of this important aspect of
standards-based instruction were many. In one such case, student achievement data
was used to help develop the Algebra Fundamentals course. At the end of the 9
th

grade, students performing poorly in their pre-algebra class were identified as being
in danger of not passing the CAHSEE. These students were placed in the Algebra
Fundamentals course, which was designed to focus on those standards most likely to
be tested on the CAHSEE. The school had developed an assignment sheet with all
assignments laid out for the whole semester and allowed students to track their own
progress. In another example, teachers used data from the most recent cumulative
quiz to identify areas for re-teaching. Teachers then went back and spent time on
instruction in those areas. In this way, re-teaching became a high priority in the math
department at MVHS.
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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?” Data analysis
for this research question is based upon the framework of Bolman and Deal’s Four
Frames of Leadership. The findings for this research question have been presented
according to these four frames which are detailed in Figure 13 (p. 111).
The Structural Frame. The structural design of the site administrative team
supported improved student achievement in couple of key ways. First, MVHS had
an assistant principal who was directly aligned to curriculum and instruction.
Interviews and an official job description confirmed that this position was in charge
of all testing and assessment at the site. In an atmosphere of high stakes testing and
accountability, allowing one person to focus efforts in this area was seen as essential
and was emphasized by Principal O’Conner and teachers interviewed who credited
this administrative structure with providing stability and consistency in the
assessment process. O’Conner reported that this process was so deeply respected at
the site that during the weeks leading up to testing, teachers knew to give AP Frisch
a wide berth since he was in “testing mode.” Department Chair Sanchez credited the
work of Frisch in preparing for high stakes testing with reducing the anxiety level of
teachers which in turn, allowed them to focus on instruction rather than
administrative issues.
In addition to the responsibilities for testing, the AP of Curriculum and
Instruction worked with the district staff to provide student achievement data to the
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teachers of MVHS. Department Chair Sanchez reported that Frisch was widely
respected by the teachers at MVHS for his ability to recall any aspect of student
achievement at MVHS when asked. Principal O’Conner reported that Frisch was
referred to as “Data Dan” for his depth of knowledge and understanding of student
achievement data issues.
O’Conner emphasized that an important aspect of the administrative team
was the need to provide adequate student support services so that the AP of
Curriculum and Instruction and the Principal could focus on academics. The
school’s structure was well-suited to this task as well. The Student Services Center
was located directly across from the principal’s office and houses all assistant
principals, the counselors and a comprehensive career center. Principal O’Conner
reported that this design was meant to ensure a student-centered approach to
education at MVHS. When the school grew beyond the ability of its Assistant
Principal of Student Services to work effectively, O’Conner lobbied the district and
was awarded with an additional AP of Student Services. O’Conner’s request was
based on his strong belief that if student discipline was not handled effectively it
would be extremely difficult to devote sufficient attention to academics. The district
agreed and invested in the additional position.
Having a facility that is designed to support academic achievement is also
important to the efforts of MVHS. In this regard, it was found that the design and
maintenance of the school facility both worked to support student achievement by
fostering a sense of pride and promoting increased teacher collaboration. The school
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was designed to be built on only 16 acres of land on the site of a former middle
school. AP Frisch and O’Conner both reported that this design had teacher
collaboration clearly in mind. One visible sign of this design was the presence of
“pods” connecting most of the classrooms to others classrooms. These pods allowed
teachers to store common materials and provided then with a place to meet and
collaborate on issues of importance.
The design of the school did not, however, prove universally effective.
O’Conner and Sanchez expressed concern that not all teachers were able to take
advantage of this since some math teachers had to move around during the day.
Teacher traveling was made necessary by a growing student population that made it
necessary to assign a few of the math teachers in another building for parts of the
school day. Despite this limitation, O’Conner and Frisch confirmed that the pods
served as useful hubs and promoted collaboration. Direct observations confirmed
that teachers frequently walk back and forth to confer with their peers and interviews
confirm the utility of these pods as well. Gutierrez told of how on several occasions,
when things had seemingly gone wrong with the graphing calculators, he was able to
help teachers in need because he was accessible. These adjustments would not have
been practical if teachers had to leave their rooms unattended in order to
communicate with their peers. Because the pods were centrally located and windows
are abundant, teachers can confer while solving such problems with students still in
direct sight.
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The pods are not the only way in which the structure and maintenance of the
school work to support student achievement. Because the school was so small, it had
an intimate atmosphere that appeared to reduce anonymity. The quad in the center of
the school served as a gathering place and appeared to encourage interaction among
students. In addition, the newness and cleanliness of the classrooms evidenced the
sense of pride students and staff have taken in their facility. This emphasis on
cleanliness was readily apparent during the research visits to the school and was
evidenced in that there was no graffiti visible at any time. Gum was not allowed
which reduced unsightly spots on the ground and trash was picked up immediately
after the lunch period in an organized and consistent fashion. The aesthetic use of
pavers instead of concrete in the parking lot and on campus added a touch of
elegance that made the school feel “upscale.”
The Human Resources Frame. One of the most important findings in this
study was that hiring practices at MVHS promoted improved student achievement in
math. The principal, assistant principal in charge of curriculum and instruction,
current and former math department chair all expressed a strong belief that hiring the
right people in the math department played a critical role in improving student
achievement in math. In his initial interview, O’Conner quoted Jim Collins
repeatedly, emphasizing that MVHS did everything it could to “Get the right people
on the bus.” Dan Frisch, Assistant Principal of Curriculum and Instruction expressed
his belief in the importance of this aspect of the school’s success by indicating that it
was an “absolutely key” ingredient to the school’s success. He elaborated by saying
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that he and the principal had hired almost every teacher at the school with only a rare
few arriving as transfers.
Former Department Chair Gutierrez was one of the original twelve teachers
hired in the school and before the school was opened, he served on a curriculum
design committee for two years. The committee was empanelled to make
recommendations about the design of the math curriculum and program. Mr.
Gutierrez expressed a deep sense of ownership of the math department at the new
school from the very beginning. Gutierrez knew his two children would be attending
the school and thus had a vested interest in the school’s success. He began the
recruiting effort by convincing an AP Physics teacher from nearby Hillside High
School to transfer to MVHS.
Both Gutierrez and current Department Chair Sanchez, gave further specific
examples of their efforts to control who was hired in their department. One example
cited by Gutierrez was that Sanchez was his former student at MVHS and was
recruited by Gutierrez to replace a teacher they both knew would retire about the
same time that Sanchez would graduate from the university. This trend continued
when Sanchez became Department Chair. Sanchez’ talent and forward thinking was
recognized and valued by Gutierrez and O’Conner who both supported transitioning
Sanchez into the leadership position. Sanchez then promoted the hiring of Aaron
Hogan, himself a former student of Sanchez at MVHS. Illustrating this point even
further, Gutierrez told of a former MVHS student currently attending a local college
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whom he has already identified as the probable successor to a current MVHS teacher
who was said to be retiring approximately four years in the future.
Two other current and two former teachers in the math department were
targeted for recruitment as participants in the Escalante Project, noted earlier. Tom
Takada and Rachel Suarez were both participants and were recruited to teach at
MVHS when current MVHS math teachers in the program became acquainted with
the quality of their work. In addition, another current math teacher at MVHS, Tina
Chow was recruited as a top prospect out of a nearby university after her successful
student teaching experience with Gutierrez.
The Political Frame. MVHS leadership and teachers found it difficult to
discuss the political aspects of change during their interviews. They consistently
indicated that there were very few political issues that they had to deal with during
the years studied. As mentioned earlier, the staff and leadership at MVHS generally
worked free from interference and there appeared to be a high degree of mutual trust
as noted in the most recent WASC report. O’Conner and Frisch both credited this
ability to work free from interference with a large part of their success. A noted
exception to this was that MVHS was forced to implement a district mandated math
intervention program.
This series of events began when the district administration directed that
MVHS implement a computer assisted instruction program designed to assist low
achieving students. This intervention program was based primarily on the use of the
software River Deep which was in use at the feeder junior high school at the time the
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decision was made. According to teachers and administrators interviewed at MVHS,
they were afforded little opportunity to participate in this process. This reportedly
caused initial reluctance to support the program.
The current department chair noted several other problems with the program
that he said contributed directly to its demise. First, students were placed in the
program based on teacher recommendations made at the middle school. Sanchez
reported that frequently, teachers at MVHS found these recommendations to be
inaccurate based on their performance in math at the high school. In one such case
cited by Department Chair Sanchez, a student had been placed in the River Deep
program who ended up being the top performing student in his Algebra I class.
Sanchez indicated that another major concern of the program was that it
required students to master one concept in the progression before moving on to
subsequent modules in the program. While in general, teachers supported the
concept of standards mastery, student data collected at the time showed that students
often went the whole semester mastering only two or three concepts. This, Sanchez
felt was due to the absence of accountability ensuring that there was steady and
consistent progress. Apparently, students were allowed to languish in the same
module for lengthy periods of time. Finally, there was a lack of communication
between classroom teachers and the math lab teacher and little coordination between
what was being taught in the regular math classroom and the efforts of the lab.
The teachers in the math department and the principal reported that they felt
strongly that these observations made continuing with the program unacceptable.
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River Deep was in place for a period of three years before Principal O’Conner made
a decision to meet with district officials and communicate his concerns. Following a
lengthy “heart to heart” discussion with district leadership, it was agreed to end the
effort after three years. O’Conner credits the district leadership with listening to the
site and allowing them to eliminate the program and instead, design an intervention
model that would be supported fully at MVHS.
Despite these initial misgivings expressed by the staff at MVHS during their
interviews, the fact remained that the River Deep intervention effort was in place
during the time the school had evidenced strong gains in student achievement in
math. This issue necessitated a more thorough investigation to determine whether
River Deep had positively impacted student achievement despite teacher and
administrative objections. Follow up interviews were held with site administrators
and the math department chair to challenge their determination that the River Deep
program was not related to the growth demonstrated by the school during the same
time the intervention was in place. These interviews and subsequent analyses of test
data and master schedules revealed the following:
1. The students enrolled in the River Deep program were almost entirely
enrolled in the school’s Pre-Algebra course.
2. All students enrolled in Pre-Algebra, and therefore River Deep, took
the Standard Math CST and not the Algebra I CST upon which the
study is based.
3. The River Deep Program did not cover the Algebra I standards.
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4. Relatively little growth was evidenced in terms of modules passed in
the program.
These four basic facts along with the existence of numerous other positive
elements supported in the data collected in this study make it highly unlikely that the
River Deep program contributed to the increased student achievement at MVHS.
That said, it was recognized that the possibility existed that River Deep helped a
limited number of students master Pre-Algebra standards during the first and second
years of the study and therefore, it could have indirectly contributed to increased
achievement in Algebra for a small number of students in the second and third years
when they were enrolled in Algebra I and took the Algebra I CST.
Another important finding related to the political frame of reference was that
MVHS was able to avoid traditional obstacles to restructuring. Assistant Principal of
Curriculum and Instruction Dan Frisch said it best during an interview when he
expressed, “MVHS didn’t restructure, we structured.” He emphasized this point to
convey his belief that MVHS was afforded the rare opportunity to build their school
from the ground up. This process occurred only a few years before the onset of
standards-based accountability. Gutierrez supported this point of view during his
interview when he elaborated on the school’s ability to select teachers of their
choosing. Since MVHS was the first high school in the district, there were no pre-
existing high school teachers in the district who had contractual rights to transfer to
the new school. Principal O’Conner expressed that a very few middle school
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teachers were granted transfers to the school, and therefore, MVHS was able to hire
whomever they felt was best.
The Symbolic Frame. Site Leadership at MVHS made strong use of
ceremonies and symbolism to promote a culture conducive to high student
achievement. From its inception, MVHS worked hard to promote a sense of pride in
the school through ceremony and ritual. Gutierrez recounted with much excitement
the blessing of the school that was carried out in a ritual performed by members of
the local tribe of Native Americans. In addition, the symbolism associated with the
school’s mascot, the eagle appeared almost everywhere in the school. The most
prominent display was a gift of a recent graduating class. A large statue of an eagle
taking flight sat prominently in the open area adjacent to the school’s entry and
served to greet everyone who entered the school. Observations noted that countless
eagles adorn the principal and assistant principals’ offices, the main office, student
center and teachers’ classrooms.
Principal O’Conner went so far as to express his strong belief that shaping the
culture of the school through symbolism was one of his greatest strengths as a leader.
In his interview, he told the story of the prairie chicken that he liked to repeat to his
students annually. In the tale, an eagle was born into a prairie chicken family and
grew up behaving as a prairie chicken would. As the story went, one afternoon the
family of prairie chickens watched as eagles soared overhead. When the eagle in the
prairie chicken family asked what kind of birds he saw in the sky, he was told by the
other prairie chickens that they were eagles and that he could never hope to be like
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them. Sadly, the eagle lived and died as a prairie chicken never realizing his
potential. Principal O’Conner said that he repeats the story as often as possible and
emphasized the point of the story that “As you think, so shall you be.” To ensure
this point was never forgotten, a figure of a chicken sits high on a shelf facing all
who enter his office with the slogan, “No Prairie Chickens Here!”
MVHS leaders also made strong use of ceremonies and school rallies to
motivate students at critical times of the year. Interviews unanimously recounted the
importance placed on the annual all-school barbecue that was meant to motivate
students to do their best on standardized tests. O’Conner elaborated on the event’s
importance in an interview by addressing potential objections this way, “If I’m the
assistant superintendent of business, I might question spending $10,000 on a school
barbecue, ‘hey is this the best use of our money?’ But if I’m a site administrator
reaping the benefits of kids doing their best on the exams, then yeah, I think it’s a
great investment.” Teachers interviewed also noted how much they felt it helped to
give students a snack – Knott’s Berry Farm cookies – before administration of the
actual CAHSEE. Frisch noted that the practice had now become an expected part of
the culture; so much so that students often asked, “Where are the cookies?” when
they knew the test was coming up.
Research Question 4: Instructional Leadership
The fourth research question asked, “How was instructional leadership
important in improving a) the math programs/strategies and b) math achievement
among students?” The framework used to analyze data for this research question
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emphasized five discreet areas of practice. Among these areas were (a) establishing
a vision for learning, (b) Supervision of Instruction, (c) community and political, (d)
Establishing a culture of teaching and learning, and (e) Making data-driven decision
making. Research at the site indicated that there were significant efforts made in all
areas except item (c) above where those interviewed repeatedly expressed that
politics and community involvement had little if anything to do with their academic
program. The findings presented in this section have been aligned to the remaining
four areas of practice.
Vision for Learning. The site leadership at MVHS engaged in effective
instructional leadership in numerous ways. One of the most important areas where
this leadership was demonstrated was in the development of a strong vision for
teaching and learning. The site leaders at MVHS worked to establish an overall
climate at the school that promoted increased student achievement. During
interviews, teachers and administrators indicated how much they respected the
principal’s efforts in this regard. One way O’Conner earned the respect of his
colleagues was in how he publicized and promoted a new school slogan each year.
These annual mantras were designed to motivate the school’s teachers and student
and ensure that they stay focused on teaching and learning. Direct observations
showed that teachers demonstrated their respect and support for these efforts by
posting these slogans in their rooms. Posters including such slogans as “Make it
Happen,” “Mind the Gap” and “Constant and Never Ending Improvement” were
displayed prominently, often directly above the central white board and always in
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direct line of sight of the students. In more than one interview, teachers reported
how much they appreciated the principal’s efforts to outdo what had been done the
year before.
Teachers actively supported the vision for teaching and learning that was
promoted by the principal and was apparent in how they responded to items in the
questionnaire. One such item asked teachers to rate the following statement: There
is a shared vision for increased student achievement. Teachers responded to this
item with a mean rating of 4.53 on the 5-point Likert scale used on the questionnaire.
Teachers rated this item sixth highest among 75 total items. Teachers also supported
this idea during their interviews. For example, when Math Department Chair
Sanchez was asked if students and teachers bought into these efforts, he replied,
“Absolutely,” and said students often challenged each other in the halls with these
slogans. AP of Curriculum and Instruction Frisch expressed said that the school’s
nationally recognized speech and debate club students often weaved these slogans
into their speeches and often won, at least once being recognized as National
Champions. What might have been seen as trite was accepted at MVHS as a
meaningful part of the culture.
Supervision of Curriculum and Instruction. Another indication that the site
leadership at MVHS provided strong instructional leadership was demonstrated in
their efforts to supervise the curriculum and instruction at MVHS. As noted earlier,
the site used student achievement data showing a lack of progress to eliminate a
course implemented at the direction of the district. In addition, the principal,
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assistant principal of curriculum and instruction and the math department chair
demonstrated regular oversight of the offerings at the site to ensure their math scope
and sequence were meeting the needs of their students. Examples of this include the
elimination of non-standards-based courses such as Consumer Math as well as the
development of new standards-based intervention courses such as Algebra
Fundamentals. The commitment to ensuring the success of these courses was
demonstrated in their efforts to outline standards-based assignments for the entire
course. In addition, formative assessments were developed to guide instruction and
emphasize re-teaching. These cumulative quizzes were used to help teachers design
subsequent lessons to re-teach concepts and intended to increase retention of content
standards over time.
MVHS leaders also engaged in effective monitoring of instruction. One way
this was accomplished was with regular visits to the classrooms. Teachers reported
that they felt trusted by the administration and Principal O’Conner reported that he
worked with his staff to establish a common language and set of expectations so that
teachers would feel comfortable with the consistency they expected when they were
evaluated. The most recent WASC report supported this finding by noting, “Teacher
evaluations are viewed as supportive and helpful.” Another important avenue for the
supervision of instruction was demonstrated in the process of teacher evaluation
which included measurable objective. O’Conner and Math Department Chair
Sanchez both reported that it was common for teachers to include measurable,
performance-based objectives in the evaluations. Examples cited included objectives
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such as establishing as an objective that a certain percentage of students in their
classes would pass the CAHSEE in their first attempt.
The Beginning Teacher Support and Assessment (BTSA) program was also
mentioned prominently in the most recent WASC report and was seen as a means of
monitoring the progress of new teachers in addition to providing much needed
support. New teachers frequently have been assigned to numerous different courses
and classrooms during their first few years, making it critical to provide support and
encouragement. On this topic the WASC Visiting Committee noted that, “BTSA
teachers have district mentors for observation and assistance. This was in addition to
the assistance provided by department chairs and other experienced staff.”
A Culture of Teaching and Learning. MVHS built a culture of teaching and
learning based on the elements included in the framework for this question included
in Table 4. O’Conner demonstrated his respect for students and staff in a number of
ways and helped build a collaborative culture in his school that included many of the
elements associated with professional learning communities. First, teachers at
MVHS focused on student learning. This was evidenced in their frequent review of
student achievement data to drive their instruction. Teaching was the variable that
was manipulated in an effort to achieve a constant high level of learning. In
addition, MVHS efforts were consistent with PLCs in their move away from
remediation and emphasis on intervention. Remedial courses were eliminated from
the curriculum and intervention courses and tutorials were implemented.
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The high level of teacher collaboration was also indicative of the site’s efforts
to implement an effective PLC at MVHS. Teachers in the math department worked
collaboratively to develop common assessments and performance rubrics. This
effort was not limited to the math department. In fact, Principal O’Conner indicated
that at least two core departments were ahead of the Math department in this regard.
Further evidence of the effectiveness related to teacher collaboration can be seen in
the resukts to the teacher questionnaire. Specifically, the following items support the
idea that teacher collaboration was a key element in the effort to increase student
achievement in math:
1. Teachers collaborate to develop common assessments and rubrics.
(4.17 on 5.0 Likert Scale)
2. Teacher Collaboration has played a key role in increasing student
achievement in math. (4.5)
3. My principal actively supports opportunities for staff members to
collaborate and plan mathematics lessons and units. (4.08)
4. The school leader encourages faculty members to dicuss effective
math instructional strategies. (4.0)
5. The school leader provides opportunities for faculty members to
discuss mathematics instruction. (4.0)
6. Our site leaders emphasize a culture of collaboration as a means of
improving instruction at our site. (3.92)
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The Math Teacher Questionnaire also revealed a pattern of perception at the
school that leaders acted on their belief that student learning was their core mission.
Professional learning communities also emphasize rigor and clearly articulated
learning goals. The teachers at MVHS demonstrated their strong belief that these
elements were in place based on their response to the following items:
1. The Master Schedule at our school is built based on student need. (4.0
on 5.0 Likert Scale).
2. Student need is a major consideration when making teacher
assignments in math at our school. (4.08).
3. The math achievement goals and measures for my school were clearly
articulated and easy to understand. (4.67).
4. Site leaders have high expectations for student achievement in math.
(4.25).
Data-Driven Decision Making. MVHS leaders emphasized the use of student
achievement data to effectively support and impact increased levels of student
achievement. The use of data to drive instruction at MVHS emphasized both
formative and summative assessments. Standardized testing, performance on final
exams and grade distributions were all used to make qualitative judgments about the
effectiveness of the instructional program at MVHS. Formative assessments such as
the cumulative quizzes noted above were used to adjust instruction and guide re-
teaching efforts. Math teachers strongly supported this element of practice when
they collectively rated the following the following item with a 4.58 on a 5.0 Likert
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scale: Our school has successfully implemented common assessments that support
increased student achievement.
Effective use of student achievement data was such an important point of
emphasis that site and district leaders worked together to prepare a detailed
presentation that was used as a way to kick off the school year. The annual
presentation highlighted student achievement data based on summative data from the
prior year was used to identify successes, outline areas of concern and set goals for
the coming year. Math Department Chair Sanchez reported in his interview that this
presentation had served as the basis for the math department’s annual goals. Former
Department Chair Gutierrez also told of the importance of this day and of how
effective it was at raising the staff’s anxiety about student achievement. Reportedly,
it was also effective at eliminating false perceptions of effectiveness and smugness
among some staff members.
Department Chair Sanchez built on this focus on summative data and applied
it to the math department in several ways. First, as noted earlier, the math
department established its annual performance goals based on the data provided to
the MVHS staff at the annual data meeting described above. In 2004-05, for
example, this data driven approach was exemplified in the following departmental
goals for math:
1. Include the Assistant Principal of Curriculum and Instruction in our
departmental meetings.
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2. Continue to develop test prep materials for the standardized tests our
students take.
3. Revise the order of curriculum to better align with standardized tests.
4. Develop lessons on the concept of standard deviation and have one of
our teachers with expertise in this area present model lessons.
5. Continue to develop success strategies for the Algebra Fundamentals
course.
6. Improve Communications with the Math Lab intervention teacher.
7. Remain current on changes to the CAHSEE in math
8. Improve student performance on standardized tests including Algebra
Formative data and in class assessments were also used to shape the direction
of the instructional program at MVHS. At the time the research was conducted, the
math department was using cumulative quizzes in Algebra, Pre-Algebra and Algebra
Fundamentals. The results of these quizzes were used to drive individualized
instruction and to design lessons to re-teach concepts that students failed to master.
These formative assessments also helped the leaders in the math department to
identify other goals for the current year that demonstrated a continued emphasis on
using formative assessment data to drive decision making at the school. Among the
additional departmental goals were:
1. Emphasize re-teaching in all courses.
2. Expand the use of graphing calculators to incorporate updated
software programs.
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3. Using CST released problems as daily warm-up activities and sponge
activities.
MVHS Math Department Chair Sanchez also worked hard to support the use
of student achievement data as a driving force by redirecting the focus of
departmental meetings away from administrativia and towards the examination of
student work and student achievement data. Math teachers who were interviewed
confirmed that issues such as the development of the cumulative quizzes and student
performance on standardized tests had now become major topics of discussion.
Using departmental time to discuss day-to-day operational issues became less
common and Sanchez indicated that such matters were now routinely handled during
the course of the regular day. Department meeting agendas and notes confirmed that
at least some time was spent discussing matters such as departmental polo shirts, but
the vast majority of items discussed were directly related to student achievement.
Research Question 5: Strategies to Overcome Lack of Subject Matter Expertise
The fifth research question asked, “How did instructional leaders respond in
academic areas in which they were not experts?” While many of the strategies
discussed in this chapter were detailed in earlier findings, the following strategies
identified in the framework for this research question were evidenced at MVHS.
The initial part of the framework for this research question involved a three-step flow
chart used to assess a principal’s relative expertise in math. During one of his
interviews, Principal O’Conner reported that he did not have a credential in math, did
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not major or minor in math, and had never taught math. Therefore his expertise level
in math was determined to be “low,” an assessment with which O’Conner agreed.
Chapter one outlined that a basic assumption of this study was that site
leaders must work in a variety of ways to overcome their own lack of expertise in a
given field of study. In this case, Principal O’Conner effectively used the following
strategies identified in the second framework for this research question detailed
earlier in Table 5.
1. Delegate Leadership to Assistant with Greater Expertise
2. Empower Department Chair
3. Emphasize Inquiry and Problem Solving
4. Emphasize Strategic Teacher Assignments
5. Emphasize Revised Course Scope and Sequence and/ or Curriculum
One of the first things the Principal at MVHS did was to effectively delegate
instructional duties to a strong assistant principal of curriculum and instruction.
Those interviewed in this study consistently pointed to this as a significant factor in
the school’s academic success. Principal O’Conner indicated that AP Frisch
demonstrated strong leadership in the following areas:
1. Tracking and disseminating student achievement data to the
department in an effort to encourage data-driven decision making.
2. Organizing the logistics of the school’s standardized testing program
in order to “take the pressure off the teachers.”
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3. Monitoring student progress and keeping them informed of their
responsibility to do their best on these high stakes testing.
4. Building the school’s master schedule with input from the department
chairs.
5. Serving as the summer school principal to ensure instructional
continuity during this important learning session.
Department Chair Sanchez indicated that Frisch worked hard to help prepare
the data-rich presentation at the beginning of the year and that subsequently served
as the basis for departmental goals and objectives. In his interview, Frisch was
reluctant to claim any credit for his ability to use student achievement data in
strategic ways, yet readily produced and referenced numerous thick binders of
student achievement data and cited what he felt were strengths and weaknesses of the
school’s academic programs at will.
Another strategy used by O’Conner to respond to the challenge of improving
student achievement was to empower the department chairs with the authority to
make decisions that positively impact student achievement. Both the former and
current department chairs reported that they felt empowered by their principal to
make important decisions that affected student achievement in math. Sanchez and
Gutierrez both played an important role in the teacher assignments noted earlier as
critical in the success evidenced at MVHS. In addition, they each described being
entrusted with major responsibility for implementing key components affecting their
discipline. Gutierrez was an integral part of implementing standards-based practices
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including the site’s strategy for meeting the challenge of preparing students to pass
the CAHSEE and the development of the Algebra Fundamentals course. Sanchez
has been instrumental in designing the cumulative quiz program and in emphasizing
the use of student achievement data, instructional technology and emphasizing re-
teaching.
Principal O’Conner confirmed the importance of these efforts and
emphasized that he has always relied on his department chairs for strong leadership
since, “They are the experts.” Assistant Principal Frisch echoed this sentiment in his
interview stating that he thought he and the principal were “facilitators” and that they
both looked to the department chairs for “real leadership.” He called them the true
“curriculum leaders.” Evidence of this leadership was demonstrated in the following
activities:
1. The Math Department Chair at MVHS played a strong role in
recommending teacher assignments that are used to build the master
schedule.
2. The Math Department Chair at MVHS led collaborative efforts to
review student achievement data and revise instruction as needed.
3. The Math Department Chair at MVHS was actively involved in
recruiting teachers for their departments.
4. The Math Department Chair at MVHS played a vital role in
curriculum development and revision.
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Another strategy identified in the framework is that MVHS promotes a
culture of inquiry and problem solving by encouraging constant reflection on student
achievement data. While examples reflecting this practice have been cited earlier in
this report, together, they reflected an overall strategy that seems to have contributed
to the improved student achievement in math at MVHS. Efforts to use student
achievement data to promote a culture of inquiry and problem solving included:
1. Using student achievement data as the basis for departmental goals
and objectives.
2. Using department meetings as a forum for reviewing student
achievement data.
3. Using student achievement data from the Cumulative Quizzes to
develop re-teaching lessons.
4. Teachers setting goals and objectives for their students’ achievement
and using them as a part of their annual evaluation.
These practices were noted in interviews and evidenced in the school’s most
recent WASC report which noted that “MVHS teachers analyze data throughout the
entire school year, and use that data to modify instructional practice.” The report
also confirmed that MVHS encourages and supports collaboration within the
departments to further develop and enhance acceptable assessment techniques.
Leaders at MVHS used strategic teacher assignments to effectively promote
increased levels of student achievement in math. An interesting and perhaps
significant practice at MVHS was that earning seniority was not equated with a
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corresponding “right” to avoid teaching the school’s most challenging students.
While in other schools it might have been commonplace for veteran teachers to
migrate towards teaching all of the upper level classes, thereby leaving the lower
level classes to new and less experienced teachers, MVHS avoided this self-
defeating trap. Current Department Chair Sanchez indicated during his interview,
“We don’t want a seniority-based system here. If you’ve been here the longest, it
means you have valuable experience that we need at the lower levels.”
AP Frisch and Sanchez indicated that during the master schedule building
process, math teachers were asked to indicate a preference of classes they wanted to
teach, but there was an expectation that one’s preference would include at least one
section of Algebra or lower. Current Math Department Chair Sanchez had been at
the school for ten years and taught a mix of classes that included both advanced
placement classes as well as Algebra and Algebra Fundamentals, the intervention
class at MVHS. Reviews of the master schedules at MVHS confirmed this
assignment pattern and revealed that this was not a new trend. Figure 24 represented
the 2002-03 master schedule grid demonstrating teaching assignments that were
typical at MVHS in math.
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Figure 24 - 2002-03 MVHS Math Department Master Schedule
Teacher Period 1 Period 2 Period 3 Period 4 Period 5 Period 6
Teacher A Alg I Geometry Alg 2 Geometry Alg I
Teacher B Alg 2 Alg Fund AP Stats Alg Fund Alg 2
Teacher C Math Lab Math Lab Math Lab Math Lab Math Lab
Teacher D PRE-CALC Calculus Geom H Alg I Alg I Alg I
Teacher E Pre Alg Alg I Geometry Geometry Geometry
Teacher F Alg 2H Choir Pre Alg Alg 2H Pre Calc
Teacher G Pre Alg Pre Calc Alg 2 Pre Alg Alg 2
Teacher H Geometry Pre Calc H Alg I Alg I Pre Calc H Pre Alg
Teacher I Alg Fund Pre Calc Geometry Geometry Geometry
Teacher J Alg I AP CALC AP CALC Alg I Alg 2
Teacher K Alg I AP CALC Alg I Pre Alg Alg I
Figure 25 shows the average teaching experience for teachers assigned to
teach each course in the department and supports the assertions of site personnel who
indicated that they worked to assign more experienced teachers to the lower level
math classes. The data showed that during the years of the study, teachers assigned
to teach Algebra Fundamentals, Pre-Algebra and Algebra I averaged more
experience than higher level courses such as Algebra 2 and Geometry. And given
that there was only one section allocated for AP statistics per year, the only course
averaging more experience for assigned teachers was Calculus which required a high
degree of math expertise to teach given its demanding subject matter. During the
years studied and continuing through the current school year, MVHS continued to
assign lower level math classes to whom they feel will best serve their neediest
students. In his interview, Sanchez indicated a preference of assigning these classes
only to teachers with at least five years of teaching experience.
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Figure 25 – Average Teaching Experience by Course.
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
Math Lab
Pre Algebra
Alg Fundamentals
Algebra I
Algebra II
Geometry
Pre Calculus
Calculus
Statistics
2002-03 2003-04 2004-05

Figures 24 and 25 above illustrate that these assignments were being made and
demonstrated a commitment not only to evenly distributing the upper and lower level
classes, but also to ensuring that lower level math classes were taught by
experienced teachers. The one exception to this was with the River Deep Math Lab
class which was taught by a new teacher for the three years of the study until the
program was ended.
A final strategy used by the leaders at MVHS to improve student
achievement in math was to adjust its instructional scope and sequence in math.
Former Department Chair Gutierrez reported in his interview that MVHS eliminated
remedial and vocational math, both classes that they valued in order to focus on
standards-based coursework. One course that was eliminated was called Math A and
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was geared towards those students with well-below grade level skills in math. This
remedial math course was eliminated in favor of a baseline course of Pre-Algebra.
This effort, in effect, raised the bar and allowed all students the chance to master
Algebra at a minimum before the end of their sophomore year.
In addition, the math department at MVHS decided to eliminate a course
called Consumer Math, which teachers felt was eminently valuable to students.
Gutierrez told of how students in Consumer Math would be taught such practical
things as balancing their checkbooks and buying a car. He recounted how he used to
bring students to the local auto dealer to do a mock purchase of an automobile,
which for many could be the largest purchase they make in their lifetime. The
decision to eliminate this course was reportedly difficult but had to be made given
the demand for standards-aligned courses and sections in the schedule for
intervention courses. Finally, the math scope and sequence was altered by adding
Algebra Fundamentals in grade 10 to add a standards-based course to the school’s
intervention effort replacing the River Deep Math Lab class.
Analysis and Discussion
The findings in this study were developed and presented by reviewing the
data collected in the context of the conceptual frameworks developed for each of the
research questions. The purpose of this section of the study was to make sense of
these findings in ways that gave them meaning and purpose. In this way, this chapter
will have addressed two basic questions about the findings. First, what were some of
the best practices in place at MVHS that fit within the frameworks developed for
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each research question; and second, what unanswered questions and areas remain
that may still need attention? These two areas of investigation are critical to learning
more about the likely reasons that the efforts undertaken at MVHS worked to bring
about the observed gains in student achievement in math.
During the data analysis process of this study, several distinct themes
emerged from the findings related to the effort to improve student achievement in
math. These themes center on “best practices” and are grounded in the literature
reviewed in Chapter 2. Other issues emerged that, if not attended to, could
potentially diminish the positive effects of the work done so far at MVHS.
Best Practices
The Importance of Human Resources. MVHS had the rare opportunity to
control to the hiring of its staff from the very outset. While many schools are subject
to transfer rights associated with collective bargaining agreements, MVHS began as
the first high school in what had previsouly been a district serving grades K-8.
Because of this, MVHS has been able to avoid the pitfalls associated with political
battles over whether teachers will “get on board” with a given change initiative.
Teachers at MVHS were selected based on the site administration’s strong belief that
they were a good “fit” for MVHS. Teachers have taken ownership of and have
actively participated in the hiring process for vacancies in their department. Teachers
have been assigned strategically to ensure that all students had access to the strongest
teachers including those enrolled in lower level classes. Hiring the right people for
the team has been a major part of the success at MVHS and has set the tone for the
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school’s ability to get everything else done with a minimum of resistance and a
maximum of buy-in.
This careful attention to the teacher selection process and the involvement of
the department chairs in the recruitment and selection process has created a situation
where teachers in the department have ownership of who is on their instructional
team. This attention was not limited to the selection process as interviews revealed
that the math department engages in self-policing and holds each other to high
standards. Current Department Chair Sanchez tells of a former staff member who
had demonstrated an unwillingness to work with the group and ultimately, these
philosophical differences were brought to the surface and the teacher resigned
recognizing the commitment of the rest of the team to continue its course.
Embracing the Era of Accountability. MVHS embraced the challenges
associated with the new era of high stakes testing and accountability and responded
to these challenges by implementing standards-based instructional practices. This
accountability was mainly school-wide in the sense that the schools were judged on
how they scored collectively on standardized tests and other related performance
measures. As noted earlier in this chapter, teachers and administrators leveraged key
state and federal policies in ways that empowered them to be successful. While
others around the state decried the lack of funding, especially for the federal
mandates associated with NCLB, MVHS saw these mandates as a way to motivate
the staff to change their practices to meet the needs of their students. Teachers
accepted responsibility for the learning of their students rather than complain about
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the system. One way this was true was in the way administrators and teachers
reported seeing the state-required CAHSEE as not merely another standardized test
to be avoided, but as a way to motivate students who had previously been
unmotivated. Embracing and supporting policies that increase accountability was a
key factor in the school’s success. In statements such as, “We liked the threat,” and
“These policies produced the pressure cooker that made us focus,” MVHS teachers
and leaders demonstrated their support for these important findings and used this
pressure to achieve to their advantage.
Standards-Based Instruction. MVHS was clear on the concept that what
happened in the classroom was what mattered most. In terms of curriculum and
instruction, no other factor was more important to the school’s success than the
implementation of standards-based instruction. These efforts included using student
achievement to develop common assessments including cumulative quizzes. They
also included revising the scope and sequence to a rigorous and standards-based path
that ensured there was no remedial “track.” MVHS also emphasized increased
student engagement using appropriate educational technology and developed its own
standards-based intervention program. By implementing SBI, MVHS successfully
ensured that all students were being taught the same rigorous standards. This fact
was confirmed in direct classroom observations made during the data collection
process.
Also of significance was MVHS’s work in providing standards-based
instructional materials – curriculum, textbooks and benchmark assessments aligned
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to California Standards – and the instructional supports designed to ensure that
students would succeed in these courses. Teachers in the math department at MVHS
worked together to select textbooks, and design benchmark assessments and
cumulative quizzes that were all aligned to the California standards. MVHS
successfully provided their students with the opportunity to learn the California
Standards and their students demonstrated that they could learn as evidenced by the
CST results detailed earlier.
Strong Instructional Leadership. Leadership is essential to effective school
reform and specific strategies have been demonstrated to be highly correlated with
student achievement. MVHS leaders demonstrated more than one of these practices
during the years studied. Department leaders in particular demonstrated their
knowledge of curriculum, instruction and assessment by implementing standards-
based strategies including benchmark assessments and rigorous curriculum that
emphasized conceptual learning using technology as a tool to engage students. In
addition, Principal O’Conner sought input by involving teachers in the design and
implementation of important decisions and policies. Teachers surveyed indicated a
strong perception that department chairs at the school were empowered to make
important decisions.
Effective leadership was also evident in the way the principal managed the
culture of the school by fostering shared beliefs and a sense of community and
cooperation. Teachers who were interviewed repeatedly reported that they felt
trusted by the principal. Teachers responded to this collegial and trusting style of
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leadership by supporting school-wide efforts to build a culture based on academics.
Posting school logos, mascots, slogans and mission statements all evidenced that
teachers had bought into the principal’s effort to maintain high standards for
students. AP Frisch reported that they, “Never had to fight with teachers” over
important issues and that this was a “huge” factor in the success of the school.
MVHS worked at developing non-threatening relationships with teachers
characterized by risk taking and eliminating the fear of making mistakes.
O’Conner’s trust in his teachers as noted above was also demonstrated in his support
for them when they wanted to eliminate an ineffective intervention model.
Department Chair Sanchez reported how much teachers at MVHS appreciated and
respected that support especially when it meant that O’Conner had to oppose the
District leadership. He further evidenced his leadership and trust in allowing the
math department to design and implement their own intervention model, which then
became the Algebra Fundamentals course.
Effective Instructional leadership involves balancing support and guidance
with building leadership capacity by creating opportunities for others to serve in
leadership roles. O’Conner demonstrated the ability to foster distributed leadership
by empowering Frisch and the Math department chair as noted earlier in this study.
O’Conner recognized that teachers are intellectuals, not merely technicians and were
due a great deal of respect and thus felt comfortable empowering his teachers and
involving them in the decision-making process. In addition, MVHS leaders
recognized and openly acknowledged their own lack of subject matter expertise in
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math and responded by supporting a model of distributed leadership. Department
chairs at MVHS were empowered to make important curricular decisions and were
respected as the experts in their field. Such teacher leadership was a respected part
of the culture at MVHS and resulted in active participation in the major decisions
affecting the department. As a result of this participation, teacher support for the
administration was high and the working environment was characterized by a high
degree of trust.
Finally, instructional leadership was demonstrated at MVHS through the
strategic use of student achievement data. MVHS leaders used student achievement
data in the form of formative and summative assessment data to effectively drive the
curriculum and instruction at their site. The use of CST scores and the development
of the cumulative quiz data to emphasize re-teaching at MVHS both support this
finding. In addition, MVHS used student achievement data to eliminate a district-
mandated intervention program precisely because data showed it was ineffective at
moving students forward in mastering content standards. Moreover, student
achievement data was instrumental in implanting student interventions and supports
such as tutoring and the Algebra Fundamentals course.
Campus Climate and Culture. MVHS leaders were skilled in creating an
atmosphere a positive campus climate that served as a solid base upon which to build
academic success. They focused on building an environment that was conducive to
teaching and learning. Leaders made excellent use of symbolism (school mascots
and annual slogans), ritual (blessing the school, prairie chicken story), and ceremony
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(Renaissance program rallies and all school barbecue) to shape the culture of the
school. As a result of these efforts, school spirit and morale were high and pride in
the school was evidenced in numerous ways.
Raising Expectations. The pattern of achievement detailed earlier in this
chapter revealed CST scores for the school-wide and significant sub-group
populations grew much more than their peers statewide. A reasonable conclusion is
that this success was based on the school’s approach to improving student
achievement in math for all students. MVHS leaders did not focus on interventions
for particular groups of students so much as they worked to improve the teaching and
learning for all students. This point is supported in the data as demonstrated by
improved student achievement for all students and not simply those who had
previously underperformed.
Overcoming Obstacles. MVHS successfully overcame traditional obstacles
to success in math. One of these obstacles was the dangers of persistent tracking.
MVHS had a standards-based scope and sequence in place for all students and while
students may have entered the system at different points, they all progressed along
the same sequence of courses. There was no remedial math track at MVHS. MVHS
also avoided the prominent pitfall represented by the fact that there are generally
fewer opportunities for African-American and Hispanic students to learn from the
best qualified teachers. At MVHS, it was well-documented that all teachers worked
across the curriculum and the most experienced and talented teachers were assigned
to teach the neediest students.
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Finally, another traditional obstacle to growth in math achievement has been
cultural discontinuity between school mathematics and the family life of diverse
student groups. At MVHS, students were taught by Hispanic and Asian math
teachers who reflected the ethnic make-up of the school. Department Chair Sanchez
reported in his interview that MESA was a strong influence on the math community
at MVHS and was made up almost entirely of Hispanic students. The four MESA
advisors were all Hispanic math teachers who reportedly worked to make cultural
relevance a key component in their program. In addition, the Golden Eagle
Engineering and Math Society (GEMS) also focused on making math and science
relevant to students. This student organization was sponsored by a science teacher
and preceded the existence of MESA on the campus. According to Sanchez, GEMS
was initially populated with Asian and Hispanic students, but when higher
performing Asian students began to dominate the group, the Hispanic students began
to drop out. MESA was introduced as a means of providing a place where students
who may not be performing t such a high level can find encouragement and support.
Items for Future Consideration
While the previous section should serve to highlight the many efforts made at
MVHS related to their increased student achievement, questions remain. These
questions arose from the data collected and from the limited nature of this study.
The following section outlines these questions and areas for attention.

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Unanswered Questions
Conceptual Knoweldge vs. Procuderal Knowledge. The review of the
literature in Chapter 2 highlighted the differences between how math is taught I the
United States versus other countries. TIMSS results emphasized the results of
programs that emphasize conceptual understanding versus the American system
which seemingly emphasizes procedural knowledge. During this study, it became
apparent that MVHS used somewhat traditional approaches to making improvement
on traditional metric such as the CST in Algebra I. The most obvious indicator of
the process used at MVHS was revealed in an interview with former Department
Chair Gutierrez who emphasized his traditional approach to instruction. And while
efforts have been made to shift to a more conceptually-based approach, it was clear
during the data collection process that such a transformation was in its infancy and
had little to do with improved test scores in Algebra. What remains unknown is
whether the demonstrated improvement in math scores at MVHS will translate into
increased conceptual understanding for individual students.
Sustained Improvement. For improvement to be truly sustained, it must be
ingrained in the culture and be a natural outgrowth of consistent efforts. MVHS had
demonstrated sustained growth during the years studied, but following this period of
time the school did not meet its academic growth targets. While the principal felt
strongly that it is a natural thing for schools to plateau every few years, it remains to
be seen whether the efforts in place will be sufficient to meet the increasing
challenges associated with these targets. In the years to come, API targets will
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increase dramatically from their current levels of 20.9% in math and 22.3% in
English/Langauge Arts. In 2008-09 the targets jump to 43.5% in math and 44.5% in
English/Language Arts.
Human Resources. MVHS emphasized that one of the most important
factors influencing their increased student achievement in math was their ability to
tightly control the hiring process and thereby the quality of teachers in their school.
It was evident in interviews that MVHS had been highly selective in this regard and
had an ample supply of strong candidates to select from. In a highly competitive
market characterized by a teacher shortage in math and an historic under funding of
education, it is questionable whether the site will be able to maintain such a high
degree of control over this area of practice. Other elements that make this process
more difficult include increased rigor of the credentialing requirements under the
HQT provision of NCLB. In addition, in the absence of large amounts of money
available for salary increases, collective bargaining tends to focus on language
benefiting teacher issues such as transfers. And while MVHS is the only high school
in the district, middle school teachers are generally able to teach in the high school.
It remains to be seen if the site can avoid dynamics such as these, which are out of
their control to a large degree, and maintain control over such an admittedly
important aspect of their success.
Professional Development. The most obvious area of need that became
evident during the data collection and analysis process was the need to plan for the
ongoing professional development needs of the staff. Like most public schools,
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MVHS has struggled to find adequate time and resources to devote to meaningful
staff development. In order to sustain the growth demonstrated during this study, the
staff at MVHS must work with the administration to plan for this need in creative
ways. Such efforts should be imbedded in practice at the site and incorporate the use
of student achievement data to drive instruction. Time for this process may be
gained through creative scheduling and possibly through grant funding as well.
Equity. Another area for attention is the need to ensure the continued equity
of educational outcomes for all students. While increased student achievement in
math was evidenced by all sub-groups, there still exists an achievement gap,
especially between Asian and Hispanic students. This division was also evidenced in
the racial make-up of the two math-related clubs that appear to be populated along
racial lines. In addition, the most recent WASC report noted that the school must
work hard to increase the diversity in an Asian dominated Advanced Placement
program in math.
Summary
This chapter reviewed the findings based on the data collected for this study
followed by a detailed analysis and discussion of the answers to the five research
questions based on how they were grounded in the literature presented earlier in this
study. The discussion included a description of policies and practices that seemed to
be related to increased student achievement in math at MVHS. Also included in this
discussion was a review of the school’s change process using Bolman and Deal’s
(1997) four frames that provided a deeper understanding of which frames served as
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major points of emphasis for the school. Finally, the discussion also looked at how
the principal worked to support such improvement when he was not an expert in
math. The findings presented in this study were based on multiple data sources
which served to strengthen their validity. It should not be surprising, then, that
MVHS experienced a great deal of success in improving its student achievement in
math. The summary, conclusions, and implications of this study are presented in the
next chapter.

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CHAPTER FIVE
SUMMARY, CONCLUSIONS AND IMPLICATIONS
For the last several decades, public education in America has been heavily
criticized for failing to meet the public’s expectations for student achievement. High
schools in particular have come under intense scrutiny as the academic progress of
students at this level has lagged behind that made in earlier grade levels.
Purpose of the Study
The purpose of the study was to learn more about how urban school leaders
brought together policy and local best practices to improve student achievement in
math. The study examined one public high school’s efforts to improve student
achievement in math. Of particular interest was the role of instructional leadership
and how leaders responded to their own lack of expertise in mathematics. The five
research questions identified by the cohort defined the areas being studied and
helped guide the research at the sites studied. The five 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 seemed 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?
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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?
Methodology
This study used a case study approach and primarily qualitative methods to
examine one school’s efforts to improve student achievement in math. Data was
collected using data collection instruments including interviews, questionnaires, site
source documents, direct observations, and quantitative data made available on the
California Department of Education’s web site. Using this wide array of data
sources allowed for triangulation of data which strengthened the validity of the
findings of the study. The questionnaires and interview guides used as the
instruments for data collection were comprised of questions that were intended to be
responsive to each of the five research questions. The conceptual frameworks and
data collection instruments were developed collaboratively by a team of eleven
doctoral students at the University of Southern California.
Sampling
The unit of analysis in this study was one public high school in southern California.
The school selected for this study was purposively selected based on its enrollment
of more than 1200 students, its diverse population and its improvement in Algebra I
CST scores between the years of 2003 and 2005. This type of sampling allowed the
researcher to develop an in depth inquiry and respond to emergent themes of inquiry.
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These factors also helped the researcher develop a rich description of the specific
efforts made by the site to improve student achievement in math.
Data Collection and Analysis
Data for the study were collected in October and November of 2006.
Conceptual frameworks were developed for each research question and served as the
basis for the instrumentation. The first conceptual framework was for RQ 2
(Appendix E) and included factors related to effective school design and effective
math program design. Effective school design was based on the work of Marsh and
Codding (1999) and included (a) student performance incentives, (b) school culture,
(C) curriculum and (d) learning activities. Effective math programs were those that
evidenced strong curriculum design, classroom practices and standards-based
instruction. Bolman and Deal’s four frames of reference served as the basis for the
framework for RQ3 dealing with the school’s change process in their search for
improved student achievement. The four frames focus on efforts relative to an
organizations structure, its human resources, its symbolism and its politics.
The framework developed for RQ 4 focused on leadership and included (a)
vision for learning, (b) supervision and monitoring instruction, (c) community and
political, (d) culture of teaching and learning and (e) data-driven decision making.
For RQ 5, the framework identified a list of twelve strategies that a leader might use
to respond to his or her own lack of expertise in math.
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These frameworks served as the basis for the development of four data
collection instruments used in the collection and analysis of data. These instruments
were:
1. The School Profile (Appendix E) served as a baseline from which to
begin consideration of the school’s pattern of achievement. The
school profile included demographic and key student achievement
data collected mostly from the CDE Data Quest web site.
2. The Key Leader Interview Guide (Appendix C) was used to interview
the four individuals in leadership positions most likely to have
impacted student achievement. These four included (a) the principal,
(b) the Assistant Principal of Curriculum and Instruction, (c) the
former math department chair and (d) the current math department
chair. The Key Leader Interview Guide was designed to allow
emergent themes to be explored and was aligned to the research
questions to facilitate data analysis.
3. The Teacher Interview Guide (Appendix D) was used to interview
math teachers at the school and was designed as an open-ended
instrument to allow teachers to talk about what they felt had impacted
student achievement. This instrument was shorter and less structured
than the Key Leader Interview Guide.

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4. The Questionnaire was designed with two versions: one for math
teachers (Appendix F) and one for all other teachers (Appendix G).
The Math teacher version included 5 items and the non-math teacher
version included 30 items. Both versions ensured that items were
aligned to the research questions to facilitate data analysis.
In addition to the data collection instruments two other methods helped with
data collection and analysis. First, source documents proved to be rich sources of
information and served to validate and confirm information shared in interviews.
Master schedules confirmed teaching assignments and course enrollment patterns
and the most recent WASC report verified numerous findings and lent support to
direct observations made during the study. Other key source documents included the
school’s curriculum guide, department meeting agendas and minutes and copies of
cumulative quizzes and other assessments. Another helpful technique used in the
study was the data collection grid (Appendix I) which served to organize findings
according to research question, conceptual framework element and data collection
instrument. Populating the grid with data made identifying themes and trends more
efficient.
Selected Findings
The data collection and analysis process used in this study led to key findings
related to each of the five research questions. This section will summarize key
findings related to each research question and note the primary data sources analyzed
that led to each of the findings.
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Research Question 1: Pattern of Achievement in Math
The first research question asked, “What was the pattern of Math
achievement for various students at the school?” Analyzing the pattern of
achievement in math for the students of Mission Valley High School was facilitated
by the wide variety of data sets readily available through the California Department
of Education. The pattern of student achievement in math began to reveal itself
during a review of the Algebra I CST results used to as the sampling criteria for the
study. This pattern continued to emerge as data was collected on items such as
course enrollment patterns and Advanced Placement Testing Results. An analysis of
this data led to the following major findings for research Question 1:
1. Students at Mission Valley High School demonstrated more growth on
the Algebra I section of the CST than did their peers statewide.
2. Asian students out gained their peers statewide by a wide margin during
the time period researched.
3. Hispanic students out gained their peers statewide by a wide margin
during the time period researched.
4. White students out gained their peers statewide by a wide margin during
the time period researched.
5. ELL students out gained their peers statewide by a wide margin during
the time period researched.
6. Enrollment in upper level math classes increased during the years studied.
7. Fewer students were enrolled in classes below Algebra I.
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8. A high percentage of students taking the Advancement Placement test
passed in the final year of the study.
9. The school dramatically improved the percentage of students passing the
CAHSEE in math.
There was strong evidence that students at Mission Valley High School
demonstrated more growth on the Algebra I section of the CST than did their peers
statewide. These gains were also realized by all significant sub-groups at the school.
Asian, Hispanic and White students all out gained their peers statewide by a wide
margin during the time period researched. English Language Learners also made
larger gains than did their peers statewide.
In addition to the pattern of achievement evidenced on the CST in Algebra I,
another indication of the school’s progress towards greater levels of achievement for
all students at the school was demonstrated by increased enrollment in all upper level
math. Improvement was demonstrated in this area school-wide and for all significant
sub-groups, with the exception of the Hispanic sub-group whose enrollment in this
area dropped proportionately with their decline in enrollment school-wide. In
addition, the school’s progress was evidenced in the changing make-up of students
enrolled in Algebra I and below. While the numbers of students enrolled in Algebra
and below remained consistent, fewer students were enrolled in Pre-Algebra and
many more students were enrolled in Algebra I. Specifically, enrollment in Algebra
increased from 290 students in 2002-03 to 335 students in 2004-05. At the same
time, enrollment in Pre-Algebra dropped from 122 students to 71.
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Research Question 2: Policy, Curriculum and Instruction
Research Question 2 asked, “What Policy initiatives as well as curriculum,
instruction and related conditions seemed to be related to improved math
achievement in the school?” MVHS demonstrated effective practice in this area as
evidenced by their efforts as follows:
1. MVHS Principal O’Conner and Math Department Leaders set the tone for
the school’s attitude towards policies related to increased accountability
for the school collectively and for its students individually.
2. The CAHSEE, in particular, was leveraged by staff to hold students
accountable for efforts to master concepts in their math classes.
3. The LPUSD implemented a multiple measures system of accountability
that rated the school’s success based on student achievement data on
discrete academic measures such as CST scores and final exam grades.
4. MVHS implemented standards-based instructional practices including
common assessments.
5. MVHS teachers served as strong role models for students.
MVHS teachers and administrators repeatedly expressed that they
appreciated the opportunity to work in an environment of high stakes assessment and
accountability. MVHS Principal Dan O’Conner indicated that these policies served
as a “Pressure Cooker,” and added that the public’s focus on standardized testing
results has forced schools to work harder and focus on academics. Current
Department Chair Gerardo Sanchez enthusiastically supported increased
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accountability for students and teachers. He felt that standardized testing provided
the impetus the teachers needed to really begin using student achievement data in a
strategic way.
The CAHSEE requirement was seen as the number one policy motivating the
practice in math at MVHS. The leadership at MVHS saw it as helpful in motivating
lower functioning students and in dealing with teachers who were resistant to
adopting a data driven and standards-based approach. The little resistance present
was met with a strong statement from the department chair who reportedly told them,
“You can disagree all you want, but it’s the law, it’s here, and we need to deal with
it.” Most teachers welcomed the accountability and felt it gave us some teeth with
unmotivated students and made them focus. The staff at MVHS responded to this
pressure by developing common finals and pacing calendars in all core areas. These
assessments made use of formats that mirrored the CST and CAHSEE exams.
In addition, the Los Padres Unified School District developed a multiple
measures system of accountability that augmented state and federal policies by rating
the success of MVHS based on three indicators each in the core areas of English and
Math. These indicators were based on academic achievement in grades 9-11. In
English, MVHS developed its own 5-point scoring rubric to rate student performance
on the final exam. In addition, students’ final grade in the course and CST score
counted as the other two measures in English. Table 6 shows the three components
used in language arts.
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In terms of curriculum and instruction, no other factor was more important to
the school’s success than the implementation of standards-based instruction.
Teachers in the math department at MVHS worked together to select textbooks, and
design benchmark assessments and cumulative quizzes that were all aligned to the
California standards. MVHS eliminated remedial math classes and designated the
same standards-based scope and sequence as the default curriculum for all students.
By implementing SBI, MVHS successfully ensured that all students were being
taught the same rigorous standards. This fact was confirmed in direct classroom
observations made during the data collection process.
At MVHS, it was well-documented that teachers at MVHS were committed
to student success and served as strong role models for students. Students were
taught by Hispanic and Asian math teachers who reflected the ethnic make-up of the
school. These teacher served as advisors and mentors in student organizations such
as MESA and provided a strong influence on the math community at MVHS. The
commitment of teachers at MVHS provided frequent opportunities to foster
meaningful interactions between math teachers and their students.
Research Question 3: Change Process
Research question 3 asked, “What change process did the school use to
enhance its math program and strategies to assist students in math?” The study used
Bolman and Deal’s four frames to analyze the data collected and make sense of the
change process. One of the most important findings in this study was that the human
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resources frame was especially important in supporting increased levels of student
achievement. This was evidenced in the following:
1. The structural design of the administrative team supported increased
student achievement at MVHS.
2. The design and size of the facility supported teacher collaboration and
reduced isolation for teachers and students.
3. MVHS site and departmental leaders maintained a collective ownership
over the hiring process and worked hard to recruit the right people for
vacant positions.
4. MVHS had minimal political obstacles with which to deal and overcame
an unsuccessful intervention effort.
5. Site Leadership at MVHS made strong use of ceremonies and symbolism
to promote a culture conducive to high student achievement.
The structural design of the site administrative team supported improved
student achievement in couple of key ways. First, MVHS had an assistant principal
who was directly aligned to curriculum and instruction. Interviews and an official
job description confirmed that this position was in charge of all testing and
assessment at the site. O’Conner reported that this process was deeply respected at
the site that during the weeks leading up to testing and math teachers credited the
work of the Assistant Principal of Curriculum and Instruction with reducing the
anxiety level of teachers which in turn, allowed them to focus on instruction rather
than administrative issues.
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Having a facility designed to support academic achievement was also
important to the efforts of MVHS. In this regard, it was found that the design and
maintenance of the school facility both worked to support student achievement by
fostering a sense of pride and promoting increased teacher collaboration. The school
was designed to be built on only 16 acres of land on the site of a former middle
school. AP Frisch and O’Conner both reported that this design had teacher
collaboration clearly in mind. One visible sign of this design was the presence of
“pods” connecting most of the classrooms to others classrooms. These pods allowed
teachers to store common materials and provided then with a place to meet and
collaborate on issues of importance.
In addition, MVHS had an intimate atmosphere that appeared to reduce
anonymity. The quad in the center of the school served as a gathering place and
appeared to encourage interaction among students. The newness and cleanliness of
the classrooms evidenced the sense of pride students and staff had taken in their
facility. This emphasis on cleanliness was readily apparent during the research visits
to the school and was evidenced in that there was no graffiti visible at any time.
Gum was not allowed which reduced unsightly spots on the ground and trash was
picked up immediately after the lunch period in an organized and consistent fashion.
The aesthetic use of pavers instead of concrete in the parking lot and on campus
added a touch of elegance that made the school feel “upscale.”
The hiring practices at MVHS promoted improved student achievement in
math. The principal, assistant principal in charge of curriculum and instruction,
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current and former math department chair all expressed a strong belief that hiring the
right people in the math department played a critical role in improving student
achievement in math. In addition, both the current and former department chairs
were actively involved in the recruitment of teacher in their department and were
able to give numerous examples of their efforts to control who was hired. One
example cited by Gutierrez was that the current department chair was a former
student at MVHS and was recruited by the former department chair. Two other
current and two former teachers in the math department were targeted for
recruitment as participants in the Escalante Project, noted earlier. In addition,
another current math teacher at MVHS was recruited as a top prospect out of a
nearby university after her successful student teaching experience at MVHS.
MVHS leadership and teachers found it difficult to discuss the political
aspects of change during their interviews. They consistently indicated that there
were very few political issues that they had to deal with during the years studied. As
mentioned earlier, the staff and leadership at MVHS generally worked free from
interference and there appeared to be a high degree of mutual trust as noted in the
most recent WASC report. O’Conner and Frisch both credited this ability to work
free from interference with a large part of their success. A noted exception to this
was that MVHS was forced to implement a district mandated math intervention
program.
Another important finding related to the political frame of reference was that
MVHS was able to avoid traditional obstacles to restructuring. Assistant Principal of
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Curriculum and Instruction Dan Frisch said it best during an interview when he
expressed, “MVHS didn’t restructure, we structured.” The school’s leaders had the
ability to select teachers of their choosing, and since MVHS was the first high school
in the district, there were no pre-existing high school teachers in the district who had
contractual rights to transfer to the new school. Principal O’Conner expressed that
only a very few middle school teachers were granted transfers to the school, and
therefore, MVHS was able to hire whomever they felt was best.
Site Leadership at MVHS made strong use of ceremonies and symbolism to
promote a culture conducive to high student achievement. From its inception,
MVHS worked hard to promote a sense of pride in the school through ceremony and
ritual. MVHS was blessed in a ceremony that was carried out in a ritual performed
by members of the local tribe of Native Americans. In addition, the symbolism
associated with the school’s mascot, the Eagle appeared almost everywhere in the
school. The most prominent was a large statue of an Eagle taking flight sat
prominently in the open area adjacent to the school’s entry and served to greet
everyone who entered the school. Observations noted that countless eagles adorn the
principal and assistant principals’ offices, the main office, student center and
teachers’ classrooms.
MVHS leaders also made strong use of ceremonies and school rallies to
motivate students at critical times of the year. Interviews unanimously recounted the
importance placed on the annual all-school barbecue that was meant to motivate
students to do their best on standardized tests. Teachers interviewed also noted how
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much they felt it helped to give students a snack – Knott’s Berry Farm cookies –
before administration of the actual CAHSEE. Frisch noted that the practice had now
become an expected part of the culture.
Research Question 4: Instructional Leadership
Research question 4 asked, “How was instructional leadership important in
improving a) the math programs/strategies and b) math achievement among
students?” MVHS leaders were effective in these areas as evidenced by:
1. MVHS developed a strong vision for student achievement.
2. MVHS leaders emphasized the supervision of instruction as a means of
increasing student achievement.
3. MVHS used student achievement data to effectively support and impact
increased levels of student achievement.
The site leadership at MVHS developed a strong vision for student
achievement and worked to promote increased student achievement. Teachers and
administrators indicated during interviews how much they respected the principal’s
efforts in this regard. A new school slogan was developed each year to motivate the
school’s teachers and students. Teachers posted these mantras prominently, often
directly above the central white board and always in direct line of sight of the
students. Students and teachers bought into these efforts and often challenged each
other in the halls with these slogans. The school’s nationally recognized speech and
debate club students often weaved these slogans into their speeches and often won, at
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least once being recognized as National Champions. What might otherwise have
been seen as trite was accepted at MVHS as a meaningful part of the culture.
The site leadership at MVHS also worked at the supervision of instruction to
effectively support increased student achievement. One way they did this was with
regular visits to the classrooms. Principal O’Conner reported that he and his
administrators have even worked to establish a common language and set of
expectations so that teachers would feel comfortable with the consistency they
expected when they were to be evaluated. The most recent WASC report supported
this finding by noting, “Teacher evaluations are viewed as supportive and helpful.”
The Beginning Teacher Support and Assessment (BTSA) program was also
mentioned prominently in the most recent WASC report and was seen as a means of
monitoring the progress of and providing support to the school’s newer teachers. On
this topic the WASC V.C. noted that, “BTSA teachers have district mentors for
observation and assistance. This was in addition to the assistance provided by
department chairs and other experienced staff.
MVHS used student achievement data to effectively support and impact
increased levels of student achievement. Site and district leaders worked together to
prepare a detailed presentation to the teachers in which student achievement data
from the prior year was used to celebrate successes, outline areas of concern and set
goals for the coming year. This presentation served as the basis for the math
department’s annual goals and was seen as an effective way to raise the staff’s
anxiety about student achievement and eliminating false perceptions and smugness.
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Department meetings were refocused on student achievement issues such as
the development of common assessments and reviewing student achievement data.
Using departmental time to discuss day-to-day operational issues became less
common and such matters were routinely handled during the course of the regular
day. Department meeting agendas and notes confirmed that the vast majority of
items discussed were directly related to student achievement.
Research Question 5: Leader’s Response to lack of Subject Matter Expertise
Research question 5 asked, “How did instructional leaders respond in
academic areas in which they were not experts?” A basic assumption of this study
was that site leaders must work in a variety of ways to overcome their own lack of
expertise in a given field of study. In this case, Principal O’Conner effectively used
the following strategies identified in the second framework for this research question
detailed earlier in Table 5.
1. Delegate Leadership to Assistant with Greater Expertise
2. Empower Department Chair
3. Emphasize Inquiry and Problem Solving
4. Emphasize Strategic Teacher Assignments
5. Emphasize Revised Course Scope and Sequence and/ or Curriculum
One of the most effective of the several strategies used by Principal
O’Conner was effectively delegating instructional duties to a strong assistant
principal of curriculum and instruction. Those interviewed in this study consistently
pointed to this as a significant factor in the school’s academic success. Principal
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O’Conner indicated that AP Frisch demonstrated strong leadership in areas such as
(a) the strategic use of student achievement data, (b) organizing the logistics of the
school’s standardized testing program, (c) monitoring student progress, (d) building
the school’s master schedule, and (e) serving as the summer school principal to
ensure instructional continuity during this important learning session.
Another strategy used by the principal to respond to the challenge of
improving student achievement was to empower the department chairs with the
authority to make decisions that positively impact student achievement. Both the
former and current department chairs reported that they felt empowered by their
principal to make important decisions that affected student achievement in math.
Both played an important role in the teacher assignments noted earlier as critical in
the success evidenced at MVHS. In addition, they each described being entrusted
with major responsibility for implementing standards-based practices including the
site’s strategy for meeting the challenge of preparing students to pass the CAHSEE
and the development of the Algebra Fundamentals course. The math department
chair was also instrumental in designing the cumulative quiz program and in
emphasizing the use of student achievement data, instructional technology and
emphasizing re-teaching. In addition, the Math department chair played a strong role
in recommending teacher assignments, led collaborative efforts to review student
achievement data and revise instruction as needed, and was actively involved in
recruiting teachers and in curriculum development as well.
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MVHS Principal O’Conner was also effective in his efforts to promote a
culture of inquiry and problem solving by encouraging constant reflection on student
achievement data. Efforts to use student achievement data to promote a culture of
inquiry and problem solving included:
1. Using student achievement data as the basis for departmental goals
and objectives.
2. Using department meetings as a forum for reviewing student
achievement data.
3. Using student achievement data from the Cumulative Quizzes to
develop re-teaching lessons.
4. Teachers setting goals and objectives for their students’ achievement
and using them as a part of their annual evaluation.
The principal also used strategic teacher assignments to effectively promote
increased levels of student achievement in math. A significant practice at MVHS
was to avoid leaving the lower level classes to new and less experienced teachers.
MVHS recognized the dangers of a seniority-based system and instead used this
valuable teaching experience by assigning veteran teachers to some of the lower
levels math classes. During the master schedule building process, math teachers were
allowed to indicate a preference of classes, but there was an expectation that one’s
preference would include at least one section of Algebra or lower.
A final strategy used by the leaders at MVHS to improve student
achievement in math was to adjust its instructional scope and sequence in math by
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eliminating remedial and vocational math in order to focus on standards-based
coursework. Eliminated courses included Math A and Consumer Math. This effort
raised the bar and allowed all students the chance to master Algebra at a minimum
before the end of their sophomore year. In addition, the math department added
Algebra Fundamentals in grade 10 to add a standards-based course to the school’s
intervention effort replacing the River Deep Math Lab class.
Conclusions
Based on data collected relevant to Research Question 1, there was strong
evidence supporting the finding that students at Mission Valley High School
demonstrated more growth on the Algebra I section of the CST than did their peers
statewide. These gains were likewise realized by all significant sub-groups at the
school. Asian, Hispanic and White students all out gained their peers statewide by a
wide margin during the time period researched. English Language Learners also
made larger gains than did their peers statewide. The enrollment pattern in higher
level math courses and in Advanced Placement classes would also support the
finding that the school made strong progress in improving student achievement in
math.
Data collected pertaining to Research question 2 also supported findings that
support the progress made in math at MVHS. Principal O’Conner and math
department leaders set the tone for the school’s attitude towards policies related to
increased accountability for the school collectively and for its students individually.
The CAHSEE, in particular, was leveraged by staff to hold students accountable for
209
efforts to master concepts in their math classes. The LPUSD also supported the
climate of accountability in its implementation of a multiple measures model that
rated the school’s success based on student achievement data on discrete academic
measures such as CST scores and final exam grades. Another significant factor in
the school’s improved student achievement in math was its implementation of
standards-based instructional practices including common assessments. In support
of these efforts, MVHS assigned its strongest teachers to its neediest students.
The change process used by MVHS leaders enhanced its math program and
student achievement in math. One of the most important findings in this study was
that the human resources frame was especially important in supporting increased
levels of student achievement. This was evidenced in that MVHS site and
departmental leaders maintained a collective ownership over the hiring process and
worked hard to recruit the right people for vacant positions. In addition, the
structural design of the administrative team supported increased student achievement
at MVHS primarily through the designation of an assistant principal in charge of
curriculum and instruction.
These personnel changes were supported by efforts in the structural and
symbolic realm as well. The design of the facility supported teacher collaboration,
an important component in professional learning communities. The small facility
supported intimacy and reduced isolation of students at MVHS. Site Leadership at
MVHS made strong use of ceremonies and symbolism to promote a culture
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conducive to high student achievement, and MVHS had minimal political obstacles
with which to deal.
Data collected in support of Research Question 4 demonstrated the
importance of instructional leadership in support of increased student achievement in
math achievement among MVHS students. MVHS leaders were effective in these
areas as evidenced by their developing and maintaining a strong vision for student
achievement. MVHS leaders emphasized the supervision of instruction in support of
this vision and used student achievement data to effectively support and impact
increased levels of student achievement. This was accomplished through the
development of curriculum and intervention programs to support students in math.
Data collected related to Research Question 5 supported the notion that
leaders must work in a variety of ways to overcome their own lack of expertise in a
given field of study. In this case, the principal at MVHS used several strategies
including effectively delegating instructional duties to a strong assistant principal of
curriculum and instruction. Those interviewed in this study consistently pointed to
this as a significant factor in the school’s academic success. Department chairs were
empowered with the authority to make decisions that positively impacted student
achievement
Another effective strategy used by the principal was to promote a culture of
inquiry and problem solving by encouraging constant reflection on student
achievement data. Efforts to use student achievement data to promote a culture of
inquiry and problem solving included (a) using student achievement data as the basis
211
for departmental goals and objectives, (b) using department meetings as a forum for
reviewing student achievement data, (c) using student achievement data from the
Cumulative Quizzes to develop re-teaching lessons, and (d) teachers setting goals
and objectives for their students’ achievement and using them as a part of their
annual evaluation.
The principal also used strategic teacher assignments to effectively promote
increased levels of student achievement in math. A significant practice at MVHS
was to avoid leaving the lower level classes to new and less experienced teachers.
MVHS used valuable teaching experience to their advantage by assigning veteran
teachers to some of the lower levels math classes. A final strategy used by the
leaders at MVHS to improve student achievement in math was to adjust its
instructional scope and sequence in math by eliminating remedial and vocational
math in order to focus on standards-based coursework.
Implications for Practice
In response to the new era of high stakes assessment and accountability, it is
likely that schools and districts will continue to work to improve teaching and
learning especially in the critical area of mathematics. This study has yielded
findings and conclusions that may serve to provide important insights to those
educators charged with the responsibility of improving the achievement of their
students. The implications listed below are presented both in terms of implications
for MVHS, and by general areas of responsibility, and include implications for
school boards and key district leaders, site administrators and teacher leaders as well.
212
Mission Valley High School
The strong growth in student achievement at MVHS during the years of the
study was followed by a year in which the school did not meet its API growth targets
for all sub-groups. In addition, changes associate with staff turn over, rapidly
increasing growth targets and collective bargaining agreements that might affect the
site’s ability to control staffing decisions are undoubtedly coming. In light of these
challenges, there are implications in this study and grounded in the literature on
lasting school improvement that would serve the school well as they seek to regain
the growth experienced during the years studied. Such efforts should include:
1. Emphasize conceptual understanding in the math department to a greater
degree than is currently occurring. By the current math department’s own
account, the school is in the initial stages of transforming its instruction in
math to a conceptual based curriculum in which instruction focuses not
on procedures and test scores, but on developing a deeper understanding
of the concepts being taught.
2. Emphasize Staff Development. In order for the teachers to make
adjustments in their instruction that allow them to implement a more
conceptual based curriculum, the school should adopt a coherent and
strategic plan for staff development that will allow more traditional
approaches to grow into those that lead to a deep understanding of the
concepts being taught in mathematics.
213
3. Transform the culture by opening up to outside ideas and developing a
professional learning community that embraces teacher collaboration and
invites the addition of outside expertise. The school should also work
more collaboratively across the departments to share best practices.
4. The school principal should consider serving more directly as the
instructional leadership as the challenges noted above begin to emerge.
Effective delegation has worked to a point, as the growth targets get more
difficult to attain, the principal will likely need to become more directly
involved in dealing with instructional issues as the urgency to change
practices increases.
District Boards and Key District Leaders
1. The implementation of Standards-Based Instruction was a key finding in this
study and as such, School Boards and key district leaders need to support site
efforts by setting policies that promote and support standards-based practices
at the site. As principals struggle with the challenge of moving schools
forward they often encounter resistance to change. Board policies can serve
as a powerful support mechanism for principals who encounter such
resistance and can have the potential positively impact schools by making
expectations more explicit for those instructors or departments who are not
actively supporting the principal’s vision. These policies should include
areas such as standards-based grading, a requirement for common
214
assessments such as final exams, and support for evaluation systems that
support collaboration and reduce isolation for teachers.
2. One of the key findings in this study was the importance of hiring the right
person for the assignment. Thus, in order to foster a site’s ability to act freely
in this regard, School Boards and key district leaders need to hire strong
instructional leaders who appreciate the importance of building an effective
instructional team. They can also support this effort by and working to
support collective bargaining agreements that free sites to select their own
personnel as opposed to allowing seniority-based transfer systems. Boards
should then support site-based decisions. The powerful combination of
leadership and teacher empowerment was evident in this study and point to
the need for district leaders to minimize micromanagement and avoid
implementing top-down mandates not supported by teachers.
3. Provide the resources necessary to support the site’s efforts to meet its
academic targets. Such support can include fiscal resources to fund
professional development and efforts geared towards increasing teacher
collaboration. Such assistance should also include providing expert advice
and guidance on data analysis and curricular programs that support what the
data reveals.
Site Administrators
1. Get the right people on the bus and in the right seats. Get the wrong people
off. The importance of having all teachers working together to implement a
215
common vision cannot be overstated. Site leaders should assign their best
teachers to their neediest students and empower teacher leaders as they work
to support a unified vision of student achievement. New teachers should be
supported and those not “on board” should be dealt with early. Every effort
should be made to remove those who refuse to work as a part of the team.
Actions in support of this effort can include:
a. Emphasize thorough hiring practices including paper screening,
attention to reference checks and recruitment. Do not simply pick
from the best pf the bunch offered by the district pool of applicants,
but aggressively pursue excellent teachers wherever they might be.
b. Work to implement walk-abouts, learning walks and similar practices
that reduce isolation and increase collaboration. When teachers know
that their peers are watching, they are more likely to be engaged in a
high level of practice. In addition, learning from peers can prove to
be a powerful form of professional development.
c. Ensure that teachers are evaluated accurately and with a focus on
standards-based practice in the classroom. Be willing to have the
courageous conversation when a teacher is not providing satisfactory
instruction.
d. Work to support a Peer Assistance and Review (PAR) process that
encourages support for weaker teachers and also provides a vehicle
for removing those unwilling to grow as professionals.
216
2. Promote standards-based instruction. Principals are well advised to ensure
that rigorous and grade-level standards-based lessons are being delivered in
every classroom. Common performance assessments including final exams
and benchmark tests should be developed and integrated with a well thought
out pacing plan to ensure all students have been taught what they need to
know. Actions in support of this area of practice should include:
a. Ensuring instruction is at grade level standard every day in every
class.
b. Ensure that assessments are directly linked to grade level content
standards and are administered in regular intervals by all core area
teachers.
3. Make Data-Driven decisions. School administrators and teacher leaders
should analyze student achievement data regularly and make academic
decisions based on student need. Such decisions include teacher
assignments, class sizes, curriculum development, and instructional materials.
Principals and other site leaders can support this effort by:
a. Regularly analyzing and disseminating benchmark assessment data.
b. Using timely and relevant student achievement data to drive
instructional units and emphasize re-teaching and individualizing
instruction to meet the needs of struggling students.
c. Focus meeting agendas on student achievement issues.
d. Assign the most talented teachers to the neediest students.
217
4. Set the tone and promote a culture of teaching and learning. Principals play a
critical role in the student achievement at their schools and even those
without specific core content area knowledge can enlist a variety of strategies
to support the focus on academics. Fostering a common vision of academic
excellence and celebrating student success in the classroom through the use
of ceremony and rituals helps everyone understand that student achievement
is the top priority at the school. Specific actions that would foster this type of
climate on campus include:
a. Use Rallies and awards ceremonies to celebrate academic stars in
addition to athletic stars.
b. Use slogans, posters and logos to advertise and promote the vision of
the school and to maintain the focus on the academic mission of the
school.
Teachers
1. One of the most important findings in this study was the manner in which
teachers embraced policies related to high stakes testing and accountability.
Consistent with this finding, teachers are encouraged to avoid the self-
defeating trap associated with blaming these policies for making their jobs
more difficult. Instead, teachers should embrace these policies as an
opportunity to motivate students and perfect their own craft to achieve
greater gains in student learning.
218
2. Consistent with the finding in this study that the implementation of
standards-based instructional practice was related to increased student
achievement, teachers are encouraged to embrace and implement such
practices including the use of standards-based lessons and common
assessments.
3. Use student achievement data to refine and perfect your craft. In order to do
this, teachers should collaborate with department members and develop
common assessments and rubrics that reflect the collective thought about
what it means to perform at standard. Such collaboration was found in this
study to be a powerful tool for growth and should be seen as supporting the
idea that teaching in isolation should become a thing of the past. Analyzing
student achievement data and working to produce common assessments and
performance rubrics are activities best done collaboratively.
4. Use student achievement data to set measurable goals for yourself and for
your department. The teachers at MVHS analyzed student achievement data
and used it to set departmental goals and included measurable student
outcomes in their individual evaluations. Rather than seeing measurement as
a threat, it should be used as a way to motivate and refine the art of
instruction. Goals not met were not seen as failure at MVHS but rather as an
opportunity to grow and this approach should be replicated wherever
possible.

219
Students
1. The findings in this study revealed that students can thrive when the climate
and culture of the school are supportive of standards-based practices.
Students, then, should come to expect a climate that is more inclusive and
celebrates academic success as well as athletic and other extra-curricular
efforts. Student leaders should seek out ways of organizing rallies and other
events that ensure such celebrations should occur. Other avenues that should
be used to promote and reward academic success include the school
newspaper and broadcast news program if present.
2. This study also demonstrated that the implementation of rigorous and
standards-based curriculum was related to student achievement at MVHS.
Students in general, should expect to be challenged and seek out the most
rigorous coursework possible.
Recommended Future Research
As data was collected and analyzed, further research was indicated in several
areas:
1. This study focused on identifying policies and practices associated with
increased student achievement in math. The study was limited to the core
area of math, but schools and districts are also struggling to meet increasing
academic demands in English/Language Arts and Science in particular.
Parallel studies in other core areas assessed on standardized tests and
incorporated into the API and AYP scores of schools would add important
220
insights into best practices in those areas and could confirm strategies
identified in this study as well.
2. The site selected for this study was chosen using a purposeful sample based
on overall gains made on Algebra I CST scores. While this methodology
served this study well, it is probable that isolated instances of success with
specific sub-groups may yield important information about what works with
specific students even when overall gains are minimal or non-existent.
Therefore, further research is indicated at schools that may have yielded
outstanding results with specific sub-groups. An example might be to
research a school that has had success demonstrating gains with special
education or ELL populations.
3. This study considered the success at a relatively new school with a
particularly unified staff. But what about a school lacking such unity but
where islands of excellence exist? Not all schools are able to control the
hiring of their teachers due to inconsistent leadership, collective bargaining
agreements that favor seniority, and a lack of qualified applicants such as is
common in inner city schools. Of interest would be internal differences at
these schools to see how some teachers succeed in light of challenges they
face.

221
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230
APPENDICES

231
Appendix A: Algebra I Objectives
Algebra I
Symbolic reasoning and calculations with symbols are central in algebra. Through
the study of algebra, a student develops an understanding of the symbolic language
of mathematics and the sciences. In addition, algebraic skills and concepts are
developed and used in a wide variety of problem-solving situations.

1.0 Students identify and use the arithmetic properties of subsets of
integers and rational, irrational, and real numbers, including
closure properties for the four basic arithmetic operations where
applicable:
1.1.1 Students use properties of numbers to demonstrate
whether assertions are true or false.
2.0 Students understand and use such operations as taking the
opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of exponents.
3.0 Students solve equations and inequalities involving absolute
values.
4.0 Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
5.0 Students solve multistep problems, including word problems,
involving linear equations and linear inequalities in one variable
and provide justification for each step.
6.0 Students graph a linear equation and compute the x- and y-
intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the
region defined by linear inequality (e.g., they sketch the region
defined by 2x + 6y < 4).
7.0 Students verify that a point lies on a line, given an equation of the
line. Students are able to derive linear equations by using the
point-slope formula.

8.0 Students understand the concepts of parallel lines and
perpendicular lines and how those slopes are related. Students are
able to find the equation of a line perpendicular to a given line that
passes through a given point.
9.0 Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically.
232
Students are able to solve a system of two linear inequalities in two
variables and to sketch the solution sets.
10.0 Students add, subtract, multiply, and divide monomials and
polynomials. Students solve multistep problems, including word
problems, by using these techniques.
11.0 Students apply basic factoring techniques to second- and simple
third-degree polynomials. These techniques include finding a
common factor for all terms in a polynomial, recognizing the
difference of two squares, and recognizing perfect squares of
binomials.
12.0 Students simplify fractions with polynomials in the numerator and
denominator by factoring both and reducing them to the lowest
terms.
13.0 Students add, subtract, multiply, and divide rational expressions
and functions. Students solve both computationally and
conceptually challenging problems by using these techniques.
14.0 Students solve a quadratic equation by factoring or completing the
square.
15.0 Students apply algebraic techniques to solve rate problems, work
problems, and percent mixture problems.
16.0 Students understand the concepts of a relation and a function,
determine whether a given relation defines a function, and give
pertinent information about given relations and functions.

17.0 Students determine the domain of independent variables and the
range of dependent variables defined by a graph, a set of ordered
pairs, or a symbolic expression.
18.0 Students determine whether a relation defined by a graph, a set of
ordered pairs, or a symbolic expression is a function and justify the
conclusion.
19.0 Students know the quadratic formula and are familiar with its
proof by completing the square.
20.0 Students use the quadratic formula to find the roots of a second-
degree polynomial and to solve quadratic equations.
21.0 Students graph quadratic functions and know that their roots are
the x-intercepts.
22.0 Students use the quadratic formula or factoring techniques or both
to determine whether the graph of a quadratic function will
intersect the x-axis in zero, one, or two points.
23.0 Students apply quadratic equations to physical problems, such as
the motion of an object under the force of gravity.
233
24.0 Students use and know simple aspects of a logical argument:
24.1 Students explain the difference between inductive and
deductive reasoning and identify and provide examples of
each.
24.1.1 Students identify the hypothesis and conclusion in
logical deduction.
24.1.2 Students use counterexamples to show that an
assertion is false and recognize that a single counterexample is sufficient
to refute an assertion.

25.0 Students use properties of the number system to judge the validity
of results, to justify each step of a procedure, and to prove or
disprove statements:
25.1.1 Students use properties of numbers to construct
simple, valid arguments (direct and indirect) for, or formulate
counterexamples to, claimed assertions.
25.1.2 Students judge the validity of an argument according
to whether the properties of the real number system and the order of
operations have been applied correctly at each step.
25.1.3 Given a specific algebraic statement involving linear,
quadratic, or absolute value expressions or equations or inequalities,
students determine whether the statement is true sometimes, always, or
never.

234
Appendix B: CST Gains and Losses for Identified Districts

District Psuedonym
Increase in
Top two
Quintiles
Decrease in
Bottom Two
Quintiles
Algebra I
Total Gains
District 1 21% -26% 47%
District 2 9% -31% 40%
District 3 13% -17% 30%
District 4 4% -22% 26%
District 5 9% -17% 26%
District 6 11% -13% 24%
District 7 6% -17% 23%
District 8 4% -16% 20%
District 9 4% -15% 19%
District 10 7% -11% 18%
District 11 6% -11% 17%
District 12 10% -7% 17%
District 13 4% -13% 17%
District 14 2% -13% 15%
District 15 4% -11% 15%
District 16 3% -12% 15%
District 17 9% -6% 15%
District 18 4% -11% 15%
District 19 2% -12% 14%
District 20 4% -10% 14%
District 21 5% -8% 13%
District 22 5% -8% 13%
District 23 10% -2% 12%
District 24 2% -10% 12%
District 25 2% -10% 12%
District 26 6% -5% 11%
District 27 0% -11% 11%
District 28 4% -7% 11%
District 29 0% -10% 10%
District 30 -1% -10% 9%
District 31 4% -5% 9%
District 32 7% -2% 9%
District 33 3% -6% 9%
District 34 2% -6% 8%
District 35 4% -4% 8%
District 36 3% -5% 8%
District 37 2% -6% 8%
District 38 -1% -8% 7%
District 39 2% -5% 7%
Algebra 1
235
District Psuedonym
Increase in
Top two
Quintiles
Decrease in
Bottom Two
Quintiles
Algebra I
Total Gains
District 40 0% -6% 6%
District 41 1% -5% 6%
District 42 1% -5% 6%
District 43 0% -6% 6%
District 44 0% -4% 4%
District 45 1% -2% 3%
District 46 1% -1% 2%
District 47 -10% -12% 2%
District 48 -2% -4% 2%
District 49 -1% -3% 2%
District 50 -2% -3% 1%
District 51 -1% -2% 1%
District 52 -1% -2% 1%
District 53 1% 0% 1%
District 54 -3% -3% 0%
District 55 -1% -1% 0%
District 56 -2% -1% -1%
District 57 -2% -1% -1%
District 58 -1% 0% -1%
District 59 -3% -2% -1%
District 60 -3% -1% -2%
District 61 -2% 0% -2%
District 62 -1% 1% -2%
District 63 1% 3% -2%
District 64 -1% 3% -4%
District 65 -2% 2% -4%
District 66 -3% 2% -5%
District 67 -2% 4% -6%
District 68 -2% 4% -6%
District 69 -1% 5% -6%
District 70 0% 7% -7%
District 71 -2% 5% -7%
District 72 -4% 4% -8%
District 73 -8% 0% -8%
District 74 -5% 4% -9%
District 75 -6% 4% -10%
District 76 -5% 5% -10%
District 77 -2% 8% -10%
District 78 -5% 7% -12%
District 79 -6% 7% -13%
Algebra 1
236
District Psuedonym
Increase in
Top two
Quintiles
Decrease in
Bottom Two
Quintiles
Algebra I
Total Gains
District 78 -5% 7% -12%
District 79 -6% 7% -13%
District 80 -8% 5% -13%
District 81 -6% 10% -16%
District 82 -6% 12% -18%
District 83 -12% 9% -21%
District 84 -10% 11% -21%
District 85 -9% 12% -21%
District 86 -5% 16% -21%
District 87 -5% 16% -21%
District 88 -21% 1% -22%
District 89 -9% 13% -22%
District 90 -12% 11% -23%
District 91 -6% 17% -23%
District 92 -13% 11% -24%
District 93 -8% 17% -25%
District 94 -9% 17% -26%
District 95 -10% 18% -28%
District 96 -14% 14% -28%
District 97 -12% 17% -29%
District 98 -15% 19% -34%
District 99 -20% 16% -36%
District 100 -20% 16% -36%
District 101 -22% 15% -37%
District 102 -21% 17% -38%
District 103 -10% 28% -38%
District 104 -18% 21% -39%
District 105 -17% 23% -40%
District 106 -17% 24% -41%
District 107 -30% 12% -42%
District 108 -17% 30% -47%
District 109 -33% 27% -60%
District 110 -60% 51% -111%
Mean -3.30% 1.07% -4.37%
Algebra 1
237
Appendix C: Key Leader Interview Guide

Key Leader Interview Guide

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

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

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

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

Are you ready?

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

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

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

4. How do you feel the CAHSEE requirement has influenced your efforts to increase
student achievement in math?
238
CHANGE PROCESS
Research Question 3: What change process did the school use to enhance its
math program and strategies to assist students in math?

“Let’s turn our attention to how you handled the change process related to your
efforts to improve student achievement in math. Specifically, I will be asking
you about different aspects of the change process as described in Bolman and
Deal’s Four frames. In case you are not familiar with this model, here is a copy
of the framework for your reference and clarification. (give the framework to
the interviewee). OK, so I will be asking you about”:
Structural changes (school design, leadership, use of facilities, etc.)
HR – Key Personal Changes
o Teacher assignments and master schedule
Political issues related to the changes made at your schools
o How did you negotiate the political aspects associated with you
change process
Symbolic Methods used to add meaning and importance to your
initiatives such as:
o Vision/mission
o Culture/climate
o Ceremonies/ awards/recognition
1. What structural changes have you made that you feel have contributed to
improved math achievement?
o School design
o Leadership
o Facilities
o CSR

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

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

4. What did you do symbolically to support and engage in the change process that
has been implemented to improve math achievement?
o Vision/mission
239
o Culture climate
o Ceremonial/awards

Leadership Instrument RQ 4

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

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

1. Who were the leaders on your campus who helped bring about the improved
achievement in math?
a. What were there roles?
2. How was the professional growth of the math teachers supported?

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

4. How has the school leadership worked to implement a professional
community on you campus?
a. Teacher empowerment
b. Teacher leadership
c. Peer collaboration
d. Reflection
5. In what ways have site leaders attempted to make the focus on student
learning and results?
240
Leadership Questionnaire RQ5

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

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

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

2. Which of the following strategies played a role in your efforts to improve student
achievement in math?

Item Strategy Approach/Source
1
Delegate Leadership to Assistant
with greater expertise
Delegation Approach
(Northouse, 2001 p. 58)
2 Empower Department Chair Teacher Leadership (Gabriel, 2005)
3 Bring in Outside Expertise
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
4
Emphasize inquiry and problem
solving
Action Research
(Stringer 1999)
5 Emphasize quality instruction
Instructional Strategies
(Marzano, 2003 pp. 78-87)
6
Emphasize strategies to engage
students in the learning process
Student Engagement
(Marzano, 2003 pp. 149-150)
7
Emphasize articulation with feeder
schools
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
8 Emphasize raised expectations
Challenging Goals and Effective
Feedback (Marzano, 2003 pp. 35-46)
9
Emphasize Strategic Teacher
Assignments
HR Frame
(Bolman & Deal, 2003)
10
Emphasize Revised Course Scope
and Sequence and/ or Curriculum
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
11
Emphasize Interventions for lower
performing students
Supplemental Services
(NCLB, 2001)
12
Emphasize Professional
Development
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
241
Appendix D: Teacher Interview Guide

Teacher Interview Guide

1. What is your current position?
2. Describe your educational background, credentials held, years of experience
and any specialized training you have had in math instruction.
3. What policy initiatives and/or curricular programs do you feel have
contributed to improved student achievement in math?
4. What teaching strategies, methods and/or instructional materials do you feel
have contributed to improved student achievement in math?
5. Over the past few years, what changes, if any do you feel have made a
significant impact on student achievement in math? How were they
implemented?
6. What role did school leaders (administrators, department chair, lead teachers,
math coaches) play in the development and implementation of the math
program?
7. What actions taken by school leaders most directly affected student
achievement
in math?
Appendix E: School Profile
Indicator Resource Data
School location LPUSD Web Site Approximately 10 miles east of Los Angeles
School size CDE Web Site 2002-03 = 1639 / 2003-04 = 1735 / 2004-05 = 1743
Ethnic Breakdown CDE Web Site Asian (49.3%) Hispanic (36.3%) White (9.4%) Other (5%)
4 Year Dropout Rate CDE Web Site .5%
Percent of FRL District/SARC 50.9%
Percent of EL Students CBEDS/SARC 504 of 1743
Percent of Special
Education students
CBEDS/SARC 131 of 1743
What are the sub-groups
as per AYP
CBEDS/SARC Asian, Hispanic, White, SES
TEACHERS 74.8 FTE
NCLB Compliant SARC/District 89% compliant based on Number of Sections
Tenured CDE Web Site 59.8 of 74.8
Probationary 1 and 2 CDE Web Site 15 of 74.8 FTE
Average years of
teaching
CDE Web Site 10.5 Years
PRINCIPAL
Taught math Key Ldr Interview No
Majored in math Key Ldr Interview No
Years in administration Key Ldr Interview 8
How many years at this
school site?
Key Ldr Interview 11
242
Indicator Resource Data
DATA
Graduation Rate CDE Web Site 99.7%
4 Year Dropout Rate CDE Web Site .5%
Algebra I CST Scores
Proficient , Advance
Proficient
CDE Website 2002-03 = 19% / 2003-04 = 21% / 2004-05 = 25%
Algebra I CST Scores
Below Basic, Far Below
Basic
CDE Website 2002-03 = 51% / 2003-04 = 46% / 2004-05 = 34%
Percentage of students
who are scoring
proficient or above on
Math CST
CDE Website 70.8%
Percent of students
taking the SAT
CDE Web Site 52.73% of Seniors
Enrollment in AP
Classes
CDE Web Site 11 sections / 311 Students
API Scores over past
three years
CDE Web Site 2002-03 = 724 / 2003-04 = 747 / 2004-05 = 769
Met AYP targets over
three years
CDE Web Site YES – School Wide
YES – All Sub Groups
243
Percentage of students
passing CAHSEE
CDE Web Site 77% Math / 61% ELA
Percent of students
meeting A-G college
entrance requirements
CDE Web Site 34.8% of Students
Percentage of students
enrolled in Algebra II or
higher
CDE Web Site 35.8%
Percent attending four
year university over
past three years- school
and sub-group
2004-05
SARC
Duplicated Count of 66.7% =Course Enrollment in
UC/CSU
244
245
Appendix F: Math Teacher Questionnaire

Math Teacher Questionnaire

Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey in the sealed envelope
provided to the principal’s secretary by November 14, 2006. Please be assured
the questionnaires will only be viewed by the researcher and not be viewed at all by
site leaders. Once again, your assistance is greatly appreciated.

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

1. The No Child Left Behind
Legislation has promoted
increased student achievement
at our school.
2. The requirement that students
pass the CAHSEE to earn a
high school diploma has
contributed to the school’s
effort to improve student
achievement.
3. Board Policies in our district
have contributed to improved
math achievement in our
school.
4. Our school has successfully
implemented common
assessments that support
increased
student achievement.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
246
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

5. Teachers at our school teach
standards-based lessons.
6. The master schedule at our
school is built based on
student need.
7. Teachers at our school use
researched-based instructional
strategies to increase student
achievement
8. Periodic benchmark
assessments provide useful
data that our teachers use to
drive instruction
9. Student need is a major
consideration when making
teacher assignments in math at
our school.
10. The NCLB Act has been one
of the main external pressures
for improved math
achievement at this school.
11. The requirement that students
pass the CAHSEE in math in
order to earn a high school
diploma has contributed to the
school’s effort to improve
math achievement.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
247
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

12. Our school’s effort to improve
student achievement in math
instruction had nothing to do
with external accountability
such as NCLB regulations and
the CAHSEE requirement.
13. Support classes have been
included in our master
schedule to improve student
achievement in math.
14. The implementation of
standards-based instruction
has served as an important
foundation in improving
student achievement in math.
15. Our school has added the use
of math coaches or experts to
assist in the effort to improve
student achievement in math.
16. Teachers collaborate to
develop common assessments
and rubrics.
17. Professional development
offerings at our site are based
on student achievement data.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Directions: Please rate each item on the following scale by circling the response of
your choice:
248
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

18. Teachers have helped
develop strategies used at our
school to improve
instructional practice in math.
19. The principal has served as a
“change agent” for improved
student achievement in math.
20. Student achievement in math
was made a priority as the
school allocated its financial
resources.
21. Our school had a clear
strategic plan to improve
student achievement in math.
22. Professional Development has
played a key role in increasing
student achievement in math
23. Teacher collaboration has
played a key role in increasing
student achievement in math.
24. Changes in the curriculum
have played a key role in
increasing student
achievement in math.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
249
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

25. Our school has implemented
effective intervention
strategies for students having
difficulty in math
26. My district supports teachers
with effective staff
development in Mathematics
Instruction.
27. My principal actively supports
opportunities for staff
members to collaborate and
plan Mathematics lessons and
units.
28. Teachers learn by watching
each other teach and
discussing best practices.
29. Our school has effective
strategies to support students
of various learning modalities
30. Our school uses math
coaches to help teachers
become more reflective with
their math instruction
31. I have gained valuable
resources from math
coaches/instructional leaders
that have improved the quality
of my math instruction.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
250
2 = Disagree Somewhat
1 = Disagree Strongly

32. My school's instructional
leader provides professional
development resources that I
use in my mathematics
instruction.
33. The school leader is aware of
the mathematics instruction
and academic progress of the
students in my class.
34. The school leader provides
opportunities for faculty
members to discuss
mathematics instruction.
35. The school instructional
leader encourages faculty
members to discuss effective
math instructional strategies.
36. My school's math
instructional practices are
developed from evidence-
based strategies.
37. I have regular support from
proven instructional leaders in
math instruction.
38. The math achievement goals
and measures for my school
were clearly articulated and
easy to understand.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
251
2 = Disagree Somewhat
1 = Disagree Strongly

39. I received coaching and
mentoring from instructional
leaders or peer coaches.
40. The district personnel, school
leaders and teachers all have a
shared vision for increased
math achievement.
41. My district and school
leaders seem knowledgeable
about instructionally effective
math practices and assessment
strategies.
42. The Math Department Chair
has been entrusted with and is
empowered to make important
curricular decisions.
43. Outside experts have been
used to promote greater
capacity in the area of math
instruction.
44. The school’s leaders
emphasize the importance of
quality instruction as a
primary mission of the school.
45. Professional Development in
math has been a key tool used
by site leaders in our effort to
improve instruction on our
campus.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
252

46. Site leaders emphasize having
high expectations for student
achievement in math.
47. Quality interventions in math
have been implemented on our site
to help students at risk of failing
academically
48. Our site leaders emphasize a
culture of collaboration as a means
of improving instruction at our
site.
49. Teacher assignments in the math
department are made strategically
and with student need in mind.
50. Our school has emphasized
articulation with our feeder
schools as a means of improving
student achievement in math
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
253
Appendix G: Non-Math Teacher Questionnaire

Non-Math Teacher Questionnaire

Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey in a sealed envelope to the
principal’s secretary by Date TBA, 2006. Please be assured the questionnaires will
only be opened by the researcher and not by viewed at all by site leaders. Once
again, your assistance is greatly appreciated.

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

1. The No Child Left Behind
Legislation has promoted
increased student achievement
at our school.
2. The requirement that students
pass the CAHSEE to earn a
high school diploma has
contributed to the school’s
effort to improve student
achievement.
3. Board Policies in our district
have contributed to improved
math achievement in our
school.
4. Our school has successfully
implemented common
assessments that support
increased
student achievement.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
254

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

5. Teachers at our school teach
standards-based lessons.
6. The master schedule at our
school is built based on
student need.
7. Teachers at our school use
researched-based instructional
strategies to increase student
achievement
8. Periodic benchmark
assessments provide useful
data that our teachers use to
drive instruction
9. In an effort to improve
instruction on our campus, our
school has focused on
ensuring that structures and
policies that support student
achievement are in place.
10. In an effort to improve
instruction on our campus, our
school has focused on
personnel issues including
hiring quality teachers and
fostering a positive working
environment amongst peers
on campus.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
255
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

11. In an effort to improve
instruction on our campus, our
school has focused on
overcoming political obstacles
and gaining the necessary
support to move the school
forward.
12. In an effort to improve
instruction on our campus, our
school has focused on
motivating students and staff
as well as celebrating
successes.
13. There is a shared vision for
increased student achievement
at our school.
14. Our school had a clear
strategic plan to improve
student achievement.
15. Student achievement is a
priority when the school
allocates its financial
resources.
16. Professional development
offerings at our site are based
on student achievement data
17. The principal works to gain
the support of the community
for the school’s academic
efforts.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
256
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

18. The school leadership works
to establish and maintain a
respect for cultural diversity
19. Students and staff are valued
and their successes celebrated.
20. The school leaders used data-
driven information to address
problems/issues related to
student achievement.
21. The principal works hard to
monitor and supervise
instruction in the classroom
22. The principal makes effective
use of the Department Chairs
and relies on their expertise
when making important
curricular decisions.
23. The principal has delegated
some curricular authority to
an assistant principal with
greater expertise in
curriculum and instruction.
24. Outside experts have been
used to promote greater
capacity in the area of
instruction.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
257
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly

25. Site leadership fosters a
culture of inquiry and
collaborative problem solving.
26. The school’s leaders
emphasize the importance of
quality instruction as a
primary mission of the school.
27. Site leaders emphasize
having high expectations for
student achievement.
28. Quality interventions have
been implemented on our site
to help students at risk of
failing academically.
29. Professional Development
has been a key tool used by
site leaders in our effort to
improve instruction on our
campus.
30. Teacher assignments are
made strategically and with
student need in mind.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
258
Appendix H: Math Teacher Questionnaire Results

Item Math Teacher Questionnaire Item Mean
1
The No Child Left Behind Legislation has promoted increased
student achievement at our school. 2.92
2
The requirement that students pass the CAHSEE to earn a high
school diploma has contributed to the school’s effort to improve
student achievement. 4.50
3
Board Policies in our district have contributed to improved math
achievement in our school. 3.42
4
Our school has successfully implemented common assessments that
support increased student achievement. 4.58
5 Teachers at our school teach standards-based lessons. 4.83
6 The master schedule at our school is built based on student need. 4.00
7
Teachers at our school use researched-based instructional strategies
to increase student achievement 4.08
8
Periodic benchmark assessments provide useful data that our teachers
use to drive instruction 4.50
9
Student need is a major consideration when making teacher
assignments in math at our school. 4.08
10
The NCLB Act has been one of the main external pressures for
improved math achievement at this school. 2.42
11
The requirement that students pass the CAHSEE in math in order to
earn a high school diploma has contributed to the school’s effort to
improve math achievement. 4.17
12
Our school’s effort to improve student achievement in math
instruction had nothing to do with external accountability such as
NCLB regulations and the CAHSEE requirement. 3.33
13
Support classes have been included in our master schedule to
improve student achievement in math. 4.08
14
The implementation of standards-based instruction has served as an
important foundation in improving student achievement in math. 4.33
15
Our school has added the use of math coaches or experts to assist in
the effort to improve student achievement in math. 1.50
16 Teachers collaborate to develop common assessments and rubrics. 4.17
17
Professional development offerings at our site are based on student
achievement data. 3.00
18
Teachers have helped develop strategies used at our school to
improve instructional practice in math. 4.42

259
Item Math Teacher Questionnaire Item Mean
19
The principal has served as a “change agent” for improved student
achievement in math. 3.83
20
Student achievement in math was made a priority as the school
allocated its financial resources. 2.58
21
Our school had a clear strategic plan to improve student achievement
in math. 4.00
22
Professional Development has played a key role in increasing student
achievement in math 3.33
23
Teacher collaboration has played a key role in increasing student
achievement in math. 4.50
24
Changes in the curriculum have played a key role in increasing
student achievement in math. 3.75
25
Our school has implemented effective intervention strategies for
students having difficulty in math 4.00
26
My district supports teachers with effective staff development in
Mathematics Instruction. 3.25
27
My principal actively supports opportunities for staff members to
collaborate and plan Mathematics lessons and units. 4.08
28
Teachers learn by watching each other teach and discussing best
practices. 3.58
29
Our school has effective strategies to support students of various
learning modalities 3.92
30
Our school uses math coaches to help teachers become more
reflective with their math instruction 1.58
31
I have gained valuable resources from math coaches/instructional
leaders that have improved the quality of my math instruction. 2.83
32
My school's instructional leader provides professional development
resources that I use in my mathematics instruction. 3.00
33
The school leader is aware of the mathematics instruction and
academic progress of the students in my class. 3.67
34
The school leader provides opportunities for faculty members to
discuss mathematics instruction. 4.00
35
The school instructional leader encourages faculty members to
discuss effective math instructional strategies. 4.00
36
My school's math instructional practices are developed from evidence-
based strategies. 3.92
37
I have regular support from proven instructional leaders in math
instruction. 3.92
260

Item Math Teacher Questionnaire Item Mean
38
The math achievement goals and measures for my school were
clearly articulated and easy to understand. 4.67
39
I received coaching and mentoring from instructional leaders or peer
coaches. 3.42
40
The district personnel, school leaders and teachers all have a shared
vision for increased math achievement. 4.00
41
My district and school leaders seem knowledgeable about
instructionally effective math practices and assessment strategies. 3.50
42
The Math Department Chair has been entrusted with and is
empowered to make important curricular decisions. 4.67
43
Outside experts have been used to promote greater capacity in the
area of math instruction. 1.92
44
The school’s leaders emphasize the importance of quality instruction
as a primary mission of the school. 4.50
45
Professional Development in math has been a key tool used by site
leaders in our effort to improve instruction on our campus. 2.83
46
Site leaders emphasize having high expectations for student
achievement in math. 4.25
47
Quality interventions in math have been implemented on our site to
help students at risk of failing academically. 3.75
48
Our site leaders emphasize a culture of collaboration as a means of
improving instruction at our site. 3.92
49
Teacher assignments in the math department are made strategically
and with student need in mind. 3.42
50
Our school has emphasized articulation with our feeder schools as a
means of improving student achievement in math 2.83

Appendix I: Data Collection Grid
RESEARCH
QUESTION Q
CONCEPT V
FRAMEWOR
Pattern of A
INSTRUMENT S
Classroom
Practices SBI
Curriculum
Design
Student
Performance Curriculum
School
Culture
Learning
Activities
TCHR
QUESTIONNAIRE
MATH
QUESTIONNAIRE
KEY LDR
INTERVIEW
TCHR INTERVIEW
Document Analysis
Master Schedules
WASC Report
Curriculum Guide
Classroom
Observations
FRAMEWORK ELEMENT
Math Program School Design
CONDITIONS RELATED TO IMPROVED STUDENT ACHIEVEMENT
RQ2
261
RESEARCH
QUESTION Q
CONCEPT V
FRAMEWOR
Pattern of A Frame Frame Frame Frame Vision Supervision Community Culture Data
INSTRUMENT S Structural HR Political Symbolic
TCHR
QUESTIONNAIRE
MATH
QUESTIONNAIRE
KEY LDR
INTERVIEW
TCHR INTERVIEW
Document Analysis
Master Schedules
WASC Report
Curriculum Guide
Classroom
Observations
RQ4
FRAMEWORK ELEMENT
LEADERSHIP
RQ3
FRAMEWORK ELEMENT
CHANGE PROCESS
262
RESEARCH
QUESTION Q
CONCEPT V
FRAMEWOR
Pattern of A FINDING STRATEGY #
INSTRUMENT
TCHR
QUESTIONNAIRE
MATH
QUESTIONNAIRE
KEY LDR
INTERVIEW
TCHR INTERVIEW
Document Analysis
Master Schedules
WASC Report
Curriculum Guide
Classroom
Observations
RQ5
COPING STRATEGIES
FRAMEWORK ELEMENT
263

Abstract (if available)

Abstract The purpose of this study was to learn more about how urban high schools successfully bring together policy initiatives and local best practice to improve math performance in their schools. In a case study of an urban high school in the Los Angeles area of Southern California, five research questions focused on the pattern of student achievement in math, policies and practices related to improved achievement in math, the change process used at the school, the leadership practices and the strategies used by the principal who was not an expert in math. Results indicated that leadership from a variety of sources all worked to focus efforts on standards-based instructional practices to move the school forward.

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Asset Metadata

Creator Rice, Roger Roy (author)

Core Title Secondary school reform and improved math achievement: a case study of site efforts at Mission Valley High School

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 04/15/2007

Defense Date 03/05/2007

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

Tag high school reform,instructional leadership,leadership,math achievement,OAI-PMH Harvest,secondary school improvement,student achievement

Language English

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

Creator Email rrice@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m392

Unique identifier UC1431763

Identifier etd-Rice-20070415 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-398407 (legacy record id),usctheses-m392 (legacy record id)

Legacy Identifier etd-Rice-20070415.pdf

Dmrecord 398407

Document Type Dissertation

Rights Rice, Roger Roy

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